What kind of transformation converts the graph of f(x) = -8x2 - 8 into the graph of g(x) =
-x² – 1?
vertical stretch
vertical shrink
horizontal stretch
horizontal shrink
Submit
Answer:
horizontal stretch
Step-by-step explanation:
For f(x) to turn into g(x), you must divide the function by 8. When we divide a function, this is known as a horizontal stretch because as you can see, the function gets wider. See the help image below with different examples.
Just a future tip: when you're in doubt, graph it out!
Horizontal stretch is the transformation which converts the graph of f(x) = -8x²- 8 into the graph of g(x) = -x² – 1. Option C is correct.
The general form of the quadratic function is f(x) = a(x - h)² + k, where (h, k) represents the vertex of the parabola.
In this case, for f(x) = -8x² - 8, the vertex is at (0, -8).
For g(x) = -x² - 1, the vertex is at (0, -1).
Comparing the two functions, you can see that the coefficient in front of x² changes from -8 to -1.
This change in the coefficient results in a horizontal stretch or compression of the parabola.
In this case, the graph has been horizontally stretched to transform from f(x) to g(x).
Hence, Option c is correct. Horizontal stretch is the transformation which converts the graph of f(x) = -8x²- 8 into the graph of g(x) = -x² – 1.
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ3
Lucy is 15 years old and has $1000, she invests in a CD paying 8% interest. How many times will her money double by the time she is 60?
Answer:
5
Step-by-step explanation:
(1 + i ) ^45 i = interest in decimal 45 = years
(1.08)^45 = ~~ 32
when she is 65 it will be worth 32 000
so it doubles 5 times (1000 2000 4000 8000 16000 32000)
Given the endpoints of a segment, find the length of each segment.
A (-3, 7) and B (-5, 2)
Step-by-step explanation:
Using the distance formula
√(x1-x2)²+(y1-y2)²
√(-3+5)²+(7-2)²
√(2)²+(5)²
√4+25
√29 units
MARK ME AS BRAINLIST
Fill in the blanks as necessary.
(a) Kaitlin is deciding how many people to take to the movies. The table below
shows the cost for different sized groups of people.
Number in group
2
3
7
Cost (in dollars)
10
15
28
The cost for each person is not always the same.
The cost for each person appears to be the same.
Predicted number in group for a cost of $40:
Answer:
The cost for each person is not always the same.10 peopleStep-by-step explanation:
Number : 2 Cost : $10
Per person = 10/2 = $5Number : 3 Cost : $15
Per person = 15/3 = $5Number : 7 Cost : $28
Per person = 28/7 = $4⇒ The cost is not always the same per person.
⇒ Predicted number in a group for cost of $40 :
⇒ Since 7 costs $28 and if we use 8, it will be $5 per head but the price difference will be too large
⇒ 10 people is more reasonable at a rate of $4 per person
NEED HELP ASAP
What is the slope of a line perpendicular to the line whose equation is 2x + 3y = 24. Fully simplify your answer.
The slope of a line perpendicular to the line whose equation is 2x + 3y = 24 is,
⇒ m = - 2/3
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The perpendicular line is,
⇒ 2x + 3y = 24
Now,
Since, Product of slopes of perpendicular line are - 1.
So, We need to find the slope of the line.
Hence, Slope of the line is,
2x + 3y = 24
y = - 2/3x + 8
m = dy/dx = - 2/3
m = - 2/3
Thus, The slope of a line perpendicular to the line whose equation is 2x + 3y = 24 is,
⇒ m = - 2/3
Learn more about the equation of line visit:
https://brainly.com/question/18831322
#SPJ2
if i have 2489 friends and 72% of those friends want burgers, and 25% of the 72% want chips too, how many want chios
Answer:
448.02
Step-by-step explanation:
72% of 2489 is 1,792.08
25% of 1,792.08 is 448.02
Enter the correct answer in the box.
Write the expression 12-2 in simplest form.
Answer: 1/144 as a fraction
Step-by-step explanation:
can someon3 help me with this it like 4 or 5 minutes
Answer:
C. 360-85=12h
Step-by-step explanation:
360=85+12h
360-85=12h
if i had 10 apples how many apples do i have?
