Step-by-step explanation:
for questions about % always find out first what 100% or what 1% are.
everything else can be calculated out of these 2 numbers.
in our case here
100% = 389 ml
1% = 100%/100 = 389/100 = 3.89 ml
18.6% = 18.6×1% = 18.6 × 3.89 = 72.354 ml
so, there are 72.354 ml of acid in the solution.
FYI
as you can see, we can combine both steps into one and do any of the following
18.6% = 18.6 × 100%/100 = 18.6 × 389/100 =
= (18.6/100) × 389 = 0.186 × 389
Sliding Ladder A 13-ft ladder i leaning againt a houe
(ee figure) when it bae tart to lide away. By the time the
bae i 12 ft from the houe, the bae i moving at the rate of
5 ft/ec
The angle between the ladder and the ground is decreasing at the rate of 1 ft/sec.
According to the question,
A sliding ladder of length let L=13ft.
Let the ladder touches the house at height h and touches the ground
x ft from the house. This is shown in the figure.
In ΔABC,
θ = [tex]cos^{-1} \frac{AB}{BC}[/tex]
⇒ θ = [tex]cos^{-1} \frac{x}{BC}[/tex]
⇒ dθ/dt= [tex]\frac{d}{dt} cos^{-1} \frac{x}{BC}[/tex]
⇒ dθ/dt= [tex]\frac{-1}{\sqrt{1 - (\frac{x}{13} )^{2} } } \frac{1}{13} \frac{dx}{dt}[/tex]
substituting the value of x=12ft and [tex]\frac{dh}{dt} = 5ft/sec[/tex] , we have
⇒ dθ/dt= [tex]\frac{-1}{\sqrt{1 - (\frac{12}{13} )^{2} } } \frac{1}{13} (5)[/tex]
⇒ dθ/dt= [tex]\frac{-1}{\frac{5}{13} } \frac{1}{13} (5)[/tex]
dθ/dt= -1
so the angle between the ladder and the ground is decreasing at the rate of 1 ft/sec.
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The complete question is:
A 13 ft. ladder is leaning against a wall when its base starts to slide away At the instant when the base is 12 ft. away from the wall, the base is moving away from the wall at the rate of 5 ft/sec. The rate at which the angle θ between the ladder and the ground is changing is -
Solve 4a^4 - 8a^2+4 = 0 for a and list all of the solutions. Explain how you got your answer.
[tex]4a^4-8a^2+4=0\implies 4(a^4-2a^2+1)=0\implies a^4-2a^2+1=0 \\\\\\ (a^2)^2-2a^2+1=0\implies (a^2-1)(a^2-1)=0\implies a^2=1 \\\\\\ a=\pm\sqrt{1}\implies a=\pm 1[/tex]
C) Assessment Practice 20. Which expressions are equivalent to -6z+(-5.5) 3.5z-5y-2.5
The given expression is not an equivalent expression.
What is an equivalent expression?
An equivalent expression is a mathematical expression that has the same value as another expression, even though they may appear to be different. Equivalent expressions are obtained by using the same operations or by making substitutions that preserve the value of the expression.
The expressions -6z + (-5.5) and 3.5z - 5y - 2.5 are not equivalent. They have different coefficients for the variables z and y, and different constants. To determine if two expressions are equivalent, you need to check that they have the same value for all possible values of the variables. If the values are the same for all inputs, then the expressions are equivalent. If the values are not the same for all inputs, then the expressions are not equivalent.
Hence, the given expression is not an equivalent expression.
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What is the quotient of 3 and 15?.
The quotient of 3 and 15 is 0.2.
The division is breaking something up into equal parts. The Dividend is the whole we start with, the Divisor is what you use to divide up the whole, and the Quotient is the answer like this:
Dividend ÷ Divisor = Quotient
So if asked that, "What is the quotient of 3 and 15?" it means sense that 3 is the Dividend, 15 is the Divisor, and you want to know the Quotient. Thus, the answer is:
3 ÷ 15 = 0.2
Therefore, the quotient of the given question, 3 and 15, that is, 3 ÷ 15 is equal to 0.2.
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If AB = 12, then A’B’ =
The solution is, A’B’ = 12 units, when AB = 12.
What is transformation?A transformation is a dramatic change in form or appearance. An important event like getting your driver's license, going to college, or getting married can cause a transformation in your life. A transformation is an extreme, radical change.
here, we have,
Given
Line segment AB = 12 units
Translation of AB → A'B' by the rule T(x +0, y+5)
This translation won't change the length of A'B' as the difference in (x2-x1) and (y2-y1) stays same
because x-coordinate stays as is and y-coordinate's change cancelled when subtracting.
