Using Equations to Compare Linear Functions
Consider the function and its inverse:
f(x) =
) = x -2
-(x) = (x + 2)
The slope, a, of the inverse function is
and the x-intercept of the inverse function is at x =
Intro
Answers
Answer:
\(a=3\) and the x-intercept of the inverse function is \(x=-2\)
Step-by-step explanation:
Given:
\(f(x)=\frac{x}{3}-2\)
\(f^{-1}(x)=a(x+2)\)
To find: slope, a, of the inverse function and the x-intercept of the inverse function
Solution:
Let \(y=f(x)=\frac{x}{3}-2\)
\(y=\frac{x}{3} -2\\\frac{x}{3}=y+2\\x=3(y+2)\\\)
So, \(f^{-1}(x)=3(x+2)\)
On comparing \(f^{-1}(x)=a(x+2)\) with \(f^{-1}(x)=3(x+2)\), \(a=3\)
To find the x-intercept of the inverse function, put \(f^{-1}(x)=0\Rightarrow 3(x+2)=0\Rightarrow x=-2\)
The slope, a, of the inverse function is 3 , and the x-intercept of the inverse function is at x = -2 .
Related Questions
How many times does 15 go int 135? who ever gets it right gets 500 points
Answers
Answer:
9 times
Step-by-step explanation:
The number 15 multiplied to the number 9 which gives the value 135.
To find the that how many 15 is to get 135, division should be performed.
So, dividing 135 by 15 gives:
= 135 ÷ 15
15 | 135 | 9
135
_______
0
Thus, the quotient is 9.
Therefore, 15 goes into 135 exactly 9 times.
Learn more about Division here:
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Pls pls help me I will give 10 points
Answers
Answer: d
Step-by-step explanation: y= +3x -6
What is the distance between3,3 and 6,3
Answers
Answer:
They are three units apart.
Step-by-step explanation:
6-3=3
Answer:3
Please explain your answer :D
don’t answer if you will not provide an explanation please :”)
Answers
Answer:
Step-by-step explanation:
QUESTION 7:
We are trying to find angles 1 and 2.
Known angle: 107˚.
In this question, we have 2 parallel lines with a transversal. A transversal is a line that passes through 2 parallel lines making it so that the angles on both sides are exactly the same.
Step 1: Find the measures of all the angles using the one we already know.
I will start with the angle adjacent (right next to) the angle that measures 107˚. As you can see, it is a supplementary angle because both of them form a straight line, or 180˚.
Therefore,
107+x= 180
x= 180-107
x= 73˚
Next, I will find the measure of the angle that is vertical to the one that measures 107˚. Note that angles that are vertical to each other are always identical, or in other words they have the same measure. Hence, the angle "vertical", or opposite to the one that measures 107˚ has to measure 107˚ as well. You can also tell this is true because they look the same.
Now I'll find the measure of the angle vertical to the one that measures 73˚. As we know, vertical angles are identical, so the one vertical to it is 73˚.
Here, I'll solve for angles 1 and 2. Like I said earlier, when a transversal crosses through 2 parallel lines, there will be 2 sets of angles that all have the same measurements.
To solve for angle 1, simply know what angle is right below it, and that is the one that measures 107˚. (If you look at the 2 lines, you will see that both angle sets are essentially duplicates of each other.) Likewise, angle 2 has to be 73˚ because the one under it is also 73˚.
Angle 1: 107˚
Angle 2: 73˚
QUESTION 8:
Again, we have a transversal that passes through 2 parallel lines. One angle measures 95˚. When there are 3 seperate angles along a straight line, the one next to the one with the given measurement will be the same as that one.
So angle 3 is 95˚. To find angle 4, find the angle measurement that's vertical to angle 3, which is 95˚. Now, since that angle and angle 4 are supplementary (both form a straight line which is always 180˚), 95+x= 180.
(x stands for angle 4)
x+95= 180
x= 180-95
x= 85
Angle 4= 85˚.
QUESTION 9:
ANGLE 5: 49˚
When there is a transversal, there are 2 identical pairs of angles. Therefore, angle 5 must be 49˚.
ANGLE 6: 131˚
angle 5 and angle 6 form a straight line which means they are supplementary angles. Therefore, both angles must add up to 180˚. So 49+x= 180
x= 180-49= 131
(x stands for angle 6)
Hope this helps!! Also I worked pretty hard on this so brainliest would be appreciated :D
Practice problems if it helps :) : https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-angles-between-lines/e/parallel_lines_1
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the values with the statistical measures for these data points.
