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3 years ago

Simplify completely''''

Mathematics

1 answer:

34kurt3 years ago

8 0

Answer:

$\displaystyle \frac{2(x + 3)}{5x - 2}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Terms/Coefficients
Factoring

Step-by-step explanation:

Step 1: Define

$\displaystyle \frac{2x^2 + 16x + 30}{5x^2 + 13x - 6}$

Step 2: Simplify

[Fraction] Factor numerator: $\displaystyle \frac{2(x + 3)(x + 5)}{5x^2 + 13x - 6}$
[Fraction] Factor denominator: $\displaystyle \frac{2(x + 3)(x + 5)}{(x + 3)(5x - 2)}$
[Fraction] Divide: $\displaystyle \frac{2(x + 3)}{5x - 2}$

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A family wants to rent a car to go on vacation. Company A charges $45.50 and 11c per mile. Company B charges $60.50 and 13c per

Maslowich

Answer: Company B charges $(15.5+0.12x) more for x miles than company A.

Step-by-step explanation:

Let x = Number of miles.

Total charge = Flat charge + (charge per mile) x (Number of miles)

Given:

For Company A ,

Flat charge= $45

Charge per mile = 11 cents = 0.11 [ 1 dollar = 100 cents i.e. 1 cent = 0.01 dollar]

Total charge = 45+0.01x

For Company B,

Flat charge= $60.50

Charge per mile = 13 cents = 0.13

Total charge = 60.50+0.13x

Difference in charge = Charge for company B - Charge for company A

= 60.50+0.13x-(45+0.01x)

= 15.5+0.12x

Hence, Company B charges $(15.5+0.12x) more for x miles than company A.

7 0

3 years ago

A tutot earns $105 for 3 hours of tutoring. How much would she earn if she tutored for

AlexFokin [52]

Answer:

$297.50

Step-by-step explanation:

If she earns 105 for three hours, she would be earning $35 an hour.

105/3=35

If she works 8.5 hours, to find the amount you would multiply the hourly rate ($35) by 8.5. So, the answer is

8.5x35=$297.50

8 0

3 years ago

Read 2 more answers

Dividing Binomials by monomials

vodka [1.7K]

The answer I got was -3x^(3)+6

8 0

3 years ago

Which expression is not equivalent to Negative 3 x minus one-half 4 y? 2 y minus 5 x minus one-half 2 y 2 x Negative 2 x minus o

Alona [7]

Answer:

The wrt=itten expressions are too difficult to interpret properly. I did my best but I don't see any of the answers as equivalent to -3x - 2y, so please check my interpretations of the answer options.

Step-by-step explanation:

"Negative 3 x minus one-half 4 y"

-3x- (1/2)4y

or -3x - 2y

=====

The answer options are too garbled for me to make sense of them. Are they:

1. 2 y minus 5 x minus one-half 2 y : 2y -5x - (1/2)2y; y -5x ?

2. 2 x Negative 2 x minus one-half 6 y : 2(-2x)- (1/2)6y; -4x - 3y ?

3. 3 x Negative 3 x minus three-fourths 4 y : 3x(-3x) - (3/4)4y; -9x -3y ?

4. one-fourth Negative 3 y minus three-fourths 7 y one-fourth minus 3 x:

(1/4)(-3y) - (3/4)7y - (1/4)(-3x); -(3/4)y -(21/4)y + (3/4)x; -(24/4)y + (3/4)x; ?

I don't see any of the answers as equivalent to -3x - 2y, so please check my interpretations of the answer options.

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2 years ago

Read 2 more answers

Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract for its new computer wheel align

sasho [114]

Answer:

Step-by-step explanation:

Hello!

The given data corresponds to the variables

Y: Annual Maintenance Expense ($100s)

X: Weekly Usage (hours)

n= 10

∑X= 253; ∑X²= 7347; $\frac{}{X}$ = ∑X/n= 253/10= 25.3 Hours

∑Y= 346.50; ∑Y²= 13010.75; $\frac{}{Y}$ = ∑Y/n= 346.50/10= 34.65 $100s

∑XY= 9668.5

To estimate the slope and y-intercept you have to apply the following formulas:

$b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} } = \frac{9668.5-\frac{253*346.5}{10} }{7347-\frac{(253)^2}{10} }= 0.95$

$a= \frac{}{Y} -b\frac{}{X} = 34.65-0.95*25.3= 10.53$

^Y= a + bX

^Y= 10.53 + 0.95X

H₀: β = 0

H₁: β ≠ 0

α:0.05

$F= \frac{MS_{Reg}}{MS_{Error}} ~~F_{Df_{Reg}; Df_{Error}}$

F= 47.62

p-value: 0.0001

To decide using the p-value you have to compare it against the level of significance:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

The decision is to reject the null hypothesis.

At a 5% significance level you can conclude that the average annual maintenance expense of the computer wheel alignment and balancing machine is modified when the weekly usage increases one hour.

b= 0.95 $100s/hours is the variation of the estimated average annual maintenance expense of the computer wheel alignment and balancing machine is modified when the weekly usage increases one hour.

a= 10.53 $ 100s is the value of the average annual maintenance expense of the computer wheel alignment and balancing machine when the weekly usage is zero.

The value that determines the % of the variability of the dependent variable that is explained by the response variable is the coefficient of determination. You can calculate it manually using the formula:

$R^2 = \frac{b^2[sumX^2-\frac{(sumX)^2}{n} ]}{[sumY^2-\frac{(sumY)^2}{n} ]} = \frac{0.95^2[7347-\frac{(253)^2}{10} ]}{[13010.75-\frac{(346.50)^2}{10} ]} = 0.86$

This means that 86% of the variability of the annual maintenance expense of the computer wheel alignment and balancing machine is explained by the weekly usage under the estimated model ^Y= 10.53 + 0.95X

Without usage, you'd expect the annual maintenance expense to be $1053

If used 100 hours weekly the expected maintenance expense will be 10.53+0.95*100= 105.53 $100s⇒ $10553

If used 1000 hours weekly the expected maintenance expense will be $96053

It is recommendable to purchase the contract only if the weekly usage of the computer is greater than 100 hours weekly.

4 0

3 years ago

Simplify completely''''​

Simplify completely''''