MATHEMATICS MIDDLE SCHOOL

A business reports a net income of –$5040 over a 9-month period. What is the average income per month for that period?

A.
$45360

B.
$560

C.
–$560

D.
–$45360

Answers

Answer 1
Answer:

The average income per month for that period will be $560.Option B is correct.

What is average?

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

It is given that,

Net income =  $5040

Time duration = 9-month

The average income per month is found as the ratio of netincome and the total time duration.

Average income per month = net income/time duration

Average income per month = $5040 / 9

Average income per month = 560
The averageincome per month for that period will be $560.

Thus option B is correct.

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Answer 2
Answer: What you do is divide -$5040 by 9 months and you get -$560.

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Find the sequence..
1,2,2,4,8

Answers

Let the n-th term be called a_n

We see that if we choose a_0=1,a_1=2 then the other numbers follow the pattern a_(n+2)=a_(n+1)\cdot a_n (see :4=2*2,8=4*2)

Hence the sequence will be 1,2,2,4,8,32,256, 8192, 2097152, 17179869184,\dots

Find the point B on AC such that the ratio of AB to BC is 2:3

Answers

Answer:

B(4, - 3 )

Step-by-step explanation:

We have A(2, - 7) and C(7, 3 )

Using the section formula to calculate the coordinates of B

x_(B) = (3(2)+2(7))/(2+3) = (6+14)/(5) = (20)/(5) = 4

y_(B) = (3(-7)+2(3))/(2+3) = (-21+6)/(5) = (-15)/(5) = - 3

Hence B(4, - 3 )

Answer:

2 1/5, 1/5

Step-by-step explanation:

khan academy

Which polynomial has (3x + 2) as a binomial factor? 6x3 + 3x2 + 4x + 2 12x2 + 15x + 8x + 10 18x3 – 12x2 + 9x – 6 21x4 + 7x3 + 6x + 2

Answers

If binomial (3x+2) is  a factor of some polynomial, then number x=-(2)/(3) is this polynomial's root. Check all polynomials:

A. For the polynomial 6x^3 + 3x^2 + 4x + 2,

6\left(-(2)/(3)\right)^3 + 3\left(-(2)/(3)\right)^2 + 4\left(-(2)/(3)\right) + 2=-(16)/(9)+(4)/(3)-(8)/(3)+2=-(10)/(9)\neq 0.

B. For the polynomial 12x^2 + 15x + 8x + 10,

12\left(-(2)/(3)\right)^2 + 23\left(-(2)/(3)\right) + 10=(16)/(3)-(46)/(3)+10=0.

C. For the polynomial 18x^3-12x^2 + 9x-6,

18\left(-(2)/(3)\right)^3 -12\left(-(2)/(3)\right)^2 + 9\left(-(2)/(3)\right) -6=-(16)/(3)-(16)/(3)-6-6\neq 0.

D. For the polynomial 21x^4 + 7x^3 + 6x + 2,

21\left(-(2)/(3)\right)^4 +7\left(-(2)/(3)\right)^3 +6\left(-(2)/(3)\right) +2=(112)/(27)-(56)/(27)-4+2\neq 0.

Answer: correct choice is B

Answer:

B 12x2 + 15x + 8x + 10

Step-by-step explanation:

Did it

The value of dollars, y, of a car x years after it was purchased can be modeled by the function y=14,000-875x

What is the meaning of the y-intercept of the linear model?

a) The initial value of the car is 14,000.
b) The average value of the car is 14,000.
c) The car’s value decreases by $875 each year after it was purchased.
d) The car’s value decreases by $16 each year after it was purchased.

Please help.

Answers

Answer:

Option a) The initial value of the car is 14,000

Step-by-step explanation:

we know that

The linear equation into slope intercept form is equal to

y=mx+b

where

m is the slope

b is the y-coordinate of the y-intercept

Remember that

The y-intercept is the value of y when the value of x is equal to zero

In this problem we have

y=14,000-875x

so

The slope is equal to m=-875(\$)/(year)

The y-intercept is b=\$14,000

therefore

\$14,000 is the value of the car for x=0  (initial value)

Translate "the sum of 6 and the product of 8 and x” into a mathematical expression

Answers

The mathematical expression is 6 + 8x

The sum of 6 and the product of 8 and x  can be written  mathematically by first  getting the product of  8 and x  which equals 8x

Sum means addition( +)

So the sum of 6 is written as 6 +

We  thus have  the mathematical expression Translated as  6 + 8x

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Final answer:

The mathematical expression for 'the sum of 6 and the product of 8 and x' is 6 + 8x.

Explanation:

A mathematical expression is a combination of numbers, variables, and mathematical operators (e.g., +, -, *, /) that represents a calculation or relationship. Expressions can be simple, like 2x + 3, or complex, serving various purposes in mathematical modeling, calculations, and problem-solving.

To translate the phrase 'the sum of 6 and the product of 8 and x' into a mathematical expression, we can use the symbols and operations of algebra. The sum of 6 and the product of 8 and x can be written as 6 + 8x. Here, 8x represents the product of 8 and x, and the addition symbol, '+', represents the sum of 6 and 8x.

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Mrs, Williams is driving on the interstate at a rate of 58 mi/h. Write an expression for the distance she will drive in x hours

Answers

Distance = speed x time
Distance = 58 mi/h * (x) hours

We are assuming that the speed is remaining constant.

Final answer:

The expression for the distance Mrs. Williams will drive in x hours is Distance = 58x (in miles).

Explanation:

To write an expression for the distance Mrs. Williams will drive in x hours, we can use the formula: Distance = Speed x Time.

In this case, the speed is 58 mi/h and the time is x hours. So, the expression for the distance she will drive is Distance = 58x (in miles).

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