C. 8- 6i
(3- i) to the power of 2 (expand the expression)
9- 6 i + i to the power of 2
calculate
9 - 6i - 1
calculate
8- 6i.
Set up a system of equations.
0.10d + 0.25q = 39.25
d + q = 250
Where 'd' represents the number of dimes, and 'q' represents the number of quarters.
d + q = 250
Subtract 'q' to both sides:
d = -q + 250
Plug in '-q + 250' for 'd' in the 1st equation:
0.10(-q + 250) + 0.25q = 39.25
Distribute 0.10:
-0.10q + 25 + 0.25q = 39.25
Combine like terms:
0.15q + 25 = 39.25
Subtract 25 to both sides:
0.15q = 14.25
Divide 0.15 to both sides:
q = 95
Now plug this into any of the two equations to find 'd':
d + q = 250
d + 95 = 250
Subtract 95 to both sides:
d = 155
So there are 95 quarters and 155 dimes.
Answer: The height of the palm tree is 21 feet.
Step-by-step explanation:
We can use a ratio to solve this:
Actual height to shadow for both objects. The fraction equivalents must be equal.
6/8 = x/28 . Cross multiply
6(28) = 8x
168 = 8x Divide both sides by 8 (8's "cancel" on the right)
168/8 =8x/8
21 = x . This gives us the tree's height as 21 feet.
<em>Another way to solve this is to use the ratios, but simplify the first fraction</em>
<em>6/8 = 3/4</em>
<em>Then multiply the length of the shadow by 3/4</em>
<em>3/4 × 28 = height</em>
<em>28÷4 = 7 7 × 3 = 21</em>
<em>21 feet= the height of the palm tree.</em>