All categories

2 years ago

Find the simplified quotient. (2x^2 + 5x +3 / x^2 - 3x -4) / (4x^2 + 2x - 6 / x^2 - 8x + 16)

Mathematics

2 answers:

irinina [24]2 years ago

8 0

ANSWER

$\frac{x - 4}{2x - 2}$

EXPLANATION

The given expression is;

$\frac{2 {x}^{2} + 5x + 3}{ {x}^{2} - 3x - 4} \div \frac{4 {x}^{2} + 2x - 6}{ {x}^{2} - 8x + 16}$

We factor to obtain;

$\frac{(x + 1)(2x + 3)}{(x - 4)(x + 1)} \div \frac{2(x - 1)(2x + 3)}{(x - 4)(x - 4)}$

Multiply by the reciprocal of the second fraction

$\frac{(x + 1)(2x + 3)}{(x - 4)(x + 1)} \times \frac{(x - 4)(x - 4)}{2(x - 1)(2x + 3)}$

Cancel out common factors to get,

$\frac{1}{1} \times \frac{(x - 4)}{2(x - 1)}$

$\frac{x - 4}{2x - 2}$

PIT_PIT [208]2 years ago

7 0

Answer:

X-4/2x-2

Step-by-step explanation:

You might be interested in

Ms. Hamby gave a quiz. Two students’ work and the answer key are shown. Ms. Hamby accepts equivalent answers in any form.

Luden [163]

Answer:

Student A and Student B both answered 2 questions correctly.

See explanation below

Step-by-step explanation:

Note: that answers in the form:

$\frac{a}{-b}=\frac{-a}{b}=-\frac{a}{b}$

ARE ALL EQUIVALENT.

First of all, 4/5 is equivalent to 0.8 if we do long division.

and 19/20 is 0.95 if we do long division.

Now, Student A:

Both of the fractions are correct and the negative sign is equivalent and makes the answer correct, so both are correct.

For Student B:

Similarly, both answers are correct for this student as well, looking at the equivalence we showed first.

Also, "-" (negative) in front of the parenthesis and inside parenthesis here doesn't matter.

Hence,

Student A and Student B both answered 2 questions correctly.

5 0

2 years ago

The slope of the line below is -5/7 Write the point-slope equation of the line using the coordinates of the labeled point.

Vesna [10]

Answer:

The answer is C) y - 2 = -5/7(x - 6)

Step-by-step explanation:

Since we have the slope (-5/7) and a point (6, 2), we can just input those in for m and (x1, y1) in point-slope form.

y - y1 = m(x - x1)

y - 2 = -5/7(x - 6)

4 0

2 years ago

Read 2 more answers

Kimani works for the city and is reimbursed for his mileage when traveling for work. In order to submit his reimbursement form,

IceJOKER [234]

The mileage from the Supermarket to the Library may be calculated using Pythagorean Theorem.

The coordinates of the Library are (7,10) and the coordinates of the Supermarket are (3,7).

So, the distance requested is √ [ (7-3)^2 + (10 - 7)^2 = √[ 4^2 + 3^2 = √ [16 + 9] =

= √25 = 5

So, he runs 5 miles.

And the reimbursement will be $0.50 / mile * 5 mile = $ 2.50.

Answer: option B) $ 2.50

5 0

2 years ago

Giselle buys two types of flowers 48 pink roses and 56 white lilies she combines the two flowers to make identical bouquets with

SSSSS [86.1K]

To solve this problem, let us first lay out all the factors of each number.

48 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

56 : 1, 2, 4, 7, 8, 14, 28, 56

The greatest number of bouquets that can be made would be equal to the greatest common factor of the two numbers. In this case it would be 8.

Answer:

8 bouquets

7 0

2 years ago