So, A'B' = 12 units.
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A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 35% salt and Solution B is 60% salt. She wants to obtain 50 ounces of a mixture that is 55% salt. How many ounces of each solution should she use?
Answer:
Step-by-step explanation:From the issue, we may deduce that:
x + y = 50 She desires to produce 50 ounces of the combination (because to this).
(0.35x) + (0.60y) = 0.55(x+y) (because we're calculating the amount of salt in each solution and the combination contains 55% salt)
We may take the first equation and replace it in the second equation:
(0.35x) + (0.60y) = 0.55(50) (50)
0.35x + 0.60y = 27.5 when x is substituted.
A system of two equations with two variables is now available:
x + y = 50\s0.35x + 0.60y = 27.5
To determine one of the variables in terms of the other, we may utilize the first equation. Let's figure out y:
y = 50 - x
We now change y in the second equation to the following expression:
0.35x + 0.60(50-x) = 27.5
Finding the value of x:
0.35x + 30 - 0.6x = 27.5
0.25x= -2.5
x= -10
Since the number of ounces cannot be negative, the answer is illogical. As a result, you should double-check your calculations or determine if the issue statement contains a mistake.
To get the answer, you can also try an alternative approach like substitution or elimination. Then, double-check your calculations.
Alex purchased 29 4 x 6 prints in 16 5 x 7 prints from an online printing service and paid $22.89. if 5 x 7 prints cost $.84 more than 4 x 6 prints, how much does a 5 x 7 print cost?
The amount of money that Alex will use to purchase the 5 x 7 print would be = $11.89.
What is online printing service?An online printing service is the service that is rendered online that helps interested individuals to prepare their printed paper works.
The number of 4 x 6 prints(X) purchased by Alex = 29
The number of 5 x 7 prints (y) purchased by Alex = 16
The total amount he paid for the whole service = $22.89
The cost of 5 x 7 prints can be calculated using this expression;
22.89 - 0.84 = 22.05/2 = 11.025
Therefore the cost of 5×7 prints = 11.05+ 0.84 = $11.89.
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Swimming Pool On a certain hot summer's day, 602 people used the public swimming pool. The daily prices are $1.50 for children and $2.50 for adults. The receipts for admission totaled $1228.00
How many children and how many adults swam at the public pool that day?
There were
children at the public pool.
1.59C + 2.25A = 786.75
C + A = 33 (even if all were the higher paying adults, that would only be 33x2.25=74.25 far less than <<786.75)
1.59C + 1.59A = 33(1.59) = 52.47 subtract to eliminate C
(2.25-1.59)A = 786.75 -52.47 = 734.28
.66A = 734.28
A = 73428/66 = 1112.55 = about 1113 adults
C = 33-1113 = -1080 children
which makes no sense. over a thousand "negative" children? the public pool gave refunds to over a thousand prepaid children who didn't show up? but a public swimming pool, no matter how large, probably wouldn't accomodate 1113 adults.
What is the difference between the largest 5 digit number and smallest 6 digit number?.
The difference between the largest 5-digit number and the smallest 6-digit number is 1.
The aim is to find the largest 5-digit and the smallest 6-digit numbers, and then we need to identify the difference between these two values.
Let's start by finding the smallest 6-digit number.
We know that 0 is the smallest digit that can not be used in the highest place value, so we will consider the next smallest digit; that is, 1 and 1 can be used in the highest place value.
Thus, we can create the required 6-digit smallest number with 0 and 1.
Hence, the smallest 6-digit number is 100000.
Now, we will discover the largest 5-digit number.
As we know, the largest digit is 9, which can be used anywhere. So, we will form the largest 5-digit number with the digit 9.
Thus, the largest 5-digit number is 99999.
Next, we need to find the difference between these two values.
So, we can determine the difference between the smallest 6-digit number and the largest 5-digit number by subtracting the smallest from the largest.
Thus, we get,
⇒100000 - 999999
⇒1
Hence, 1 is the difference between the smallest 6-digit and the largest 5-digit numbers.
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please help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!! piecewise function
Answer:
Undefined
Step-by-step explanation:
The function is defined in the domain (1, +∞)
Any value in the range of (-∞, 1] is undefined
31.002 in expanded form
Answer: 30+1+.002
Step-by-step explanation:
Just break it up into number groups. Like tens, ones, or hundreds
To produce function g, function f was reflected over the x-axis and. Function g is defined as.
