Select All equivalent expressions to 4( x + 2)

Factorization involves breaking down an expression.

The sum of cubes is given as:

[tex](a^3 + b^3) = (a + b)(a^2 -ab + b^2)[/tex]

(a) Verify the formula

Expand the expression on the right-hand side

[tex](a^3 + b^3) = a^3 -a^2b + ab^2 +a^2b - ab^2 + b^3[/tex]

Collect like terms

[tex](a^3 + b^3) = a^3 -a^2b +a^2b+ ab^2 - ab^2 + b^3[/tex]

[tex](a^3 + b^3) = a^3 + b^3[/tex]

The formula has been verified

(b) Factorized 8x^3+ 27

We have:

[tex]8x^3 + 27[/tex]

Express 27 as 3^3

[tex]8x^3 + 27 =8x^3 + 3^2[/tex]

Express 8 as 2^3

[tex]8x^3 + 27 =2^3x^3 + 3^3[/tex]

Rewrite as:

[tex]8x^3 + 27 =(2x)^3 + 3^3[/tex]

Given that:

[tex](a^3 + b^3) = (a + b)(a^2 -ab + b^2)[/tex]

The expression becomes

[tex]8x^3 + 27 =(2x + 3)((2x)^2 - (2x)3 +3^2)[/tex]

[tex]8x^3 + 27 =(2x + 3)(4x^2 -8x3 +9)[/tex]

(c)The other factor of 2^3 - b^3

By difference of cubes, we have:

[tex]x^3 - y^3=(x-y)(x^2+xy+y^2)[/tex]

So, the equation becomes

[tex]2^3 - b^3=(2-b)(2^2+2b+b^2)[/tex]

This gives

[tex]2^3 - b^3=(2-b)(4+2b+b^2)[/tex]

Hence, the other factor of [tex]2^3 - b^3[/tex] is [tex]4+2b+b^2[/tex]

(c) Factor x^3 - 1

We have:

[tex]x^3 - y^3=(x-y)(x^2+xy+y^2)[/tex]

Express 1 as 1^3 in x^3 - 1

[tex]x^3 - 1 =x^3 - 1^3[/tex]

[tex]x^3 - y^3=(x-y)(x^2+xy+y^2)[/tex] becomes

[tex]x^3 - 1^3=(x-1)(x^2+x+1^2)[/tex]

[tex]x^3 - 1^3=(x-1)(x^2+x+1)[/tex]

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Mathematical processes are the steps used to determine the result of operations

The dimension of the rectangle is given as:

[tex]Length = 5x^2 - 8x + 9[/tex]

[tex]Width = x + 5[/tex]

(1) The perimeter of the triangle

This is the sum of the side lengths of the rectangle.

So, we have:

[tex]Perimeter = 2 \times (Length + Width)[/tex]

This gives

[tex]Perimeter = 2 \times (5x^2 - 8x + 9 + x + 5)[/tex]

Collect like terms

[tex]Perimeter = 2 \times (5x^2 - 7x + 14)[/tex]

Open brackets

[tex]Perimeter = 10x^2 - 14x + 28[/tex]

Hence, the perimeter of the rectangle is [tex]10x^2 - 14x + 28[/tex]

(2) The area of the triangle

This is the product of the dimensions of the rectangle.

So, we have:

[tex]Area = Length \times Width[/tex]

This gives

[tex]Area = (5x^2 - 8x + 9) \times (x + 5)[/tex]

Open brackets

[tex]Area = 5x^3 - 8x^2 + 9x +25x^2 - 40x + 45[/tex]

Collect like terms

[tex]Area = 5x^3 - 8x^2 +25x^2+ 9x - 40x + 45[/tex]

[tex]Area = 5x^3 +17x^2 -31x + 45[/tex]

Hence, the area of the rectangle is [tex]5x^3 +17x^2 -31x + 45[/tex]

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The transactions that would leave the initial balance the same are a deposit of $278 followed by a withdrawal of $278.

