The graph of y=|x| is transformed as shown in the graph below. Which equation represents the transformed function?
Answers
After transformation the vertex becomes at (-3,-2)
Apply axes transformation from (0,0) to (h,k)
So, the transformation rule is (x,y) → (x-h, y-k)
(h,k) will be equal (-3,-2)
∴ y=|x| ⇒ (y-(-2)) = |x-(-3)|
∴(y+2) = |x+3|
∴ y = |x+3|-2
So, the correct answer is option 2
we have that
the original function [tex]y=\left|x\right|[/tex] has the vertex at point [tex](0,0)[/tex]
The transformed function has the vertex at point [tex](-3,-2)[/tex]
so
the rule of the translation is equal to
[tex](x,y)------> (x-3,y-2)[/tex]
That means
The translation is [tex]3[/tex] units to the left and [tex]2[/tex] units down
therefore
the answer is
the transformed function is [tex]y=\left|x+3\right|-2[/tex]
Related Questions
The current size of an image on Samuel's computer is shown below: A rectangle is shown. The length of the rectangle is labeled as length equal to 8 inches and the width is labeled as width equal to 10 inches. What are the dimensions of the image at fraction 1 over 2 times its current size
Answers
You can just divide each by 2.
Answer:
The length and the width of image is 4 inches and 5 inches respectively
Step-by-step explanation:
Given : Length of rectangle is 8 inches
Width of rectangle is 10 inches
To Find: What are the dimensions of the image at fraction [tex]\frac{1}{2}[/tex] times its current size
Solution:
Length of rectangle is 8 inches
Since we are given that the dimensions of the image at fraction [tex]\frac{1}{2}[/tex] times its current size
So, Length of image = [tex]\frac{1}{2} \times 8 = 4[/tex]
Thus the length of image is 4 inches.
Width of rectangle is 10 inches
Since we are given that the dimensions of the image at fraction [tex]\frac{1}{2}[/tex] times its current size
So, width of image = [tex]\frac{1}{2} \times 10 = 5[/tex]
Thus the width of image is 5 inches.
Hence the length and the width of image is 4 inches and 5 inches respectively.
Ben runs around the track at a pace of 1 lap every 80 seconds. Sally runs on the track in the opposite direction. The two meet every 30 seconds. How long does it take Sally to run each lap around the track?
Answers
How would the expression x^3+8 be written using Sum of Cubes?
Answers
x³ + 8
8 is the cube of 2, so we can write the above expression as sum of two cubes as:
x³ + 2³
Using the formula of sum of cubes, we can write:
x³ + 2³ = (x + 2)(x² - 2x + 4)
Thus, option B gives the correct answer
hey can you please help me posted picture of question
Answers
f⁻¹(x) = [tex] \frac{x+6}{7} [/tex]
Explanation:
To get the inverse of a function, we will follow these steps:
1- replace f(x) with y
2- swap the x and y variables
3- solve for y
replace y with f⁻¹(x)
Applying this to the given as follows:
f(x) = 7x - 6
Step 1: replace f(x) with y:
y = 7x - 6
Step 2: swap the x and y variables:
x = 7y - 6
Step 3: solve for y:
7y = x + 6
y = [tex] \frac{x+6}{7} [/tex]
Step 4: replace y with f⁻¹(x):
f⁻¹(x) = [tex] \frac{x+6}{7} [/tex]
Hope this helps :)
it took a ball 1 minute to roll 90 feet. what was ths balls average rate of speed in feet per second
Answers
Divide the 90 by 60.
Looking at the ping-pong ball toss board below, whats the probability of landing on a gray square? (Note the board contains 5 rows of 5 squares.)
Answers
answer
D. 1/5
Answer:
Option D. [tex]\frac{1}{5}[/tex] is the correct option.
Step-by-step explanation:
Total number of solution sets n(S) (sample space) = 5×5 = 25
(Since a ping-pong ball can land on any block of the toss board so total number of events which can occur will be = 25)
Now preferred events n(E) = 5
(Since number of grey squares where ping-pong ball can land are = 5)
Therefore probability of landing of ping pong ball on a grey square P(E) = [tex]\frac{n(E)}{n(S)}[/tex]
P(E) = [tex]\frac{5}{25}[/tex]
P(E) = [tex]\frac{1}{5}[/tex]
Therefore, Option D. [tex]\frac{1}{5}[/tex] will be the answer.
