Simplify 9x^2 - 25/3x-5

1 answer:

4 0

First, we are going to write it like this:
$\frac{9x^2-25}{3x-5}$
Then, we are going to do something like factoring, but it's not factoring. An example would be: $x^2-y^2=\left(x+y\right)\left(x-y\right)$
If we apply it, we would be left with:
$=\frac{\left(3x+5\right)\left(3x-5\right)}{3x-5}$
We cancel the common factors, and we are left with:
$=3x+5$
That's our final answer.

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Thanks!
-TetraFish

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An artist creates a cone-shaped sculpture for an art exhibit. If the sculpture is 8 feet tall and has a base with a circumferen

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Answer:

The volume of the cone-shaped sculpture is equal to 114.631 ft³.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Geometry

Circumference Formula:
$\displaystyle C = 2 \pi r$

r is radius

Volume Formula [Cone]:
$\displaystyle V = \frac{\pi r^2 h}{3}$

r is radius
h is height

Step-by-step explanation:

Step 1: Define

Identify given.

h = 8 ft

C = 23.236 ft

Step 2: Find Radius r

[Circumference Formula] Substitute in variables:
$\displaystyle \begin{aligned}C = 2 \pi r & \rightarrow 23.236 \ \text{ft} = 2(3.14)r \\\end{aligned}$
Solve [Equality Properties]:
$\displaystyle \begin{aligned}C = 2 \pi r & \rightarrow 23.236 \ \text{ft} = 2(3.14)r \\& \rightarrow r = 3.7 \ \text{ft} \\\end{aligned}$

Step 3: Find Volume

[Volume Formula - Cone] Substitute in variables:
$\displaystyle \begin{aligned}V = \frac{\pi r^2 h}{3} & \rightarrow V = \frac{(3.14)(3.7 \ \text{ft})^2(8 \ \text{ft})}{3} \\\end{aligned}$
Evaluate:
$\displaystyle \begin{aligned}V = \frac{\pi r^2 h}{3} & \rightarrow V = \frac{(3.14)(3.7 \ \text{ft})^2(8 \ \text{ft})}{3} \\& \rightarrow V = \boxed{ 114.631 \ \text{ft}^3 } \\\end{aligned}$