Identify a transformation of the function f(x) = (x) by observing the equation of the function g(x) = (x)+56.

A: a vertical shift 56 units upwards

B: a horizontal shift 56 units to the left

C: a horizontal shift 56 units to the right

D: a vertical shift 56 units downward

Answer:

Y=2x^2

Step-by-step explanation:

The following equations represent a parabola with vertex (0,0): y=2x², x=-2y² and x=2y².

The quadratic function can be represented by a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

A parabola also can be represented by a quadratic equation. The vertex of an up-down facing parabola of the form ax²+bx+c is [tex]x_v=\frac{-b}{2a}[/tex] . Knowing the x-coordinate of vertex, you can find the y-coordinate of vertex.

The another form for describing a parabola is [tex]4p\left(x-h\right)=\left(y-k\right)^2[/tex], where h and k are the vertex coordinates.

You should analyse each one of the options, considering the equations that can be represented a parabola.

Letter A - y=2x²

The coefficients of the quadratic equation are:

a=2, b=0, c=0

Then,

[tex]x_v=\frac{-b}{2a}\\ \\ x_v=\frac{-0}{2*2}=0[/tex].

If x-coordinate of vertex is equal to 0, from y=2x²you can:

[tex]y_v=2x^2\\ \\ y_v=2*0^2=0[/tex]

Therefore, the given equation ( y=2x²) represents a parabola with vertex (0,0).

Letter B - x=-2y²

From equation [tex]4p\left(x-h\right)=\left(y-k\right)^2[/tex], you can rewrite the given equation parabola for vertex (0,0) in:

[tex]4p(x-0)=(y-0)^2\\ \\ 4*\frac{-1}{8} x=y^2\\ \\ \frac{-1}{2} x=y^2\\ \\ x=-2y^2[/tex]

Therefore, the given equation ( x=-2y²) represents a parabola with vertex (0,0).

Letter C - x=2y²

From equation [tex]4p\left(x-h\right)=\left(y-k\right)^2[/tex], you can rewrite the given equation parabola for vertex (0,0) in:

[tex]4p(x-0)=(y-0)^2\\ \\ 4*\frac{1}{8} x=y^2\\ \\ \frac{1}{2} x=y^2\\ \\ x=2y^2[/tex]

Therefore, the given equation ( x=2y²) represents a parabola with vertex (0,0).

Letter D - y=-2

The degree of equation is not equal 2. Therefore, it does not represent a parabola.

Only the equations of letter A, B and C represent a parabola with vertex (0,0). See the attached image.

Read more about the vertex of parabola here:

https://brainly.com/question/4551229

Answer:

N/A

Step-by-step explanation:

No figures below.

Answer:

84

Step-by-step explanation:

To find the range, find the difference between the largest value and the smallest value.

544 - 460 = 84

y = mx+b

(5-8)/(9-0) = -1/3 which is m

solve point slope to find slope intercept by using one of the points (0,8)

y-y1=m(x-x1)

y-8 = -1/3(x-0)

y-8 = -1/3x

Answer: y = -1/3x + 8

Answer:

I’m sorry, but it’s a black screen.

Step-by-step explanation:

The benefit: Savings accounts typically have higher interest rates than checking, making it easy for you to grow your money faster. ... Going over that limit can result in a fee or, if you do it multiple times, your bank might convert the account to checking.

Answer:

The answer is "Option C"

Step-by-step explanation:

Please find the complete question in the attached file.

In this question its value of P is 0.0644, the significance level is higher than 0.05. Which doesn't reject [tex]H_o[/tex],

Answer: C

Step-by-step explanation: EDGE 2022

Answer:

1733.33

Step-by-step explanation:

The volume of a pyramid is (length*width*height) divided by 3

Answer:

1733.33

Step-by-step explanation:

v = (lwh)/3

v = (20 x 20 x 13)/3 = 5200/3 = 1733.33

Answer:

18

Step-by-step explanation:

This is actually pretty easy. Keep this in mind.

There are 34 total students. 16 of them like bananas and the rest like apples. All you really need to do is count up from 16 to 34 to find the answer.

The simple equation for this is: 34-16

Thus, the answer is 18.

Answer:

.02

Step-by-step explanation:

Answer:

Step-by-step explanation:

To be a function x can't repeat with a different y so in a every element of x is mapped to a different y so it is a function.

For choice B, -4 is paired with both 7 and 8 so it is not a function.

Choice C is a function since each x is paired with a different y.

Answer:

- 14

Step-by-step explanation:

c² - d² ← is a difference of squares and factors as

= (c + d)(c - d) ← substitute values for factors

= 7 × - 2

= - 14

Answer:

the answer is no. D

Step-by-step explanation:

Answer:

Oh, yes it is D

Answer:

y=4x+5

Step-by-step explanation:

y=mx+c

gradient =m

y intercept=c

m=4

c=5

so

y=4x+5

Answer:

y=4x+9

Step-by-step explanation:

y=mx+b

y=4x+b

5=4(-1)+b

5=-4+b

b=9

y=4x+9

Answer:

1.5% of 4000 or 60

Step-by-step explanation:

Answer:

The tree is 8 foot long

hope this helps

good day mate

Answer:

8

Step-by-step explanation:

12:6 = x:4

2:1 = x:4

x=8

Answer:

[tex]\frac{x+20}{x+4}[/tex]

Step-by-step explanation:

Can't cancel out terms like that

need to factor out the top and bottom

[tex]\frac{x^{2} +16x-80}{x^{2} -16}[/tex] = [tex]\frac{(x+20)(x-4)}{(x-4)(x+4)}[/tex]   now cancel out the (x-4) from the top and bottom

= [tex]\frac{x+20}{x+4}[/tex]

Answer & Explanation:

Error: individual terms in an equation in a fraction cannot be directly canceled out.