What is the letter ƒ in mathematics?
Answers
Example: f(x) = x + 1
It is a fancier/more proper replacement for the variable 'y'. The same is used for the letter g as in g(x) and h as in h(x).
OR
It could just be a regular ole variable
Example: f + 1 = 7, solve for f
The letter f usually indicates that the equation is a function in the notation f(x).
Example: f(x) = x + 1
It is a fancier/more proper replacement for the variable 'y'. The same is used for the letter g as in g(x) and h as in h(x).
OR
It could just be a regular ole variable
Example: f + 1 = 7, solve for f
What is the area of the figure?
Answers
plz help ill give u brainlist plz some one help fast it is esy in just dume
Answers
If there are 5 questions and you want to pick the right one the probability is 1/5. If you don't know how to find that, let your calculator walk you to the answer.
1
÷
5
=
And it will tell you that it is 0.2.
So if you blindly (not brainly) fill in the multiple choice answer sheet, the number you will get right is
(P(0.2) * The total number of questions or
0.2 * 70 = 14
Just pure dumb luck will give you 14 correct answers.
hello can you please help me posted picture of question
Answers
Total number of numerals to be used = 6
We are to find the number of different codes that can be formed and those can be found by permutations.
We have to find the permutations of 10 numerals taken 6 at a time. So we are to find 10P6.
10P6 = 151200
So, 151200 different codes can be formed.
So the answer to this question is option A
which best describes the meaning of the term theroem?
Answers
which transformations are needed to change the parent some function to the sine function below?
Answers
Vertical compression of 1/2 compresses the range from -1/2 to 1/2
Phase shift of pi/2 to the left
Horizontal stretch to a period of 4pi, as the crests are at -4pi, 0, 4pi
Vertical shift of 1 unit up moves the range to 1/2 to 3/2
So the first choice looks like a good answer.
Solution:the function y = sin x, which would have range from -1 to 1 and period of 2pi:
So the answer would be:Vertical compression of 1/2 compresses the range from -1/2 to 1/2Phase shift of pi/2 to the leftHorizontal stretch to a period of 4pi, as the crests are at -4pi, 0, 4piVertical shift of 1 unit up moves the range to 1/2 to 3/2
Suppose that the demand equation for a certain item is 1p+1x2−160=0. evaluate the elasticity at 65:
Answers
Here, the question has omitted to define variables, so we will ASSUME
p=price
x=variable,
and we're given
p+x^2-160=0
We calculate
[tex]\delta{x}/\delta{p}[/tex] by implicit differentiation with respect to p:
1+2x (dx/dp)=0
=>
E(x)=(dx/dp)=-1/(2x)
Therefore the price elasticity at x=65 is
E(65)=1/(2*65) =-1/130 (approximately -0.00769)
The required value of elasticity at x = 65 is -0.007.
Given that,
The demand equation for a certain item is [tex]1p + 1x^{2} -160 = 0[/tex].
We have to determine,
The value of elasticity at 65.
According to the question,
The price elasticity of demand is calculated as the percentage change in quantity divided by the percentage change in price.
Therefore,
Price of elasticity = [tex]\frac{dp}{dx}[/tex]
Calculate change by differentiation with respect to p:
[tex]\dfrac{d(p+x^{2} -160)}{dx}\\\\1 + 2x\frac{dp}{dx} = 0\\[/tex]
Then,
[tex]E(x) = \frac{dp}{dx} = \frac{-1}{2x}[/tex]
Therefore, The elasticity at x = 65 is ,
[tex]E(65) = \frac{-1}{2(65)} = -0.007[/tex]
Hence, The required value of elasticity at x = 65 is -0.007.
For more information about Elasticity click the link given below.
https://brainly.com/question/14547451
the cost of internet access at a cafe is a function of time the cost for 8, 25, and 40 minutes are shown write the equation in slope-intercept form that represents the function then find the cost of surfing the web at the cafe for one hour
Answers
Answer:
?
Step-by-step explanation:
Where is the graph?
For spring break this year your family decided to visit Michigan, but it snows the first weekend you are there. You decide to make a snowman. If the bottom ball is 3 feet across, the middle ball is 2 feet across, and the top is 1 foot across, how much snow is needed to build the whole snowman? Round your answer to the nearest cubic foot.
