Answer:
The answer is D
Step-by-step explanation:
The parent function will be reflected over the x-axis, compressed by a factor of 0.4, and translated into 2 units right.
It is given that the two functions one is the parent function [tex]\rm y = \sqrt[3]{-x}[/tex] and the transformed function [tex]\rm y = -0.4 \sqrt[3]{-x-2}[/tex].
It is required to find the transformation rules.
What is a function?It is defined as a special type of relationship and they have a predefined domain and range according to the function.
We have parent function:
[tex]\rm y = \sqrt[3]{-x}[/tex]
and transformed function:
[tex]\rm y = -0.4 \sqrt[3]{-x-2}[/tex]
If we multiply the parent function with a negative value it will f(x) over the x axis.
By the transformation rules of the function y = -f(x) reflects f(x) over x-axis.
After applying the transformation to the parent function:
[tex]\rm y = -\sqrt[3]{-x}[/tex]
By the transformation rules of the function if multiply the function with less than the unit value it will be compressed by the multiplied factor ie.
y = k f(x) and k<1, the function will be compressed by the k factor hence:
[tex]\rm y = -0.4\sqrt[3]{-x}[/tex] (after applying the second transformation)
As we can see the transformed function is subtracted by -2
By rules of transformation, for y=f(x-A) it would be a horizontal translation of 'A' unit to the right.
After applying this transformation we get:
[tex]\rm y = -0.4 \sqrt[3]{-x-2}[/tex] which is a transformed function derived after applying the transformation to the parent function.
Thus, the parent function will be reflected over the x-axis, compressed by a factor of 0.4, and translated into 2 units right.
Learn more about the function here:
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HELP ASAP PLEASE
The graph of a linear function passes through the points (7,0) and (-8, 45). A second linear function is
shown on this graph.
What is the distance, in units, between the y-intercepts of the two functionS?
distance : 15 units
coordinates : (7,0) and (-8, 45)
slope:
[tex]\sf \rightarrow \dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\sf \rightarrow \dfrac{45-0}{-8-7}[/tex]
[tex]\sf \rightarrow -3[/tex]
equation:
[tex]\hookrightarrow \sf y - 0 = -3(x-7)[/tex]
[tex]\hookrightarrow \sf y = -3x+21[/tex]
the y-intercept of this function:
[tex]\hookrightarrow \sf y = -3(0)+21[/tex]
[tex]\hookrightarrow \sf y =21[/tex]
distance between both y-intercept :
21 - 615The coach of Darnel's baseball team recorded how many runs the team scored in each game last season. This box plot shows the results. please
The fraction of the game that Daniel's team scores 2 or more runs is 1/4 of the game.
What are box plots?A box plot is used to study the distribution and level of a set of scores. Scores are distributed into 4 groups. Each group has a value of 25%
The first quartile, is the first line on the box. The first quartile represents 1/4 of the score.
To learn more about box plots, please check: https://brainly.com/question/27215146
use the terms 8 , 3x , 3/2 and 4x to complete the expression below so that’s is equivalent to 9x - 12
Answer:
A quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign. The solutions to quadratic inequality always give the two roots. The nature of the roots may differ and can be determined by discriminant (b2 – 4ac).
What is the area of the given quadrilateral?
Answer:
20 square units
Step-by-step explanation:
as its a square, we just add all the sides together. like a+b+c+d..
5+5+5+5=20 units
The following double line graph represents the enrollment of students at Jefferson Middle School for 2006 through 2009. If enrollment continues in the same trend, which of the following is a good prediction for eighth grade enrollment in 2010?
130
200
165
75
Considering the double line graph, it is found that a good prediction for eighth grade enrollment in 2010 is of 165.
What does the graph state?It states that:
The number of students enrolled in the 7th grade is falling by about 20 students per year.The number of students enrolled in the 8th grade is increasing by about 20 students per year.In 2009, there were 150 students enrolled in the 8th grade, hence an estimate for 2010 should be of about 165 or 170 students.
More can be learned about graphs at https://brainly.com/question/24808124
Answer:
165
Step-by-step explanation:
Determine the root of the equation by factoring 3x^2-x-4=0.
I have both of the roots solved, but when I verify it does not come out to a zero. Why is this?
Answer:
The roots you found should be [tex](3x-4)(x+1)=0[/tex], which shows that [tex]x = \frac{4}{3} \\ x=-1[/tex]
Step-by-step explanation:
You likely messed up when trying to one or both of the roots back into the equation.
How do I solve for x and y?
Answer:
x = 69y = 21Step-by-step explanation:
To solve for x and y, take advantage of the relationships between angles and diagonals in a rhombus. Each diagonal bisects the vertex angle, and the acute angles in each right triangle are complementary.
