The each angle measure of the trigonometric ratios are obtained.
Define the term trigonometric ratios?A mathematical discipline called trigonometry examines connections between triangles' sides and angles. Due to the fact that every straight-sided form can be decomposed into a group of triangles, trigonometry may be found across all of geometry.The given values is:
sin x = 0.7547,
Using trigonometric properties,
cos x = √(1 - sin²x)
= √(1 - 0.7547²)
cos x = 0.6560
Cosec x = 1 / sin x
= 1 / 0.7547
Cosec x = 1.3250
Now,
1 + cot²x = cosec²x
cot x = √(cosec²x - 1)
= √(1.3250² - 1)
cot x = 0.8692
tan x = 1 / cot x
= 1 / 0.8692
tan x = 1.1544
Thus, the each angle measure of the trigonometric ratios are obtained.
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Each of the 39 students in the eighth grade at Lincoln Middle School has one dog or one cat or both a dog and a cat. Twenty students have a dog and 26 students have a cat. How many students have both a dog and a cat?
Number of 7 students have both a dog and a cat, out of the 39 eighth grade students at Lincoln Middle School.
Total number of 8th grade students: 39
Number of students with a dog: 20
Number of students with a cat: 26
Number of students with both a dog and a cat: 20 + 26 - 39 = 7. Therefore, 7 have both a dog and a cat.
There are 39 students in the 8th grade at Lincoln Middle School. Of those students, 20 have a dog, 26 have a cat, and 7 have both a dog and a cat. To calculate this number, we added the number of students with a dog (20) and the number of students with a cat (26) and then subtracted the total number of students (39). The result of this calculation, 7, is the number of students who have both a dog and a cat. This means that 7 out of 39 8th grade students at Lincoln Middle School have a dog and a cat.
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Find the volume of the rectangular prism.
Answer:
Q9:
[tex]\boxed{V = \dfrac{7}{96}\;cubic\;feet}}[/tex]
Q10
[tex]\boxed{V = \dfrac{64}{125}\;cubic\;yards}[/tex]
Step-by-step explanation:
For a rectangular prism, the volume = length x width x height
Given these 3 dimensions simply multiply them to get the volume
Q9
[tex]V = \dfrac{7}{8} \cdot \dfrac{2}{3} \cdot \dfrac{1}{8}\\\\[/tex]
[tex]V = \dfrac{7\cdot 2\cdot 1}{8\cdot 3 \cdot 8}\\\\V = \dfrac{14}{192}\\\\[/tex]
Divide numerator and denominator to reduce to lowest fraction
[tex]V = \dfrac{14 \div 2}{192\div 2}\\\\\boxed{V = \dfrac{7}{96}\;cubic\;feet}}[/tex]
Q10
This is a cube since each side is the same length
For a cube of side a, the volume = a³
So for this particular cube
[tex]V = \left(\dfrac{4}{5}\right)^3\\\\\\\boxed{V = \dfrac{64}{125}\;cubic\;yards}[/tex]
first we translate b and place its tail at the tip of a, being careful to draw a copy of b that has the same length and direction. then we draw the vector a b (see the middle figure) starting at the ---select--- point of a and ending at the terminal point of the copy of
First, we translate b and place the tail at the tip of a, being careful to draw a copy of b that has the same length and direction. then we draw the vector a+b (see the middle figure) starting at the initial point of a and ending at the terminal point of the copy of b.
Alternatively, we could place b so it starts where a start and construct a+b by the parallelogram law as in the bottom figure.
The parallelogram law says that if we place two vectors so they have the same initial point, and then complete the vectors into a parallelogram, then the sum of the vectors is the directed diagonal that initiates at the same point as the vectors.
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draw the dot plot of the distribution of possible data values that has the largest possible standard deviation (there were ten people at the talk, so there should be ten dots on your dot plot)
The dot plot consists of ten dots, each representing the data value of a single person at the talk. The data values are spread out as far as possible, resulting in the largest possible standard deviation.
