This problem is an example of solving equations with variables on both sides. To solve, we must first set up an equation for both the red balloon and the blue balloon.
Since the red balloon rises at 2.6 meters per second, we can represent this part of the equation as 2.6s. The balloon is already 7.3 meters off of the ground, so we just add the 7.3 to the 2.6s:
2.6s + 7.3
Since the blue balloon rises at 1.5 meters per second, we can represent this part of the equation as 1.5s. The balloon is already 12.4 meters off of the ground, so we just add the 12.4 to the 1.5:
1.5s + 12.4
To determine when both balloons are at the same height, we set the two equations equal to each other:
2.6s + 7.3 = 1.5s + 12.4
Then, we solve for s. First, the variables must be on the same side of the equation. We can do this by subtracting 1.5s from both sides of the equation:
1.1s + 7.3 = 12.4
Next, we must get s by itself. We work towards this by subtracting 7.3 from both sides of the equation:
1.1s = 5.1
Last, we divide both sides by 1.1. So s = 4.63.
This means that it will take 4.63 seconds for both balloons to reach the same height. If we want to know what height that is, we simply plug the 4.63 back into each equation:
2.6s + 7.3
= 2.6 (4.63) + 7.3
= 19.33
1.5s + 12.4
= 1.5 (4.63) + 12.4
= 19.33
After 4.63 seconds, the balloons will have reached the same height: 19.33 meters.
9514 1404 393
Answer:
B. 50
Step-by-step explanation:
The alternate interior angles at transversal t across parallel lines AB and CD will be congruent.
2x +40 = x +90
x = 50 . . . . . . . . . . . subtract x+40
The value of x is 50.
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<em>Check</em>
2x+40 = 2×50 +40 = 140
x+90 = 50 +90 = 140 . . . . so the obtuse angles are congruent, as they should be
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<em>Additional comment</em>
The lines AB and CD are not shown as being parallel. We have to assume they are, or we cannot work the problem.
Answer:
Judy = $5/hr
Ben = $4/hr
Step-by-step explanation:
Judy's hours at work - x
Ben's hours at work - y
8x + 10y = 80
9x + 5y = 65
Given these two equations above, we get:
10y = 80 - 8x, which means y = 8 - 0.8x.
Substitute y in the second equation with 8 - 0.8x, so we have:
9x + 5 (8 - 0.8x) = 65
9x + 40 - 4x = 65
5x = 25
x = 5
Come back to the first equation, substitute x:
8*5 + 10y = 80
10y = 80 - 40
y = 4
Scale factor is a ratio. The correct option is C.
<h3>How are
scale drawings formed?</h3>
For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.
Then it means
All feet measurements will then be multiplied by s/k to get the drawing's corresponding lengths.
The length of AB can be written as,
AB = √[(1-4)²+ (1-1)²]
AB = 3
Since the length A'B' is 6 units, therefore, the scale factor will be,
Scale factor = (Length after transformation)/(Length before transformation)
Scale factor = 6 /3 = 2
Hence, the correct option is C.
Learn more about Scale factors:
brainly.com/question/8765466
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