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
Simplify, and list any restrictions on the variable: (2x(x-4)/(4x^2-64)
uysha [10]

Answer:

WHEN SIMPLIFIED THE ANSWER WILL BE:

Step-by-step explanation:

(X)/(2(X+4)

8 0
3 years ago
A cone is a solid that has one circular base and only one face. true or false
bearhunter [10]
The answer for this is true 
4 0
3 years ago
Read 2 more answers
How would you solve (-1,4),y=3x+5
astraxan [27]

Answer:

y = 12x

Step-by-step explanation:

-1 times 4 equals -4 so you have -4,y = 3x + 5 so you do 5 + 3 so it is 8x then you have -4,y = 8x so you add 4 to each side and it becomes y = 12x

5 0
3 years ago
If the subject without diabetes eats a high-carb food such as the candy bar or orange smoothie, then the blood glucose levels wi
zysi [14]

Answer:

1. The right answer is stay the same.

In a healthy subject, a diet rich in sugar (such as starch and fast sugars) increases blood sugar in the first two hours after ingestion and then stabilizes after the third hour with the action of the patient. insulin which has a hypoglycemic action. But over time the pancreas (the organ that secretes insulin) will get tired over time if these foods are eaten excessively.

2. The right answer is stay the same.

In a healthy person, a diet of low-sugar foods (such as fiber) does not increase blood glucose (or very little) and helps maintain normal blood glucose levels. These foods are good for the health because they preserve the pancreas as long as there is not much solicitude by the presence of a hause of glucose in the blood.

3. The right answer is increase.

In a type 1 diabetic patient, the pancreas does not secrete insulin appropriately, and this is due to self-destruction of the organ by the immune system (autoimmune disease). This implies that during the ingestion of foods rich in sugars, the blood sugar will be hard to regain its normal level, that is why it remains elevated after three hours after ingestion.

4. The right answer is stay the same.

Foods low in carbohydrates are very good for the health and is recommended in the subjects diabetic (type 1 and 2) and even for the healthy subjects to avoid the appearance of the diabetes afterwards. These foods help diabetics to have controlled blood glucose levels when their degradation does not give glucose.

6 0
3 years ago
What are the transformations to this quadratic function y= (x+4) power of 2 - 8
I am Lyosha [343]

Answer:

Horizontal shift of 4 units to the left.

Vertical translation of 8 units downward.  

Step-by-step explanation:

Given the quadratic function, y = (x + 4)² - 8, which represents the horizontal and vertical translations of the parent graph, y = x²:

The vertex form of the quadratic function is y = a(x - h)² + k

Where:

The vertex is (h , k), which is either the <u>minimum</u> (upward facing graph) or <u>maximum</u> (downward-facing graph).

The axis of symmetry occurs at <em>x = h</em>.

<em>a</em> =  determines whether the graph opens up or down, and makes the graph wider or narrower.

<em>h</em> = determines how far left or right the parent function is translated.

<em>k</em> = determines how far up or down the parent function is translated.

Going back to your quadratic function,

          y = (x + 4)² - 8

  • The vertex occrs at (-4, -8)
  • a is assumed to have a value of 1.
  • Given the value of <em>h</em> = -4, then it means that the graph shifted horizontally by <u>4 units to the left</u>.  
  • Since k = -8, then it implies that the graph translated vertically at <u>8 units downward</u>.

Please mark my answers as the Brainliest, if you find this helpful :)

4 0
2 years ago
Other questions:
  • When rolling a fair number cube with numbers 1 through 6, what is the probability of rolling a number greater than 5?
    13·2 answers
  • Fund the separate equation and angles between them
    13·1 answer
  • Find the center of the circle whose equation is x² - 10x + y² - 10y = -1 A)(5,5) B)(10,10) C)(10,1)
    5·1 answer
  • Pls help
    14·2 answers
  • Solve the question belo , thanks
    7·1 answer
  • A cell phone tower casts a shadow 150 feet long. A tree nearby that is 30 feet tall casts a shadow that is 20 feet long. How tal
    5·2 answers
  • The axis of symmetry for this parabola<br><br> Y equals -5xsquared plus 10x-14
    15·1 answer
  • Two dice are tossed 432 times. How many times would you expect to get a sum of 4?
    15·2 answers
  • Pedro brought 8 tickets to a basketball game. He paid a total of $208.
    6·1 answer
  • Geometry
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!