Answers
Answer:
Min = 32
lower quartile = 38
median = 46.5
upper quartile = 59
Max = 62
Step-by-step explanation:
The first thing to do is organize the numbers from the smallest number to the largest number. The median is in the middle its going to come down to (48-45)/2 =46.5 and the lower quartile is in between the median and the minimum which will be 38 and the upper quartile is between the median and the maximum which is 59
lower quartile = 38
median = 46.5
upper quartile = 59
Max = 62
Step-by-step explanation:
The first thing to do is organize the numbers from the smallest number to the largest number. The median is in the middle its going to come down to (48-45)/ 2 =46.5 and the lower quartile is in between the median and the minimum which will be 38 and the upper quartile is between the median and the maximum which is 59
Can someone please help me with this
Answers
Answer:
1. 96 inches squared
2. h=324
3. 85
Step-by-step explanation:
1. v=lwh
v=8•3•4
v=96
2. 345- 21
h=324
3. 1,012/12
=84.3
hope this helped!
Which of the following points are solutions to the inequality below check all that apply
Answers
Answer:
A, C, and D
Step-by-step explanation:
By substituting the values of each of the points into the inequality, you can determine that A, C, and D are the correct answers.
Which table shows a proportional relationship between the value of x and
Y
Answers
Answer:
The answer is B (1 , 3) , (2 , 6) , (4 , 12) , (5 , 15)
Step-by-step explanation:
∵ X : 1 , 2 , 4 , 5
∵ Y : 3 , 6 , 12 , 15
∵ 2/6 = 1/3
∵ 4/12 = 1/3
∵ 5/15 = 1/3
∴ 1/3 = 2/6= 4/12 = 5/15 = 1/3 ⇒ all are proportion
∴ Answer B is in proportional relationship
The answer is B (1 , 3) , (2 , 6) , (4 , 12) , (5 , 15)
please help 20 points
Answers
Answer:
your best bet is A
You could do divideding to solve
an then think of another stratigy
Step-by-step explanation:
Solve the following equation for x.
7x-3y=-13
Answers
Answer:
x = 3/7y - 13/7
Step-by-step explanation:
7x-3y=-13
+3y +3y Add 3y to both sides
7x = 3y - 13 Divide both sides by 7
x = 3/7y - 13/7
Earn points, answer both questions!
Answers
Answer:
Area of five squares = 1289.09 square units
Perimeter = 194.6 units
Step-by-step explanation:
Area of square and perimeter:
First find the length of each square, then find the area of each square.
To find the area of five squares, add all the area of each square.
Side of square1 = 27 units
\(\sf Side \ of \ square2 = \dfrac{2}{3}*27=2*9 = 18 \ units\\\\Side \ of\ square3= \dfrac{2}{3}*18=2*6=12 \ units\\\\Side \ of \ square4=\dfrac{2}{3}*12=2*4=8 \ units\\\\Side \ of \ square5=\dfrac{2}{3}*8=\dfrac{16}{3}=5.3 \ units\)
Area of square1 = 27*27 = 729 square units
Area of square2 = 18*18 = 324 square units
Area of square3 = 12*12 = 144 square units
Area of square4 = 8*8 = 64 square units
Area of square5 = 5.3*5.3 = 28.09 square units
Area of five squares = 729 + 324 + 144 + 64 +28.09
= 1289.09 square units
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Perimeter of the composite figure = (27 + 27+27+9) + (18+18+6) +(12+12+4) + (8+8+2.7)+ (5.3+5.3+5.3)
= 90 + 42 + 28 + 18.7 + 15.9
= 194.6 units
the perimeter is 194.6 units
The pharmacist has a 2.8 L bottle of cough syrup. If she fills a bottle that is 1,200 ml, how many ml of cough syrup does the pharmacist have left?
160 ml
400 ml
1,600 ml
4,000 ml
Answers
Answer: 1,600 ml
Step-by-step explanation:
You can arrive at this answer by subtracting the amount of cough syrup used (1,200 ml) from the initial amount in the bottle (2.8 L, which is 2,800 ml).
2,800 ml - 1,200 ml = 1,600 ml
I hope this helps :)
Answer: 1,600 mL
Step-by-step explanation:
1. convert the 1,200 mL to L, which is 1.2 L.
