Solve each system of equations using the elimination method

10x-6y=54
-4x+3y=-24

The total employee benefits of Trevor with no job expenses and gross pay of $28600 is 17.1%. Option d is the correct option.

Total employment compensation is equal to the sum of gross pay and employment benefit subtracted with any job expenses.

Trevor’s total employment compensation is $33,500. Trevor has no job expenses and his gross pay is $28,600.

Let the total employee benefits is x. Therefore, using the above definition of total employment compensation,

[tex]33500=28600+x-0\\[/tex]

Solve it for x as,

[tex]x=33500-28600\\x=4900[/tex]

In the percentage form,

[tex]x=\dfrac{4900}{28600}\times100\\x=17.1\%[/tex]

Hence, the total employee benefits of Trevor with no job expenses and gross pay of $28600 is 17.1%. Option d is the correct option.

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Answer: a = 75 b = 60

Step-by-step explanation:

b + 120 = 180

b = 60

a + 105 = 180

a = 75

Three friends decide to share the cost to rent an apartment equally. The apartments that they are considering cost at least 1 200 per month. Write and solve an inequality to represent each person's share of the rental cost​

Lets highlight some key words.

There are three friends and they equally have to share an unknown amount of number to earn up to the 1200 per month,

X=Amount needed to pay the rent fee.

Since there are 3 friends and they have to split we have to multiply,

3x, "At least" is less than or equal to so .

3x [tex]\leq[/tex]

Additionally theres 1200 per month so the friends need to share there rent and 1200 is the total it should be put as

3x [tex]\leq[/tex] $1200

To add up to the rent, and to solve the inequality

we have to do the opposite of multiplication, and divide.

1200/3 = 400, x [tex]\leq[/tex] 400

Africa and Asia

I did it today in my class

Answer:

i think it is $106,800.00

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 6.5%/100 = 0.065 per year.

Solving our equation:

A = 60000(1 + (0.065 × 12)) = 106800

A = $106,800.00

The total amount accrued, principal plus interest, from simple interest on a principal of $60,000.00 at a rate of 6.5% per year for 12 years is $106,800.00.

The simple interest rate for this loan is 78%.

It is the interest calculated on the principal at a given rate for a time period.

We have,

If Steven borrows $60,000 at an interest rate of 6.5%, the total amount of interest he will pay over 12 years can be calculated as:

I = Prt

where I is the interest, P is the principal amount borrowed ($60,000), r is the interest rate as a decimal (0.065), and t is the time period in years (12). Substituting the given values, we get:

I = 60000 x 0.065 x 12

I = $46,800

The simple interest rate is the ratio of the total interest paid to the principal borrowed, expressed as a percentage:

simple interest rate = (total interest/principal borrowed) x 100

Substituting the given values, we get:

simple interest rate = (46800 / 60000) * 100

simple interest rate = 78%

Therefore,

The simple interest rate for this loan is 78%.

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Using the power of zero property, we find that:

a) The simplification of the given expression is 1.

b) Since , equivalent expressions are:  and .

--------------------------------

The power of zero property states that any number that is not zero elevated to zero is 1, that is:

Thus, at item a, , thus the simplification is .

At item b, equivalent expressions are found elevating non-zero numbers to 0, thus  and .

Answer:

153/4=38 Remainder 1

Answer:

38 r 1

Step-by-step explanation:

Hope this helped! Have a nice day!

:3

Answer:

The correct answer is

A. The income would need to be at least $1000.

Step-by-step explanation:

Correct on Edge.

Answer:

43.65 grams

Step-by-step explanation:

43.65 grams of bird feed containing 5% seed must be added to get 43.65 grams

Answer:

a) 130m    b)1.3m/s²

Step-by-step explanation:

area under graph = distance

area of trapezium = a+b/2 x h

6+20/2 x 10

13 x 10 = 130m

acceleration = gradient

gradient = change in y/ change in x

4/3 = 1.3 m/s²

Answer:

Our answer should be this :

[-7 18]

[-1. -16]

Answer:

  see attached

Step-by-step explanation:

Your calculator, spreadsheet, or any number of apps or web sites can compute a matrix product for you. The requirement for the product to exist is that the number of columns in the left matrix match the number of rows in the right matrix.

The product term at location (row, column) = (j, k) in the product is the dot-product of row j in the left matrix with column k in the right matrix. For example, in this matrix product, term (1,2) in the product is the dot-product ...

  [1, -2]·[4, -7] = (1)(4) +(-2)(-7) = 4 +14 = 18 . . . product term (1, 2)

__

The attachment shows the full product.

