At the bank, Derek made 7 withdrawals, each in the same amount. His brother, John, made 5 withdrawls, each in the same amount.
Let x be the amount of one of Derek's withdrawals
Each of John's withdrawals was $5 more than each withdrawal that Derek made.
x + 5 is t the amount of one of John's withdrawals
Derek made 7 withdrawals
So amount withdraw 7 times = 7x
John made 5 withdrawals
So amount withdraw 5 times = 5(x+5)
Both Derek and John withdrew the same amount of money in the end
(A) 7x = 5(x+5)
(B) Solve for x
7x = 5x + 25
Subtract 5x from both sides
2x = 25
Divide by 2
x = 12.5
(C) check your solution
we plug in 12.5 for x in 7x= 5x + 25
7(12.5) = 5(12.5) + 25
87.5 = 62.5+ 25
87.5 = 87.5
(D) Each brother withdrawal 87.5 dollars
Answer:
They are both proportional.
Tank A = .00375 minutes/gallon
Tank B = 2/600 or ~0.003 minutes/gallon
Step-by-step explanation:
They are both proportional because as time increases, the amount of gallons increases.
Tank A unit rate
Tank B unit rate
Rate = rise / run
Choose points on the graph that has definite points.
Tank A = (1.5 mins - 0.75 mins) / 200 gallons
Tank A = .00375 minutes/gallon
Tank B = (2 mins - 0 mins) / 600 gallons
Tank B = 2/600 or .003 minutes/gallon
When applying indirect proofs, we assume the negation of the conclusion is true, and show that this assumption would lead to nonsense, or contradiction.
In our case we assume a is not smaller than 7, that is we assume a≥7.
a≥7 then, multiplying both sides by 3:
3a≥21, then, adding both sides 7:
3a+7≥28,
which is a contradiction because 3a+7 is smaller than 28.
So our assumption is wrong, which means the opposite of it is correct.
Answer: assume a≥7
Answer:
19/54
Step-by-step explanation:
- 7/27 + 11/18
LCM of the 27, 18 is 54
- 7/27 * (2/2) + 11/18 * (3/3)
- 14/54 + 33/54
33 - 14/54
19/54
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Step-by-step explanation:
the area of a triangle
baseline × height / 2
in our case
baseline × height / 2 = 60 in²
height = 6×baseline - 16
baseline × (6×baseline - 16) / 2 = 60
baseline × (3×baseline - 8) = 60
3×baseline² - 8×baseline = 60
baseline = x
3x² - 8x - 60 = 0
general solution to a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 3
b = -8
c = -60
x = (8 ± sqrt(64 - 4×3×-60))/(2×3) =
= (8 ± sqrt(64 + 720))/6 = (8 ± sqrt(784))/6 =
= (8 ± 28)/6
x1 = (8 + 28)/6 = 36/6 = 6
x2 = (8 - 28)/6 = -20/6 = -10/3
x2 as a negative number is not a valid solution for a length in a geometric shape.
so, x = 6 in is our solution for the baseline.
height = 6x - 16 = 6×6 - 16 = 36 - 16 = 20 in
base = 6 in
