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2 years ago

Find the area of the following shape. Show work.

Mathematics

1 answer:

Serga [27]2 years ago

6 0

Answer:

The total area:

12 units²

Step-by-step explanation:

There are three parts on this shape:

1 big right triangle

1 rectangle

1 small right triangle

Big right triangle:

area = (4*4)/2 = 16/2 = 8units²

Rectangle:

area = 2*1 = 2units²

Small right triangle:

area = (2*2)/2 = 2units²

Total area

8+2+2 = 12 units²

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Find an expression for a cubic function f if f(4) = 96 and f(-4) = f(0) = f(5) = 0. Part 1 of 4 A cubic function generally has t

Bezzdna [24]

Given a polynomial $p(x)$ and a point $x_0$ , we have that

$p(x_0) = 0 \iff (x-x_0) \text{\ divides\ } p(x)$

We know that our cubic function is zero at -4, 0 and 5, which means that our polynomial is a multiple of

$(x+4)(x)(x-5) = x(x+4)(x-5)$

Since this is already a cubic polynomial (it's the product of 3 polynomials with degree one), we can only adjust a multiplicative factor: our function must be

$f(x) = ax(x+4)(x-5),\quad a \in \mathbb{R}$

To fix the correct value for a, we impose $f(4)=96$ :

$f(4) = 4a(4+4)(4-5) = -32a = 96$

And so we must impose

$-32a=96 \iff a = -\dfrac{96}{32} = -3$

So, the function we're looking for is

$f(x) = -3x(x+4)(x-5)=-3x^3+3x^2+60x$

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2 years ago

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Step-by-step explanation:

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2 years ago

Below is a diagram of the base of gazebo hunter is building in his backyard

Brilliant_brown [7]

Full Question: Below is the diagram of the base of gazebo. Hunter is building for his backyard. He plans on gazebo having a height of 4 meters with a pyramid shaped roof that is an additional 2 meters high. He needs to order shingles for the roof and needs to know how much area is covered by shingles.

Answer:

$2784$ $m^{2}$