Prove:
Using mathemetical induction:
P(n) = 
for n=1
P(n) = 
= 6
It is divisible by 2 and 3
Now, for n=k, 
P(k) = 
Assuming P(k) is divisible by 2 and 3:
Now, for n=k+1:
P(k+1) = 
P(k+1) = 
P(k+1) = 
Since, we assumed that P(k) is divisible by 2 and 3, therefore, P(k+1) is also
divisible by 2 and 3.
Hence, by mathematical induction, P(n) = is divisible by 2 and 3 for all positive integer n.
Let x be equal to the number of drinks Yasmine consumed.
Jose had 2 times that drink so his number of consumed drink would be represented by 2x.
Sally had 3 fewer drink than Jose so her number of consumed drinks would be represented by 2x-3.
Altogether, the three of them consumed 72 drinks so your equation would be:
x+2x+(2x-3)=72
add like terms together:
5x-3=72
have the term with x be alone on one side of the equation, in this case by adding three to both sides:
5x=75
now divide both sides by five for the value of x and your answer is.....
x=15
Answer:
f(4) = 1
Step-by-step explanation:
f(4) = what?
So if we know that x, aka 4, is technicially f is greater then 2, so you can plug in x as 4. So that means 5(4) - 19 = 20 - 19 = 1, so f(4) = 1
Answer:
The answer is 8 quarters, 16 nickles, and 32 dimes
Step-by-step explanation:
- First, the equation would be (2/4d) x 5 +d x 10 +1/4d x 25= 600 (Don't put 6.00, that's dollars. We put 6 dollars into cents to make it easier.)
- Then we slowly start to solve: 10/4d + 10d + 25/4d = 600
- 10d+40d+25d/4 = 600 (Put all of that over 4, not first 25d)
- 75d= 600 x 4
- d=600 x 4/75 (same here put everything over 75)
- d=32
- So then n= 2 x 32/4 = 16
- Then n would be equal to : 1/4d= 1/4 x 32 = 8
- So your answer would be 8 quarters, 16 nickles, and 32 dimes.
Hope this helped :)
<h3>
Answer: -19, -15, -9, -1, 9 (choice A)</h3>
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Explanation:
If we plug in x = -2, then we get,
y = x^2 + 7x - 9
y = (-2)^2 + 7(-2) - 9
y = 4 - 14 - 9
y = -10 - 9
y = -19
So x = -2 leads to y = -19. The answer is between A and D.
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If you repeat those steps for x = -1, then you should get y = -15
Then x = 0 leads to y = -9
x = 1 leads to y = -1
Finally, x = 2 leads to y = 9
The outputs we get are: -19, -15, -9, -1, 9 which is choice A
Choice D is fairly close, but we won't have a second copy of -15, and we don't have an output of -19.