To produce g, function was reflected over the x-axis and | shifted up 3 units . Function g can be defined as g(x)=f(x-1)+4.
What is axis ?
An axis is a straight line around which an object or a geometric shape can rotate or be symmetrical. In a coordinate system, an axis is a line that serves as a reference for the location of points in space.
When a function f(x) is reflected over the x-axis, it changes the sign of the y-coordinate values. By reflecting the graph of f(x) over the x-axis, the new function g(x) will have the same shape as f(x) but with all y-coordinate values inverted.
Additionally, by shifting the function up 3 units, it means that the y-coordinate values of the new function g(x) will be 3 units greater than the y-coordinate values of the original function f(x).
So the transformation can be represented as:
g(x) = f(x-1) + 4
It is the horizontal shift of 1 unit to the right, and a vertical shift of 3 units up
To produce g, function was reflected over the x-axis and | shifted up 3 units . Function g can be defined as g(x)=f(x-1)+4.
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In the following function defined by an equation in the form y = a x squared + b x + c, identify the values of a, b, and c. y = two-thirds x squared + 3 a. a = 0, b = two-thirds, c = 3 b. a = two-thirds, b = 0, c = 3 c. a = 0, b = 3, c = two-thirds d. a = two-thirds, b = two-thirds, c = 3
b. a = two-thirds, b = 0, c = 3 c is correct
We have to find the values of a, b, and c of the equation:
y = 2/3 x square + 3 (Given)
y = 2/3 x square + 3 which is in the form of y = ax square + bx +c
y = 2/3 x square + (0)b + 3
therefore, a = 2/3 , b = 0, c= 3
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HELP PLEASE!
At the beginning of a storm, a pond was 8 cm deep. During the storm, the depth increased by 1.5 cm every hour for 8 hours.
Click "Show your work" to graph the function in the whiteboard.
What are the law of exponential and logarithmic function?.
The law of exponential and logarithmic function is that the logarithmic functions are the inverses of the exponential functions.
According to the first law, we can multiply two exponential functions with the same base by adding their respective exponents. According to the second law, the exponents must be subtracted in order to divide two exponential functions with the same base.
According to the third law, we must multiply the exponents in order to raise a power to a new power. According to the fourth and fifth laws, we must raise each factor to the same power in order to raise a product or quotient to that power.
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Quadrilateral DEFG is similar to quadrilateral HIJK. Find the measure of side IJ.
Figures are not drawn to scale.
D
E
6
F
H
23.6
I
J
Answer:
23.6 units.
Step-by-step explanation:
Since quadrilateral DEFG is similar to quadrilateral HIJK, the ratios of corresponding sides are equal. We can use this information to find the measure of IJ.
We know that:
DF/HJ = EF/IJ = 6/23.6 = 2/8 = 1/4
So we can set up the proportion:
IJ/EF = HJ/DF
IJ/6 = 23.6/6
IJ = 23.6/6 * 6 = 23.6
For babysitting, Nicole charges a flat fee of $3, plus $5 per hour. Write an equation in slope-intercept form that models this situation.
Answer:
Step-by-step explanation:
y=5x(dollars per hour)+3(flat fee)
y=5x+3
Samuel has 1 cup of rubbing alcohol and will use the entire amount. He plans to store the cleaning solution in containers that each hold a maximum of 6 cups. How many containers does he need.
