X^2 + 2x < 8 x^2 + 2x - 8 < 0 (x + 4)(x - 2) < 0 ,, {x + 4 < 0 and x - 2 > 0} or {x + 4 > 0 ,,and x - 2 < 0} ,, {x < -4 and x > 2} or {x > -4 and x < 2},, Discard x < -4 and x > 2 because it has no solutions, leaving just x > -4 and x < 2 ,, -4 < x < 2

6 0

3 years ago

While exercising victor walked 3/4 of a mile in 1/5 of an hour. at this rate how far will he have traveled after an hour

Marina86 [1]

(1 / 5) hour is 12 minutes and five times this equals 1 hour.
So the distance times 5 equals miles per hour.
(3 / 4) * 5 = 15 / 4 = 3.75 mph

4 0

3 years ago

The city council plans to build a new water storage tank for the community. The tank is cylindrical with a base diameter of 25 f

Stella [2.4K]

Answer:

a. $14726.216ft^{3}$

b. $110446.62gal$

Step-by-step explanation:

I attach the diagram of the new water tank.

a. In order to find the volume of the tank in cubic feet, we will need to calculate the volume of a cylinder. We know that its base measures $25ft$ and its height is $30ft$ .

The volume ''V'' of a cylinder is :

$V=(\frac{\pi D^{2}}{4}).(H)$

Where '' $D$ '' is the diameter of the base and '' $H$ '' is the height of the cylinder.

If we replace all the data in the equation :

$V=\frac{\pi .(25ft)^{2}}{4}.(30ft)=14726.216ft^{3}$

We found out that the volume of the tank in cubic feet is $14726.216ft^{3}$

b. We know that 1 cubic foot of water is equal to 7.5 gallons. To find the amount of gallons that the new tank can hold, we need to do an unit conversion.

This equivalence is given to us :

$1ft^{3}=7.5gal$ ⇒ Using the equivalence ⇒

$(14726.216ft^{3}).(\frac{7.5gal}{1ft^{3}})=110446.62gal$

Finally, the new tank will hold $110446.62gal$ of water.

7 0

4 years ago