Answer:
That (blank) is 9.
Step-by-step explanation:
Please write 8x^2 - 48x = -104, with " ^ " indicating exponentiation. Thanks.
This sounds like a perfect example of "completing the square."
First, factor 8x^2 - 48x = -104: 8(x^2 - 6x = -13).
If we focus SOLELY on x^2 - 6x = -13, it's just a little easier to "complete the square." Take half of the coefficient of x (which here is -6), and square that result (which here is (-3)^2, or 9. Now add 9 both sides of x^2 - 6x = -13:
x^2 - 6x + 9 = -13 + 9. Note: The "blank" in the problem statement is 9.
We could go ahead and solve this, tho' we weren't asked to do so. Rewrite x^2 - 6x + 9 as (x - 3)^2:
x^2 - 6x = -13 then becomes (x - 3)^2 = 4. To solve for x, take the sqrt of both sides of this latest result, obtaining x - 3 = plus or minus 2. Add 3 to both sides to isolate x: x = 3 plus or minus 2.
Thus, x = 5 or x = 1.
We are given the set of points
<span>{(1, 60), (2, 240), (3, 960), (4, 3840)}{(1, 60), (2, 240), (3, 960), (4, 3840)}
If w is the function name and t is the input variable, then the equation has the form
w = k a^t
Plugging in any two of the points to solve for k and a
Choosing </span>(1, 60) and (2, 240)<span>
60 = k a
k = 60 / a
240 = k a^2
Substituting
240 = 60/a (a^2)
a = 4
and
k = 60 / 4 = 15
The function is
w = 15 (4^t)</span>
Answer:
Sierra studied 3 hours
William studied 2 hours
Step-by-step explanation:
jonah studied 6 hours.
He also studied 3 hours longer than sierra meanining sierra studied 3 hours less than 6 hours.
So, 6 hours minus 3 hours is equals to 3 hours.
With that being said, Sierra has studied 3 hours.
Sierra = 3 hours
The question then states that Jonah studied 3 times as many hours as William.
Reminder: Jonah studied 6 hours in total.
This means that jonahs' hours (6 hours) is equals to 3 times williams hours (3x)
6 hours= 3x
x= williams hours
we divide both sides by 3 to see what x is equals to
in other words, we divide Jonahs' hours to see what williams hours are
With that being said, William studied for 2 hours
2 hours = x
Answer:
a] is 8cm
Step-by-step explanation:
A=2a2+4ah
a=8cm
h=15cm
therefore A=608
From the information given,
3 pounds = $18
Therefore, 1 pound = 18/3 = $6 (this can be treated as a constant of proportionality) such that,
Cost,C = 6*Weight, W (pounds)
Equation;
C = 6W, where C = Cost in $, and W = Weight in pounds.