Samuel needs a total of 6 containers for his plan
How to determine the number of container he needs?The complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
1 cup of rubbing alcohol = 1/(1/2) = 2 shares
Also, we have
1 cup of rubbing alcohol contains = 1 + 1/2 + 16 = 17.5
For the 2 shares calculated above, we have
2 shares = 17.5 * 2
Evaluate
2 shares = 35
Given that each can hold a maximum of 6 cups, the number of containers needed is
Container = 35/6
This gives
Container = 5.83
Round up
Container = 6
Hence, he needs 6 containers
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Solve each equation and please answer like (x,y) x=smaller number y=larger number:
1: x(x-32)=0
2: (y-3) (y+2) =0
3: (2y+5)(y-4)=0
4: 2z^2+20z=0
5: 9x^2 =27x
Quadratic equations' solutions are x=0, x=32 , y=3, y=-2 , [tex]y=-\frac{5}{2}, y=4$$[/tex] , z=0, z=-10 , and x=0, x=3
What is the quadratic equation ?[tex]$$x(x-32)=0 \quad: \quad x=0, x=32$$[/tex]
Steps
x(x-32)=0
If a b=0, then either a=0 or b=0, according to the Zero Factor Principle.x=0 or x-32=0
Solve x-32=0: x=32
The following are the quadratic equation's solutions:
x=0, x=32
2 . [tex]$$(y-3)(y+2)=0 \quad: \quad y=3, y=-2$$[/tex]
Steps
(y-3)(y+2)=0
If a b=0, then either a=0 or b=0, according to the Zero Factor Principle. y-3=0 or y+2=0
Solve y-3=0 : y=3
Solve y+2=0 : y=-2
The following are the quadratic equation's solutions:
y=3, y=-2
3. [tex](2 y+5)(y-4)=0 \quad: \quad y=-\frac{5}{2}, y=4$$[/tex]
Steps
(2 y+5)(y-4)=0
If a b=0, then either a=0 or b=0, according to the Zero Factor Principle. 2 y+5=0 or y-4=0
Solve 2 y+5=0: y=-[tex]\frac{5}{2}[/tex]
Solve y-4=0 : y=4
The following are the quadratic equation's solutions:
[tex]y=-\frac{5}{2}, y=4$$[/tex]
4.[tex]$$2 z^2+20 z=0 \quad: \quad z=0, z=-10$$[/tex]
steps
[tex]$$2 z^2+20 z=0$$[/tex]
The following are the quadratic equation's solutions:
[tex]$$z_{1,2}=\frac{-20 \pm \sqrt{20^2-4 \cdot 2 \cdot 0}}{2 \cdot 2}$$$$\sqrt{20^2-4 \cdot 2 \cdot 0}=20$$$$z_{1,2}=\frac{-20 \pm 20}{2 \cdot 2}$$[/tex]
Distinguish the answers
[tex]$$\begin{aligned}& z_1=\frac{-20+20}{2 \cdot 2}, z_2=\frac{-20-20}{2 \cdot 2} \\& z=\frac{-20+20}{2 \cdot 2}: 0 \\& z=\frac{-20-20}{2 \cdot 2}:-10\end{aligned}$$[/tex]
The following are the quadratic equation's solutions:
z=0, z=-10
5 .
[tex]$$\begin{aligned}& 9 x^2=27 x: x=0, x=3 \\& \text { Steps } \\& 9 x^2=27 x\end{aligned}$$[/tex]
Move 27 x to the left side
[tex]$$9 x^2-27 x=0$$[/tex]
[tex]$$\begin{aligned}& \text { Factor } 9 x^2-27 x: \quad 9 x(x-3) \\& 9 x(x-3)=0\end{aligned}$$[/tex]
If a b=0, then either a=0 or b=0, according to the Zero Factor Principle. x=0 or x-3=0
Solve x-3=0: x=3
The following are the quadratic equation's solutions
x=0, x=3
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in the figure PQ is parallel to RS the length of PQ is 2 cm; the length of RS is 6 cm; the length of QT is 4 cm what is the length of TS
The length of TS in ΔTRS using Similarity of triange is 12 cm .
What is Similarity of Triangles ?If two items have the same shape or have the same shape as their mirror images, they are said to be Similar. One can be produced from the other more accurately by evenly scaling it, perhaps with the addition of further translation, rotation, and reflection.
If the sides are in the same ratio or proportion and the angles are equal (corresponding angles), two triangles will be comparable (corresponding sides). Similar triangles may have varying individual side lengths, but they must have equal angles and the same scale factor or matching ratio of the side lengths. If two triangles resemble one another, then
Triangles with similar angle pairings have all the same angles.Triangles have proportionate sides on all matching sides.In ΔTPQ and ΔTPS
∠T is common in both triangle
PQ ║ RS
∴∠TPQ = ∠TRS (Corresponding Angles)
similarly ,
∠TQP = ∠TSR
∴ Δ TPQ ~ ΔTRS
So,
PQ/ RS = TQ/ TS
⇒ 2/ 6 = 4 / TS
⇒TS = (4*6)/2 = 12
The length of TS in ΔTRS using Similarity of triange is 12 cm .
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The length of TS in ΔTRS using Similarity of triangel is 12 cm .
What is meant by length ?
