Answer:
The value of 
Step-by-step explanation:
Being the general expression of the sequence:
We replace the value n=12 to get
Answer:
(a) t = 7 sec approximately; (b) t = 6 sec
Step-by-step explanation:
(a) Set h(t)= -16(t-3)^2 + 288 = 0 and solve for t:
16(t-3)^2 = 288
After simplification, this becomes (t - 3)^2 = 18, or t - 3 = ±3√2.
Because t can be only zero or positive, t = 3 + 3√2 = 7 seconds
(b) Solve h(t)= -16(t-3)^2 + 288 = 150:
-16(t-3)^2 = - 162
or (t - 3)^2 = 10.125, or
t - 3 = ±3.18, or, finally, t = 6.18 sec (discard t = -0.18 sec)
Answer:
9 units
Step-by-step explanation:
If you assume the solution is an integer, then you are looking for factors of 27 that differ by 6. You don't have to look far:
27 = 1×27 = 3×9
If the length is 9 units and the width is 3 units, the width is equal to the length minus 6 units.
The length is 9 units.
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<em>Alternate solutions</em>
You can write an equation for the area using L to represent the length. The area is the product of length and width, so is ...
A = LW
27 = L(L-6) = L^2 -6L
You can "complete the square" by adding the square of half the L coefficient:
27 +3^2 = L^2 -6L +3^2
36 = (L -3)^2 . . . . . simplify a bit
6 = L -3 . . . . . . . . . positive square root
9 = L . . . . . . . . . . . . add 3
The length is 9 units.
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You can also put the quadratic equation into standard form:
L^2 -6L -27 = 0
To factor this, you're looking for factors of -27 that have a sum of -6. From above, we know these are -9 and +3. So the factorization is ...
(L -9)(L +3) = 0
The solutions are the values of L that make these factors be zero:
L -9 = 0 ⇒ L = 9
L +3 = 0 ⇒ L = -3
Only the positive solution is useful as a measure of length. The length is 9 units.
There are 20 nickels and 10 pennies.
20 cents x 5 is $1.00 and 10 cents x 1 is 10 cents so it is $1.10 because a nickel is 5 cents so 20x5 is a dollar and a penny is worth 1 cent and 10 pennies is 10 cents so $1.00+$0.10=$1.10 brainliest is appreciated! :)
Answer:
74
Step-by-step explanation:
What I'm getting at, is that you need to add all the hour sold cups up, and then double it because she expects to sell twice as much. 15 + 11 +5 +6 = 37, and 37 doubled is 74
