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3 years ago

Simplify the expression. (x^2 - 9)/(x^2 + 2x - 15)

Mathematics

1 answer:

tia_tia [17]3 years ago

4 0

Answer:

We have

$\frac{x^2-9}{x^2+2x-15}$

$\frac{\left(x+3\right)\left(x-3\right)}{x^2+2x-15}$

$\frac{\left(x+3\right)\left(x-3\right)}{\left(x-3\right)\left(x+5\right)}$

$\frac{x+3}{x+5}$

∴The answer is D

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Consider the following problem: a box with an open top is to be constructed from a square piece of cardboard, 3 feet wide, by cu

Alecsey [184]

Answer:

) See annex

b) See annex

x = 0,5 ft

y = 2 ft and

V = 2 ft³

Step-by-step explanation: See annex

c) V = y*y*x

d-1) y = 3 - 2x

d-2) V = (3-2x)* ( 3-2x)* x ⇒ V = (3-2x)²*x

V(x) =( 9 + 4x² - 12x )*x ⇒ V(x) = 9x + 4x³ - 12x²

Taking derivatives

V¨(x) = 9 + 12x² - 24x

V¨(x) = 0 ⇒ 12x² -24x +9 = 0 ⇒ 4x² - 8x + 3 = 0

Solving for x (second degree equation)

x =[ -b ± √b²- 4ac ] / 2a

we get x₁ = 1,5 and x₂ = 0,5

We look at y = 3 - 2x and see that the value x₂ is the only valid root

then

x = 0,5 ft

y = 2 ft and

V = 0,5*2*2

V = 2 ft³

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3 years ago

It says If 496 people voted in the election, how many were over 65 years old . I have a graph that say Over 65 is 25%

Dennis_Churaev [7]

Answer:

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Step-by-step explanation:

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alina1380 [7]

Answer:

Step-by-step explanation:

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3 years ago

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3 years ago

A square of side length s lies in a plane perpendicular to a line L. One vertex of the square lies on L. As this square moves a

user100 [1]

Answer:

Part (A) The required volume of the column is $s^2h$ .

Part (B) The volume be $s^2h=\frac{s^2h}{2}+\frac{s^2h}{2}$ .

Step-by-step explanation:

Consider the provided information.

It is given that the we have a square with side length "s" lies in a plane perpendicular to a line L.

Also One vertex of the square lies on L.

Part (A)

Suppose there is a square piece of a paper which is attached with a wire through one corner. As you blow it up it spins around on the wire.

This square moves a distance h along L, and generate a corkscrew-like column with square.

The cross section will remain the same.

So the cross section area of original column and the cross section area of twisted column at each point will be the same.

The volume of the column is the area of square times the height.

This can be written as:

$s^2h$

Hence, the required volume of the column is $s^2h$ .

Part (B) What will the volume be if the square turns twice instead of once?

If the square turns twice instead of once then the volume will remains the same but divide the volume into two equal part.

$s^2h=\frac{s^2h}{2}+\frac{s^2h}{2}$

Hence, the volume be $s^2h=\frac{s^2h}{2}+\frac{s^2h}{2}$ .

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3 years ago