A dot plot is a graph that is used to represent the distribution of data. It consists of dots, each of which represents a single data value. In this case, the dot plot represents the distribution of possible data values from a talk with ten people. To achieve the largest possible standard deviation, the data points should be spread out as far as possible. Each dot should be placed on the graph in such a way that the difference between any two adjacent data points is maximized. This is done by placing the highest and lowest values at opposite ends of the graph, and then evenly spacing out the remaining data points in between. All of this should result in the largest possible standard deviation of the data set.
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the cup on the 9th hole of a golf course is located dead center in the middle of a circular green which is 30 feet in radius. your ball is located as in the picture below. the ball follows a straight line path and exits the green at the right-most edge. assume the ball travels 8 ft/sec. introduce coordinates so that the cup is the origin of an xy-coordinate system. provide numerical answers below with two decimal places of accuracy. (a) the x-coordinate of the position where the ball enters the green will be . (b) the ball will exit the green exactly 9.014 incorrect: your answer is incorrect. seconds after it is hit. (c) suppose that l is a line tangent to the boundary of the golf green and parallel to the path of the ball. let q be the point where the line is tangent to the circle. notice that there are two possible positions for q. find the possible x-coordinates of q: smallest x-coordinate
A circle is formed by all points on a plane equidistant from a given point
The possible x-coordinates of Q are -134.71 and +134.71
Known parameters are;
The radius of the golf course, r = 30 feet
Point the ball exits the green = The right-most edge
Speed of the ball = 8 ft./sec
Location of the cup = The origin (0, 0)
Location the ball starts = (-40. -50)
Required:
To find the possible x-coordinates of Q, the point where the line L parallel to the path of the ball is tangent to the circle
The coordinates of the rightmost edge of the golf course = (30, 0)
[tex]slope,m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
the slope of the path: [tex]m=\frac{-50-0}{-40-30}[/tex]
m=-50/-70
m=5/7
The equation of a circle is (x - h)² + (y - k)² = r²
The center of the circular green, (h, k) = (0, 0)
The equation of the given circle is (x - 0)² + (y - 0)² = x² + y² = 30²
the slope of the radius at the tangent Point [tex]m_{r} =-\frac{1}{m}[/tex]
The equation of the radius at a tangent point is therefore;
[tex]y=-\frac{7}{5} .x[/tex]
Which gives the equation of the circle as follows;
[tex]x^{2} +(-\frac{7}{5} .x)^2=30^2\\\\\frac{31.x^2}{25} =30^2\\\\x=\frac{\sqrt{30^2*25} }{31} \\\\x=\frac{750}{31}*\sqrt{31}[/tex]
x=±134.70
The possible x-coordinates of point Q are -134.70 and +134.70
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A construction company purchases a crane for $450,000. An accountant for the company figures the crane loses 30% of its value every year. The value of the crane can be computed after x years using the function V ( x ) = 450 , 000 ( 1 − 0.3 ) x . Use the graph to answer the following questions What is the value after 5 years? cells When will the value decline below $140000? (round to the nearest tenth).
The value of the company after 5 years is given as follows:
$75,631.5.
The value will decline below $140,000 when:
3.27 years.
What is the exponential function?The exponential function for this problem is defined as follows:
V(x) = 450000(0.7)^x.
The value after 5 years is found replacing the lone instance of x by 5, hence:
V(5) = 450000(0.7)^5
V(5) = $75,631.5.
The value will decline below $140,000 when at x for which V(x) = 140000, hence:
140000 = 450000(0.7)^x.
(0.7)^x = 140000/450000
(0.7)^x = 0.311111
xlog(0.7) = log(0.311111)
x = log(0.311111)/log(0.7)
x = 3.27 years.
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Repost but with a photo
Show your work
Simplify the equation below:
Answer:
With work shown...
Answer: 2^23 + 12 / 2
Step-by-step explanation:
WORK:
(1) -A negative base raised to an odd power equals a negative.
