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3 years ago

Write a system of equations to describe the situation below, solve using substitution, and fill in the

Mathematics

1 answer:

Oksi-84 [34.3K]3 years ago

5 0

Answer:

R=5

Step-by-step explanation:

3r+21

2r+26

3r+21=2r+26

r=5

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Kate is a wage earner. One year she earned $72 000. She works 36 hours/week.

Lemur [1.5K]

Answer:

Kate's possible hourly rate of pay: $34.75

Hours of overtime: 100

Step-by-step explanation:

In order to find Kate's hourly wage, we can set up an equation based on the number of hours she works per week and the estimated number of overtime hours to equal her total pay for the year. If Kate works 36 hours/week and there are 52 weeks in a year, her total hours for one year are: 36 x 52 = 1872. Setting up an equation based on her total earnings of $72,000:

1872x + 100(2x) = 72000, where 'x' is the hourly rate and '2x' is her overtime rate which is double time.

Combine like terms: 1872x + 200x = 72000 or 2072x = 72000

Divide both sides by 2072: 2072x/2072 = 72000/2072

Solve for x: x = $34.75

Kate's hourly rate is estimated at $34.75. We can check to see if this is correct by putting this value back into our original equation:

1872(34.75) + 100(2)(34.75) = 65052 + 6950 = 72002

The answer of $72,002 is very close to $72,000 and the best estimate of Kate's hourly wage and overtime hours.

8 0

3 years ago

If f(x) = 2(34) + 1, what is the value of f(2)? <br>

larisa86 [58]

I believe that f(2) is 34.5

f(2) = 2(34) + 1
f(2) = 68 + 1
f(2) = 69
f = 69/2
f = 34.5

I AM NOT SURE

3 0

3 years ago

Two of the side lengths of a triangle are x = 10 and y = 5. Which side length could not represent z, the third side of the trian

pentagon [3]

A i got this question on my test and i put A

8 0

3 years ago

The least common denominator of 1/3, 5/8, and 1/2 is:

andrey2020 [161]

Answer: 24

Step-by-step explanation:

You need to find the common denominator. In the case 24 is the least one because when you multiply 3 by 8, you finally have a common denominator for all three.

If you found this answer helpful, give it a five-star rating and a thanks! It would really mean a lot!

8 0

3 years ago

HELP ASAP TIMED !!!! What is the exact value of cos(c + d), given Sine c = StartFraction 24 Over 25 EndFraction for c in Quadran

Keith_Richards [23]

9514 1404 393

Answer:

Step-by-step explanation:

In the second quadrant, ...

c = 180° -arcsin(24/25) ≈ 106.26°

In the third quadrant, ...

d = 360° -arccos(-3/4) ≈ 221.41°

Then cos(c+d) = cos(327.67°) ≈ 0.84498

This is a positive irrational number, greater than 21/100, so the only reasonable choice is the last one:

$\dfrac{21+24\sqrt{7}}{100}\approx 0.84498$

_____

Perhaps you want to work this out using the trig identities.

cos(c) = -√(1 -sin(c)²) = -7/25

sin(d) = -√(1 -cos(d)²) = -(√7)/4

Then the desired cosine is ...

cos(c+d) = cos(c)cos(d) -sin(c)sin(d)

cos(c+d) = (-7/25)(-3/4) -(24/25)(-√7/4)

cos(c+d) = (21 +24√7)/100 . . . . matches choice D

8 0

3 years ago