Given the original amount and the percent of change, find the new amount, $25; 300%

-y-22-13 6< X/2-2 I need help solving both

AveGali [126]

Answer: The first one is y≤11 and the second question is x>16 Hope that helps Goodbye!

Step-by-step explanation: 1. Add 22 to both sides.

-13+2

−y≥−13+2

2 Simplify -13+2−13+2 to -11−11.

-y\ge -11

−y≥−11

3 Multiply both sides by -1−1.

y\le 11

y≤11

1 Add 22 to both sides.

6+2<\frac{x}{2}

6+2<

2

x

2 Simplify 6+26+2 to 88.

8<\frac{x}{2}

8<

2

x

3 Multiply both sides by 22.

8\times 2<x

8×2<x

4 Simplify 8\times 28×2 to 1616.

16<x

5 Switch sides.

x>16

5 0

3 years ago

What is the domain of f in the equation F(x)=5/x2-18x+45

Hitman42 [59]

$f(x)=\dfrac{5}{x^2-18x+45}\\\\The\ domain:\\\\x^2-18x+45\neq0\\\\x^2-15x-3x+45\neq0\\\\x(x-15)-3(x-15)\neq0\\\\(x-15)(x-3)\neq0\iff x-15\neq0\ \wedge\ x-3\neq0\\\\\boxed{x\neq15\ \wedge\ x\neq3}\to\boxed{x\in\mathbb{R}-\{3,\ 15\}}$

6 0

3 years ago

Let y = 5e5z

jekas [21]

Answer:

$\displaystyle dy = 25e^{5x}dx\\dy = 3.27 \cdot 10^7$

General Formulas and Concepts:

Math

Rounding
Euler's Number e - 2.71828

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Calculus

Derivatives

Derivative Notation

Differentials

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

eˣ Derivative: $\displaystyle \frac{dy}{dx}[e^u] = u'e^u$

Step-by-step explanation:

Part A

Step 1: Define

$\displaystyle y = 5e^{5x}$

Step 2: Differentiate

[Function] eˣ Derivative: $\displaystyle \frac{dy}{dx} = \frac{dy}{dx}[5x] \cdot 5e^{5x}$
[Derivative] Basic Power Rule: $\displaystyle \frac{dy}{dx} = 5x^{1 - 1} \cdot 5e^{5x}$
[Derivative] Simplify: $\displaystyle \frac{dy}{dx} = 5 \cdot 5e^{5x}$
[Derivative] Multiply: $\displaystyle \frac{dy}{dx} = 25e^{5x}$
[Derivative] [Multiplication Property of Equality] Isolate dy: $\displaystyle dy = 25e^{5x}dx$

Part B

Step 1: Define

[Differential] $\displaystyle dy = 25e^{5x}dx$

[Given] x = 3, dx = 0.4

Step 2: Evaluate

Substitute in variables [Differential]: $\displaystyle dy = 25e^{5(3)}(0.4)$
[Differential] [Exponents] Multiply: $\displaystyle dy = 25e^{15}(0.4)$
[Differential] Evaluate exponents: $\displaystyle dy = 25(3.26902 \cdot 10^6)(0.4)$
[Differential] Multiply: $\displaystyle dy = (8.17254 \cdot 10^7)(0.4)$
[Differential] Multiply: $\displaystyle dy = 3.26902 \cdot 10^7$
[Differential] Round: $\displaystyle dy = 3.27 \cdot 10^7$