Answers
Answer:
transformed function, g (x) =1/7x+5
Step-by-step explanation:
Related Questions
Mike is loading a moving van by walking up a ramp. The ramp is 10 feet long and the bed of the van is 2.5 feet above the ground. How far does the ramp extend past the back of the van?
Answers
Using the Pythagorean theorem, the ramp extends 9.68 feet past the back of the van.
What is the Pythagorean theorem?
Pythagoras Theorem (also called Pythagorean Theorem) is an important topic in Mathematics, which explains the relation between the sides of a right-angled triangle. The sides of the right triangle are also called Pythagorean triples. Pythagoras theorem is basically used to find the length of an unknown side and the angle of a triangle. By this theorem, we can derive the base, perpendicular and hypotenuse formulas.
Pythagoras formula:-
Hypotenuse² = Perpendicular² + Base²
c² = a² + b²
Where “a” is the perpendicular,
“b” is the base,
“c” is the hypotenuse
Now,
For given situation,
Hypotenuse=10feet, perpendicular=2.5feet and we have to find base
Therefore
10^2=b^2+2.5^2
b^2=100-6.25
b=√93.75
b=9.68 feet
Hence,
The ramp extends 9.68 feet past the back of the van.
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Factor the trinomial by grouping. -
5x² - 28x+15
a. Find two numbers whose product is 5.15= 75 and whose sum is - 28.
b. Write - 28x using the factors from part (a).
c. Factor by grouping.
Answers
a. The two numbers whose product is 75 and whose sum is -28 are -25 and 3.
b. -28x = -25x + 3x
c. -5x² - 25x + 3x + 15
= -5x(x-5) + 3(x-5)
= (3x-15) + (-5x+25)
= (-5x+3x) + (25-15)
= -2x +10
The trinomial -5x² - 28x + 15 can be factored by grouping as (-2x+10)
Grace purchased a chocolate cheesecake costing $17.04. She gave the cashier $19.68. How much change did the cashier give back to Grace?Grace purchased a chocolate cheesecake costing $17.04. She gave the cashier $19.68. How much change did the cashier give back to Grace?
Answers
Answer:
2.64
Step-by-step explanation:
.
graph with the x axis labeled time in hours and the y axis labeled height of candlestick in inches and a line going from the point 0 comma 8 through the point 3 comma 6
Find and interpret the slope and y-intercept in this real-world situation.
The slope is 8, and the y-intercept is negative two thirds. The candle starts at a height of two thirds of an inch and decreases 8 inches every hour.
The slope is 8, and the y-intercept is negative three halves. The candle starts at a height of three halves of an inch and decreases 8 inches every hour.
The slope is negative two thirds, and the y-intercept is 8. The candle starts at a height of 8 inches and decreases two thirds of an inch every hour.
The slope is negative three halves, and the y-intercept is 8. The candle starts at a height of 8 inches and decreases three halves of an inch every hour.
Answers
The correct statement regarding the slope and the intercept of the linear function are is given as follows:
The slope is negative two thirds, and the y-intercept is 8. The candle starts at a height of 8 inches and decreases two thirds of an inch every hour.
How to interpret the y-intercept of a linear function?The two most important features of a linear function are the slope and the intercept, and their meaning is explained as follows:
Slope: rate of change of the output variable relative to the input variable.Intercept: value assumed by the output variable when the input variable assumes a value of zero.The input and output variables for this problem are given as follows:
Input: time in hours.Output: height in inches.Two points of the function are:
(0, 8) and (3,6).
Given two points, the slope is calculated as the change in y divided by the change in x, hence:
m = (6 - 8)/(3 - 0)
m = -2/3.
Meaning that the candle's height decays at a rate of 2/3 of an inch an hour.
When x = 0, y = 8, hence the intercept of b = 8 represents the initial height of the candle.
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Mariam wants to rent out her house. She researches similar listings in an online rental marketplace and sees that she can rent her home for $210$ per night or $1300 per month. Mariam's house is near a beach in a moderate-sized city with good weather year-round, a famous aquarium, a water park, and lots of restaurants.
To figure out if she should list her home as a short-term rental or a long-term rental, first Mariam divides 1300 by 210.
1300/210=6.2
She needs to rent her home 6-7 nights per month to match the revenue from a long-term rental. Since Mariam lives in a location likely to have tourists, she should find plenty of renters. She lists her home as a short-term rental.
