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nikitadnepr [17]
3 years ago
15

The equation y^2+8y−x+18=0 represents a parabola. Drag and drop the expressions into the boxes in the equation to rewrite the eq

uation of this parabola in standard form.
x= ( )^2 + ___
Mathematics
1 answer:
mario62 [17]3 years ago
4 0

Answer:

The equation of parabola is standard form is x=\left(y+4\right)^2+2

Step-by-step explanation:

Given equation of parabola is,

y^2+8y-x+18=0

In order to find the equation of parabola in standard form, eliminate x from left side of equation and use completing square method to find the equation.

First step is to add x on both side of equation.

y^2+8y-x+18+x=0+x

y^2+8y+18=x

Rewriting,

x=y^2+8y+18

Now applying completing square method as follows.

Following are the steps for calculation of this method.

Find the last term of above equation by using below formula,

Last\:term\:of\:square=\left(\dfrac{coefficient\:of\:y}{2}\right)^{2}

Now coefficient of y is 8.

\therefore Last\:term\:of\:square=\left(\dfrac{8}{2}\right)^{2}

Simplifying,

Last\:term\:of\:square=\left(4\right)^{2}

Last\:term\:of\:square=16

Second step is to add and subtract the last term.

x=y^2+8y+18+16-16

Rewriting,

x=y^2+8y+16+18-16

Since \left(a+b\right)^{2}=a^{2}+2ab+b^{2}

Using above formula,

x=\left(y+4\right)^{2}+2

Therefore, the equation of parabola in standard form is x=\left(y+4\right)^{2}+2

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If f(x) = 4x^3 + Ax^2 + 7x - 1 and f(2) = 3, what is the value of A?<br> (^ = powers)
bekas [8.4K]

Answer:

A = -10.5

Step-by-step explanation:

To find the value of "A", you can plug x = 2 and f(x) = 3 into the equation. This will allow you to simplify and find the value of "A".

f(x) = 4x³ + Ax² + 7x - 1                     <---- Original equation

3 = 4(2)³ + A(2)² + 7(2) - 1                 <---- Plug x = 2 and f(x) = 3 into equation

3 = 4(8) + A(4) + 14 - 1                      <---- Solve 2³ and 2²

3 = 32 + A(4) + 14 - 1                        <---- Multiply 4 and 8

3 = 45 + A(4)                                    <---- Combine like terms

-42 = A(4)                                         <---- Subtract 45 from both sides

-10.5 = A                                         <---- Divide by 4

If A = -10.5, the final equation would look like this:

f(x) = 4x³ - 10.5x² + 7x - 1

8 0
2 years ago
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Arte-miy333 [17]

Answer:

x=76 being exterrior alternate angle

6 0
2 years ago
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Please anybody help please
wel

Answer:

x= -3 and y = 6

Step-by-step explanation:

so basically what you are trying to do is reduce into finding x and y

what you do is you want to find a number to multiply one of the equations in order to get the same x or y value does not matter which

so,...

we can do

either 20x or 15y

we will go with the smallest 15y

so for both equations multiply the whole thing by 5 for the first equation and by 3 for the second

5 x 5x+3y=3 --> 1

3 x 4x+5y=18 --> 2

we then get

25x+15y = 15 -->1

12x + 15y = 54 -->2

then now that you have the same Y values you can subtract ! which cancels out both the 15y

25x+15y = 15 -->1

- 12x + 15y = 54 -->2

13x =-39

so now x=-3 and all you have to do with x = -3 is sub this into either one of the equations that you started with  !

x = -3

5(-3) +3y =3

-15 + 3y = 3

3y = 3+15

3y=18

y = 6!

5 0
2 years ago
It is currently 0 degrees outside and the temperature is dropping 4 degrees every hour. The temperature after h hours is -4h. Ex
Ymorist [56]

Answer:

-4x3.5=-14

Step-by-step explanation:

divide -14 by -4 wich = 3.5

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Answer:

Step-by-step explanation:

A.

C.

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