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3 years ago

Find the value of x for the given value of y:A: y=6x-4;y=20B:y=x/2+3;y=1

Mathematics

2 answers:

aleksandrvk [35]3 years ago

6 0

Answer:

Step-by-step explanation:

y = 6x - 4......y = 20

20 = 6x - 4

20 + 4 = 6x

24 = 6x

24/6 = x

4 = x

y = x/2 + 3.....y = 1

1 = x/2 + 3

1 - 3 = x/2

-2 = x/2

-2 * 2 = x

-4 = x

Karo-lina-s [1.5K]3 years ago

5 0

The answer is
A. x=4
B. x=-4

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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

Andreas93 [3]

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:
$\displaystyle \begin{aligned}V = \frac{\pi r^2 h}{3} & \rightarrow V = \frac{(3.14)(3.7 \ \text{ft})^2(8 \ \text{ft})}{3} \\& \rightarrow V = \boxed{ 114.631 \ \text{ft}^3 } \\\end{aligned}$