In her reasoning, Mariam divided 1300 by 210. If this is correct, explain why. If this is not correct, explain what she should have done.
Answers
This is absolutely correct as dividing the rate per month by the rate per night gives the number of nights per month needed for the revenues to match: [tex]$$month$\div $night=r/month \cdot \ $night/r$=# $nights/month$$[/tex]
What is revenue?A company's income is the cash that is generated by its operations. Depending on the accounting technique used, there are various methods for calculating revenue.
Sales made with credit will be counted as revenue when it comes to the delivery of goods or services to the customer in accrual accounting. Even if payment hasn't yet been received, revenue may still be recognised in accordance with certain rules.
To evaluate how successfully a business collects debt, it is important to review the cash flow statement. Contrarily, sales are only recorded as revenue in cash accounting after money has been exchanged. A "receipt" is the term for a sum of money given to a business. Receivables without income are possible.
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Use the given transformation to evaluate the integral.
u= x+y, v= -2x+y;
R\int \int5y dxdy where R is the parallelogram bounded by the lines y= -x+1, y=-x+4, y= 2x+2, y= 2x+5
a. 85/4
b. 65/4
c.85/2
d.65/2
Answers
After evaluating the integral answer is 85/4. thus, option A is the answer.
The given transformation is a change of variables from (x, y) to (u, v). To evaluate the integral using the transformation, we need to use the Jacobian determinant. The Jacobian determinant is the absolute value of the determinant of the matrix of partial derivatives of the transformation.
du/dx = 1, du/dy = 1
dv/dx = -2, dv/dy = 1
The determinant of the matrix of partial derivatives is det(J) = du/dx * dv/dy - du/dy * dv/dx = (1)(1) - (1)(-2) = 3
So the Jacobian determinant is |J| = |3| = 3.
The integral becomes:
R\int \int 5y dx dy = (1/3) R\int \int 5v du dv
where R is the region in the uv-plane that corresponds to the region in the xy-plane bounded by the lines y= -x+1, y=-x+4, y= 2x+2, y= 2x+5
The integral evaluates to (1/3) R\int \int 5v du dv = (1/3) * 85/2 = 85/6 = 85/4
Therefore the correct answer is 85/4
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Marge simplified the expression as show. -8b+15b+14=21b. What mistake did marge make, what is the correct simplified version of the expression
Answers
The value of expression is 1 of the equation -8b+15b+14=21b
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given expression is -8b+15b+14=21b
Minus eight times of b plus fifteen b plus forteen equal to twenty one.
In the given expression b is the variable and minus and plus are the operators.
-8b+15b+14=21b
Take the variable terms on one side and constant on other side.
-8b+15b-21b=-14
-14b=-14
Divide both sides by -14
b=1
Hence, the value of expression is 1 of the equation -8b+15b+14=21b
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an even number. each card is worth a different number of points (this point value is written on the card). alice and bob then take turns removing either the leftmost or rightmost card from the row, until all the cards are gone. at that point, the player who has collected the most points is declared the winner.
Answers
The best strategy for Alice is to take the card with the highest point value. This will maximize her chances of winning, since she can then choose the last card from the remaining cards. Bob should take the card with the lowest point value, as this will minimize Alice's chances of winning.
Alice always takes the first turn. Bob can either take the leftmost card or the rightmost card. If Alice takes the leftmost card and Bob takes the rightmost card, then Alice will have the advantage of being able to make the last move. If Bob takes the leftmost card and Alice takes the rightmost card, then Bob will have the advantage of being able to make the last move.
The best strategy for Alice is to take the card with the highest point value. This will maximize her chances of winning, since she can then choose the last card from the remaining cards. Bob should take the card with the lowest point value, as this will minimize Alice's chances of winning.
Alice should also be aware of Bob's strategy and try to anticipate what card he will take. If Alice can guess correctly, she can adjust her strategy to ensure she takes the card with the highest point value. If she guesses incorrectly, she should still attempt to take the card with the highest point value.
Alice should take the card with the highest point value and Bob should take the card with the lowest point value. Alice should also anticipate Bob's strategy and adjust accordingly to ensure she takes the card with the highest point value.
