Answer:
![\large\boxed{Common\ factors:\ 1,\ 2,\ 4,\ a,\ 2a,\ 4a}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7BCommon%5C%20factors%3A%5C%201%2C%5C%202%2C%5C%204%2C%5C%20a%2C%5C%202a%2C%5C%204a%7D)
Step-by-step explanation:
![16a=2\cdot2\cdot2\cdot2\cdot a\\Factors:\boxed1,\ \boxed2,\ \boxed4,\ 8,\ 16,\ \boxed{a},\ \boxed{2a},\ \boxed{4a},\ 8a,\ 16a\\\\20ab=2\cdot2\cdot5\cdot a\cdot b\\Factors:\boxed1,\ \boxed2,\ \boxed4,\ 5,\ 10,\ 20,\ \boxed{a},\ \boxed{2a},\ \boxed{4a},\ 5a,\ 10a,\ 20a,\\b,\ 2b,\ 4b,\ 5b,\ 10b,\ 20b,\ 2ab,\ 4ab,\ 5ab,\ 10ab,\ 20ab\\\\Common\ factors:\ 1,\ 2,\ 4,\ a,\ 2a,\ 4a](https://tex.z-dn.net/?f=16a%3D2%5Ccdot2%5Ccdot2%5Ccdot2%5Ccdot%20a%5C%5CFactors%3A%5Cboxed1%2C%5C%20%5Cboxed2%2C%5C%20%5Cboxed4%2C%5C%208%2C%5C%2016%2C%5C%20%5Cboxed%7Ba%7D%2C%5C%20%5Cboxed%7B2a%7D%2C%5C%20%5Cboxed%7B4a%7D%2C%5C%208a%2C%5C%2016a%5C%5C%5C%5C20ab%3D2%5Ccdot2%5Ccdot5%5Ccdot%20a%5Ccdot%20b%5C%5CFactors%3A%5Cboxed1%2C%5C%20%5Cboxed2%2C%5C%20%5Cboxed4%2C%5C%205%2C%5C%2010%2C%5C%2020%2C%5C%20%5Cboxed%7Ba%7D%2C%5C%20%5Cboxed%7B2a%7D%2C%5C%20%5Cboxed%7B4a%7D%2C%5C%205a%2C%5C%2010a%2C%5C%2020a%2C%5C%5Cb%2C%5C%202b%2C%5C%204b%2C%5C%205b%2C%5C%2010b%2C%5C%2020b%2C%5C%202ab%2C%5C%204ab%2C%5C%205ab%2C%5C%2010ab%2C%5C%2020ab%5C%5C%5C%5CCommon%5C%20factors%3A%5C%201%2C%5C%202%2C%5C%204%2C%5C%20a%2C%5C%202a%2C%5C%204a)
Answer:
f(t) = 4(t − 1)2 + 4; the minimum height of the roller coaster is 4 meters from the ground
Step-by-step explanation:
The function is a quadratic where t is time and f(t) is the height from the ground in meters. You can write the function f(t) = 4t2 − 8t + 8 in vertex form by completing the square. Complete the square by removing a GCF from 4t2 - 8t. Take the middle term and divide it in two. Add its square. Remember to subtract the square as well to maintain equality.
f(t) = 4t2 − 8t + 8
f(t) = 4(t2 - 2t) + 8 The middle term is -2t
f(t) = 4(t2 - 2t + 1) + 8 - 4 -2t/2 = -1; -1^2 = 1
f(t) = 4(t-1)^2 + 4 Add 1 and subtract 4 since 4*1 = 4.
The vertex (1,4) means at a minimum the roller coaster is 4 meters from the ground.
- f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 2 meters from the ground
- f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 4 meters from the ground
- f(t) = 4(t − 1)2 + 4; the minimum height of the roller coaster is 1 meter from the ground
- f(t) = 4(t − 1)2 + 4; the minimum height of the roller coaster is 4 meters from the ground
X intercept will be 30
Y intercept will be 105
Slope is -3.5
Answer:
a. ratio of the amount in dollars to the number of apples (r)
r= 1.25 dollars/apple
b. Akia can buy 8 apples
c. Christian can buy 4 apples
Step-by-step explanation:
Nomenclature
C: Total cost of apples ( dollars)
n: number of apples (units)
r : ratio of the amount in dollars to the number of apples (dollars/number of apples)
Formula : r = C/n
Problem deveopment
a. ratio of the amount in dollars to the number of apples
r = C/n= 1.25 dollars /1 apple = 1.25 dollars/apple
b. Apples that Akia can buy
r = C/n
n=C/r
![n=\frac{10 dollars}{1.25\frac{dollars}{apples} }](https://tex.z-dn.net/?f=n%3D%5Cfrac%7B10%20dollars%7D%7B1.25%5Cfrac%7Bdollars%7D%7Bapples%7D%20%7D)
n= 8 apples
Akia can buy 8 apples
c. Apples that Christian can buy
n=C/r
n=6/1.25
n= 4.8
The number must be an integer, then, Christian can buy 4 apples
There are 3 feet in 1 yard
3 x 3 = 9 + 1 = 10
There are 12 inch in 1 feet
10 x 12 = 120
120 in > 100 in.
False, 3yd 1ft is greater than 100 in by 20 in
hope this helps