2. Subtract that value from 2.8 L, equaling 1.6 L
3. Convert the 1.6 L back into mL by multiplying by 1000, which is equivalent to 1600 mL.
Which describes the sequence of transformations used to obtain the image (triangle A’) from the pre-image (triangle A)?
dilation by a scale factor of 2, then rotation of 180° about the origin
dilation by a scale factor of 2, then a reflection over the x-axis
dilation by a scale factor of 1/2, then a rotation of 180° about the origin
dilation by a scale factor of 1/2. then a reflection over the x-axis
Answers
Answer:
C : dilation by a scale factor of 1/2, then a rotation of 180° about the origin
Step-by-step explanation:
8th grade math i mark as brainliest
Answers
Answer:
We start with 4 cards. The probability of picking the 4 is 1/4. That card is put back, so we again have 4 cards. The probability of picking the 6 (the number greater than 5) is 1/4.
Therefore, the probability of picking a 4 and then a 6 is (1/4)(1/4) = 1/16.
Answer:
1/16
Step-by-step explanation:
PLZ HELP ME AGAIN
whats the relationship between 1,6 and 1,3
Answers
Answer:
their from the 3's
Step-by-step explanation:
Distribute the negative number and simplify.
-7(2 - 3x)
Answers
-14+21x
Hope this helps
Use the Midpoint Rule with \(n=5\) to estimate the volume obtained by rotating about the y-axis the region under the curve \(y=\sqrt{1+x^3}\), \(0\leq x\leq 1\).
Answers
To estimate the volume using the Midpoint Rule with \(\displaystyle n=5\), we need to divide the interval \(\displaystyle 0\leq x\leq 1\) into \(\displaystyle n\) subintervals of equal width. Since \(\displaystyle n=5\), each subinterval will have a width of \(\displaystyle \Delta x=\frac{1-0}{5}=\frac{1}{5}\).
Now, let's calculate the volume using the Midpoint Rule. The formula for the volume obtained by rotating about the y-axis is:
\(\displaystyle V\approx 2\pi \sum _{i=1}^{n}y_{i}\Delta x\)
where \(\displaystyle y_{i}\) represents the value of the function \(\displaystyle y=\sqrt{1+x^{3}}\) evaluated at the midpoint of each subinterval.
First, let's find the midpoints of the subintervals. Since the width of each subinterval is \(\displaystyle \Delta x=\frac{1}{5}\), the midpoint of the \(\displaystyle i\)-th subinterval is given by:
\(\displaystyle x_{i}=\frac{\Delta x}{2}+\left( i-\frac{1}{2}\right) \Delta x=\frac{1}{10}+\left( i-\frac{1}{2}\right) \frac{1}{5}\)
Substituting \(\displaystyle x_{i}\) into the function \(\displaystyle y=\sqrt{1+x^{3}}\), we obtain:
\(\displaystyle y_{i}=\sqrt{1+\left( \frac{1}{10}+\left( i-\frac{1}{2}\right) \frac{1}{5}\right) ^{3}}\)
Now, we can calculate the approximate volume using the Midpoint Rule:
\(\displaystyle V\approx 2\pi \sum _{i=1}^{5}y_{i}\Delta x\)
Substituting the values of \(\displaystyle y_{i}\) and \(\displaystyle \Delta x\) into the formula, we can evaluate the sum and compute the estimated volume.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
Which of the following choices is an example of a unit rate?
A. 10 miles per gallon
B. 1 gallon per 10 miles
C. 10 miles per 10 gallons
Answers
Answer:A
Step-by-step explanation:
Simplify this answer please
Answers
9 . 13 = 117
x^12 . x^2 = x^14 (add the powers)
y^3 . y^2 = y^5 (add the powers)
Answer: 117 x^14 y^5
Before you multiply or divide a fraction by a mixed number, you have to make sure they are both in the same___________?
Answers
Answer:
Step-by-step explanation:
form. Meaning you need make both fractions improper
please answer quickly
Answers
Answer:
37.5
Step-by-step explanation:
cosФ = \(\frac{A}{H}\)
cos(33°35') = \(\frac{m}{45}\)
m = 45 × cos(33°35')
m = 37.5 (1d.p.)
Which expression shows a way to find 20% of 950? Please I need help thanks.