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in the expansion of (2a 4b)8, which of the following are possible variable terms? explain your reasoning. a2b3; a8; a5b3; ab8; a3b5; a7b; a6b5; b8
Answers
The possible variable terms are a2b3, a5b3, ab8, a3b5, a7b, and a6b5. These terms all contain the same number of a's and b's as the original expression, (2a4b)8.
The expansion of (2a 4b)8 can be found by multiplying the a coefficients and b coefficients by 8. The a coefficients would increase by a factor of 8 and the b coefficients would increase by a factor of 8. This means that the possible variable terms for (2a 4b)8 are all those that have 8 a's and 8 b's. This includes a2b3, a5b3, ab8, a3b5, a7b, and a6b5. These terms all contain the same number of a's and b's as the original expression, (2a4b)8, but with the coefficients multiplied by 8. For example, the term a2b3 would be the result of multiplying 2a4b by 8, which results in 16a32b. This can be simplified to a2b3. Similarly, a5b3 would be the result of multiplying 2a4b by 8, which results in 16a32b. This can be simplified to a5b3.
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a line which joins the midpoints of two sides of a triangle is _?
Answers
A line which joins the midpoints of two sides of a triangle is Midsegment
A triangle's midsegment is a line formed by joining any two of the triangle's sides at their midpoints. All three sides of a triangle can be divided (split in half) in any triangle, whether it be right, isosceles, or equilateral. The midpoint of each side is the point that is equally spaced from either vertex.
Triangles can have three midsegments because they have three sides. Any two sides can be joined at their midpoints. Half the length of the base is represented by one midsegment (the third side not involved in the creation of the midsegment). That is the only intriguing aspect. It also:
Is consistently parallel to the triangle's third side; the base
Creates a tiny triangle that resembles the primary triangle.
The area of the smaller, comparable triangle is one-fourth that of the larger triangle.
Half of the original triangle's circumference is contained within the smaller, comparable triangle.
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65% as a fraction in simplest form
Answers
Answer:
13/20
Step-by-step explanation:
Answer:
65/100
Step-by-step explanation:
65/100 because if you try to divide it by 2 u get 32.5
Relationships between short- and long-term exposure to violent video games and desensitization, as measured through components of moral evaluation, were examined. Sixty-six children aged 5-12 years old completed questionnaires assessing video game experience and preferences and empathy and attitudes toward violence. The children played a violent or nonviolent video game and then responded to vignettes about everyday occurrences. Vignette responses were coded for aggression and empathy. Preexisting empathy and attitudes towards violence were positively related to the corresponding vignette scores. Long-term exposure to violent video games contributed to lower empathy vignette scores. Playing a violent versus a nonviolent game did not affect vignette responses. Results suggest that long-term exposure to violent video games may be associated with desensitization as reflected in lower empathy, although the direction of causality remains unclear.What is the main IV?What is the main DV?
Answers
This study examines the relationship between long-term exposure to violent video games and desensitization as measured by empathy and attitudes to violence in children aged 5 to 12 years.
They completed a questionnaire assessing their experience and preference for video games and their empathy and attitudes toward violence. Children then played violent or non-violent video games and responded to snippets of everyday events.
vignette reactions were coded for aggression and empathy. Results showed that pre-existing empathy and attitudes toward violence were positively associated with the corresponding vignette scores.
Prolonged exposure to violent video games has been found to reduce empathy vignette scores. However, the study found no significant difference in vignette responses depending on whether children played violent or non-violent games.
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A ball dropped vertically fall d meters in t seconds. D is directly proportional to the square of t the ball drops 80 meters in the first 4 seconds . how far does the ball drop in the next 8 seconds
Answers
The distance the ball drops in the next 8 seconds is 320 meters.
What is direct proportion?Direct proportion is when two variables move in the same direction. If one variable increases, the other variable increases.
The equation that is used to represent direct proportion is: D = kt²
Where: k is the constant of variation
80 = k4²
80 = 16k
k = 80 / 16
k = 5
Distance the ball drops in the next 8 seconds : 5 x 8²
= 64 x 5 = 320 meters
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find the values of x and y
Answers
The value of x is 1.75 and y is 5. The solution is obtained using properties of congruent triangles.
What is a congruent triangle?
Two triangles that are congruent will have precisely the same three sides and three angles.
The dimensions of the triangles' sides and angles determine whether two or more triangles are congruent. A triangle's size is determined by its three sides, and its shape by its three angles. Pairs of corresponding sides and corresponding angles in two triangles are said to be equal if they are congruent. They share a similar size and shape. In triangles, there are numerous congruence conditions.
