Tomas learned that the product of the polynomials (a + b)(a2 – ab + b2) was a special pattern that would result in a sum of cubes, a3 + b3. His teacher put four products on the board and asked the class to identify which product would result in a sum of cubes if a = 2x and b = 1.Which product should Tomas choose?

(2x + 1)(2x2 + 2x – 1)
(2x + 1)(4x3 + 2x – 1)
(2x + 1)(4x2 – 2x + 1)
(2x + 1)(2x2 – 2x + 1)

Answers

Answer 1

Answer: This is a simple substitution problem. Clearly the answer here is (2x + 1)(4x2 – 2x + 1). We just have to replace a with 2x and b with 1. The tricky part here is the first term in the second group of terms. 2x is to be squared. Common mistake here is raising the x with 2 and not including the coefficient.

Answer 2

Answer:

The product that Tomas should choose given that the pattern resulted in a sum of cube is (2x + 1)(4x² – 2x + 1)

Data obtained from the question

Polynomial => (a + b)(a² – ab + b²)
a = 2x
b = 1
Product =?

How to determine the product

(a + b)(a² – ab + b²)

But

a = 2x

b = 1

Substituting the value of a and b, we have

(a + b)(a² – ab + b²)

(2x + 1)[(2x)² – (2x × 1) + 1²]

(2x + 1)(4x² – 2x + 1)

Thus, the product that Tomas should choose is (2x + 1)(4x² – 2x + 1)

Learn more about polynomial:

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A social worker earns $760 gross pay. If he is married and claims 1 dependent, his state tax rate is 7%, and FICA is 7.65%, what is his net
pay?

Answers

I believe the net pay is $648.66.
$760×.07 for sales tax rate =53.20
$760×0.0765 for FICA= 58.14
(7.65÷100=0.0765)
now 760-53.20-58.14= 648.66

Solve the equation. –3x + 1 + 10x = x + 4

Answers

Answer:

x = 1/2 = 0.5

Step-by-step explanation:

We must solve x in the following equation:

–3x + 1 + 10x = x + 4

We'll try to get the terms with x on the left and the independent terms on the right by performing the opposite operations on both sides of the equation:

–3x + 1 + 10x -x = x + 4 -x

–3x + 1 + 10x -x -1 = 4 -1

6x = 3

Now lets isolate x, again by performing the opposite operation, that is dividing by 6 on both sides:

6x /6 = 3/6

x = 1/2 = 0.5

10x-3x= 8x

8x + 1 = x + 4

subtract x in both side

7x + 1 = 4

subtract 1 on both side

7x = 3

divide 7 on both side

x = 3/7

or

.43 in decimal

How do I solve this math problem you and your friend are selling magazine subscriptions for a fundraiser. After w weeks , you have sold (7w = 6) subsriptions and your friend has sold ( 9w = 2) subscriptions. Whats the diffrence written in simple expression form?

Answers

Answer:

The diffrence written in simple expression form is 40/63

Step-by-step explanation:

To solve for the difference normally you have to subtract your own subscription from that of your friends,

Let's perform this operation step wise

Now your subscription is

(7w = 6)

w=6/7

Your friends own is

( 9w = 2)

w=2/9

So the difference in simple form is

6/7-2/9

The LCM is 63 I.E 9*7=63

=54-14/63

=40/63

Can anyone help please :)

Answers

Answer:

Explanation:

There is a theorem in geometry that says:

In a circle, if two chords are equal in measure, then their corresponding minor arcs are equal in measure.

Those small tick marks on each of the chords means that they are equal in measure. So, following the theorem, the arcs are also equal in measure.

If they are equal and

arc AB = arc CB

arc AB = 24 feet

Then

arc CB = 24 feet

by substitution.

The length of a rectangle is 3 inches more than twice its width, and its area is 65 square inches. What is the width?If w = the width of the rectangle, which of the following expressions represents the length of the rectangle?

2w + 3
2(w + 3)
3(2w)

Answers

Let L be the length of the rectangle and W be its width. Translating the first sentence into mathematical expressions, we get, L=2W+3. To get the area of a rectangle, we will use the formula A=L*W. Since we are already given with the area, we will substitute this value to the formula, together with the expression of L in terms of W. Thus, 65=(2W+3)*(W). Further simplification would yield

65=2W^2+3W
2W^2+3W-65=0

We have a quadratic equation, hence, we will solve for its factors. We have,

(2w+13)(w-5)=0

The two roots of the equation are: -13/2 and 5. Since we can only have positive numbers for dimensions, the width of the rectangle is 5 in.

The expression for the length of the rectangle is 2W+3.

Event B is dependent on event A, and event A occurs before event B. Which expression is equal to the probability of event A?

Answers

An event is the result of a random experiment or a group of shared results.
It could be defined as every subset of a sample space because the sample space is a collection of all possible results of a random experiment.

When the event B is dependenting on event A,

$\to \bold{P(B \cap A) \neq P(B)* P(A)}\n\n$