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11Alexandr11 [23.1K]
3 years ago
9

To estimate your average monthly salary, divide your yearly salary by the number of months in a year. Write and solve an equatio

n to determine your yearly salary when your average monthly salary is $4,559.
Mathematics
1 answer:
sasho [114]3 years ago
7 0

Answer:

yearly salary = $54,708

Step-by-step explanation:

Let monthly salary be x

Let yearly salary be y

Let number of months be n

To estimate your average monthly salary, divide your yearly salary by the number of months in a year. This can be written as

x = y divided by n

x = \frac{y}{n}

Therefore, writing an equation to determine yearly salary is the same as making the yearly salary 'y' the subject of the formula above:

x = \frac{y}{n}\\cross-multiplying\\n\ \times\ x= y\\y\ =\ nx

where y = ???

x = $4,559

n = 12 months

y =  4,559\ \times\ 12 \\= \$\ 54,708

Therefore yearly salary = $54,708

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What is the equation of the line that has a slope of m = 2 and passes through the point (-5, -6)?
Alenkinab [10]

Answer:

y=2x+4

Step-by-step explanation:

You can solve this two ways: insert the values into point-slope form and simplify to solve for y, converting it to slope-intercept form, <em>or</em><em> </em>insert the values into slope-intercept form, solve for b, and insert b. We'll do both :)

<em><u>Point-slope form:</u></em>

y-y_{1}=m(x-x_{1})

Where:

  • m is the slope
  • x_{1} and y_{1} are corresponding coordinate points (x,y)

Insert the given values:

m=2\\\\(-5_{x_{1}},-6_{y_{1}})\\\\y-(-6)=2(x-(-5))\\\\y+6=2(x+5)

Solve for y. Expand the right sie using the distributive property:

y+6=2(x)+2(5)\\\\y+6=2x+10

Isolate the variable. Subtract 6 from both sides, canceling out the 6 on the left:

y+6-6=2x+10-6\\\\y=2x+4

<em>OR</em>

<em></em>

<em><u>Slope-intercept form:</u></em>

y=mx+b

Where:

  • m is the slope
  • b is the y-intercept
  • x and y are corresponding coordinate points (x,y)

Insert the given values:

m=2\\\\(-5_{x},-6_{y})\\\\-6=2(-5)+b

Simplify the multiplication:

-6=-10+b

Solve for b. Add 10 to both sides, canceling out the 10 on the right:

-6+10=-10+10+b\\\\4=b

The value of b is 4. Insert the appropriate information into the equation. When using slope-intercept form, you don't plug in the coordinate points:

y=2x+4

:Done

4 0
3 years ago
PLEASE HELP! THANKS! The measures, in degrees, of the 3 angles of a triangle are given by 2x +1, 3x - 3, and 9x. What is the mea
drek231 [11]
So all of the internal angles of a triangle will add up to 180 degrees.  So if we add all of the expressions given and set them equal to 180, we can solve for x, then solve for each angle...

(2x + 1) + (3x - 3) + 9x = 180
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14x - 2 = 180
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x = 13

Now we can substitute 13 into each expression to find the value of each angle...

2x + 1 =
2(13) + 1 =
26 + 1 = 27 degrees

3x - 3 =
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9x =
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So the 3 angles are 27 degrees, 36 degrees, and 117 degrees.

The smallest is 27 degrees

** Note-- I don't see 27 degrees in the answer choices you gave, so I double checked my math (I didn't find any mistakes).  Please check to see that the question is written correctly (pay close attention to plus and minus signs).
7 0
3 years ago
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