The triangles are congruent by SAS congruency because
AC = CD (Given)
∠ACB = ∠DCE ( Vertically opposite angles)
BC = CE (Given)
Thus, Triangle ABC ≅ Triangle DEC
Since, the triangles are congruent, therefore
⇒AC = CD
⇒4y-6 = 2x+6 ...(1)
Also, BC = CE
⇒3y+1 = 4x
⇒(3y+1)/4 = x ...(2)
Now, substituting the value of x in (1), we get,
⇒4y-6 = 2(3y+1)/4+(6)
⇒4y-6 = (6y+2 +24)/4
⇒16y-24 = 6y+2 +24
⇒10y = 50
⇒y = 5
Now putting the value of y in (2), we get
⇒(3(2)+1)/4 = x
⇒7/4 = x
⇒ x = 1.75
Hence, the value of x is 1.75 and y is 5.
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I need it asap please answer it
Answers
The Surface area this of cylinder with radius 11cm and height 30 cm is 2833.71 cm².
What is a cylinder?Two parallel, identical bases connected by a curved surface form a 3D solid shape known as a cylinder. Similar to a disc in shape, these bases. The axis of the cylinder shape is a line drawn through the middle of, or connecting, two circular bases. Perpendicular distance is the measurement separating the two bases, and it is denoted by the letter "h," which stands for height. The distance between the two circular bases' centres and outer edges is known as the cylinder's radius and is denoted by the letter "r".
Surface area of cylinder = 2πr(r+ h)
= 2π11(11+ 30)
= 2833.71 cm²
Thus, the Surface area this of cylinder with radius 11cm and height 30 cm is 2833.71 cm².
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Use the graph to answer the following questions.
(a) Over which intervals is the function increasing? Choose all that apply.
(-∞, -9) (-6, -2) (-2, 3) (3, 7) (-2,7) (7, ∞0)
(b) At which x-values does the function have local minima? If there is more than one
value, separate them with commas.
-6,3
(c) What is the sign of the function's leading coefficient?
(Choose one)
(d) Which of the following is a possibility for the degree of the function? Choose all
that apply.
04
8
05
6
7
9
X
Answers
a) Over the intervals (−∞,−9),(-6,-2) and (3,7) the function is increasing.
b) At x-values x=-6 and x=3 the function have local minima.
c) The sign of the function's leading coefficient is negative.
d) The possibility for the degree of the function is 5 or 7.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
A function is said to increasing if the value of y increases as the value of x increases.
From the graph, the function is increasing on (−∞,−9),(-6,-2) and (3,7)
The local minima is a point where the function has minimum value in its local neighbour.
From the graph, the function has a local minima at x=-6 and at x=3.
In the end, the value of f(x) decreases as the value of x increases therefore the sign of the function's leading coefficient is negative.
The graph intersects the x-axis 2 times and also the function have 5 turning points both the these information indicates that the function is of 5 degrees or 7 degrees.
Therefore, interval, local minima, coefficient value and degree of function is obtained.
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What is the value of log3 9?
O A.
О в. 1
O C. 2
OD. 3
27
Answers
[tex]question[/tex]
What is the value of log3 9 ?[tex]answer[/tex]
Option c is correct answer.C. 2Hope it's help......✨
The value of expression log₃9 is 2, Option B is correct.
What is Expression?An expression is combination of variables, numbers and operators.
We know that 3 raised to what power equals 9.
We can write this as:
3ˣ = 9
Taking the logarithm of both sides with base 3, we get:
log₃(3ˣ) = log₃ 9
x = log₃9
So, the value of log3 9 is the exponent x that satisfies the equation 3ˣ = 9.
Since 3²= 9, we have:
log₃ 9 = 2
Hence, the value of expression log₃9 is 2.
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parallel to line y=-3x+5 passes through (-4,5) point slope form
Answers
The equation of line in point slope form will be -
y - 5 = - 3(x + 4).
What is geometry?Geometry is a branch of mathematics that deals with shapes, sizes, angles, and dimensions of objects.
Given is a equation of a line → y = -3x + 5 passing through point (-4, 5).