Answers
Combine volumes up (1ft times 3.14) + (2ft times 3.14) + (3ft times 3.14)
18.8 >. rounded to the nearest cubic foot of 19
Find the measure of the missing angle of a triangle, if two of its angles are 75 degree and 65 degree respectively. please show work
Answers
75° +65° +(missing angle) = 180°
(missing angle) = 180° -75° -65°
(missing angle) = 40°
Which of the following is the prime factored form of the lowest common denominator of?
A.2 x 2 x 2 x 3
B.2 x 4 x 2 x 3
C.8 x 6
D.2 x 12
Answers
2 x 2 x 2 x 3 factored form is the prime factored form.
What is a prime number?"A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers."
The given factored forms are:
A. 2 x 2 x 2 x 3
Here, all the numbers are prime numbers.
Therefore, this factored form is the prime factored form.
B. 2 x 4 x 2 x 3
Here, all the numbers are not prime numbers.
Therefore, this factored form is not the prime factored form.
C. 8 x 6
Here, not a single number is prime number.
Therefore, this factored form is not the prime factored form.
D. 2 x 12
Here, all the numbers are not prime numbers.
Therefore, this factored form is not the prime factored form.
Learn more about prime number here: https://brainly.com/question/10454590
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A cyclist rides a bicycle with a wheel radius of 0.500 m across campus. a piece of plastic on the front rim makes a clicking sound every time it passes through the fork. if the cyclist counts 320 clicks between her apartment and the cafeteria, how far has she traveled? (a) 0.50 km (b) 1.5 km (c) 1.0 km (d) 0.80 km (e) 1.8 km
Answers
circumference=2*pi*r
for r=0.50 m
circumference=2*pi*0.50-----> pi m
1 click correspond to a length of--------> pi meter
320 click---------------> x
x=320*pi-----> x=1005.31 meters-------> 1 km
the answer is
the option (c) 1.0 km
One aluminum can weights 1/25 pound. If your school starts a recycling drive how many cans will your school need to collect to recycle one ton?
Answers
First you have to find how many cans make a pound
1/25 * 25 = 1
It takes 25 cans to get to 1 pound
There are 2000 pounds in a ton
Multiply the amount of cans to make a pound by the amount of pounds in a ton
25 * 2000 = 50000
The answer is 50,000 aluminum cans
Hope this helps!
please help me answer these!!!
Answers
1. Checking selection "a",
265 =? 35 +20*7 = 35 +140 = 175
a (7, 265) is NOT a solution
2. Checking selection "a",
18 =? 5*4 -2 = 20 -2 = 18
a (4, 18) IS a solution
Q10 Q2.) Find the standard form of the equation of the parabola satisfying the given conditions.
Answers
1. You have that the standard form of the equation of the parabola must satisfy the following conditions given in the exercise above:
Focus: (-1,4) and Directrix: y=2
2. Therefore you have:
√(x0-(-1))²+(y0-4)²=|y0-2|
(x0+1)²+(y0-4)²=(y0-2)²
3. When you simplify the expression above and clear y0, you obtain:
y0=y
y=1/4(x²+2x+13)
y=(x²/4)+(x/2)+(13/4)
Therefore, the answer is: y=(x²/4)+(x/2)+(13/4)
5-2i and 7+6i find the midpoint
Answers
So that would be ((5+7) / 2, (-2+6) / 2) = (6, 2)
So then answer would be 6+2i
The midpoint between the complex numbers 5-2i and 7+6i is 6 + 2i.
Explanation:To find the midpoint between two complex numbers, we can use the formula:
Midpoint = (Re(z1) + Re(z2))/2 + (Im(z1) + Im(z2))/2i
Applying the formula to the given complex numbers 5-2i and 7+6i, we have:
Midpoint = (5 + 7)/2 + (-2 + 6)/2i
Midpoint = 12/2 + 4/2i
Midpoint = 6 + 2i
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A test has forty questions worth 100 points.The test consists of True/False questions worth 3 points each and multiple choice questions worth 2 points each. How many multiple choice questions are on the test?
Answers
Answer:
20 multiple choice questions
Step-by-step explanation:
I hope this help you out
A video posted on the internet is becoming very popular,and the total number of views is increasing by 40% every hour if the video currently has 38,000 views how many views will it have in 2 hours
Answers
Final answer:
The video with an initial 38,000 views will have approximately 74,480 views in 2 hours when it is increasing by 40% every hour.
