1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Slav-nsk [51]
3 years ago
11

LOTS OF POINTS Simplify the expression by factoring, showing the steps in your work

Mathematics
1 answer:
julia-pushkina [17]3 years ago
8 0

Answer:

\frac{3x+7}{4x+1}

Step-by-step explanation:

\frac{12x^2+31x+7}{16x^2+8x+1}

First you factor 12x^2+31x+7:

=\left(12x^2+3x\right)+\left(28x+7\right)

Then you factor out 3x from 12x^2+3x:

12x^2+3x

=12xx+3x

=3\cdot \:4xx+3x

=3x\left(4x+1\right)

Then you factor out 7 from 28x+7:

28x+7

=7\cdot \:4x+7

=7\left(4x+1\right)

=3x\left(4x+1\right)+7\left(4x+1\right)

Factor out common term 4x+1:

=\left(4x+1\right)\left(3x+7\right)

\frac{\left(4x+1\right)\left(3x+7\right)}{16x^2+8x+1}

Factor 16x^2+8x+1:

=4^2x^2+8x+1

=4^2x^2+8x+1^2

=\left(4x\right)^2+8x+1^2

=\left(4x\right)^2+2\cdot \:4x\cdot \:1+1^2

Use the perfect square formula:

=\left(4x+1\right)^2

\frac{\left(4x+1\right)\left(3x+7\right)}{\left(4x+1\right)^2}

Cancel out common factor 4x+1:

=\frac{3x+7}{4x+1}

You might be interested in
The width of a rectangle is 6 kilometers less than twice its length. if its area is 108 square​ kilometers, find the dimensions
Art [367]
Hi there!

Answer:
length = 9 kilometres
Width = 12 kilometres

Let's solve this problem step by step!
To find our answer we need to set up and solve an equation.

Let the length of the rectangle be represented by x.
The width of the rectangle can therefore be expressed by 2x - 6.

The area of a rectangle can be found by using the formula:
A = width × length

Plug in the data from the formula
A = x (2x - 6).

Simplify using rainbow technique.
x(2x - 6) = 2 {x}^{2} - 6x

Now we've found the simplified expression that expresses the area of the rectangle. Therefore, we can now set up and start solve the equation.

2 {x}^{2} - 6x = 108
Subtract 108

2 {x}^{2} - 6x - 108 = 0
Divide by 2.

{x}^{2} - 3x - 54
(x - 9)(x + 6) = 0
Rule AB = 0, gives A is 0 or B is 0.

x - 9 = 0 \\ x = 9 \\ \\ x + 6 = 0 \\ x = - 6

The length of the rectangle, which was represented by x, must be 9 (since it cannot be a negative number).

Length
x = 9
Width
2x - 6 = 2 \times 9- 6 = 18 - 6 = 12

Answer:
length = 9 kilometres
Width = 12 kilometres

~ Hope this helps you!
6 0
3 years ago
Solve the attached question<br><br>#yohaniJaman<br><br><br><br>​
aksik [14]

HETY is a parallelogram.

HT and EY are diagonals. We know that diagonals divides the parallelogram into two equal parts.

So ar(HET) = ar(HTY)

And, ar(HEY) = ar(EYT) now, in AHET, diagonal EY bisects the line segment HT and also the AHET,

∴ar(AHOE) = ar(AEOT)

Similarly in AETY

ar(ΔΕΟΤ) = ar(ΔΤΟΥ)

And in AHTY,

ar(ATOY) = ar(AHOY)

That means diagonals in parallelogram divides it into four equal parts.

Hence Proofed.

5 0
2 years ago
a person driving along the road moves rates of 56 miles per hour driven.How far does the person drive in 1.5 hours?
tester [92]
56 miles : 1 hour
/2. /2
28 miles : 30 minutes
56+28. 1h+30m
84 miles : 1 hour 30 minutes

84 is the answer
8 0
3 years ago
Read 2 more answers
An athlete eats 75 g of protein per day while training. How much protein will she eat during 21 days of training? Write your ans
lisov135 [29]

Answer:

1.575 kg

Step-by-step explanation:

75g x 21

1575 g

convert to kg

1.575 kg

Brainliest Appreciated!

7 0
3 years ago
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 111
BabaBlast [244]

Answer:

I’m not sure m a

Step-by-step explanation:

4 0
2 years ago
Other questions:
  • Sharon has a rectangular bedspread that measures 3 feet by 5 feet. She wants to
    13·1 answer
  • The first term of an Arithmetic Series is 6 and the third term is 12. What is the second term in the series?
    14·1 answer
  • Solve the equation <br>50=4(x-7)-6(3x-6)
    7·2 answers
  • (x-3)^2+ (y-5)^2 = 144 <br> is it (3,5) or (-3,-5)
    13·2 answers
  • The function f(x = 2x + 1 is defined over the interval [2, 5]. if the interval is divided into n equal parts, what is the value
    8·2 answers
  • A tanks length is 3 feet longer than its width. The height is 1 foot less than the width. The volume of the tank is 160 cubic fe
    13·1 answer
  • Write a 2 two column proof. Given: 4y = 2x -10; y = 6 Prove : x = 17
    9·1 answer
  • Find the area of the figure . Sides meet at right angles .
    7·2 answers
  • Jack wants to abopt all kittens that weigh more than 4 ounces how many kittens will he abopt
    9·1 answer
  • The first person to answer this gets brainliest
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!