Correction:

the easy way (solve the quadratic equation in the numerator and complete the square in the denominator):

(x^2 + 16x - 80) / (x^2 - 16)

(x+20)(x-4) / (x+4)(x-4)

x+20 / x+4

the complicated way (manipulate the exponents and common factors):

(x^2 + 16x - 80) / (x^2 - 16)

(x^2 - 4x + 20x - 80) / x^2 - 2^4

x(x^2-1 - 2^2)+4*5(x - 2^4-2) / (x - 2^2)(x + 2^2)

x(x-4)+20(x-4) / (x-4)(x+4)

x(x-4)+(2^2 (5))(x-4) / (x-4)(x+4)

(x-4)(x + 2^2 (5)) / (x-4)(x+4)

(x-4)(x+20) / (x-4)(x+4)

x+20 / x+4

A. Find the unknown term of each proportion.

1. Answer: X=5

Step-by-step explanation:

x/7=15/21 ==> 21x=7(15) ==> 21x=105

21x/21=105/21 ==> x=5

2. Answer: X=40.5

Step-by-step explanation:

27/x=x/3 ==> 27(3)=x(x) ==> 81=2x

81/2=2x/2 ==> x=40.5

3. Answer: X=16

Step-by-step explanation:

8/x+2=4/9 ==> 8(9)=4(x+2) ==> 72=4x+8

72-8=4x+8-8 ==> 64=4x ==> 64/4=4x/4 ==> x=16

4. Answer: X=8

Step-by-step explanation:

3/x=30/80 ==> 3(80)=30x ==> 240=30x

240/30=30x/30 ==> x=8

5. Answer: M=56

Step-by-step explanation:

m/8=m+7/9 ==> 9m=8(m+7) ==> 9m=8m+56

9m-8m=8m-8m+56 ==> m=56

B. Solve the following.

1. Answer: 80 and 100

Step-by-step explanation:

4:5 ==> 4x+5x=180 ==> 9x=180

9x/9=180/9 ==> x=20

4(20)= 80            5(20)=100

2. Answer: 235.29

Step-by-step explanation:

3400/8 ==> 425

100,000/425= 235.29

Answer:

Step-by-step explanation:

Question says that it uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides. Putting this into equation, we have something like this.

120 = L + 2W

Where

LW = area.

Again, in order to maximize the area with the given fencing, from the equation written above, then Width, w must be = 30 feet and length, l must be = 60

On substituting, we have

A = LW = (120 - 2W) W

From the first equation, making L the subject of the formula, we have this

L = 120 - 2W, which then we substituted above.

On simplification, we have

L = 120W -2W²

Differentiating, we have

A' = 120 - 4W = 0

Remember that W = 30

So therefore, L = 120 - 2(30) = 60 feet

The required length of the rectangular garden is 60 feet

According to the question, the school uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides.

Substitute into the perimeter of the rectangle will give:

120 = L + 2W

Area = LW

In order to maximize the area with the given fencing, from the equation written above, then w = 30 feet and l = 60

On substituting, we have;

A = LW = (120 - 2W) W

L = 120 - 2W,

On simplification, we have

L = 120W -2W²

Differentiating, we have

A' = 120 - 4W = 0

Remember that W = 30

So therefore, L = 120 - 2(30) = 60 feet

Hence the required length of the rectangular garden is 60 feet

Learn more on area of rectangular garden here: https://brainly.com/question/386401

Answer:

I believe its 10 but forgive me if I'm wrong

Answer

Use the fact that 45 times 1/9 = 5. Them multiply by 8 to get the answer, 40.

Step-by-step explanation:

Answer:

11 square units

Step-by-step explanation:

Find the diagram attached

First we need to find the side length of the square with known areas.

Area of a square = L²

L is the side length of the square

For the green square

44 = L²

Lg = √44

For the purple square

Ap = Lp²

33 = Lp²

Lp = √33

Get the length (L) of the unknown square using pythagoras theorem;

Lg² = L²+Lp²

(√44)² = L²+(√33)²

44 = L²+33

L² = 44-33

L² = 11

Since Al = L²

Hence the area of the square adjacent to the third side of the triangle is 11 square units

Answer:

180in3 (180 inch cubed)

Step-by-step explanation:

12 x 5 x 3

Answer: I would assume the answer would be 180

Step-by-step explanation: The formula for volume is Length x Width x Height. So multiply all the number above and the answer will be 180

Answer:

I believe it would be 4.563 x 10^8

Answer:

117+x=180°(sum of straight line)

Step-by-step explanation:

x=180-117

x=63

Answer:

1.202

Step-by-step explanation: