Answer:
10
Step-by-step explanation:
Yesterday, Priya successfully made 6 free throws.
Today, she made 75% as many as yesterday.
We are asked to calculate the number of successful free throws that Priya made today.
So, the number will be 
.
Since it is the number of successful free throws, so it will be 10 throws. ( Answer )
The second equation is correct. Nina initally had 17 marbles in her bag. Her mother placed m marbles into her bag. After counting, she now has 34 marbles. Part of this 34 marbles is already her initial 17 marbles. Therefore, 17 marbles initially + m unknown marbles = 34 marbles. The equation <span>17 + m = 34 is the answer.</span>
Answers:
x = -8/5 or x = 8/5
Sum of the first ten terms where all terms are positive = 4092
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Explanation:
r = common ratio
- first term = 4
- second term = (first term)*(common ratio) = 4r
- third term = (second term)*(common ratio) = (4r)*r = 4r^2
The first three terms are: 4, 4r, 4r^2
We're given that the sequence is: 4, 5x, 16
Therefore, we have these two equations
Solve the second equation for r and you should find that r = -2 or r = 2 are the only possible solutions. If r = -2, then 5x = 4r solves to x = -8/5. If r = 2, then 5x = 4r solves to x = 8/5.
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To find the sum of the first n terms, we use this geometric series formula
Sn = a*(1 - r^n)/(1 - r)
We have
- a = 4 = first term
- r = 2, since we want all the terms to be positive
- n = 10 = number of terms to sum up
So,
Sn = a*(1 - r^n)/(1 - r)
S10 = 4*(1 - 2^10)/(1 - 2)
S10 = 4*(1 - 1024)/(-1)
S10 = 4*(-1023)/(-1)
S10 = 4092
1/4 because 6/24 can be simplified all the way down to 1/4