The given equation is -
y = -3x + 5
Slope of the line parallel to this line -
m{p} = - 3
We can write the equation of line in point slope form as -
y - 5 = -3(x + 4)
Therefore, the equation of line in point slope form will be -
y - 5 = - 3(x + 4).
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At what height above the surface of the earth, the value of g becomes 64% of its value on the surface is the earth? (Radius of the earth is 6400km )
O 1600kmO 2650kmO 3200kmO 9038km
Answers
The value of g becomes 64% of its value on the surface of the earth when it is at a height of 3200km above the surface, with the radius of the earth being 6400km.
Radius of Earth = 6400 km
Height above the surface of Earth = 3200 km
Gravitational Acceleration on surface of Earth = 9.8 m/s2
Gravitational Acceleration at 3200 km above the surface of Earth = 9.8 x 0.64 = 6.272 m/s2
The gravitational acceleration (g) on the surface of the earth is 9.8 m/s2. This value is constant, regardless of the height of an object above the surface. However, as the height of an object increases, the gravitational force experienced by the object decreases. The radius of the earth is 6400 km, so at a height of 3200 km above the surface, the gravitational acceleration experienced by an object is 64% of its value on the surface of the earth, which is 6.272 m/s2. This is because the gravitational force decreases as the object moves further away from the surface, and at 3200 km the force is only 64% of the force at the surface.
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Can somebody help me? I am learning about Basic Exponent Properties in Algebra and I do not understand how to solve equations with exponents. Please tell me how to do it?
Here are some examples:
1. (4xy²)(-2x²y³)
2. 6y³/18x · 2xy
3. Which expression has the greater value? 2³ · 2(exponent 5) or 4(exponent 7)/4³
4. (3x)exponent1/3 · (3x)exponent7/3 / (3x)exponent2/3
Please Answer ASAP!! I will give 40 points!!
Answers
Answer:
Provided an explanation below.
The examples are not asking you to solve, only to simplify the expression
For the examples you posted, not sure if you want the solutions are not; I have gone ahead and simplified
[tex]1.\; -8x^3y^5\\\\2\; \dfrac{2y^3}{3}\\\\3.\; They are both equal\\\\4.\; 3x^2\\\\[/tex]
Step-by-step explanation:
First let's understand what an exponent is.
When a number or a term or an expression is multiplied repeatedly by itself, an exponent can be used to represent this situation
for example,
5 x 5 x 5 x 5 x 5 x 5 = 5⁶ since 5 is multiplied by itself 6 times
Here the number being multiplied(5) is called the base and the number of times it is multiplied(6) is called the exponent.
There are some rules regarding exponentiation
1 Zero Exponent
Any number raised to the power zero is 1
[tex]4^0 = 1\\\\123.456^0 = 1\\\\x^0 = 1[/tex]
2. Negative Exponent
If the exponent if negative, the expression is equivalent to the reciprocal of the term raised to the positive exponent
In general
[tex]a^{-m} = \dfrac{1}{a^m}\\\\and\\\\\dfrac{1}{a^{-m}} = a^m\\\\[/tex]
Examples:
[tex]x^-1 = \dfrac{1}{x}\\\\\left({x + y}\right)^{-a} = \dfrac{1}{(x+y)^a}[/tex]
[tex]\dfrac{1}{x^{-3}} = x^3[/tex]
3. Product Rule
When you multiply exponents with the same base the exponents get added
In general
[tex]\displaystyle {a^m a^n = a^{m + n}}[/tex]
Examples
[tex]x^3x^6 = x^{(3+6)} = x^9\\\\[/tex]
4. Quotient Rule
When you divide an exponentiated term by another exponentiated term with the same base the resulting exponent is the difference between the two exponents:
In general
[tex]\dfrac{a^m}{a^n} = a^{m-n[/tex]
Examples
[tex]\dfrac{y^3}{y^2} = y^{3-2} = y^1 = y[/tex]
5. Power Rule 1
An exponent term raised to another power will be the base raised to the product of the two exponents
In general
[tex](a^m)^n = a^{mn}[/tex]
[tex](x^3)^4 = x^{3 \cdot 4} = x^{12}[/tex]
6. Power Rule 2
If the base is the product of two or more terms and the whole expression is raised to a power then each individual term gets raised to that power.