Answers
Answer:
the answer of the expression is 190
Step-by-step explanation:
Given expression as :
20 % of 950
Or, \(\frac{20}{100}\) times 950
Or, \(\frac{20}{100}\) × 950
Or, 20 × \(\frac{950}{100}\)
or, 20 × 9.5
∴ 190
Answer:
1/5 times 950
Step-by-step explanation:
I did this on iready and got it correct
8(x + 5) = 16
Apply the Distributive Property and simplify.
- 8(x + 5) = 16
-8x +___= 16
Answers
Answer:
-40
Step-by-step explanation:
Just multiply
-8x-40=16
please help asap asap
Answers
Answer:
No, it's not because 6 x 4 = 24 and 2 x 3 = 6.
Step-by-step explanation:
In order for it to be equivalent, the simplified ratio needs to be multiplied by the same number, meaning because 6 x 4 = 24, the next number needs to be the product of 2 x 4, not 2 x 3.
Answer:
24:6 is equivalent to 6:2 because 6 times 4 is 24 and 2 times 3 is 6
ZEARNNNNNN
Step-by-step explanation:
5(3m - 6) when simplify
Answers
Answer:
15m-30
have a nice day
The expression in simplified form, obtained from the distributive property of multiplication over addition is; 15·m - 30
What is the distributive property?The distributive property of multiplication over addition states that for numbers, a, b, and c, we get;
a·(b + c) = a·b + a·c
The expression, 5·(3·m - 6) can be simplified by applying the distributive property of multiplication as follows;
5·(3·m - 6) = 5 × 3·m + 5 × (-6) = 15·m - 30
The simplified form of the expression is therefore; 15·m - 30
Learn more on the distributive property here: https://brainly.com/question/2807928
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A quarter circle is attached to the side of a square as shown.
What is the best approximation for the area of this figure?
Use 3.14 to approximate pi.
A.)28.6 m²
B.)41.1 m²
C.)66.24 m²
D.)116.5 m²
Note: I helping my brother math work so i hope you can answer this question
Answers
Answer: A
Step-by-step explanation: You have to find the area first, after you use pie and you get 28.6
Answer:
D
Step-by-step explanation:
Just did this good luck
7th grade math I'll give brainliest
Answers
Answer:
Step-by-step explanation:
Rise over run is the slope, m
m=2/5
a) the slope is 2/5 = .4 which is below the boundary guideline. So no this is not with in carpenter's guidelines
b) the image below show a line with slope 2/5 but with intercept 3
c) the stairs can be draw on the line with rise 2 run 5 from the line. see image
d)equation is in image
2.
a) count the squares
horizontal distance =3
vertical distance =3
b) slope is vertical distance over horizontal distance so m= 3/3 =1
Luis is cutting construction paper into rectangles for a project. He needs to cut one rectangle that is 12 inches × 13
1
3
inches. He needs to cut another rectangle that is 10
1
2
inches by 10
1
3
inches. How many total square inches of construction paper does Luis need for his project?
Answers
Answer: 356 total square inches
Step-by-step explanation: (12*13)+(10*10)=156+100=356 square inches
I NEED HELP ASAP with a science experiment give me ideas what experiments (mini-labs) I could do based on the task! READ THE SCREENSHOT
Answers
Answer: You should do a representation of how the heat and light waves reach humans on earth and keep us warm.
Step-by-step explanation:
all your answers are already in the task introduction.
1. Make earth out of styrofoam ball (buy at a dollar store) and paint. (blue and green). (If you want to make humans out of popsicle sticks)
2. Use velvet pipe cleaners (blue for cold air and red for hot air) to represent convection and conduction.
3. Use yellow pipe cleaners for solar energy to represent radiation.
4. Rest is up to you for how you want it to look.
Henry was playing with his marble collection, and decided to challenge his friend Andrew to figure out how many of each color marbles he had. Henry gave Andrew the following clues. "I have x blue marbles. I have four times as many red marbles as blue marbles. I have 5 less green marbles then I do blue marbles." Altogether I have 91 marbles. How many green marbles does Henry have?
Answers
Answer:
11
Step-by-step explanation:
First, set up an equation. Since all the blue marbles+red marbles+green marbles= total number of marbles, we have: x+4x+x-5=91.
x+4x+x-5=91
6x-5=91
6x=96
x=16
Since there are x-5 green marbles, we get the number of green marbles=16-5=11.