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cyndiann2002
15.03.2022 •
Mathematics
Margaret and Donovan are twins. They have each kept track of their heights every year since they were 5.
Donovan wrote an equation to track his height: h = 105 + 4.25(a - 5)
Based on the evidence shown, which statement correctly compares the twins' rates of growth?
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Ответ:
Don’t even know I need help
Myself
Ответ:
B
Explanation:What we know:
Donovan's height can be expressed through the equation H = 105 + 4.25(a - 5) where H is height and a is ageMargaret's height is expressed through a given tableHow to solve:
We need to create a table for Donovan's height, compare it to Margaret's table, and then choose the appropriate statement. H will represent height, and a will represent age. B and c are constant values, and x is a coefficient to a-c
Process:Part 1 - DataSimplifying equation
Set up equation H = 105 + 4.25(a - 5)
Distribute H = 105 + (4.25a - 21.25)
Age 5
Set up equation H = 105 + (4.25a - 21.25)
Substitute H = 105 + [(4.25*5) - 21.25]
Simplify H = 105 + (21.25 - 21.25)
Simplify H = 105
Age 6
Set up equation H = 105 + (4.25a - 21.25)
Substitute H = 105 + [(4.25*6) - 21.25]
Simplify H = 105 + (25.5 - 21.25 )
Subtract H = 105 + 4.25
Solve H = 109.25
Age 7
Set up equation H = 105 + (4.25a - 21.25)
Substitute H = 105 + [(4.25*7) - 21.25]
Simplify H = 105 + (29.75 - 21.25)
Subtract H = 105 + 8.5
Solve H = 113.5
Continue for the following ages (8-10)
Part 2 - Table Comparison1. Create a table for both sets of data. Example:
Age | 5 | 6 | 7 | 8 | 9 | 10 |
Mar. height (cm) | 101 | 105 | 109 | 113 | 117 | 121 |
Don. height (cm) | 105 | 109.25 | 113.5 | 117.75 | 122 | 126. 25 |
2. Find which statement applies
2a. Margaret did not grow faster than Donovan
2b. Donovan did grow faster than Margaret
2c. Margaret and Donovan did not grow at the same rate
2d. There is enough data to draw a conclusion
Solution: BCheck:
We came to this conclusion by putting Donovan's data into a chart. We can check by writing an equation for Margaret's height. Then, use that equation with Donovan's to see the difference
Margaret's equation:
H = 4a + 81
Comparison (using ages 8 & 9):
8:
H= 4a + 81 | H = 105 + (4.25a - 21.25)
H = (4*8) + 81 | H = 105 + [(4.25*8) - 21.25)
H = 32 + 81 | H = 105 + 12.75
H = 113 | H = 117.75
9:
H = 117 | H = 122
113 < 117.75
117 < 122
Because the statement still holds true, answer B is correct.
Ответ:
I don't know I'm kinda lost. but I got 126