The transactions that would leave the initial balance the same are transactions that net to zero. Withdrawals reduce the balance in the account. Deposits increase the value of the balance in the account.

Option A: Net balance

$275 - $232 + 132 = $175

Option B: Net balance

$275 + $278 - $278 = $275

Option C: Net balance

$275 - $115 + $312 = $472

Option D: Net balance

$275 + $205 - $317 = $163

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Check the picture below.

Answer:

Angles are [tex]67^0,53^0[/tex]

Step-by-step explanation:

Let the angles be [tex]x,y[/tex]

One fifth of sum of two angles is 24

[tex]\frac{x+y}{5} =24\\\\x+y=120[/tex]

The  difference is [tex]14[/tex]

[tex]x-y=14[/tex]

[tex]2x=134\\\\x=67^0[/tex]

[tex]y=120-67\\\\=53^0[/tex]

[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \log_4(q)=m\implies 4^m = q[/tex]

Answer:

C. x is y less than z

Step-by-step explanation:

x+y=z

by using transposition

x = z-y

whatever x is, it is equal to the value of y taken from z

The give quadratic function is dilated by the given coefficient, and shifted

horizontally to the left.

(a) The transformation of the common function f(x) are;

Please find attached the required graph created with MS Excel

(b) Where t = 0, represent the year 2,000 we have;

(c) The mortgage debt in the year 2014 is M ≈ $5.622 trillion

Reasons:

The given function is f(t) = 0.0037·(t + 14.979)²

Year 1990 is t = 0

(a) The given common function is; f(x) = x²

The transformation of the quadratic function are;

The coefficient 0.0037 widens the common function such that f(t) is wider

than f(x).

The constant, 14.979 added to the variable, t, shifts the graph of the

common function horizontally to the left.

Therefore;

Please find attached the required graph over the interval 0 ≤ t ≤ 19 created with MS Excel.

(b) The amount of mortgage debt in 2,000 is given as follows;

With t' = 0 represent the year 2,000, we have;

At year 1990, t' = -10

Which gives, t' = t + 10

From which we have;

f(t) = 0.0037·(t + 14.979)² = 0.0037·(t' + 10 + 14.979)²  = 0.0037·(t' + 24.979)²

Therefore;

The function with t = 0 representing the year 2,000 is presented as follows;

f(t) = 0.0037·(t + 24.979)²

(c) In the year 2014, we have;

t = 2014 - 2000 = 14

Which gives;

f(14) = 0.0037·(14 + 24.979)² ≈ 5.622

The mortgage debt in the year 2014 is M ≈ $5.622 trillion dollars

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Answer:

6c+2(5-7c)=6c+10-14c

A. -8c+10 is correct option.

Answer:

linear = 3x+y = 12, y = x/2 -3, y=x

nonlinear y = 6/x -2, y=3x³+5

Answer:

Well your Hypotenuse is 10 and your other angle is 8 so it is most likely 6 because you see a change in 2 each time and it is about 2 units smaller because all right triangles follow a pattern

Step-by-step explanation:

if it was too go even higher it would go to 12,14,16 etcetera

Answer:

723 -> 01011010011

Step-by-step explanation:

Answer:

A = 12√3

Step-by-step explanation:

first find the limits by finding the zeros

0 = 9 − 3x²

3x² = 9

x² = 3

x = ±[tex]\sqrt{3}[/tex]

[tex]A = \int\limits^a_b ({9 - 3x^2\\}) - 0\, dx[/tex]

where b = [tex]-\sqrt{3}[/tex] and a = [tex]\sqrt{3\\}[/tex]

A = 9x - x³ [tex]\left \{ {{\sqrt{3} } \atop {-\sqrt{3} }} \right.[/tex]

[tex]A = 9\sqrt{3} - \sqrt{3} ^3 - (9(-\sqrt{3)} - (-\sqrt{3} )^3)[/tex]

[tex]A = 9\sqrt{3} -3\sqrt{3} +9\sqrt{3} - 3\sqrt{3}[/tex]

[tex]A = 12\sqrt{3}[/tex]

Answer:

D. x = negative eleven-halves plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction

Step-by-step explanation:

Evaluate 0 and 1 (xe+ex)Dx

==========================================================

Explanation:

The ratio 3:2 scales up to 3x:2x for some positive whole number x.