__
The angles created by the diagonal at the lower left vertex are congruent:
y° = 21°
__
The angles x° and y° are complementary:
x° = 90° -21°
x° = 69°
Solve the equation k^2-6k=11 by completing the square
Answer:
k = ±2√5 + 3
Step-by-step explanation:
k² - 6k + 9 = 11 + 9(k - 3)² = 20k - 3 = √20k - 3 = ±2√5k = ±2√5 + 3[tex]k=3+2\sqrt5\ or\ k=3-2\sqrt5[/tex]
Step-by-step explanation:
[tex]k^2-6k=11[/tex]
_______________________________________________
Add one term in order to complete the square[tex]k^2-6k+(6\times\frac{1}{2})^2=11+(6\times\frac{1}{2})^2[/tex]
________________________________________________
Calculate[tex]k^2-6k+3^2=11+3^2[/tex]
_________________________________________________
Factor the expression using [tex]a^2\pm 2ab+b^2=(a\pm b)^2[/tex][tex](k-3)^2=11+3^2[/tex]
__________________________________________________
Calculate the power[tex](k-3)^2=11+9[/tex]
___________________________________________________
Calculate the sum or difference[tex](k-3)^2=20[/tex]
______________________________________________________
Split into two equations[tex]k-3=\sqrt{20}\ or\ k-3=-\sqrt{20}[/tex]
________________________________________________________
Move variables to the left side of the equation:[tex](k-3=\sqrt{20})[/tex]
[tex]k=\sqrt{20}+3\\ k=2\sqrt{5}+3[/tex]
____________________________________________________
Move variables to the left side of the equation:[tex](k-3=-\sqrt{20})[/tex]
[tex]k=\sqrt{20}+3\\ k=-2\sqrt{5}+3[/tex]
_____________________________________________________
So far:[tex]k=2\sqrt{5}+3\ or\ k=-2\sqrt{5}+3[/tex]
_____________________________________________________
Find the union of the solutions[tex]k=2\sqrt{5}+3\ or\ k=-2\sqrt{5}+3[/tex]
_____________________________________________________
I hope this helps you
:)
Deondre drops a nickel from a balcony that
is 125 meters in the air. The function
y = -512 + 125 can be used to represent y, the
height of the coin in meters after t seconds.
Write and solve an equation to find the time it
will take for the coin to hit the ground.
The function [tex]y = -5t^2 + 125[/tex] of the nickel is quadratic function
It will take 5 seconds for the coin to hit the ground
How to determine the time the nickel hits the ground?
The function is given as:
[tex]y = -5t^2 + 125[/tex]
When the nickel hits the ground, the value of the function is:
y = 0
So, we have:
[tex]-5t^2 + 125 = 0[/tex]
Subtract 125 from both sides
[tex]-5t^2 =- 125[/tex]
Divide both sides by -5
[tex]t^2 =25[/tex]
Take the square root of both sides
[tex]t = 5[/tex]
Hence, it will take 5 seconds for the coin to hit the ground
Read more about quadratic functions at:
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At one farmer’s market, bananas cost $0. 80 per pound. At another farmer’s market, bananas are sold in 5-pound bags for $4. 50 per bag. Which explains how to find the better buy? Divide 4. 50 by 5 to find the unit rate for the 5-pound bag, and compare that number to $0. 80 per pound. Divide 0. 80 by 5 to find the unit rate for the 5-pound bag, and compare that number to $0. 80 per pound. Multiply 4. 50 by 5 to find the cost for 5 pounds, and compare to $4. 50 per bag. Multiply 4. 50 by 0. 80 to find the cost for 5 pounds, and compare to $4. 50 per bag.
To find the better buy divide 4.50 by 5 to find the unit rate for the 5-pound bag, and compare that number to $0. 80 per pound.
The cost price per pound is the amount of money required to buy one pound of a brand or goods.
To find the cost price per pound, divide the total amount of cost of the goods to the total number of goods.
At one farmer’s market, bananas cost $0.80 per pound.
At another farmer’s market, bananas are sold in 5-pound bags for $4. 50 per bag. To compare it with first market price, divide the 5 pound bags with $4.50.
The cost of one bag in this market is,
[tex]C=\dfrac{4.50}{5}\\C=0.5625[/tex]
As this cost is less, thus, the cost of this market for one banana is less than the first market and so this is the better buy.
Hence, to find the better buy divide 4.50 by 5 to find the unit rate for the 5-pound bag, and compare that number to $0. 80 per pound.