4^7 x (-8^3) + 12 / 2
(2) -Multiplying two negatives equals a positive: (-) x (-) = (+)
2^14 x 2^9 + 12 / 2
(3) -Calculate the product
2^23 + 12 / 2
The solution is located at the top.
Hope this helped <3
Use the number line to find the missing value. +(-4)=-1
The value of the missing number will be 3.
What is a number line?A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R."
It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.
The equation for the missing number is given as x + (-4) = -1. the missing number will be calculated as:-
x + (-4) = -1
x -4 = -1
x = 4 - 1
x = 3
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Solve the following radical equation
√4z²-13z+9+3=3z
To solve the radical equation √4z²-13z+9+3=3z, we need to get rid of the radical sign in order to isolate the variable.
First, we can add 9 to both sides to get:
√4z²-13z+12=3z+9
Then we can square both sides of the equation:
4z²-13z+12 = 9z²+27z+81
Now, we can rearrange the equation to get:
9z²-40z+69 = 0
Now we can use the quadratic formula to find the solutions for z:
z = (40 ± √(40²-4969)) / 2*9
z = (40 ± √(1600-2772)) / 18
z = (40 ± √(-1172)) / 18
Since the square root of a negative number is an imaginary number, this equation has no real solutions, which means that there are no values of z that will make the equation true.
So the radical equation √4z²-13z+9+3=3z doesn't have any solution.
The distance on the map from Chicago to NY is 1.5 inches. In reality, the distance from
Chicago to NY is 816 miles. On the map, the distance from Chicago to STL is 0.5 inches. How far in reality is the distance from Chicago to STL?
inches Inches
miles = miles
Answer: 272 miles
Step-by-step explanation:
The scale factor is [tex]\frac{816}{1.5}=544[/tex] inches per mile.
So, the distance from Chicago to STL is [tex]544(0.5)=272[/tex] miles.
In the given circle, the diameter EB is parallel to DC, and AB is parallel to ED. The angles AEB and ABE are in the ratio 4 : 5. What is the degree measure of angle BCD?
The degree measure of angle BCD is 130.
What is the measure of angle?
An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
Here, we have
Given: the diameter EB is parallel to DC, and AB is parallel to ED. The angles AEB and ABE are in the ratio 4: 5.
We can let ∠AEB be 4x and ∠ABE be 5x because they are in the ratio 4: 5.
When an inscribed angle contains the diameter, the inscribed angle is a right angle. Therefore by the triangle sum theorem,
= 4x+5x+90 = 180
x = 10 and
∠ABE = 50.
∠ABE =∠BED because they are alternate interior angles and AB||ED.
Opposite angles in a cyclic quadrilateral are supplementary,
so ∠BED + ∠BCD = 180
Use substitution to get ∠ABE + ∠BCD = 180
50 + ∠BCD = 180
∠BCD = 130
Hence, the degree measure of angle BCD is 130.
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The inventory of Royal Decking consisted of five products. Information about the December 31, 2021, inventory is as follows:
Per Unit
Product Cost Selling Price
A $ 130 $ 150
B 170 190
C 130 170
D 90 120
E 50 70
Costs to sell consist of a sales commission equal to 10% of selling price and shipping costs equal to 10% of cost.
Required:
What unit value should Royal Decking use for each of its products when applying the lower of cost or net realizable value (LCNRV) rule
The unit value should Royal Decking use for each of its products,
Product A: $8 (loss),
Product B: $16 (loss),
Product C: $10 (profit),
Product D: $9 (profit),
Product E: $8 (profit).
What is the unit value?The sum of the quantities divided by the total value of purchases and sales yields the unit value of a group of similar goods. As a result, it represents a quantity-weighted average of the various prices at which the good is bought and sold.