Answer:
10 apples
Step-by-step explanation:
Help I have a d in this class
2. Elana's Family. Elana's Family.
Solve for 1/4 of x is 6
Answer: x=24
Step-by-step explanation:
1/4x=6x=6/0.25x=24Other way to do it is 6x4=24(3×1/2) + (6×3/4) + (3×1) + 1 1/4 +1 1/2=
What are the dimensions of the large rectangle and the small rectangle?
Answer:
there is no picture to give an answer
Answer:
I need the picture to answer the question...
Step-by-step explanation:
Which of the following statements about closure is false?
Polynomials are closed under addition. When you add polynomials, the result will always be a polynomial.
Polynomials are closed under subtraction. When you subtract polynomials, the result will always be a polynomial.
Polynomials are closed under division. When you divide polynomials, the result will always be a polynomial.
Polynomials are closed under multiplication. When you multiply polynomials, the result will always be a polynomial.
Using the concept of closure, it is found that the false statement is given by:
Polynomials are closed under division. When you divide polynomials, the result will always be a polynomial.
What is the closure of a polynomial?A polynomial is said to be closed under an operation if the operation always results in a polynomial. It holds true for the addition, subtraction and multiplication operations.
As for the division, if the degree of the numerator is lower than the degree of the denominator, the result of the division will have a negative exponent, which is not a polynomial, hence the division operation is not closed.
More can be learned about closure of polynomials at https://brainly.com/question/9438778
A company makes three sizes of juice bottles: small, medium, and large.
• The ratio of small bottles to medium bottles made is 2:3.
• The ratio of medium bottles to large bottles made is 3:5,
The company makes s small bottles every minute.
Enter an expression in terms of s to represent the number of large bottles the company makes every minute.
An expression in terms of s that represents the number of large bottles is : L = [tex](\frac{15s}{2} /3})[/tex]
Ratio of different sizes of bottlesThe company makes s small bottles every minute
let ; M represent the number of medium bottles made every minute
L represent the number of large bottles made every minute
small bottles to medium = 2 : 3
small bottles to medium = s : M
M is the unknown, so to find how many medium bottles that has been made, we must cross multiply
2M = 3s
M = [tex]\frac{3s}{2}[/tex] medium bottles made every minute
medium bottles to large bottles = 3 : 5
medium bottles to large bottles = M : L
where M = [tex]\frac{3s}{2}[/tex]
The equation becomes:
3 : 5
[tex]\frac{3s}{2}[/tex] : L
L is the unknown, so to find how many Large bottles that has been made, we must cross multiply
3L =( [tex]\frac{3s}{2}[/tex] ) * 5
L = [tex](\frac{15s}{2} /3})[/tex]
L = ( [tex]\frac{5}{2}[/tex] s)
L = 2.5 s
therefore the large bottles the company makes every minute is 2.5s large bottles
we can conclude that the expression for the number of large bottles the company makes every minute with respect to s is : L = 2.5 s
Learn more about Ratio : https://brainly.com/question/1509142
if sin18=0.3090, cos 18=0.9511, sin 22=0.3746, and cos22=0.9272, then what is sin4
Answer:
[tex]0.6428[/tex]
Step-by-step explanation:
Using the addition formula for sine[tex]sin(x + y) = sinxcosy + cosxsiny[/tex]
[tex]sin40 = sin(18 + 22)[/tex]
[tex]= sin18cos22 + cos18sin22= (0.3090 * 0.9272) + (0.9511 * 0.3746)= 0.2865 + 0.3563= 0.6428[/tex]
Find the perimeter of the figure.
Step-by-step explanation:
perimeter=(8cm×5)+24cm
=40cm+24cm
=64cm
PLEASE HELP ASAP
Subtract 5y2 – 64 – 11 from 6y2 + 2y + 5.
Your answer should be a polynomial in standard
form.