Explanation:
To calculate the number of views a video will have in 2 hours if it is increasing by 40% every hour, we will use the formula for percentage growth. Initially, the video has 38,000 views. After one hour, the views will be increased by 40%, and after two hours, this new amount will again be increased by 40%. The formula for calculating the number of views after each hour is:
Views after n hours = Initial views × [tex](1 + growth rate)^n[/tex]
Where:
Initial views = 38,000
Growth rate = 40% = 0.40 (as a decimal)
n = number of hours
After 1 hour:
Views after 1 hour = 38,000 × (1 + 0.40)^1
Views after 1 hour = 38,000 × 1.40 = 53,200
After the second hour, we will use the number of views from the first hour to calculate the increase:
Views after 2 hours = 53,200 × [tex](1 + 0.40)^1[/tex]
Views after 2 hours = 53,200 × 1.40 = 74,480
Therefore, the video will have approximately 74,480 views in 2 hours.
a band that will be the opening act for a concert charges a $700.00 flat fee as well as 16% of all ticket profits from ticket sales. if the band earned $1,200, how much was made in total ticket sales for the show?
Answers
1. Subtract the flat fee 1,200-700 =500
2. 500 is what just the band made. Divide that by .16 (16%) to get the total ticket amount... 500 divided by .16 = 3,125
The total ticket amount was $3,125.
Jamie has applied for a credit card. The APR of the card is 20%. What will be the monthly interest rate?
Answers
20/12 = 1.67%
Answer:
1.67%
Step-by-step explanation:
The APR of a card is the Annual Percentage Rate. This is the yearly rate of interest that a person has to pay on the money he or she borrowed. Interest is a price that is paid for borrowing money. In this case, if the APR is 20%, we would need to divide this number by the number of months in a year in order to get the monthly interest rate:
20 / 12 = 1.67 %
jose bought 8 bags of oranges.each bag weighed 12 ounces. there are 16 ounces in a pound.how many pounds of oranges did jose buy
Answers
First you have to find the amount of ounces the oranges weigh
To find this you multiply the amount of oranges by the how much they weigh
12 * 8 = 96
Divide this by the amount of ounces is in a pound
96 / 16 = 6
The answer is 6 pounds
Hope this helps!
What is the value of y?
11.6 ft
12.5 ft
16.5 ft
17.5 ft
Answers
in the triangle BCD
cos C=8/14
C=arc cos (8/14)-----> C=55.15°
sin C=BD/14---------> BD=14*sin 55.15------> BD=11.49 ft
in the triangle ABC
180=∡A+∡B+∡C
∡A=180-(90+55.15)-----> ∡A=34.85°
tan A=BD/y-------> y=BD/tan A-----> y=11.49/tan 34.85----> y=16.50 ft
the answer is
y=16.50 ft
1. First, you must apply the Pythagorean Theorem to calculate the heigth of the triangle, as below:
a^2=b^2+c^2
b=√(a^2-c^2)
b=√(14)^2-(8)^2
b=√132
b=11.48
2. Now, you must calculate the angle ∠BC, as below:
Sin(α)^-1=opposite/hypotenuse
Sin(BC)^-1=8/14
∠BC=34.84°
3. Therefore, the angle ∠BA is:
∠BA=90°-34.84°
∠BA=55.15°
4. Then, you have:
Tan(55.15°)=y/11.48
y=16.48
Which of the points listed is the same distance from the y-axis as the point (−1.5, 6)?
Answers
we know that
the distance from a point to line (y-axis) is the perpendicular line against y-axis, which is the absolute value of x-coordinates
in this problem
the point (−1.5, 6)
the absolute value of x-coordinates is 1.5
hence
the distance is 1.5
therefore
the answer is
the option B) the point (1.5,-3)
Question 11 Unsaved
Find the domain, period, range, and amplitude of the cosine function.
y = -6cos4x
Answers
y = -6cos4x
The function is defined for all values of x, therefore, the domain is:
(-inf, inf)
The range of the function is:
For x = 0
y = -6cos (4 (0))
y = -6cos (0)
y = -6 (1)
y = -6
For x = pi / 4
y = -6cos (4 (pi / 4))
y = -6cos (pi)
y = -6 (-1)
y = 6
The range of the function is:
[-6, 6]
The amplitude of the function is:
6
Answer:
Domain: (-inf, inf)
Range: [-6, 6]
Amplitude: 6