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3 years ago

Each square represents one square foot. Estimate the area of the figure below.

Mathematics

1 answer:

JulijaS [17]3 years ago

5 0

The estimated area of the figure is 36 square foot.

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The product of (4z^2 + 7z - 8) and (-z + 3) is -4z^3 + xz^2 + yz - 24. What is the value of x? What is the value of y?

ycow [4]

Answer:

$x=5+\frac{29}{z}-\frac{y}{z}$

$y=5z+29-xz$

Step-by-step explanation:

Given: $(4z^2+7z-8)(-z+3)=-4z^3+xz^2+yz-24$ ; find x and y.

Let's start with finding x first. Let's distribute the left side of the equation.

$-4z^3+5z^2+29z-24=-4z^3+xz^2+yz-24$

Let's move everything we can to the left side of the equation. Some things will cancel out.

$5z^2+29z=xz^2+yz$

Now, let's move the term that includes $x$ to the left side of the equation. Everything else should be moved to the right.

$-xz^2=-5z^2-29z+yz$

Let's get rid of the negative sign in front of $x$ by dividing both sides by -1.

$xz^2=5z^2+29z-yz$

To get $x$ completely isolated, divide both sides by $z^2$ .

$\frac{xz^2}{z^2}=\frac{5z^2}{z^2}+\frac{29z}{z^2}-\frac{yz}{z^2}$

Simplify.

$x=5+\frac{29}{z}-\frac{y}{z}$

Let's solve for y. We will start with the distributed and simplified equation to make it easier.

$5z^2+29z=xz^2+yz$

Now, let's move the term that includes $y$ to the left side of the equation. Everything else should be moved to the right.

$-yz=-5z^2-29z+xz^2$

Again, let's get rid of the negative sign in front of the $y$ by dividing both sides by -1.

$yz=5z^2+29z-xz^2$

To isolate y, divide both sides by z.

$\frac{yz}{z}=\frac{5z^2}{z}+\frac{29z}{z}-\frac{xz^2}{z}$

Simplify.

$y=5z+29-xz$

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Step-by-step explanation:

(2 x 6) + ( $\sqrt{16\\}$ - 8 ÷ 2^2) =

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12 + (4 - 2)

12 + 2

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Y and x have a proportional relationship, and y = 12 when x = 8.

OleMash [197]

Answer: x is 12

Step-by-step explanation:

For directly proportional relationship, both variables change in the same direction. It means that an increase in one variable will result to an increase in the other variable. A decrease in one variable will result to a decrease in the other variable.

y and x have a proportional relationship,

We will introduce a proportionality constant and replace the proportionality symbol with an equal to symbol. Thus

y = kx

When y is 12, x is 8

Substituting into the equation,

12 = k × 8

k = 12/8 = 1.5

The equation becomes

y = 1.5x

The value of x when y is 18 will be

18 = 1.5x

x = 18/1.5 = 12

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3 years ago