The term "length" is used to describe an object's size or the separation between two points.For instance, the length of a ruler is revealed in the table below.The distance separating an object's ends is its length. The longest dimension is this one. The width of an object is the separation between its two sides. The shortest dimension is this one.Using measuring instruments like a ruler, measuring tape, etc., one may measure the length of any object. A ruler can be used to determine, for instance, how many inches a pencil is long. A foot scale can be used to gauge the height of each student in a class.In ΔTPQ and ΔTPS
∠T is common in both triangle
PQ ║ RS
∴∠TPQ = ∠TRS (Corresponding Angles)
similarly ,
∠TQP = ∠TSR
∴ Δ TPQ ~ ΔTRS
So,
PQ/ RS = TQ/ TS
⇒ 2/ 6 = 4 / TS
⇒TS = (4*6)/2 = 12
The length of TS in ΔTRS using Similarity of triange is 12 cm.
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Is AABC AQRP? Explain
A No, SSA is not a thing
B Yes, by SAS
C) Yes, by HL
D No, not enough information
There are 4 boxe of apple there are 10 apple in each box how many apple are there in all
By using the multiplication formula, the number of apples in all 4 boxes are 40.
Aside from addition, subtraction, and division, multiplication is also considered to be one of the four fundamental mathematical operations. Multiplying in mathematics refers to the process of repeatedly adding together groups of the same size.
The multiplication formula is expressed as:
Multiplicand × Multiplier = Product
Where:
Multiplicand: The first number (factor)
Multiplier: The second number (factor)
Product: The final result after multiplying the multiplicand and multiplier
In this case, we are given that:
Multiplicand = 4 boxes
Multiplier = 10 apples
Thus, the number of apples in 4 boxes are:
Product = 4 x 10
Product = 40
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A patio has an area of 214
2
1
4
square yards. 34
3
4
of the patio is carpeted. What is the area of the carpeted part of the patio?
The area of the carpeted part of the patio is 1 [tex]\frac{11}{16}[/tex] square yards.
What are Mixed Fractions?Mixed fractions are type of fractions which consist of a whole number part and a fractional part.
Mixed fractions are of the form a b/c where a is the whole number part and b/c is the fractional part.
Given that,
Area of the patio = 2 1/4 square yards
= (2 × 4 + 1) / 4 square yards
= 9/4 square yards
Also given that, 3/4 of the patio is carpeted.
Area of the carpeted part of the patio = 3/4 (9/4)
= 27/16 square yards
= 1 11/16 square yards
Hence the area of the carpeted part is 1 [tex]\frac{11}{16}[/tex] square yards.
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The complete question is as follows :
A patio has an area of 2 1/4 square yards. 3/4 of the patio is carpeted. What is the area of the carpeted part of the patio?
How do you find the sine of an angle in a right triangle?.
To find the sine of an angle in a right triangle, we can use the following relationship:
[tex]sin(angle) = opposite side / hypotenuse\\[/tex]
What is right triangle?
A right triangle is a type of triangle that has one angle that measures exactly 90 degrees (also known as a right angle). This angle is formed by the intersection of two legs of the triangle, which are not the hypotenuse of the triangle. The side opposite the right angle is called the hypotenuse and it is always the longest side of the triangle.
To find the sine of an angle in a right triangle, you can use the following relationship:
[tex]sin(angle) = opposite side / hypotenuse\\[/tex]
This relationship holds true for any angle in a right triangle, not just the acute angles.
For example, if you have a right triangle with an angle of 30 degrees and the opposite side is 5 units and the hypotenuse is 12 units, you can find the sine of the angle by dividing the opposite side by the hypotenuse:
[tex]sin(30) = 5/12 = 0.4166\\[/tex]
It's also important to note that the sine of an angle is always between -1 and 1, and the sine of an acute angle is always positive.
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To find the sine of an angle in a right triangle, we can use the following relationship:
sine = opposite side / hypotenuse side
What is right triangle?
A right triangle is a type of triangle that has one angle that measures exactly 90 degrees (also known as a right angle). This angle is formed by the intersection of two legs of the triangle, which are not the hypotenuse of the triangle. The side opposite the right angle is called the hypotenuse and it is always the longest side of the triangle.
To find the sine of an angle in a right triangle, you can use the following relationship:
sine = opposite side / hypotenuse side
This relationship holds true for any angle in a right triangle, not just the acute angles.
For example, if you have a right triangle with an angle of 30 degrees and the opposite side is 5 units and the hypotenuse is 12 units, you can find the sine of the angle by dividing the opposite side by the hypotenuse:
sin(30) = 5/12 = 0.4166
It's also important to note that the sine of an angle is always between -1 and 1, and the sine of an acute angle is always positive.
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Factor the algebraic expression 15a+12=
Answer:
3(5a + 4)
Step-by-step explanation:
Given expression: 15a + 12
The common factor for both is 3.