Given inventory,
Product Cost Selling Price
A $130 $150
B $170 $190
C $130 $170
D $90 $120
E $50 $70
a sales commission equal to 10% of the selling price and shipping costs equal to 10%,
Product A :
the unit value is given by,
Value = selling price - (product cost + sales commission + shipping cost)
= $150 - ($130 + 10% x selling price + 10% x product cost)
= $150 - ($130 + 10% x $150 + 10% x $130)
= $150 - ($130 + $15 + $13)
= -$8 = $8 (loss)
Product B :
Value = selling price - (product cost + sales commission + shipping cost)
= $190 - ($170 + 10% x selling price + 10% x product cost)
= $190 - ($170 + 10% x $190 + 10% x $170)
= $190 - ($170 + $19 + $17)
= -$16 = $16 (loss)
Product C :
Value = selling price - (product cost + sales commission + shipping cost)
= $170 - ($130 + 10% x selling price + 10% x product cost)
= $170 - ($130 + 10% x $170 + 10% x $130)
= $170 - ($130 + $17 + $13)
= $10 = $10 (profit)
Product D :
Value = selling price - (product cost + sales commission + shipping cost)
= $120 - ($90 + 10% x selling price + 10% x product cost)
= $120 - ($90 + 10% x $120 + 10% x $90)
= $120 - ($90 + $12 + $9)
= $9 = $9 (profit)
Product E :
Value = selling price - (product cost + sales commission + shipping cost)
= $70 - ($50 + 10% x selling price + 10% x product cost)
= $70 - ($50 + 10% x $70 + 10% x $50)
= $70 - ($50 + $7 + $5)
= $8 = $8 (profit)
Hence unit value for each product is -$8, -$16, $10, $9, and $8.
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HELP ME BRO PLEASE this due tonight ion even know what to do frfr
Answer: (-1, 5)
Step-by-step explanation: I wrote down all the explanations refer to the image please
the sum of a number with the square of its following algebraic language
[tex]\bold{n + (n+1)^{2}}[/tex]
Step by step explanation:An unknown number can be interpreted with any letter of the alphabet, they will be our unknowns to be able to form an algebraic expression.
Well, in this case, I will use the variable n, to name the unknown number.
Let "n" be the number, the square of it is; n² and the following number results from adding the unit; then (n + 1) will be the next of the number.
(grouping the data the following algebraic expression is obtained):
[tex]\bold{n + (n+1)^{2}}[/tex]
Answer:
(n + 1 )
Let "n" be the number, the square of it is; n² and the following number results from adding the unit; then (n + 1) will be the next of the number.
(strang 5.2.15) consider the determinants of the n-by-n tridiagonal matrices containing only 1s for the nonzero elements:
The determinant of an n-by-n tridiagonal matrix containing only 1s can be calculated by iterating over the diagonal elements and summing the products of each element and its corresponding power of 1
The determinant of an n-by-n tridiagonal matrix containing only 1s as nonzero elements is given by the formula:
det(A) = 1^n-2 + 1^n-3 + ... + 1^2 + 1
For example, consider the 3x3 matrix:
A = [1 1 0; 1 1 1; 0 1 1]
Using the formula above, the determinant of A can be calculated as:
det(A) = 1^2 + 1 = 2
More generally, the determinant of an n-by-n tridiagonal matrix containing only 1s can be calculated by iterating over the diagonal elements and summing the products of each element and its corresponding power of 1. This sum can then be taken to the power of 1 to obtain the determinant of the matrix.
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Classify these events. Some businesses have large stores and some businesses have large parking lots. These events would be considered:SubjectiveIndependentDependentClassical
These events would be considered as: Subjective, Independent, Dependent, Classical
Subjective event: An event that is based on individual opinion or belief. This event would not be represented by a formula or calculation.
Independent event: An event that is not influenced by other events. This event can be represented by a formula such as P(A) = P(A) which calculates the probability of an event occurring on its own.
Dependent event: An event that is influenced by other events. This event can be represented by a formula such as P(A|B) = P(A ∩ B) / P(B) which calculates the probability of an event occurring given that another event has already occurred.