[tex](ab)^m = a^mb^m\\\\(2x^3y^2z^4)^4 = 2^4x^{3.4}y^{2.4}z^{4.4} = 16x^{12}y^8z^{16}[/tex]
7. One exponent
Any term raised to the power 1 is itself
[tex]a^1 = a[/tex]
example: 5¹ = 5
x¹ = x
You may have to use some or all of the rules when confronted with a specific problem
There are plenty of excellent resources on the web which can explain far more lucidly than I can.
Here are a few. Just search for them and you will get the site links
LibreTexts, OpenStax, cK-12.org etc
As for the specific examples you posted:
[tex]1. (4xy^2)(-2x^2y3)\\[/tex]
Multiply the constant coefficients: 4 x -2 = -8Multiply each term with the same base by the other term with the same base[tex]x\cdot x^2 =x^1x^2 = x^{1 + 2} = x^3\\\\\\y^2 y3 = y {2 + 3} = y^5\\\\[/tex]
Combine all these to get the final answer:
[tex](4xy^2)(-2x^2y^3) = -8x^3y^5[/tex]
[tex]\textrm{2. }\dfrac{6y^2}{18x}\cdot 2xy[/tex]
[tex]\mathrm{Cancel\:}\dfrac{6y^2}{18x}:\quad \dfrac{y^2}{3x}\\\\[/tex]Then the expression becomes
[tex]=\dfrac{y^2}{3x}\cdot \:2xy[/tex][tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \:a\cdot \dfrac{b}{c}=\dfrac{a\cdot \:b}{c}[/tex]
[tex]\dfrac{y^2}{3x}\cdot \:2xy = =\dfrac{y^2\cdot \:2xy}{3x}[/tex]
Cancel the x above and the x below to get
[tex]\dfrac{y^2\cdot \:2y}{3}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}[/tex]
[tex]y^2y=y^{2+1} = y^3[/tex]
Putting all the terms together we get
[tex]\textrm{2. }\dfrac{6y^2}{18x}\cdot 2xy =\dfrac{2y^3}{3}[/tex]
3. Which expression has the greater value?
[tex]2^3.2^5 \; or\; \dfrac{4^7}{4^3}[/tex]
[tex]2^3\cdot2^5 = 2^8\\\\\dfrac{4^7}{4^3}= 4^{7-3}=4^4\\\\\mathrm{Since \;4 = 2^2, 4^4 = (2^2)^4=2^8}[/tex]
[tex]4. \dfrac{\left(3x^{\frac{1}{3}}\cdot 3x^{\frac{7}{3}}\right)}{3x^{\frac{2}{3}}}[/tex]
[tex]\\\\\\\mathrm{Cancel\:the\:common\:factor:}\:3[/tex]==> [tex]\dfrac{3x^{\frac{1}{3}}x^{\frac{7}{3}}}{x^{\frac{2}{3}}}[/tex]
[tex]\mathrm{Simplify\:}\dfrac{x^{\frac{1}{3}}}{x^{\frac{2}{3}}}[/tex]
[tex]\longrightarrow \dfrac{x^{\frac{1}{3}}}{x^{\frac{2}{3}}} = x^{\frac{1}{3} - \frac{2}{3} }= x^{-\frac{1}{3}} = \dfrac{1}{x^\frac{1}{3}}\\\\\\\longrightarrow \dfrac{3x^{\frac{7}{3}}}{x^{\frac{1}{3}}} =3x^{\frac{7}{3}-\frac{1}{3}} = 3x^2[/tex]
If so, what are the two expressions being cubed? In other words, if the expression is rewritten In the form (p^3 - q^3), what are p and q?
Answers
The two expressions being cubed are p and q. The expression (p^3 - q^3) is equivalent to cubing both p and q. This means that the expression can be written as (p * p * p - q * q * q). Rewriting it in the form (p^3 - q^3) shows that the two expressions being cubed are p and q.
The expression (p^3 - q^3) is equivalent to cubing both p and q. This means that the expression can be written as (p * p * p - q * q * q). Rewriting it in the form (p^3 - q^3) shows that the two expressions being cubed are p and q.
The expression (p^3 - q^3) is the result of cubing two different expressions, p and q. This is equivalent to multiplying each expression by itself three times. Rewriting the expression in the form (p^3 - q^3) indicates that the two expressions being cubed are p and q. In other words, the expression is the result of taking p and raising it to the third power and then taking q and raising it to the third power. The result is then subtracting q^3 from p^3. This is commonly referred to as cubing both p and q, and the two expressions being cubed are p and q.