We have 3x white pieces, 2x black pieces, and 3x+2x = 5x pieces total. Set this equal to the 15 mentioned and solve for x.

5x = 15

5x/5 = 15/5

x = 3

Therefore, there are 3x = 3*3 = 9 white pieces and 2x = 2*3 = 6 black pieces, which gives 9+6 = 15 total. The ratio 9:6 reduces to 3:2 after dividing both parts by the GCF 3.

Answer:

c

Step-by-step explanation:

it just is that's the right book

Answer:

2.5x+73=235.5

2.5x=162.5

x=65

ANSWER NUMBER 500 L GOOOOOOOO!!!!!!!!!!!!!!!!!

Hope This Helps!!!

The equation will be 2.5x+73=235.5 and the value of x will be 65.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Malik needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 2.5 hours and charged him $73 for parts. The total was $235.50.

The equation can be written as below:-

2.5x+73=235.5

2.5x=162.5

x=65

Therefore, the equation will be 2.5x+73=235.5 and the value of x will be 65.

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Answer:

You get more points by answering people's questions. You use points to get help from other people.

Answer: Answer people's questions to get points and use those points to get an answer to your question.

Answer:

unfortunately i cannot tell you the exact answers; however, i can suggest something instead. my suggestion is that if there's any math notes that are available, maybe you could look over them-then apply that to the problems.

Step-by-step explanation:

I hope this helps you!

Answer:

B

Step-by-step explanation:

Using the combination formula and the probability concept, it is found that there is a 0.1259 = 12.59% probability that she gets at least two red ones, given that she gets at least one green one.

Combination formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Desired outcomes:

Hence:

[tex]D = C_{3,2}C_{3,1}{C_{10,1}} = \frac{3!}{2!1!} \times \frac{3!}{1!2!} \times \frac{10!}{1!9!} = 90[/tex]

Total outcomes:

Four marbles are taken from a set of 13, hence:

[tex]T = C_{13,4} = \frac{13!}{4!9!} = 715[/tex]

Then, the probability is:

[tex]p = \frac{D}{T} = \frac{90}{715} = 0.1259[/tex]

0.1259 = 12.59% probability that she gets at least two red ones, given that she gets at least one green one.

To learn more about the use of the combination formula and the probability concept, you can check combination formula and the probability concept,

Answer:

85*65=5525

85*43=3655

5525-3655=1870

Hope This Helps!!!

[tex]f[/tex](x) = 0.20x + 35 : 29.5

Answer:

0.7 is 7/10 Example out of ten cookies 7 are chocolate chip

0.07 is 7/100 Example out of 100 cookies 7 are chocolate chip

Hope This Helps!!!

Answer:

the answer would be 12 I say this because 72 divied by 6 would equal 12

Answer:

12 dollars

Set up a proportion.

6/72=1/x

Solve by cross-multiplying (my preferred method) and then you will end up with the final answer of x=12.

12 is the answer :)

PLEASE MARK BRAINLIEST!

THANK YOU & HAVE A WONDERFUL DAY :))

Answer:

your trying to find out how much each cookie cost

from looking at this we can see that 2 cookies is 1 dollar so each cookie is 50 cents

Hope This Helps!!!

Answer:

See explanation

Step-by-step explanation:

Dilation of 1.5 about the origin. (Each new point is 1.5 times as far from the origin.)

G (-1, 3)  G' (-1.5, 4.5)

F (-2, -2)  F' (-3, -3)

G'x / Gx = -1.5/-1 = 1.5

G'y / Gy = 4.5 / 3 = 1.5

F'x / Fx = -3 / -2 = 1.5

F'y / Fy = -3 / -2 = 1.5