Answer:
[tex]y^2 + 2y + 80[/tex]
Step-by-step explanation:
[tex]6y^2 + 2y + 5 - (5y^2 - 64 - 11)[/tex]
[tex]6y^2 + 2y + 5 - 5y^2 + 64 + 11[/tex] [pay attention to the signs :)
[tex]y^2 + 2y + 80[/tex]
HELP ASAP!!
Person A leaves a $16 tip for a meal that costs $123. Person B leaves a tip of $12 for a meal that costs $89. Who is the better tipper? Explain.
Calculate the interest rate for an account that was
compounded semi-annually, had an initial deposit of
$9,000 and was worth $13,373.53 after 10 years.
Answer:
Intrest rate is 3645%
20(36.45%) = $4374
Step-by-step explanation:
Semi-annualy = 6 months
Start: $9,000
After 10-years (120 months): $13,373.53
Since it's gaining money every 6 months, it gains money over 20 months.
(120/6 = 20)
After removing the starting cost, it gains $4,373.53 over 20 months.
(13,373.53 - 9,000 = 4,373.53)
$4,373.53 spread out over 20 months equals around $218.68 every 6 months.
(4,373.53 ÷ 20 = 218.6765)
(218.6765 ≈ 218.68)
$218.68 over 6 months equals about $36.45 every month
(218.68 ÷ 6 = 36.44666)
(36.4666 ≈ 36.45)
The intrest rate is 3645%
(3645% ÷ 100% = 36.45)
You need to arrange of your favorite books along a small shelf. How many different ways can you arrange the books, assuming that the order of the books makes a difference to you?
Question content area bottom
Part 1
enter your response here ways
(Type a whole number.)
Answer:
The answer is 8! ("eight factorial") = 8*7*6*5*4*3*2*1 = 40320, which is the number of permutations of 8 objects.
(8 ways to put the first book in the first place, then 7 ways to put the second book in the second place, then 6 ways to put the third book in the third place, and so on).
James bought a car for $17.528 which included a 4.5% tax
a) How tax did he pav? b) He received a 15% discount off the
original price of the car. What was the original price?
Answer:
(1) the tax is 788.76
(2) 19312.23
Step-by-step explanation:
Hope this helps
Find the surface area of each of the following figures using the given values.
Answer:
Step-by-step explanation:
1. the surface area of a square is 6 * s^2
a. 6 * 5^2 = 150 sq ft
b. 6 * 6^2 = 216 sq in
c. 6 * 12^2 = 864 sq mm
2. the surface area of a rectangle is 2(l*w + w*h + l*h)
a. 2(2*5 + 5*7 + 2*7) = 118 sq ft
b. 2(16*11 + 11*10 + 16*10) = 892 sq in
3. the surface area of a sphere is 4pi * r^2
a. 4pi * 12^2 = 576pi or 1809.6 units sq
b. 4pi * 16^2 = 1024pi or 3216.99 units sq
c. d = 2r, r = 5, 4pi * 5^2 = 100pi or 314.2 units sq
4. the surface area of a cylinder is (2pi * r^2) + (2pi*r * h)
a. (2pi * 6^2) + (2pi * 6 * 12) = 216pi or 678.6 units sq
b. (2pi * 2^2) + (2pi * 2 * 10) = 48pi or 150.8 units sq
c. (2pi * 3^2) + (2pi * 3 * 5) = 48pi or 150.8 units sq
5. r = d/2 = 0.5, using formula from question 4:
(2pi * 0.5^2) + (2pi * 0.5 * 4) = 4.5pi or 14.14 ft sq
Which one has a greater quantity:
The volume of a prism with a base area of 24.3 cm2 and height 14 cm or
The volume of a pyramid with a base area 24.3 cm2 and height 14 cm
Answer:
The volume of a prism with a base area of 24.3 cm2 and height 14 cm
# 5 pls !!
find dy/dx by implicit differentiation
Step-by-step explanation:
[tex]5. {x}^{3} - xy + {y}^{2} = 4[/tex]
[tex] \frac{dy}{dx} ( {x}^{3} - xy + {y}^{2} ) = \frac{dy}{dx} (4)[/tex]
[tex]3 {x}^{2} - x(1) \frac{dy}{dx} + 1(y) + 2y \frac{dy}{dx} [/tex]
Combine the dy/dx.
