Answer:
6% , 800$
Step-by-step explanation:
to answer the question we can use this proportion :
x : 100 = 30 : 500
x = (100*30)/500
x = 6%
for calculate the amount after 10 years we can use this formula
A = P(1+rt)
where P indicates the initial amount, r the rate (in decimal) and t the time of investment
A = 500(1 + 0,06 x 10) = 500(1 + 0,6) = 500(1,6) = 800 $
The future value of cash whose initial value is $845, at the rate of 11.3% for 7 years will be calculated using the compound interest rate, that is:
A=p(1+r/100)^n
where:
A=future amount
r=rate=11.3%=0.113
time=7 years
thus the future value of our cash will be:
A=845(1+0.113)^7
A=845(1.113)^7
A=$1,787.82
7x - 44 = 4x + 4
Add both sides 44
7x - 44 + 44 = 4x + 4 + 44
7x = 4x + 48
Subtract both sides 4x
7x - 4x = 4x - 4x + 48
3x = 48
Divide both sides by 3
3x ÷ 3 = 48 ÷ 3
<h2>x = 16 </h2>
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Suppose that the angle between 39 and 4x + 4 is t degrees as you know they make a straight line together thus :
39 + t + 4x + 4 = 180
39 + t + 4(16) + 4 = 180
39 + t + 64 + 4 = 180
39 + t + 68 = 180
t + 107 = 180
Subtract both sides 107
t + 107 - 107 = 180 - 107
<h2>t = 73 </h2>
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8y - 43 = 4x + 4 + t
8y - 43 = 4(16) + 4 + 73
8y - 43 = 64 + 4 + 73
8y - 43 = 68 + 73
8y - 43 = 141
Add both sides 43
8y - 43 + 43 = 141 + 43
8y = 184
Divide both sides by 8
8y ÷ 8 = 184 ÷ 8
<h2>y = 23 </h2>
Answers:
x = 7
The measure of angle D is 14 degrees
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Angle C and angle D are complementary, which means they add to 90 degrees.
(angle C) + (angle D) = 90
(12x-8) + (3x-7) = 90
12x-8 + 3x-7 = 90
(12x+3x) + (-8-7) = 90
15x-15 = 90
15x-15+15 = 90+15
15x = 105
15x/15 = 105/15
x = 7
So you have the correct x value. Nice work.
Now use this x value to find the measure of angle D
angle D = 3*x - 7
angle D = 3*7 - 7
angle D = 21 - 7
angle D = 14 degrees
