Find the GCF of 45, 90, 75: which is 15
So he can make 15 stones total.
Divide each of the color numbers by 15 to get the number of tiles he uses in each stone
By evaluating, we will see that for x = 7 h(x) exceeds g(x).
<h3>
For which value of x does h(x) first exceed g(x)?</h3>
We have:
h(x) = 2*(2)^x
g(x) = 22x - 4
Now we can evaluate both function in the different options:
h(5) = 2*(2)^5 = 64
g(5) = 22*5 - 4 = 106
We can see that for x = 5, h(x) does not exceed g(x), let's try the next one.
h(6) = 2*(2)^6 = 128
g(6) = 22*6 - 4 = 128
So, for x = 6 both functions have the same output, then for x = 7 we will see that h(x) exceeds g(x).
The correct option is B.
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Answer:
874.6
Step-by-step explanation:
total sales = 1045
1045 * .12 = 125.4
fuel = 9 * 5 = 45
1045 - 125.4 - 45 = 874.6
The constant of variation is 1/8.
<h3>What is variation?</h3>
The discrepancy among an ideal and real scenario is referred to as the Law of Variation. The most frequent manifestations of variation or variability are changes in the data, anticipated results, or minor changes in the quality of the output.
The types of variation are given below-
- Where a variable is a fixed multiple of another, this is known as direct variation. For instance, my income varies directly (or proportionally) with the amount of hours I put in.
- When one of the variables rises, the other one falls—this is known as inverse and indirect variation (product is constant). For instance, the length of time an air conditioner is operating has an indirect (equal or inverse) impact mostly on temperature in my home.
- Joint variation occurs when at least two factors are directly associated. For instance, a triangle's base and height are both related to the triangle's area.
According to the question;
A quantity m varies jointly with p and r which shows that p and r in joint variation with m.
m ---> pr
m = kpr
where, k is the constant of variation.
m = 1, p = 2, r = 4.
Substitute the values in the relation,
1 = k(2)(4)
1 = 8k
k = 1/8
Therefore, the constant of variation is 1/8.
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Answer:
15/56x^(-4/7) + 32x^3 + 6.
Step-by-step explanation:
Using the rule for algebraic differentiation:
If y = ax^n, dy/dx = anx^(n-1).
So :
If y = 5/8x^3/7 + 8x^4 + 6x - 9
dy/dx = 5/8* 3/7 x^(3/7-1) + 8*4 x^(4-1) + 6x(1-1)
= 15/56x^(-4/7) + 32x^3 + 6.