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3 years ago

Which of the following is the quotient of the rational expressions shown below?

1 answer:

soldier1979 [14.2K]3 years ago

7 0

We have two rational expressions. One in numerator and one in denominator.
Dividing by a fraction is equivalent to multiplying by its reciprocal. The rational expression in the denominator can be multiplied by taking its reciprocal to simplify the overall expression as shown below.

$\frac{ \frac{4x+1}{6x} }{ \frac{x}{3x-1} } \\ \\ 
= \frac{4x+1}{6x} * \frac{3x-1}{x} \\ \\ 
= \frac{(4x+1)(3x-1)}{6 x^{2} }$

There are no common factors, so the expression can be simplified any further.

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Complete the synthetic division problem below.

rewona [7]

Answer:

Step-by-step explanation:

- 2 | 2 2 - 2 4

↓ - 4 4 - 4

--------------------------

2 - 2 2 0 ← remainder

Since the remainder = 0 then (x + 2) is a factor

quotient = 2x² - 2x + 2

4 0

2 years ago

Find the third side in simplest radical form

klasskru [66]

Answer:

$2 \sqrt{71} \: units$

Step-by-step explanation:

Given is a right angled triangle in which third side is the hypotenuse.

Therefore, by Pythagoras theorem:

$thid \: side = \sqrt{ {15}^{2} + ( \sqrt{59} )^{2} } \\ \\ = \sqrt{225 + 59} \\ \\ = \sqrt{284} \\ \\ = \sqrt{ {2}^{2} \times 71 } \\ \\ = 2 \sqrt{71} \: units$

3 0

2 years ago

Express the given linear equation in slope intercept form and identify the slope and y- intercept of -2x+7y=28

AlekseyPX

Slope-intercpet is y=mx+b where m=slope
b=y intercept
convert
-2x+7y=28
add 2x to both sides
7y=2x+28
divide both sides by 7
y=2/7x+4
slope=2/7
y-intercept=4 or the point (0,4)

4 0

3 years ago

11 You are renting a car for a trip. You call two different rental car places about prices. Each

Sonja [21]

Answer:

Step-by-step explanation:

m is number of miles

A: 45+0.21m (45 is the initial cost)

B: 28+0.38m (28 is the initial cost)

To know how in many miles the cost will be equal,

45+0.21m=28+0.38m

0.38m-0.21m=45-28

0.17m=17

m=17/0.17 = 100

So, at 100 miles the cost will be same for company A and B.

4 0

2 years ago

Henrietta bought 5 cupcakes and 2 brownies for $16.25. She went back to the bakery the next day and bought 7 cupcakes and 6 brow

serious [3.7K]

Answer:

cost of one cupcake = $2.75

cost of one brownie = $1.25

Step-by-step explanation:

Let c = number of cupcakes

Let b = number of brownies

Equation 1: 5c + 2b = 16.25

Equation 2: 7c + 6b = 26.75

Multiply equation 1 by 3:

⇒ 15c + 6b = 48.75

Now subtract equation 2 from this equation to eliminate 6b:

⇒ 8c = 22

Divide both sides by 8:

⇒ c = 2.75

Substitute c = 2.75 into one of the original equations and solve for b:

⇒ 5(2.75) + 2b = 16.25

⇒ 13.75 + 2b = 16.25

⇒ 2b = 2.5

⇒ b = 1.25

Therefore, cost of one cupcake = $2.75 and cost of one brownie = $1.25

6 0

2 years ago