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A cylinder has a base diameter of 16cm and a height of 20cm. What is its volume in cubic cm
Answer:320 cubic cm
Step-by-step explanation: if you multiply 16x20m you get 320 cm
On a coordinate plane ,the segment with endpoints (10,40) and (70,120) is dilated by a factor of 4/5,with the origin as the center of dilation. What is the length of the resulting segment ?
A-80
B-100
C-112
D-125
The length of the dilated line segment is 80 units.
What is dilation?Dilation is the increase or decrease in the size of a figure or object.
The segment with endpoints (10,40) and (70,120) is dilated by a factor of 4/5 to get (8, 32) and (56, 96).
The distance between points (8, 32) and (56, 96) is:
[tex]Distance = \sqrt{(96-32)^2+(56-8)^2} =80\ units[/tex]
The length of the dilated line segment is 80 units.
Find out more on dilation at: https://brainly.com/question/10253650
A box has a square base with side x cm , height 4 cm and volume 289 cm^3. Find x
Answer:
8.5 cm
Step-by-step explanation:
volume = height × area of base
since this a square, area of base = x²
so 289 = 4 × x²
x² = 289 ÷ 4
x² = 72.25
so x = √72.25
x = 8.5cm
hope this helps
Please help will give brainlest! locks in 30 min!
Answer:
1
Step-by-step explanation:
[tex] \tan( \frac{5\pi}{4} ) \times \frac{\pi}{180} = 1.19[/tex]
The question wants in radian, not in degrees since using the unit circle. Hope this helps
Answer:
a) 1
Step-by-step explanation:
Tan 5pi/4: 1
Tan (-5pi/4): -1
Tan 5pi/4 in degrees: tan (225°)
Select the set of equations that is NOT equivalent to 8k = 20
Based on her results, what is the probability that a student randomly picked in her class chose comedy as their favorite?
1. 1/14
2. 2/7
3. 1/2
4. 1/7
Explanation:
8 people picked comedy out of 14+8+2+4 = 28 people total.
8/28 = (4*2)/(4*7) = 2/7 is the probability of randomly selecting someone who picked comedy as their favorite.
Hello I'm just here to say if a question asks "circle all of the expressions that are equivalent to some type of math question do i pick more than one?
what is the area of this figure?
Answer:
234 square millimeters
Step-by-step explanation:
You want the area of the irregular polygon shown.
CompositionThere are always several ways you can find the area of a figure like this. In the attachment we have shown extensions of the vertical and horizontal lines that will divide the figure into a triangle and two rectangles.
Triangle areaThe triangle has a base of 12 mm and a height of 13 mm. Its area is ...
A = 1/2bh
A = 1/2(12 mm)(13 mm) = 78 mm²
Rectangle areaThe upper rectangle has a width of 8 mm and a length of 14 mm. Its area is ...
A = LW
A = (14 mm)(8 mm) = 112 mm²
The lower rectangle has a width of 4 mm and a length of 11 mm. Its area is ...
A = (4 mm)(11 mm) = 44 mm²
Total areaThe area of the figure is the sum of the areas of its parts:
total area = triangle area + upper rectangle + lower rectangle
total area = 78 mm² + 112 mm² + 44 mm² = 234 mm²
The area of the figure is 234 square millimeters.
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Can someone please help me with this
Definition of a trapezoid: a quadrilateral with one pair of parallel sides
Thus PQRS is a trapezium because Line PQ is parallel to line SR
Hope that helps!
help please and thank you!
Answer:
A (0,3)
Step-by-step explanation:
The Y-intercept is where X equals 0
When X equals zero, Y equals 3.
Helpp me with my sister's math
Answer:
the 1/2w +22 one is a binomial
Step-by-step explanation:
a binomial is a equation with one two separate numbers AFTER simplifcation. so "1+1" is not a binomial because its equal to just 2, but "1 + x" is a binomial because its simplifed
Find an equation for the plane that contains the line and is perpendicular to the plane
For the line and the plane to be perpendicular, they have to meet at right angles
The equation for the plane is x + 2y + 3z= 26
How to determine the equation?From the complete question, we have:
Point = (5,0,7)
Plane perpendicular to ⟨1,2,3⟩
The general equation is:
a * x+b * y+c * z = d
So, we have:
d = 5 * 1 + 2 * 0 + 7 * 3
Evaluate
d = 26
Recall that:
d = 5 * 1 + 2 * 0 + 7 * 3
Replace the points with x, y and z.
So, we have:
d = x * 1 + 2 * y + 3 * z
Evaluate
d = x + 2y + 3z
So, we have:
d = x + 2y + 3z and d = 26
Equate both equations
x + 2y + 3z= 26
Hence the equation for the plane is x + 2y + 3z= 26
Read more about perpendicular planes at:
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6x + 4 - 8x + 9(4 - x)
-
Answer:
6x - 8x + 4 + 36 - 9x
= 40 - 11x
Whats the equation of a circle with the center point of 1, -1 and a radius of. 5
Step-by-step explanation:
For this problem, we need to use the fact that the circle with center (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2.