Factorize:
=> 3(5a) + 3(4)
Take out the common factor: (3)
=> 3(5a + 4)
Answer:
3(5a+4)
Step-by-step explanation:
Firstly, find the highest common factor between 15a and 12, which is 3 and write it in brackets, which is:
3(5a+4)
The brackets are 5a+4 because 3×5a=15a and 3×4=12, which gives you the algebraic expression 15a+12
Determine the degree of the following polynomial: -7xy^3z^2
Answer:
The given expression is -7xy^3z^2
The degree of x is 1
The degree of -7 is 0
The degree of y^3 is 3
The degree of z^2 is 2
The degree of a polynomial is the highest exponent of its variables. In the case of the polynomial -7xy^3z^2, the degree is the highest exponent among x, y, and z.
The highest exponent is 3, which is the exponent of y. So the degree of the polynomial -7xy^3z^2 is 3.
It's worth noting that the coefficient -7 has no effect on the degree of the polynomial. The degree of a polynomial is determined by the exponents of its variables, not its coefficients.
Hi,please help !
Simplify : 10c³de² ÷ 2cde =
Step 1: Think about this as four separate division questions:
[tex]\dfrac{10c^3de^2}{2cde} =\dfrac{10}{2} \cdot \dfrac{c^3}{c} \cdot\dfrac{d}{d}\cdot \dfrac{e^2}{e}[/tex]
Step 2: Simplify each of the four, one at a time:
[tex]\begin{aligned}\dfrac{10c^3de^2}{2cde} &=\dfrac{10}{2} \cdot \dfrac{c^3}{c} \cdot\dfrac{d}{d}\cdot \dfrac{e^2}{e}\\[0.5em]&=5 \cdot c^{3-1} \cdot1\cdot e^{2-1}\\[0.5em]&=5 c^{2} e\end{aligned}[/tex]
NEED HELP IMMEDIATELY PLEASE!!! Question 6 of 25
f(x) = 5x + 3. Find the inverse of f(x).
O A. f¹(x)=3-5x
OB. f-¹(x) = x-5/3
OC. f¹(x) = 5x - 3
OD. f-¹(x) = x-3/5
It is option D (f-¹(x) = x-3/5)
ABCD is a parallelogram. Solve for m_BCA:
A
D
39°
107°
B
с
Can somebody pls answer this question and give a brief explanation on what to do so I can try to understand it a little more?
While the moving platform rotates, the shape of the quadrilateral ABCD does not change, only its shape. Therefore, ABCD is a parallelogram by the Parallelogram Opposite Sides Converse because both pairs of opposite sides are congruent. A parallelogram has the following dimensions: — AB — DC.
What is Parallelogram?An amusement park ride includes four swinging arms and a moving platform.The platform swings back and forth, getting higher and higher, until it crosses the top and circles. AD and BC are two of the swinging arms, and DC is parallel to the ground (line l). Why does the movable platform AB always remain parallel to the ground?While the moving platform rotates, quadrilateral ABCD's shape changes, but its side lengths remain constant. Because the Parallelogram Opposite Sides Converse shows that both sets of opposite sides are congruent, ABCD is a parallelogram.A parallelogram is defined as AB DC —. The Transitive Property of Parallel Lines states that while DC and AB are parallel to line, they are also parallel . This means that the moving platform is parallel to the ground.The Complete Question is Parallelogram.
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What transformation has changed the parent function f(x) = (0.5)x to its new appearance shown in the graph? exponential graph passing through point negative 3, 2 and negative 2, 1 a f(x) − 2 b f(x + 2) c f(x) + 1 d −1 • f(x)
Correct option is A, f(x) -2 has changed the parent function f(x) = (0.5)x to its new appearance.
What modification has caused the parent function to change?The parent function f(x) = log5x has been modified by reflecting it over the x-axis, extending it vertically by a factor of three, and moving it down by three units.
In the picture below you can see the blue line is the graph of the function
f(x) = log(5x) and the green line is the graph of the function
g(x) = log[5(x + 4)] - 2
Since the function f passes at point (2, 1), we must reduce it by 2 units to ensure that it also passes at position (-2, -1). To do this, we add 2 to the function f.
We only need to add 4 to the variable x to have the function go left when we obtain log(5x) - 2.
The function shifts to the left when you add a number to x;
The function moves to the right when you remove a number from x;
The function increases when you add a number to it;
The function decreases when you take a number away from it.
Then we get a function g(x) = log[5 (x + 4)] - 2.
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