Select all points that lie on line y = 8x

Two large and 1 small pumps can fill a swimming pool in 4 hours. One large and 3 small pumps can also fill the same swimming poo

kolezko [41]

Let x and y be the unit rates at which one large pump and one small pump works, respectively.

Two large/one small operate at a unit rate of

(1 pool)/(4 hours) = 0.25 pool/hour

so that

2x + y = 0.25

One large/three small operate at the same rate,

(1 pool)/(4 hours) = 0.25 pool/hour

x + 3y = 0.25

Solve for x and y. We have

y = 0.25 - 2x ==> x + 3 (0.25 - 2x) = 0.25

==> x + 0.75 - 6x = 0.25

==> 5x = 0.5

==> x = 0.1

==> y = 0.25 - 2 (0.1) = 0.25 - 0.2 = 0.05

In other words, one large pump alone can fill a 1/10 of a pool in one hour, while one small pump alone can fill 1/20 of a pool in one hour.

Now, if you have four each of the large and small pumps, they will work at a rate of

4x + 4y = 4 (0.1) + 4 (0.05) = 0.6

meaning they can fill 3/5 of a pool in one hour. If it takes time t to fill one pool, we have

(3/5 pool/hour) (t hours) = 1 pool

==> t = (1 pool) / (3/5 pool/hour) = 5/3 hours

So it would take 5/3 hours, or 100 minutes, for this arrangement of pumps to fill one pool.

6 0

3 years ago

Which of the following represents the zeros of f(x) = x3 − 11x2 + 38x − 40?

Delvig [45]

The answer is 5, 4, 2

Among all choices we have 5, so
x = 5
x - 5 = 0
Let's divide the expression by (x - 5) using the long division:
x³ - 11x² + 38x - 40
(x - 5) * x² = x³ - 5x² Subtract
____________________________
-6x² + 38x - 40
(x - 5) * (-6x) = -6x² + 30x Subtract
____________________________
8x - 40
(x - 5) * 8 = 8x - 40 Sutract
____________________________
0

Thus: x³ - 11x² + 38x - 40 = (x - 5)(x² - 6x + 8)

Now, let's simplify x² - 6x + 8.

x² - 6x + 8 = x² - 2x - 4x + 8 =
= x² - 2*x - (4*x - 4*2) =
= x(x - 2) - 4(x - 2) =
= (x - 4)(x - 2)

Hence:
x³ - 11x² + 38x - 40 = (x - 5)(x - 4)(x - 2)
To calculate zero:
x³ - 11x² + 38x - 40 = 0
(x - 5)(x - 4)(x - 2) = 0
x - 5 = 0 or x - 4 = 0 or x - 2 = 0
x = 5 or x = 4 or x = 2

3 0

3 years ago

How do you solve 3 1/4 - 1 5/6

rjkz [21]

Answer:

to solve $3\frac{1}{4} -1\frac{5}{6}$ you would first need to convert them from mixed numbers to improper fractions. You can do this by multiplying the denominator with the whole number and then adding the numerator. Then you should make sure that the denominators are the same. You can do this by first finding a number that they will both multiply into. In this example it is 12. And when changing the denominator you must apply it to the numerator. So if you multiplied the denominator by 3 then you must multiply the numerator by 3. After you can just minus the numerators. However remember to keep the denominator the same. Then you can change it back into a mixed number by dividing the numerator by the denominator and having that whole number on the side of the fraction . lets say it is $\frac{13}{6}$ then you would divide 13 by 6 which is 2 and a decimal and then minus the number that is multiplied by the numerator and it will give a number that is smaller than the denominator and then it would become $2\frac{1}{6}$ .