The different between three times a number and five is equal to the product of four times the number increased by two.

Simplify the expression y * y^-2 * y^5

castortr0y [4]

add the exponents

y^(1-2+5)

y^(4)

6 0

3 years ago

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If f(x)f(x) is an exponential function where f(-0.5)=27f(−0.5)=27 and f(1.5)=21f(1.5)=21, then find the value of f(0.5)f(0.5), t

vovikov84 [41]

Given:

f(x) is an exponential function.

$f(-0.5)=27$

$f(1.5)=21$

To find:

The value of f(0.5), to the nearest hundredth.

Solution:

The general exponential function is

$f(x)=ab^x$

For, x=-0.5,

$f(-0.5)=ab^{-0.5}$

$27=ab^{-0.5}$ ...(i)

For, x=1.5,

$f(1.5)=ab^{1.5}$

$21=ab^{1.5}$ ...(ii)

Divide (ii) by (i).

$\dfrac{21}{27}=\dfrac{ab^{1.5}}{ab^{-0.5}}$

$\dfrac{7}{9}=b^2$

Taking square root on both sides, we get

$\dfrac{\sqrt{7}}{3}=b$

$b\approx 0.882$

Putting b=0.882 in (i), we get

$27=a(0.882)^{-0.5}$

$27=a(1.0648)$

$\dfrac{27}{1.0648}=a$

$a\approx 25.357$

Now, the required function is

$f(x)=25.357(0.882)^x$

Putting x=0.5, we get

$f(0.5)=25.357(0.882)^{0.5}$

$f(0.5)=23.81399$

$f(0.5)\approx 23.81$

Therefore, the value of f(0.5) is 23.81.

6 0

3 years ago

It takes three identical water pumps 8 hours to fill a pool. How long would it take four of the same pumps to fill the pool?

patriot [66]

Itll take four pumps 6 hours to fill the pool with water. And heres how we get to that conclusion: Logically, the thing that would make calculating how much time would it take for four (or any other number) pumps to fill the pool much, much simpler, would be knowing how much water goes through one pump in one hour. And luckily, this can be calculated from the data given above. Basically, if three pumps fill the pool in 8 hours, this means one pump fills 1/3 of the pool in this time. Now, since the exact amount of water goes through the pump at any point, this means that in order to fill 1/3 of the pool with one pump, thered be 1/8 of the total amount of water that goes through it (in this case, 1/3 of the pool) every hour. Or, one pump would fill 1/8 * 1/3 in one hour. This is 1/24. And its just smooth sailing from here on. If one pump fills 1/24 of the pool in an hour, four pumps fill 4*1/24, or 1/6 in the same time. So if the four pumps fill out 1/6 of the pool in one hour, theyd need to do this 6 times to fill the whole pool. Or, rather, 6 hours.

3 0

3 years ago

What is the solution to 0.6(24x-32)=0.8(24-6x)?

Helen [10]

You would have to move terms which will bring you to 14.4 x - 19.2 = 19.2 - 4.8x the you would combine like terms then you would get 19.2x= 38.4 then you divide both sides by 19.2 and get 2 as your answer.

5 0

3 years ago

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Choose the equation of the horizontal line that passes through the point (2,4)

Tanzania [10]

Answer:

y = 4

Step-by-step explanation:

The point (2, 4) has the x intercept = 2 and y intercept = 4.

A horizontal line has a slope of 0, therefore every point on a horizontal line has the same value and a slope of 0.

So to find the equation of the horizontal line, we use the value of y intercept which can be written in the form y = b where point is (a, b).

Since the point given here is (2, 4), therefore the equation of the horizontal line which passes through it will be y = 4.