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Select which step should be completed first in the simplification process for each of the expressions.
Choices parentheses exponents multiplication/division addition/subtraction
Answers
The evaluation of the expression using the order of operations, indicates the operations that come first as follows;
(5 + 5)² + 15 - 10 Parenthesis
40 ÷ 8 · 4 + 2; Division
4 - 2 + 3 · 5; Multiplication
(3² + 8) ÷ 7 - 5; Parenthesis
What is the order of performing mathematical operations?The order of operations is a rule that serves as a guide for the correct sequence of performing operations in an equation or expression.
The evaluation expressions can be presented as follows;
First operation;
(5 + 5)² + 15 - 10
The order of operations, PEMDAS, indicates that we get;
1) Parenthesis first
2) Exponents
3) Multiplication and division
4) Addition and subtraction
Based on the above PEMDAS order of operation, the step that should be completed first is the operation within the parenthesis, which is the addition operation (5 + 5)
The correct option is; Parenthesis
(5 + 5)² + 15 - 10 ParenthesisSecond expression;
40 ÷ 8 · 4 + 2
The operations in the expression are; division, multiplication, and addition
The order of operations indicates that division, which comes first, from the left, should be performed first. The correct option is therefore;
40 ÷ 8 · 4 + 2; division
Third expression;
4 - 2 + 3 · 5
The subtraction is the first operation from the left, but the order of operations, PEMDAS, indicates that the multiplication, 3 · 5 should be performed first, therefore;
4 - 2 + 3 · 5; MultiplicationFourth expression;
(3³ + 8) ÷ 7 - 5
The parenthesis which comes first in the order of operations and first among the operations from left to right comes first
Therefore, the parenthesis comes first;
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the product of two consecutive natural numbers is 1.5 times the square of the lesser number. find the two numbers.
Answers
The two consecutive natural numbers that satisfy the given equation are 3 and 4.
Let the two numbers be x and x+1
x(x+1) = 1.5x^2
x^2 + x - 1.5x^2 = 0
x^2 - 0.5x = 0
(x-3)(x+0.5) = 0
x = 3, x+1 = 4
The given equation is the product of two consecutive natural numbers, which is equal to 1.5 times the square of the lesser number.
Therefore, we can set up an equation by substituting x for the lesser number and x+1 for the greater number.
x(x+1) = 1.5x^2
We can then simplify the equation by subtracting 1.5x^2 from both sides.
x^2 + x - 1.5x^2 = 0
We can then factor this equation to find the solution.
x^2 - 0.5x = 0
(x-3)(x+0.5) = 0
The solutions to this equation are x = 3 and x+1 = 4. Therefore, the two consecutive natural numbers are 3 and 4.
The two consecutive natural numbers that satisfy the given equation are 3 and 4.
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Calculate the acceleration produced by a bus moving with velocity of 72 km / hr to stop a distance of 50
Answers
As a result, the bus accelerates at a rate of -4 m/s2, and it travels 50 m after applying the brakes.
Find the acceleration ?Bus's initial speed was 72 km/h.
Bus's last speed is 0 km/h.
(Therefore, the bus driver stops)
Bus travel time, t=5 s
To Locate
Bus acceleration and the distance it travels before stopping once the brakes are applied
Solution:
Final velocity is v.
Initial velocity is u.
Acceleration is a.
It takes time.
displacement is s.
Considering that
u = 20m/s
v = 0 m/s
Bus acceleration should be "a"
When using the first law of motion on a bus, we obtain
Let d represent the bus's distance traveled after braking.
a = -4 m/s²
Thus, when we use the third equation of motion on a bus, we obtain
As a result, the bus accelerates at a rate of -4 m/s2, and it travels 50 m after applying the brakes.
d = 50 m
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is the solution of b x 5/6 = 25 greater than or less than 25
Answers
The value of the equation is b = 30 , which is greater than 25
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
b x ( 5/6 ) = 25 be equation (1)
On simplifying the equation , we get
Multiply by 6 on both sides of the equation , we get
5b = 25 x 6
5b = 150
Divide by 5 on both sides of the equation , we get
b = 150 / 5
b = 30
So , the value of b is 30 and is greater than 25
b > 25
Hence , the equation is b = 30
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A total of $6000 is invested: part at 7% and the remainder at 11 %. How much is invested at each rate if the annual interest is $460?