Classical event: An event that is determined by predetermined probabilities or odds. This event can be represented by a formula such as P(A) = n(A) / n(S) which calculates the probability of an event occurring based on the number of favorable outcomes divided by the total number of outcomes.
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A randomly selected sample of 1,000 college students was asked whether they had ever used the drug Ecstasy. Sixteen percent (16% or 0.16) of the 1,000 students surveyed said they had. Which one of the following statements about the number 0.16 is correct?Select one:A. It is a randomly chosen numberB. It is a population proportionC. It is a sample proportionD. It is a margin of error
It is a sample size proportion. 0.16 is the proportion of the 1,000 college students that reported using Ecstasy, which is a measure of the sample.
The number 0.16 is a sample proportion. This means that it is the proportion of the sample of 1,000 college students that reported using the drug Ecstasy. A sample proportion is a measure of the sample, not of the population. It is not a randomly chosen number and it is not a margin of error. A margin of error is a measure of how accurate a sample statistic is likely to be, usually expressed as a percentage or a number of standard deviations. A population proportion is the proportion of the total population that holds a certain characteristic or has had a certain experience. Thus, 0.16 is a sample proportion and not a population proportion, margin of error, or randomly chosen number
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[References]
a. When 36.714 and 98.77 are multiplied, the answer should have
Enter the answer, using the correct number of significant figures:
36.714 x 98.77 =
=
[Review Topics]
b. When 36.714 and 98.77 are summed, the answer should have
point.
Enter the answer, using the correct number of decimal places:
36.714+98.77=
significant figure(s).
digit(s) after the decimal
36.714 x 98.77 = 3627.7198
36.714 + 98.77 = 135.484 (4 decimal places)
4
10 points
(x-3)²
O x² - 6x +9
O x²-9
Ox+9
O x² +9
The correct expression is a) [tex]x^2-6x+9[/tex].
What is expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
Here the given expression is ,
=> [tex](x-3)^2[/tex]
Now using formula [tex](a-b)^2=a^2-2ab+b^2[/tex] then
=> [tex]x^2-2.x.3+3^2[/tex]
=> [tex]x^2-6x+9[/tex]
Hence the correct answer is a) [tex]x^2-6x+9[/tex].
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the following equation has two different solutions. solve the equation by factoring and place one solution in each answer box. the larger answer goes in box 1. the smaller solution should go in box2. solve for x: x^2 +16x + 63 = 0Box1 (Larger Solution): Box2 (Smaller Solution):
Box1: x = -9 Box2: x = 7
For this equation, we need to factor the left side of the equation to solve it. To do this, we need to find two numbers that multiply to give us 63 and add to give us 16.
The two numbers are -9 and +7.
So, the factored equation is (x - 9)(x + 7) = 0.
For this equation, we need to factor the left side of the equation to solve it. To do this, we need to find two numbers that multiply to give us 63 and add to give us 16.
To solve the equation, we set each factor equal to zero and solve for x.
x - 9 = 0 -> x = 9
x + 7 = 0 -> x = -7
Therefore, the larger solution is x = -9, and the smaller solution is x = 7.
Therefore, the answer is Box1: x = -9 and Box2: x = 7.
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a boy has color blindness and has trouble distinguishing between blue and green. there are 75 blue pens and 25 green pens mixed together in a box. given that he picks up a blue pen, there is a 80% chance that he thinks it is a blue pen and a 20% chance that he thinks it is a green pen. given that he picks a green pen, there is an 90% chance that he thinks it is a green pen and a 10% chance that he thinks it is a blue pen. assume that the boy randomly selects one of the pens from the box.
a) There is a 60% probability that the boy picks up a blue pen and recognizes it as blue.
b) There is a 62.5% probability that the boy chooses a pen and thinks it is blue.
c) Given that the boy thinks he chose a blue pen, there is a 96% probability that he actually chose a blue pen.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
The following probabilities are given -
A 75% probability that a pen is blue.
A 25% probability that a pen is green.