[tex] \frac{dy}{dx} ( - x + 2y) + y + 3 {x}^{2} [/tex]
[tex] \frac{dy}{dx} ( - x + 2y) = - 3 {x}^{2} - y[/tex]
[tex] \frac{dy}{dx} = \frac{ - 3 {x}^{2} - y}{ - x + 2y} [/tex]
[tex] \frac{3 {x}^{2} + y }{x - 2y} [/tex]
Answer:
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{y-3x^2}{2y-x}[/tex]
Step-by-step explanation:
using the product rule to differentiate - xy then
3x² - (x[tex]\frac{dy}{dx}[/tex] + y(1) ) + 2y[tex]\frac{dy}{dx}[/tex] = 0
3x² - x[tex]\frac{dy}{dx}[/tex] - y + 2y[tex]\frac{dy}{dx}[/tex] = 0
3x² + [tex]\frac{dy}{dx}[/tex] (2y - x) - y = 0 (subtract 3x² - y from both sides )
[tex]\frac{dy}{dx}[/tex] (2y - x) = y - 3x² ← divide both sides by (2y - x)
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{y-3x^2}{2y-x}[/tex]
Write an equation for the translation of "left 7 units
Y=|x|
i need the answer to this lol
Help help math math maths
Answer: X = 7
Step-by-step explanation:
1) 20 / 5 = 4
2) X - 2 = 5
3) 7 - 2 = 5
4) 4 x 5= 20
6) 20 / 5 = 4
7) X = 7
Rearrange the equation so x is the independent variable. -4x-6=-5y+9 y=
-4x-6=-5y+9y
-4x-6= 4y
-4x= 4y+6
4x=-4y-6
x= (-4y-6)/4
SOLVE THE EQUATION and explain YOUR ANSWER
Using the given quadratic function, it is found that:
a) The vertex is (-2.5, -15.5).
b) The y-intercept is of -3.
c) The solutions are x = -0.28, x = 5.28.
What is the quadratic function?It is modeled by:
f(x) = 2x² - 10x - 3.
Which means that the coefficients are a = 2, b = -10, c = -3.
What is the vertex of the function?It is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex]
[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]
Hence:
[tex]x_v = -\frac{-10}{4} = -2.5[/tex]
[tex]y_v = -\frac{(-10)^2 - 4(2)(-3)}{8} = -15.5[/tex]
The vertex is (-2.5, -15.5).
What is the y-intercept of the equation?It is the value of coefficient c, hence it is of -3.
What are the solutions?[tex]\Delta = b^2 - 4ac = (-10)^2 - 4(2)(-3) = 124[/tex]
[tex]x_1 = \frac{10 + \sqrt{124}}{4} = 5.28[/tex]
[tex]x_2 = \frac{10 - \sqrt{124}}{4} = -0.28[/tex]
The solutions are x = -0.28, x = 5.28.
More can be learned about quadratic functions at https://brainly.com/question/24737967
On a standardized exam, the scores are normally distributed with a mean of 450 and a standard deviation of 25. Find the z-score of a person who scored 470 on the exam.
A Z-score helps us to understand how far is the data from the mean. The z-score of a person who scored 470 on the exam is 0.8.
What is Z-score?A Z-score helps us to understand how far is the data from the mean. It is a measure of how many times the data is above or below the mean. It is given by the formula,
[tex]Z = \dfrac{X- \mu}{\sigma}[/tex]
Where Z is the Z-score,
X is the data point,
μ is the mean and σ is the standard variable.
Given the mean is 450, while the standard deviation is 25, therefore, the value of the z-score can be written as,
[tex]Z = \dfrac{X- \mu}{\sigma}\\\\Z(X=470) = \dfrac{470- 450}{25} = 0.8[/tex]
Hence, the z-score of a person who scored 470 on the exam is 0.8.
Learn more about Z-score:
https://brainly.com/question/13299273
#SPJ1