Answers
Based on a system of equations, the investment at each rate is as follows:
At 7% = $5,000At 11% = $1,000.What is a system of equations?A system of equations, also known as simultaneous equations, yields the solutions to two or more equations solved concurrently or simultaneously.
We use the let statements to state the variables of simultaneous equations.
The total investment = $6,000
The total interest earned = $460
Interest rates:
A = 7%
B = 11%
Let investment A = a and investment B = b
Equations:0.07a + 0.11b = 460 ... Equation 1
a + b = 6,000 ... Equation 2
Multiply Equation 2 by 0.07:
Equation 3: 0.07a + 0.07b = 420
Subtract Equation 3 from Equation 1:
0.07a + 0.11b = 460
-
0.07a + 0.07b = 420
0.04b = 40
b = 1,000
= $1,000
From Equation 2:
a + b = 6,000
a + 1,000 = 6,000
a = 5,000
= $5,000
Thus, whereas $5,000 is invested at 7%, $1,000 is invested at 11%.
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Which of the following is the graph of the region 1
Answers
The graph of the region 1 <|x - 3| < 4 is a line segment from x = -1 to x = 7.
1. The equation |x - 3| = 1 can be rewritten as x - 3 = 1 or x - 3 = -1.
2. Solving for x, x = 4 or x = 2.
3. The equation |x - 3| = 4 can be rewritten as x - 3 = 4 or x - 3 = -4.
4. Solving for x, x = 7 or x = -1.
5. The graph of the region 1 <|x - 3| < 4 is a line segment from x = -1 to x = 7.
The graph of the region 1 <|x - 3| < 4 is a line segment from x = -1 to x = 7. To find the two endpoints of the line segment, we need to solve for x in the equations |x - 3| = 1 and |x - 3| = 4. The equation |x - 3| = 1 can be rewritten as x - 3 = 1 or x - 3 = -1, and solving for x gives us x = 4 or x = 2. The equation |x - 3| = 4 can be rewritten as x - 3 = 4 or x - 3 = -4 and solving for x gives us x = 7 or x = -1. Therefore, the graph of the region 1 <|x - 3| < 4 is a line segment from x = -1 to x = 7.
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the complete question is
Which of the following is the graph of the region 1 <|x - 3| < 4
A 6-sided die is rolled 2 times. What is the probability of getting 1 both times? (Give your answer as a fraction in simplest form.
Answers
Answer:1/36
Step-by-step explanation:
you have a 1 in 6 chance to get one out of a 6 sided die. U double that to get 1/36.
(2x^5+3y^4)(-4x^2+9y^4)
Answers
The simplified form of the expression (2x⁵ + 3y⁴)(- 4x² + 9y⁴)
is 36y⁸ - 8x⁷ + 18x⁵y⁴ - 12x²y⁴.
What is a polynomial?A polynomial is an algebraic expression.
A polynomial of degree n in variable x can be written as,
a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.
Given, A multiplication of two polynomials (2x⁵ + 3y⁴)(- 4x² + 9y⁴).
= 2x⁵(- 4x² + 9y⁴) + 3y⁴(- 4x² + 9y⁴).
= - 8x⁷ + 18x⁵y⁴ - 12x²y⁴ + 36y⁸. (multiplication of the same base is the
addition of exponents)
= 36y⁸ - 8x⁷ + 18x⁵y⁴ - 12x²y⁴.
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Which of the following are options you can select in the Top Values list for a query? Select all the options that apply.a. all b. 25% c. 5 d. none
Answers
All, 25%, and 5 are all valid options that can be selected in the Top Values list for a query.
All will display all the values in the query, 25% will display the top 25% of the values, and 5 will display the top 5 values.
To calculate 25%, we can use the formula (value/total)*100. For example, if the total number of values is 20, then 25% would be (20/20)*100 = 100. This would display all 20 values in the query. Similarly, if the total number of values is 50, then 25% would be (50/50)*100 = 100, which would also display all 50 values.
To calculate 5, we can use the same formula (value/total)*100. For example, if the total number of values is 20, then 5 would be (5/20)*100 = 25. This would display the top 5 values in the query. Similarly, if the total number of values is 50, then 5 would be (5/50)*100 = 10, which would also display the top 5 values.
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