If a pen is blue, an 80% probability that the boy thinks it is a blue pen.
If a pen is blue, a 20% probability that the boy thinks it is a green pen.
If a pen is green, a 90% probability that the boy thinks it is a green pen.
If a pen is green, a 10% probability that that the boy thinks it is a blue pen.
a) The probability that the boy picks up a blue pen and recognizes it as blue.
There is a 75% probability that he picks up a blue pen.
There is a 80% probability that he recognizes a blue pen as blue.
So, the equation will be -
P = 0.75 × 0.8
P = 0.6
Therefore, there is a 60% probability.
b) The probability that the boy chooses a pen and thinks it is blue.
There is a 75% probability that he picks up a blue pen.
There is a 80% probability that he recognizes a blue pen as blue.
There is a 25% probability that he picks up a green pen
There is a 10% probability that he thinks a green pen is blue.
So, the equation will be -
P = (0.75 × 0.80) + (0.25 × 0.10)
P = 0.6 + 0.025
P = 0.625
Therefore, there is a 62.5% probability.
c) Given that he thinks he chose a blue pen, the probability that he actually chose a blue pen.
There is a 62.5% probability that he thinks that he choose a blue pen.
There is a 60% probability that he chooses a blue pen and think that it is blue.
So, the equation will be -
P = 0.6/0.625
P = 0.96
Therefore, there is a 96% probability.
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A boy has color blindness and has trouble distinguishing blue and green. There are 75 blue pens and 25 green pens mixed together in a box. Given that he picks up a blue pen, there is a 80% chance that he thinks it is a blue pen and a 20% chance that he thinks it is a green pen. Given that he picks a green pen, there is an 90% chance that he thinks it is a green pen and a 10% chance that he thinks it is a blue pen. Assume that the boy randomly selects one of the pens from the box.
a) What is the probability that he picks up a blue pen and recognizes it as blue?
b) What is the probability that he chooses a pen and thinks it is blue?
c) (Given that he thinks he chose a blue pen, what is the probability that he actually chose a blue pen?
given: - > 10. choose the solution set. {x | x < -40/7} {x | x > -35/2} {x | x < -35/2} {x | x > -40/7}
The solution set is {x | x < -35/2} and {x | x > -40/7}.
To find the solution set of these two inequalities, first we need to solve them.
The first inequality is x < -40/7. To solve this inequality, we need to divide both sides of the inequality by -7. This gives us x > -40/7.
The second inequality is x > -35/2. To solve this inequality, we need to divide both sides of the inequality by 2. This gives us x < -35/2.
Therefore, the solution set is {x | x < -35/2} and {x | x > -40/7}.
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compare the values of the method of moments estimate and the maximum likelihood estimate if a random sample of size 5 consists of the numbers 17, 92, 46, 39, and 56
The method of moments estimate and the maximum likelihood estimate are the same.
The method of moments estimate is the sample mean, which can be calculated by adding the numbers together and dividing by 5. In this example, the mean is 52. The maximum likelihood estimate is the mean of the population distribution, which can be estimated by maximizing the likelihood function. This involves taking the partial derivatives with respect to the parameters and solving for the values that make the derivative equal to zero. In this example, the maximum likelihood estimate will also be 52. Thus, the method of moments estimate and the maximum likelihood estimate are the same.
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If you dissolved 50 grams of sugar in 30 grams of water. What would the sugar concentration be?
According to the information, the concentration of sugar in this solution is 62.5%.
How to calculate the concentration of sugar?To calculate the concentration of sugar we have to divide the mass of the solute by the mass of the solution and then multiply it for 100.
Equation:
(Mass of solute / Mass of the solution ) x 100Mass of the solute (sugar) = 50gMass of the solvent (water) = 30gMass of the solution (sugar + water) = 30g + 50g = 80gThe sugar concentration = 50g/80g x 100 = 62.5%
Therefore, the sugar concentration is 62.5%.