Answer:

$6,480

Step-by-step explanation:

[tex]180(12)(3)=6,480[/tex]

Hope this helps

Answer:

#540

Step-by-step explanation:

Alan saved $180 in each month

and we have 12 months in a year so we say

$180=12

x=36

here we cross multiply then we have 180 * 36 which is equal to $6480 after that we divide it by 12 and that's $540

Note: I got 36 months because 12 months in a year so multiply by three years that's 36 months

Answer:

a counter-clockwise 90 degree rotation about the origin

Step-by-step explanation:

Answer:

ANSWER IS C The transformation below that caused AB to transform into A'B' is a reflection across the y-axis

How to translate a coordinate point to another

Given the following coordinates

A = (6, 2)

B = (2, 6)

A' = (-6, 2)

B' = (-2, 6)

According to the reflection rule, the reflection over y axis is given as:

Note that the x-coordinate was negated as seen from the translation A to A' and B to '.

Hence the transformation below that caused AB to transform into A'B' is a reflection across the y-axis

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Step-by-step explanation:

Answer:

the 3 and the 22 should be negative

Step-by-step explanation:

Firstly take the unknown angle be x

now x + 138° = 180° {: linear pair}

x = 180-138

x = 42

now , angle 1+ angle x + 18 = 180 { because of angle sum property }

=> angle 1 +42 +18 = 180

=> angle 1 +60 = 180

=> angle 1 = 180-60

=> angle 1 = 120

With respect to the diagram in question

Exterior Angle property

Exterior angle of triangle is equal to sum of two opposite interior angle .

[tex] \angle{A} + \angle{ B} = ext \angle C \\ putting \: the \: value \\ 3x - 13 + 2x + 4 = 116 \\ 5x - 9 = 116 \\ 5x = 125 \\ x = \frac{125}{5} \\ x = \frac{ \cancel{125} {}^{ \: \: 25} }{ \cancel5} \\ x = 25[/tex]

For Angle A :- 3x-13

[tex] \angle A = 3x-13 \\ \angle A = 3(25)-13 = 75 - 13 \\ \angle A = 62 \degree[/tex]

Answer:

Step-by-step explanation:

Answer:

84

Step-by-step explanation:

Because 3 people are making 21 shirts

If there were 12 people then your timesing the answer by 4 so 21=3 people so whats 3 people x 4=12 so then times the shirts by 4

Whats 21 x 4=84 so there is your answer.

Hope it helps have a great day:)

The solution is, 84 long will it take 12 people.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Because 3 people are making 21 shirts

If there were 12 people then your timesing the answer by 4

so 21=3 people so whats 3 people x 4=12

so then times the shirts by 4

21 x 4=84 so there is your answer.

Hence, The solution is, 84 long will it take 12 people.

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Answer:

0.05

Step-by-step explanation:

If dividing 9 by 0.45, basically .45/9, then you would get 0.05. :) You would need to use division, and move the places 2 over since there is a decimal.

The requried, 0.45 divided 9 gives the quotient of 0.05.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
To divide 0.45 by 9, we can write it as a fraction and simplify it:

0.45 ÷ 9 = 0.45/9

We can simplify the fraction by dividing both the numerator and denominator by 9:

0.45/9 = (0.45 ÷ 9)/(9 ÷ 9)
         = 0.05/1 = 0.05

Therefore, 0.45 divided by 9 is equal to 0.05.

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Answer:

10*4-6*2=28

Step-by-step explanation:

Answer:

x=-1, y=1

Step-by-step explanation:

x-2y=-3
multiply both all terms by -2
-2x+4y=6
-2x+4y+2x-3y=6-5
simplify to get y=1
replace y with 1 in the original equation of your choice and solve for x
x-2(1)=-3
x-2=-3
x=-1

Given the second difference, the table is quadratic.

A linear function is a function that has a single variable raised to the power of 1. An example is x + 2. A quadratic function is a function that usually has a single variable and it is raised to the power of 2. An example is 2x² + 10x + 25.

First differences:

21 - 11 = 10

35 - 21 = 14

53 - 35 = 18

75 - 53 = 22

Due to the fact that the first difference is not the same, the function is not a linear function.

Second difference:

14 - 10 = 4

18 - 14 = 4

22 - 18 = 4

Due to the fact that the second difference is fairly constant, the function is a quadratic function.

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Answer:

Your answer would be:
C.) 4 - 12x

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

hmm wait for my answer

Step-by-step explanation:

wait

Answer:  [tex]y + 1 = \frac{4}{3}\left(x - 3\right)\\\\[/tex]

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

Explanation:

The given slope is [tex]m = \frac{4}{3}[/tex] and the line goes through the point [tex](x_1,y_1) = (3,-1)[/tex]

This means [tex]x_1 = 3 \ \text{ and } \ y_1 = -1[/tex]

We will plug this information into the point-slope formula below and simplify.

