Use the distributive property to write two expressions that are equivalent to 12 +30x. Describe the steps you followed

Sarah is a computer engineer and manager and works for a software company. She receives a

daser333 [38]

Answer:

a) Number of projects in the first year = 90

b) Earnings in the twelfth year = $116500

Total money earned in 12 years = $969000

Step-by-step explanation:

Given that:

Number of projects done in fourth year = 129

Number of projects done in tenth year = 207

There is a fixed increase every year.

a) To find:

Number of projects done in the first year.

This problem is nothing but a case of arithmetic progression.

Let the first term i.e. number of projects done in first year = $a$

Given that:

$a_4=129\\a_{10}=207$

Formula for $n^{th}$ term of an Arithmetic Progression is given as:

$a_n=a+(n-1)d$

Where $d$ will represent the number of projects increased every year.

and $n$ is the year number.

$a_4=129=a+(4-1)d \\\Rightarrow 129=a+3d .....(1)\\a_{10}=207=a+(10-1)d \\\Rightarrow 207=a+9d .....(2)$

Subtracting (2) from (1):

$78 = 6d\\\Rightarrow d =13$

By equation (1):

$129 =a+3\times 13\\\Rightarrow a =129-39\\\Rightarrow a =90$

Number of projects in the first year = 90

b)

Number of projects in the twelfth year =

$a_{12} = a+11d\\\Rightarrow a_{12} = 90+11\times 13 =233$

Each project pays $500

Earnings in the twelfth year = 233 $\times$ 500 = $116500

Sum of an AP is given as:

$S_n=\dfrac{n}{2}(2a+(n-1)d)\\\Rightarrow S_{12}=\dfrac{12}{2}(2\times 90+(12-1)\times 13)\\\Rightarrow S_{12}=6\times 323\\\Rightarrow S_{12}=1938$

It gives us the total number of projects done in 12 years = 1938

Total money earned in 12 years = 500 $\times$ 1938 = $969000

8 0

1 year ago

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frozen [14]

$\sqrt{-4}$ can also be written as 2i
where i = √-1

$\frac{2i}{4-2-3i} = \frac{2i}{2-3i}$

Rationalizing denominator,

$\frac{2i(2+3i)}{(2-3i)(2+3i)} = \frac{4i-6}{4+9} = \frac{4i-6}{13}$

8 0

2 years ago

What is 800-5x divided by 6.5

MA_775_DIABLO [31]

Answer:10 over 13 x

Step-by-step explanation: convert the decimal number into a fraction 800-5x divided by 13 over 2

to divided by a fraction , multiply by the reciprocal of that fraction 800-5x x2 over 13

factor out 5 from the expression 5(160-x x2over 13) use the commutative property to reorder the terms 5(160-2over 13x) factor out 1 over 13 from the expression 5x 1 over 13x(2080-2x)factor out 2 from the expression 5x 1 over13 x2(1040-x)use the commutative property to recorder the terms 5*2x 1 over 13x (1040x) calculate the product 10 over 13x(1040-x) solution 10 over 13x (1040-x)

for simplify expression: covert the decimal number into a fraction 800-5x divided by 13 over 2 to divide by a fraction , multiply by the reciprocal of that fraction 800-5x x2 over 13 calculate the product 800- 10 over 13x

solution: 800-10 over 13x so your answer would still be

8 0

2 years ago

SOMEONE PLEASE HELP ME ASAP PLEASE!!!!!

Liula [17]

Answer:

T(x, y) = (x - 5, y - 6)

Step-by-step explanation:

The transformation T is a translation that creates an image P' of original point P by adding 5 to the x-coordinate and 6 to the y-coordinate of the original point P.

Now you want to transform point P' into point P, so you are undoing the first transformation. You need to do the opposite of what the transformation above does. You need to subtract 5 from the x-coordinate and subtract 6 from the y-coordinate.

Answer: T(x, y) = (x - 5, y - 6)

5 0

2 years ago

A high school has a total of 850 students. there are 60 more female students than there are make students?

Mrac [35]

Hey. Let me help you on this one.

Let's break this problem down so it's easier for us to comprehend it.

There are 850 students in the school, and the amount of female students equals to the amount of male students + sixty additional females.

Amount of students in school = 850 students

Male students = $X$

Female students = $X+60$

Let's form an equation so we can work with what we have.

$X+(X+60)=850$

Subtract 60 from both sides.

$X+X=790$

Simplify

$2X=790$

Divide both sides by 2.

$X=395$

Answer: There are 395 male students, and 455 female students.

3 0

2 years ago

Use the distributive property to write two expressions that are equivalent to 12 +30x. Describe the steps you followed​

Use the distributive property to write two expressions that are equivalent to 12 +30x. Describe the steps you followed