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2 years ago

A) Find the value of y.b) Hence, find the surface area of this trapezoidal prism?

Mathematics

1 answer:

Ilya [14]2 years ago

5 0

Answer:

<h2>A)FIND THE VALUE OF Y.</h2>

Step-by-step explanation:

<h2>#CARRY ON LEARNING</h2><h2>#MARK BRAINLITS</h2>

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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

2 years ago

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Morgan is walking her dog on an 8-meter-long leash. She is currently 500 meters from her house, so the maximum and minimum dista

Gnom [1K]

Given:
Morgan = 500 meters from her house
Length of leash = 8 meters

minimum distance of the dog from the house 500 - 8 = 492 meters.
maximum distance of the dog from the house 500 + 8 = 508 meters.

7 0

3 years ago

Find the remainder when f(x) = x^3 + 14x^2 − 7x − 10 is divided by x − 3.

Elanso [62]

Answer:

122

Step-by-step explanation:

(3)³ + 14(3²) - 7(3) - 10

122

Used remainder theorem

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3 years ago

PLZ HELP QUICK!!!

Viktor [21]

Answer:

9-8

Step-by-step explanation:

60 divided by 7 is 8.5

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3 years ago

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Can anybody help me please

Sliva [168]

Hello, your answer would be (-5, 5)

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2 years ago

A) Find the value of y.b) Hence, find the surface area of this trapezoidal prism?​

A) Find the value of y.b) Hence, find the surface area of this trapezoidal prism?