(1, 3.5 ) and (3, 3.5 )
the endpoints of the midsegment are at the midpoints of DE and DF
using the midpoint formula with D(0, 7), E(2, 0), F(6, 0)
midpoint of DE = [
(0 + 2),
(7 + 0)] = (1, 3.5)
midpoint of DF = [
(0 + 6),
(7 + 0)] = (3, 3.5)
Answer:
a) 40 = 8b
b) b = 5
Step-by-step explanation:
(b) 40 = 8 × b
40 ÷ 8 = b
5 = b
Answer:
8x+7
Step-by-step explanation:
Answer:
- $5000 at 10%, $10000 at 12% and 10000 at 16%
Step-by-step explanation:
- <em>One part of $ 25,000 is invested at 10% interest, another part at 12%, and the rest at 16%. The total annual income from the three investments is $ 3,200. Also, the income from the investment at 16% is equal to the income from the other two investments combined. How much was invested at each interest rate?</em>
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Let the parts be x, y and z
<u>As per given we get below system of equations:</u>
- x + y + z = 25000
- 0.1x + 0.12y + 0.16z = 3200
- 0.1x + 0.2y = 0.16z
<u>Substitute 0.1x + 0.2y in the second equation:</u>
- 0.16z + 0.16z = 3200
- 0.32z = 3200
- z = 3200/0.32
- z = 10000
<u>Now we have:</u>
- x + y + 10000 = 25000 ⇒ x + y = 15000
and
- 0.1x + 0.12y + 0.16*10000 = 3200 ⇒ 0.1x + 0.12y = 1600
<u>Multiply the second equation and then subtract the first one:</u>
- 10(0.1x + 0.12y) = 10(1600) ⇒ x + 1.2y = 16000
- x + 1.2y - (x + y) = 16000 - 15000
- 0.2y = 1000
- y = 10000
Then
<u>So the parts are:</u>
- $5000 at 10%, $10000 at 12% and 10000 at 16%
Answer: plane 1: 420 mph; plane 2: 500 mph
Step-by-step explanation:
This is a physics exercise, but in order to solve this problem, you need to identify both planes first:
Let's call the plane 1 speed X
V1 = X
And V2 would be:
V2 = V1 + 80 = X + 80
If we combine both speeds:
V = V1 + V2 = X + X + 80 = 2X + 80
Now that we have an expression for the combined speed, let's see the rest of the data:
Distance: d = 1380 mile
Time: t = 1.5 h
We also know that the formula to get speed is:
V = d/t
We have the combined speed, so, let replace it in the above formula to solve for X:
2X + 80 = 1380/1.5
2X + 80 = 920
2X = 920 - 80
2X = 840
X = 840/2
X = V1 = 420 mph
We have V1, so to get V2:
V2 = 420 + 80 = 500 mph