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2 years ago

9

Justine earned $28,000 during the first year of her job at city hall. After each year she received a 6% raise. Find her total ea

rnings during the first five years on the job.

1 answer:

Verdich [7]2 years ago

5 0

Answer:

$ 157838.60 in 5 years

Step-by-step explanation:

r = 1.06

sum of geometric seq = a1 ( 1-r^n)/(1-r) n = 5

28000 ( 1 - 1.06^5) / ( 1-1.06) = 157838.60

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Ghella [55]

$10-\frac{3x-1}{2} =\frac{6x+3}{11}$

$10 = \frac{6x+3}{11} + \frac{3x-1}{2}$

$10 = (\frac{6x+3}{11} \times \frac{2}{2} ) + (\frac{3x-1}{2} \times \frac{11}{11} )$

$10 = ( \frac{2(6x + 3)}{22} ) + ( \frac{11(3x - 1)}{22} )$

$10 = \frac{12x + 6}{22} + \frac{33x - 11}{22}$

$10 = \frac{12x + 6 + 33x - 11}{22}$

$10 = \frac{(12 x + 33x) + (6 - 11)}{22}$

$10 = \frac{45x - 5}{22}$

$10 \times 22 = 45x - 5$

$220 = 45x - 5$

$220 + 5 = 45x$

$225 = 45x$

$\frac{225}{45} = x$

$\frac{45}{9} = x$

$5 = x$

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2 years ago

Why is subtracting an expression similar to distributing a –1?

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6. Meg started her trip with 112 gallons of gas in her car's gas tank. She bought an additional 6 gallons on her trip and arrive

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3 years ago

How do you determine the quadratic equation having roots that are real numbers and equal

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3 years ago

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Prove that sinA-sin3A+sin5A-sin7A/cosA-cos3A-cos5A+cos7A= cot2A

MAVERICK [17]

Write the left side of the given expression as N/D, where
N = sinA - sin3A + sin5A - sin7A
D = cosA - cos3A - cos5A + cos7A
Therefore we want to show that N/D = cot2A.

We shall use these identities:
sin x - sin y = 2cos((x+y)/2)*sin((x-y)/2)
cos x - cos y = -2sin((x+y)/2)*sin((x-y)2)

N = -(sin7A - sinA) + sin5A - sin3A
= -2cos4A*sin3A + 2cos4A*sinA
= 2cos4A(sinA - sin3A)
= 2cos4A*2cos(2A)sin(-A)
= -4cos4A*cos2A*sinA

D = cos7A + cosA - (cos5A + cos3A)
= 2cos4A*cos3A - 2cos4A*cosA
= 2cos4A(cos3A - cosA)
= 2cos4A*(-2)sin2A*sinA
= -4cos4A*sin2A*sinA

Therefore
N/D = [-4cos4A*cos2A*sinA]/[-4cos4A*sin2A*sinA]
= cos2A/sin2A
= cot2A

This verifies the identity.

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3 years ago