[tex]y - y_1 = m\left(x - x_1\right)\\\\y - (-1) = \frac{4}{3}\left(x - 3\right)\\\\y + 1 = \frac{4}{3}\left(x - 3\right)\\\\[/tex]

We stop here since your teacher wants the answer in point-slope form. As the name implies, point-slope form is very handy to quickly spot the slope and a point on the line.

If your teacher wanted the answer in slope-intercept form, then you'd solve for y to get it into y = mx+b form.

Answer:

Step-by-step explanation:

w + a + d = 14

d = 3w

200w + 150a + 140d = 2230

w + a + 3w = 14

4w + a = 14      Eq. 1

200w + 150a + 140d = 2230

20w + 15a + 14(3w) = 223

62w + 15a = 223   Eq. 2

Eq. 1 & Eq. 2

4w + a = 14

62w + 15a = 223

-60w - 15a = -210

62w + 15a = 223

2w = 12

w = 6.5

A half a night is not allowed. Are you sure of rates in each city?

Is it Washington $200,

Dallas $140

Atlanta $150

It doesn't work.

Answer:

  9x + 30 ≤ 22

Step-by-step explanation:

Let x be "a number."

"the sum of a number times 9" is 9x +

"and 30"                                          9x + 30

"is at most 22"                                 9x + 30 ≤ 22

Answer:

  90° CCW

Step-by-step explanation:

The angle from C to the origin to C' is a right angle when measured counterclockwise (in the usual direction).

ΔA'B'C' is a rotation of ΔABC 90° CCW.

__

This is fully equivalent to a rotation of 270° CW.

[tex] \huge \mathbb{\green{\fbox{\pink{ANSWER}}}} [/tex]

[tex] \\ \: \: \implies \: sin^{4} \: \theta + cos^{4} \: \theta \rightarrow \blue{ \frac{1}{2} } [/tex]

[tex] \\ \\ \: \large \mathfrak \green{Solution} : [/tex]

[tex] \\ \bf \: Given : [/tex]

[tex] \\

\sf \: \: \bf sin \: \theta - cos \: \theta = 0 [/tex]

[tex] \\ \sf \rightarrow \: sin \: \theta = cos \: \theta [/tex]

[tex] \\ \sf \rightarrow \: \frac{sin \: \theta} {cos \: \theta} = 1 [/tex]

[tex] \\ \sf \rightarrow \: tan \: \theta = 1 [/tex]

[tex] \\ \sf \rightarrow \: tan \: \theta = tan \: 45 \degree [/tex]

[tex] \\ \sf \rightarrow \: \theta = 45 \degree [/tex]

[tex] \\ \\ \therefore \: sin^{4} \: \theta + cos^{4} \: \theta [/tex]

[tex] \\ \sf \rightarrow \: sin^{4} \: 45 \degree + cos^{4} \: 45 \degree [/tex]

[tex] \\ \\

\sf \rightarrow \: (\frac{1}{ \sqrt{2} } ) ^{4} +(\frac{1}{ \sqrt{2} } ) ^{4} [/tex]

[tex] \\ \sf \rightarrow \: ( \frac{1}{ \cancel {\sqrt{2} }} )^{ \cancel{2}} ( \frac{1}{ \cancel{ \sqrt{2} }} )^{\cancel{2}} + ( \frac{1}{ \cancel {\sqrt{2} }} )^{ \cancel{2}} ( \frac{1}{ \cancel{ \sqrt{2} }} )^{\cancel{2}} [/tex]

[tex] \\ \\

\sf \rightarrow \: \frac{1}{2} × \frac{1}{2} + \frac{1}{2}× \frac{1}{2} [/tex]

[tex] \\ \\ \sf \rightarrow \: \frac{1}{4} + \frac{1}{4} [/tex]

[tex] \\ \\ \sf \rightarrow \: {\cancel \frac{2} {4}}[/tex]

[tex] \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \fbox{\pink {\frac{1}{2}}} [/tex]

The value of [tex]sin^4\theta+cos^4 \theta[/tex] will be [tex]\frac{2}{(\sqrt{2})^4}[/tex]

Given the expression

sin θ – cos θ = 0

This can be simplified further as:

sin θ = cos θ

sin θ/cosθ = cosθ/cosθ
tanθ = 1

θ = arctan(1)

θ = 45 degrees

To evaluate [tex]sin^4\theta+cos^4 \theta[/tex], substitute the value of theta into the expression to have:

[tex]sin^4\theta+cos^4 \theta\\=sin^445+cos^4 45\\=(\frac{1}{\sqrt{2}} )^4+(\frac{1}{\sqrt{2}} )^4\\=2(\frac{1}{(\sqrt{2})^4} )[/tex]

Hence the value of [tex]sin^4\theta+cos^4 \theta[/tex] will be [tex]\frac{2}{(\sqrt{2})^4}[/tex]

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Answer: 80

Step-by-step explanation:

1 cm is 10 millimeters. 8*10 is 80