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3 years ago

2x (y^2+3)-5 (3+y^2)

Mathematics

1 answer:

Irina18 [472]3 years ago

3 0

Use distributive property a(b + c) = ab + ac.

$2x(y^2+3)-5(3+y^2)=(2x)(y^2)+(2x)(3)+(-5)(3)+(-5)(y^2)\\\\=2xy^2+6x-15-5y^2$

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Could someone help me rnnn?

GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola: $y=3x^2-4$

Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

(where (h, k) is the vertex and $a$ is some constant)

Substitute point (0, -4) into the equation:

$\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}$

Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$

Substitute point (1, -1) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}$

Equate to find h:

$\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}$

Substitute found value of h into one of the equations to find a:

$\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}$

Substitute found values of h and a to find k:

$\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}$

Therefore, the equation of the parabola in vertex form is:

$\implies y=3(x-0)^2-4=3x^2-4$

So the vertex of the parabola is (0, -4)

5 0

3 years ago

Read 2 more answers

the glass gauge on a cylindrical coffee maker shows there are 45 cups left when the coffee maker is 36% full. How many cups of c

Nadya [2.5K]

Answer:

125 cups

Step-by-step explanation:

45 is 36% of what number?

45 = 0.36n

n = 45 / 0.36

n = 125

4 0

3 years ago

What is the value of -10 - (-11) ?

Luda [366]

Step-by-step explanation:

Hey there!

Answer: 1

Here;

= -10 - (-11)

= -10 +11 [ (-)×(-)= +]

= 1

Hope it helps...

6 0

3 years ago

The side lengths of Triangle B are the side lengths of Triangle A. Which statement is not true about Triangle A and Triangle B?

Minchanka [31]

Answer:

They are not similar.

Step-by-step explanation:

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3 years ago

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Galina-37 [17]

Answer:

Step-by-step explanation:

Hello, we know that if the equation is

$y=a(x-h)^2+k$

Then the vertex is the the point (h,k)

Here, the vertex is the point (-2,-20) so we can write, a being a real number that we will have to find,

$y=a(x-(-2))^2-20=a(x+2)^2-20$

On the other hand, we know that the y-intercept is (0,-12) so we can write

$-20=a(0+2)^2-12=4a-12\\\\\text{We add 12 and we divide by 4.}\\\\4a = -20+12=-8\\\\a = \dfrac{-8}{4}=-2$

So the equation becomes.

$\boxed{y=-2(x+2)^2-12}$

And we can give the standard form as below.

$y=-2(x+2)^2-12=-2(x^2+4x+4)-12\\\\=-2x^2-8x-8-12 \ \\\\\boxed{y=-2x^2-8x-20}$

Thank you.

7 0

4 years ago