MATHEMATICS MIDDLE SCHOOL

Consider the polynomial p(x)=8x3+12x2+2x+3.Part A: What is the correct factorization of p(x)=8x3+12x2+2x+3 over the integers?

Part B: What method is used to factor p(x)=8x3+12x2+2x+3?

Select one answer for Part A and select one answer for Part B.

B: perfect-square trinomial
B: grouping
A: (2x+3)(4x+1)
B: sum of cubes
A: (4x2+1)(2x+3)
A: (2x+3)(4x2+6x+1)

Answers

Answer 1

Answer:

A: $(4x^2+1)(2x+3)$

B: grouping

Step-by-step explanation:

We are given the polynomial: $p(x)=8x^3+12x^2+2x+3$

Part A: What is the correct factorization of $p(x)=8x^3+12x^2+2x+3$ over the integers?

We need to factorize the term $p(x)=8x^3+12x^2+2x+3$

Factorizing by grouping:

$p(x)=8x^3+12x^2+2x+3$

$p(x)=(8x^3+12x^2)+(2x+3)$

$p(x)=4x^2(2x+3)+1(2x+3)$

$p(x)=(4x^2+1)(2x+3)$

So, factors of the term $p(x)=8x^3+12x^2+2x+3$ are $p(x)=(4x^2+1)(2x+3)$

Part B: What method is used to factor p(x)=8x3+12x2+2x+3?

The method used to factor the given polynomial is grouping.

We group the terms and then find the common terms in that specific group

So, the answers are:

A: $(4x^2+1)(2x+3)$

B: grouping

Keywords: Finding Factors

Learn more about finding factors at:

#learnwithBrainly

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Relationship B has a greater rate than Relationship A. The graph represents Relationship A.Which table could represent Relationship B?

A.
Time (weeks) -2- -5- -6- -9-
Plant growth (in.) -1.2- -3 -3.6- -5.4-

B.
Time (weeks) -2- -5- -6- -9-
Plant growth (in.) -1.4- -3.5- -4.2- -6.3-

C.
Time (weeks) -2- -5- -6- -9-
Plant growth (in.) -1.6- -4- -4.8- -7.2-

D.
Time (weeks) -3- -4- -6- -9-
Plant growth (in.) -1.5- -2- -3- -4.5-

Answers

The table that could represent Relationship B to have a greater rate than Relationship A is;

Table C

To find the rates of the various tables, we will use the formula;

Rate = Δy/Δx

Using the coordinates on the graph (4, 3) and (8, 6), we have;

Rate = (6 - 3)/(8 - 4)

Rate = 3/4

Rate = 0.75

For Table A;

From the graph, we can see the y-axis represents plant growth while the x-axis represents time.

Thus, using the coordinates (2, 1.2) and (5, 3), we have;

Rate = (3 - 1.2))/(5 - 2)

Rate = 0.6

For Table B;

Using the coordinates (2, 1.4) and (5, 3.5)

Rate = (3.5 - 1.4)/(5 - 2)

Rate = 0.7

For Table C;

Using the coordinates (2, 1.6) and (5, 4) gives;

Rate = (4 - 1.6)/(5 - 2)

Rate = 0.8

For Table D;

Using the coordinates (3, 1.5) and (4, 2) we have;

Rate = (2 - 1.5)/(4 - 3)

Rate = 0.5

Read more at; brainly.com/question/12559989

The rate would be the gradient, defined by dy/dx.
For graph A this would be (6-3)/(8-4)= 3/4.
So any table showing a gradient of over 3/4 would have a faster rate.
Table A: (3-1.2)/(5-2)= 1.8/3= 0.6, less than 0.75
Table B: (3.5-1.4)/(5-2)= 2.1/3= 0.7, still less than 0.75
Table C: (4-1.6)/(5-2)= 2.4/3= 0.8.
This is a higher gradient than 0.75 in graph A. therefore table C shows a faster rate.

A Bag of Halloween Candy weighs 4.7 pounds, how much would 3.4 bags weigh

Answers

You could multiply the two numbers to get a product of 15.98 pounds.

Can someone help me with 24 please?

Answers

Answer:

A(-3, -7) B(2,-1) C(-2,0) D(-5,6)

Step-by-step explanation:

A(3,7) B(-2,1) C(2,0) D(5,-6)

180 rotation around origin = (-x,-y)

A(3,7) - A(-3,-7)

B(-2,1) - B(2,-1)

C(2,0) - C(-2,0)

D(5,-6) - D (-5,6)

Answer:

A(-3, -7) B(2,-1) C(-2,0) D(-5,6)

Step-by-step explanation:

A(3,7) B(-2,1) C(2,0) D(5,-6)

180 rotation around the origin would equal (-x,-y)

A(3,7) - A(-3,-7)

B(-2,1) - B(2,-1)

C(2,0) - C(-2,0)

D(5,-6) - D (-5,6)

An isosceles trapezoid has legs that measure 10 cm and bases of 12 cm and 2 cm. The base angles measure 60°. Find the height and the area of the trapezoid.

Answers

I hope this helps you

-15 + 12x = 5x + 7 -3x
SOLVE FOR X

Answers

Answer:

$x = 2.2$

Step-by-step explanation:

$- 15 + 12x = 5x + 7 - 3x \n + 12x - 5x + 3x = 15 + 7 \n 10x = 22 \n (10x)/(10) = (22)/(10) \n x = 2.2$

Answer: $x=(11)/(5)$

Simplify both sides of the equation

$-15+12x=5x+7+-3x$

$12x-15=(5x+-3x)+(7)$ (Combine Like Terms)

$12x-15=2x+7$

Subtract 2x from both sides

$12x-15-2x=2x+7-2x\n10x-15=7$

Divide both sides by 10

$(10x)/(10) =(22)/(10)$

$x=(11)/(5)$

What is the least common denominator for the fractions 1/6 and 3/4 20 points

Answers

The least common denominator for 1/6 and 3/4 would be 12.

If you were going to convert both of your original fractions to have this common denominator, they would be

1/6 = 2/12

3/4 = 9/12

12 is the least common denominator (lcd) for the fractions 1/6 and 3/4

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In your own words, explain the steps you would need to take to find slope from data in a table. The sample response is… Start by choosing two data points. Calculate the difference between the second y value and the first y value. Then divide that by the difference between the second x value and the first x value.But at the end it says you should include this info… Choose two sets of data (x and y values). Calculate the difference between the two y values. Calculate the difference between the corresponding two x values. Slope is the difference in y values / difference in x values.Use this information to your advantage.Hope this helps! :))