The landscaper charges a rate of $40 per hour to plant trees.

A group of friends buys 15 movie tickets for a total of $147.66, which

Vedmedyk [2.9K]

Answer: $9.20

Step-by-step explanation:

Divide the full tax price by the sales tax (7% or .07) plus 1 (always add 1 to the tax) thus

$147.66 / 1.07 = $138.00

So $138.00 is the full price without tax.

Now divide $138.00 by the amount of tickets (15) to find a single ticket price before tax!

138.00/15 = $9.20

Remember to always add 1 to the tax percentage above when dividing to get the *pre-tax* price.

7 0

3 years ago

The problem is attached, thanks.

NeX [460]

Answer:

$\displaystyle \frac{dy}{dx} \bigg| \limit_{(1, 4)} = 2$

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)
Exponential Rule [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$
Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Implicit Differentiation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

$\displaystyle \sqrt{x} - \sqrt{y} = -1$

Point (1, 4)

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle x^{\frac{1}{2}} - y^{\frac{1}{2}} = -1$
[Implicit Differentiation] Basic Power Rule: $\displaystyle \frac{1}{2}x^{\frac{1}{2} - 1} - \frac{1}{2}y^{\frac{1}{2} - 1}\frac{dy}{dx} = 0$
[Implicit Differentiation] Simplify Exponents: $\displaystyle \frac{1}{2}x^{\frac{-1}{2}} - \frac{1}{2}y^{\frac{-1}{2}}\frac{dy}{dx} = 0$
[Implicit Differentiation] Rewrite [Exponential Rule - Rewrite]: $\displaystyle \frac{1}{2x^{\frac{1}{2}}} - \frac{1}{2y^{\frac{1}{2}}}\frac{dy}{dx} = 0$
[Implicit Differentiation] Isolate y terms: $\displaystyle -\frac{1}{2y^{\frac{1}{2}}}\frac{dy}{dx} = -\frac{1}{2x^{\frac{1}{2}}}$
[Implicit Differentiation] Isolate $\displaystyle \frac{dy}{dx}$ : $\displaystyle \frac{dy}{dx} = \frac{2y^{\frac{1}{2}}}{2x^{\frac{1}{2}}}$
[Implicit Differentiation] Simplify: $\displaystyle \frac{dy}{dx} = \frac{y^{\frac{1}{2}}}{x^{\frac{1}{2}}}$

Step 3: Evaluate

Substitute in point [Derivative]: $\displaystyle \frac{dy}{dx} = \frac{(4)^{\frac{1}{2}}}{(1)^{\frac{1}{2}}}$
Exponents: $\displaystyle \frac{dy}{dx} = \frac{2}{1}$
Division: $\displaystyle \frac{dy}{dx} = 2$

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Implicit Differentiation

Book: College Calculus 10e

6 0

3 years ago

Which ordered pair is a solution of the inequality y > 13x + 3

solong [7]

Answer:

x<y-3/13

Step-by-step explanation:

Switch sides'

13x+3<y

Subtract 3 from both sides

13x+3-3<y-3

Simplify

13x<y-3

Divide both sides by 13

13x/13<y/13-3/13

Simplify

x<y-3/13

(13,3)

Hope this helped!!

8 0

3 years ago

A copy machine makes 45 copies in 25 seconds .Find the unit rate of copies per second

katen-ka-za [31]

Answer:

1.8

Step-by-step explanation:

45 divided by 25

5 0

4 years ago

What is the solution to Multiply (Y-1)(y+8)

Setler79 [48]

whats is y? I can't solve the problem without it

4 0

3 years ago