This gives us that the equation of the circle is (x-1)^2 + (y-1)^2 = 25.
can yall help me please
I suppose, your answers are already given at the bottom of this page..
what’s the missing side length?
A. 10
B. 7.1
C. 4
D. 35.4
Answer:
ans is 10
Step-by-step explanation:
by using pythagoras theorm
26^2=a^2+24^2
a^2=100
a=10
Manny does not eat 4/9 of his orange at lunch. Josh does not 5/9 of his orange at lunch. How much orange do Manny and Josh have left over?
The amount of orange that Manny and Josh have leftover after eating lunch is 1.
What are fractions?A fraction is a non-integer. A fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below
How much orange is leftover?Oranges Manny has left = 1 - 4/9 = 5/9
Oranges Josh has left = 1 - 5/9 = 4/9
Oranges they both have left = 5/9 + 4/9 = 1
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You make commission working at Footlocker. On Saturday you sold
$1,500 worth of merchandise and made $120 in commission. On
Sunday you sold $1,300 worth of merchandise. If you made the same percent commission,how much did you earn on Sunday?
A. $8
B. $86. 66
C. $104
D. $1,039. 99
Answer:
C. $104
Step-by-step explanation:
First, we need to figure out what percent $120 is of $1500.
120 ÷ 1500 = 0.08 = 8%. So, $120 is 8% of $1500, and this is the percentage that'll be used to calculate Sunday's commission.
0.08 (8%) × 1300 = 104
Thus, you earned $104 on Sunday.
1. D=5.9 ft.
calculate the circumference of the circle.
2. D=3.2 ft.
calculate the circumference of the circle.
3. D= 6.1 ft.
calculate the circumference of the circle.
4. R= 3.7 m.
Calculate the circumference of the circle.
5. R=6.2
Calculate the circumference of the circle.
6. R=5.1 Ft.
Calculate the circumference of the circle.
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Here's the solution ~
As we know, we can calculate the circumference of a circle in terms of its diameter as :
[tex]\qquad \sf \dashrightarrow \:c = \pi d[/tex]
where, c = circumference and d = diameter
And also, circumference of circle is terms of radius (r) is :
[tex]\qquad \sf \dashrightarrow \:c = 2\pi r[/tex]
Now, let's move on to questions ~
First[tex]\qquad \sf \dashrightarrow \:3.14 \times 5.9 [/tex]
[tex]\qquad \sf \dashrightarrow \: \approx18.53 \: ft[/tex]
・ ．━━━━━━━†━━━━━━━━━．・
Second[tex]\qquad \sf \dashrightarrow \:3.14 \times 3.2[/tex][tex] \qquad \sf \dashrightarrow \: \approx10.048 \: ft[/tex]
・ ．━━━━━━━†━━━━━━━━━．・
Third[tex]\qquad \sf \dashrightarrow \:3.14 \times 6.1[/tex]
[tex]\qquad \sf \dashrightarrow \: \approx19.15 \: ft[/tex]
・ ．━━━━━━━†━━━━━━━━━．・
Fourth[tex]\qquad \sf \dashrightarrow \:2×3.14 \times 3.7[/tex]
[tex]\qquad \sf \dashrightarrow \: \approx2×11.62 \: m[/tex]
[tex]\qquad \sf \dashrightarrow \: \approx23.24 \: m[/tex]
・ ．━━━━━━━†━━━━━━━━━．・
Fifth[tex]\qquad \sf \dashrightarrow \:2×3.14 \times 6.2[/tex]
[tex]\qquad \sf \dashrightarrow \: \approx2× 19.47 \: units[/tex]
[tex]\qquad \sf \dashrightarrow \: \approx38.94 \: m[/tex]
・ ．━━━━━━━†━━━━━━━━━．・
Sixth[tex]\qquad \sf \dashrightarrow \:2×3.14 \times 5.1[/tex]
[tex]\qquad \sf \dashrightarrow \: \approx2×16.01 \: ft[/tex]
[tex]\qquad \sf \dashrightarrow \: \approx \: 32.02m[/tex]
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
The area of a circular fountain is 121π square feet.
What is the diameter of the fountain?
Answer:
22 feet
Step-by-step explanation:
The area of a circle is π · r².
So, step one is to figure out the radius, so taking that equation, we can say π · r² = 121π.
Divide both sides by π to get r² = 121
Then, you take the square root of both sides to leave r = 11.
The diameter is twice as long as the radius, so multiply 11 · 2 to get 22.
The diameter is 22 feet long.