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2 years ago

Given the function f(x) = 3|x – 2| + 6, for what values of x is f(x) = 18?

Mathematics

2 answers:

oksian1 [2.3K]2 years ago

7 0

Answer:

Step-by-step explanation:

x = -2 x = 6

got it right on EDGE

Nikolay [14]2 years ago

4 0

Answer:

x = -2, x = 6

Step-by-step explanation:

18 = 3|x - 2| + 6

12 = 3|x - 2|

4 = |x - 2|

4 = x - 2 and -4 = x - 2

x = 6 and x = -2

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How do I determine the 50th term for the sequence -5, -1, 3, 7, 11

Mademuasel [1]

The sequence is going up by 4 so u have to multiply each term by four and the -5 is it’s 0th term as well it’s beginning so you have to input that in the equation as well
4(50) - 5 = 200 - 5 = 195
I’m not very good at explaining so I hope u get it

5 0

3 years ago

The edge of each cube used to build this rectangular prism is 13

kolbaska11 [484]

Answer:

$\frac{3}{3} * \frac{2}{3} *\frac{3}{3} =\frac{2}{3} \ in^3$

====================================================

Step-by-step explanation:

The question is missing the attached figure.

The edge of each cube used to build this rectangular prism is 1/3 inch long. Based on the attached figure.

the volume of the prism = length × height × width

length = $3 * \frac{1}{3} = \frac{3}{3}$

height = $3 * \frac{1}{3} = \frac{3}{3}$

width = $2 * \frac{1}{3}= \frac{2}{3}$

So the volume of the prism = $\frac{3}{3} *\frac{3}{3} *\frac{2}{3} =\frac{2}{3} \ in^{3}$

∴ The equation that shows the volume of the prism, in cubic inches

= $\frac{3}{3} * \frac{2}{3} *\frac{3}{3} =\frac{2}{3} \ in^3$

8 0

3 years ago

Read 2 more answers

If the gradient of the tangent to

Marizza181 [45]

Answer:

Point A(9, 3)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

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

Algebra I

Coordinates (x, y)
Functions
Function Notation
Terms/Coefficients
Anything to the 0th power is 1
Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$
Exponential Rule [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle y = \sqrt{x}$

$\displaystyle y' = \frac{1}{6}$

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y = x^{\frac{1}{2}}$
Basic Power Rule: $\displaystyle y' = \frac{1}{2}x^{\frac{1}{2} - 1}$
Simplify: $\displaystyle y' = \frac{1}{2}x^{-\frac{1}{2}}$
[Derivative] Rewrite [Exponential Rule - Rewrite]: $\displaystyle y' = \frac{1}{2x^{\frac{1}{2}}}$
[Derivative] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y' = \frac{1}{2\sqrt{x}}$

Step 3: Solve

Find coordinates of A.

x-coordinate

Substitute in y' [Derivative]: $\displaystyle \frac{1}{6} = \frac{1}{2\sqrt{x}}$
[Multiplication Property of Equality] Multiply 2 on both sides: $\displaystyle \frac{1}{3} = \frac{1}{\sqrt{x}}$
[Multiplication Property of Equality] Cross-multiply: $\displaystyle \sqrt{x} = 3$
[Equality Property] Square both sides: $\displaystyle x = 9$