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Suppose that $5,800 is invested at 4.6% annual interest rate, compounded monthly. How much money will be in the account in (A) 6 months? (B) 4 years?
Answer:
Step-by-step explanation:
5800 divided by 100=58x4.6=126 something like that
Which equation has exactly two real and two nonreal solutions?
We got two real solutions (-3,+3) and two non real solutions (-2i,+2i)
Therefore, x³+2x² +x-7=0 is correct answer.
What is real and nonreal solution?An a non real solution uses non real numbers to solve the equation, which cannot be solved with real numbers. Back to the school answer: A non-real solution to a math equation is a solution that has “imaginary numbers” (also called “complex numbers”) in it because it cannot be solved with real numbers.
Step1
We need to find equation that has exactly two real and two non real solutions
2 real and 2 non real solution means 4 solutions
x³ equation has maximum of 3 solutions
So we ignore equation that has largest exponent x³
We ignore options B and D
Let check option A
x⁴ 36x² =0
factor the left hand side
Factor out x^2
x² (x² -36)=0
WE set each factor =0 and solve for x
x² =0 so x=0
x² - 36 =0 so x= +-6
So solutions are x=0, x=6 , x= -6. Only 3 real solutions we got
LETS check with option C
x⁴ - 5x² -36=0
Factor left hand side
(x² -9)(x² +4)=0
set each factor =0 and solve for x
x² -9 =0 so x= -3, + 3
x² + 4 =0 , x² = -4, so x= +2i, -2i
So we got two real solutions (-3,+3) and two non real solutions (-2i,+2i)
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10 points
Find the product of (x + 5)(x - 5). (1 point)
x² - 10x + 25
x² + 10x + 25
Ox²-25
Ox²+25
Find the product of (2x + 5y)(2x - 5y). (2 points)
4x² - 20xy + 25y²
4x²+20xy + 25y²
4x²+25y²
4x²-25y²
Answer:
Solution in attached photo.
Step-by-step explanation:
SolutionTo expand the brackets, we will use the rainbow expansion method.
Which function is the inverse of
f(x)= sq x-2
6
The inverse function of the function f(x) will be f⁻¹(x) = 36x² + 2. Then the correct option is A.
What is the inverse function?Let the function f is given as
y = m(x + a) + c
Then the inverse function of the function f will be given by swapping x with y and y with x.
The function is given below.
f(x) = √(x - 2) / 6
Replace x with y and f(x) with x. Then the inverse function is given as,
x = √(y - 2) / 6
6x = √(y - 2)
36x² = y - 2
y = 36x² + 2
f⁻¹(x) = 36x² + 2
The inverse function of the function f(x) will be f⁻¹(x) = 36x² + 2. Then the correct option is A.
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The complete question is given below.
Translate this sentence into an equation 12 more than Craig’s score is 70 use the variable c to represent his score
Reason:
c = Craig's score
c+12 = twelve more than Craig's score
c+12 = 70 because the key term "is" translates to "equals". As an example, saying "x is 5" means "x = 5".
use the ressult of the simulation to explain why you think the smaple orvoideso r does not provide evidence that the standard deviation of the uice dispened exceeds .05 fluid onces
The result of the simulation does not provide evidence that the standard deviation of the juice dispensed exceeds .05 fluid ounces because the simulation does not indicate any instances where the standard deviation of the juice dispensed was greater than .05 fluid ounces. This indicates that the variability of the juice dispensed was within the acceptable sum range of .05 fluid ounces or less.
The simulation did not indicate any instances where the standard deviation of the juice dispensed was greater than .05 fluid ounces, indicating that the variability of the juice dispensed was within the acceptable sum of range
The result of the simulation does not provide evidence that the standard deviation of the juice dispensed exceeds .05 fluid ounces because the simulation does not indicate any instances where the standard deviation of the juice dispensed was greater than .05 fluid ounces. This indicates that the variability of the juice dispensed was within the acceptable range of .05 fluid ounces or less.
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