Answer:
a)
i) we have the equation:
3*x - 2*y
We want to find a common multiple of 3 and 2.
One can be:
3*6 = 18
2*9 = 18
And both numbers 6 and 9 are on the list, then if we take:
x = 6, y = 9
we get:
3*6 - 2*9 = 18 - 18 = 0
The solution is x = 6, y = 9.
ii) The greatest possible value of:
3*x - 2*y
Will be when x is the largest value of the list (because it is on the positive term) and y is the smallest value on the list (because it is on the negative term)
then we need to have x = 10, y = 5
The value will be:
3*10 - 2*5 = 30 - 10 = 20
iii) Now we want to have the smallest value on x, and the largest one on y, then:
x = 5, y = 10
The smallest value of the equation will be:
3*5 - 2*10 = 15 - 20 = -5
B) We want to solve:
5*(a - 4*b)
when:
a = -7
b = 1/4
This is kinda easy, we just need to replace the variables in the equation to get:
5*(a - 4*b) = 5*(-7 - 4*(1/4)) = 5*(-7 - 4/4) = 5*-8 = -40
Answer:
y + 4/7 
6x
Step-by-step explanation:
Answer:
Step-by-step explanation:
Interest earned is proportional to the interest rate, so if the interest earned is the same, the amounts invested must be inversely proportional to the interest rates. That is, for the 3% and 2% accounts, the ratio of money invested is 2:3.
In other words, 2/5 of the money ($3200) was invested at 3%, and 3/5 of the money ($4800) was invested at 2%.
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If you need an equation, you can let x represent the amount invested at the highest rate. Then 8000-x is the amount invested at the lower rate. For the interest in the two accounts to be equal, we have ...
3%·x = 2%·(8000-x) . . . . . the amounts of interest earned are the same
3/2·x = 8000 -x . . . . . . . . divide by 2%
5/2·x = 8000 . . . . . . . . . . . add x and simplify
x = 8000·(2/5) = 3200 . . . multiply by the inverse of the x coefficient
8000-x = 8000 -3200 = 4800 . . . . the amount invested at the lower rate
Tamara invested $3200 in the 3% account and $4800 in the 2% account.
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She earned $96 in each account for the year.
We know that h = 65 ft and the angle of elevation to the top is α = 56°.
x - the length of the support wire;
x · cos 56° = 65
x = 65 / cos 56°
x = 65 / 0.5592
x = 116.237 ≈ 116.2 ft ( to the nearest tenth )
Answer: The support wire is 116.2 ft long.
The number is 14. You can put it in an equation by writing 14 + (14 ÷ 2) = 21
