Please answer the questions on the Photo

A rectangle swimming pool is 8 feet deep. One side of the pool is 4.5 times longer than the other. The amount of water needed fo

wel

The side lengths of the pool 10 ft and 45 ft.

<u>SOLUTION: </u>

Given, a rectangle swimming pool is 8 feet deep.

One side of the pool is 4.5 times longer than the other.

Let the length of pool be n feet, the width will be 4.5n feet

The amount of water needed for the swimming pool is 3600 cubic ft

We have to find the dimensions of the pool. Now, we know that,

$\begin{array}{l}{\text {volume of pool}=\text {depth} \times \text {length } \times \text {width}} \\\\ {\rightarrow 3600 \text { cubic } f t=8 \text { feet } \times \text { n feet } \times(4.5 n) \text { feet }} \\\\ {\rightarrow 8 n \times 4.5 n=3600} \\\\ {\rightarrow 36 n^{2}=3600} \\\\ {\rightarrow n^{2}=100}\end{array}$

On taking square root on both sides we get,

$\begin{array}{l}{\rightarrow\sqrt{n^{2}}=\sqrt{100}} \\\\ {\rightarrow n=10 \mathrm{ft}}\end{array}$

So, the width will be $4.5 n=4.5 \times 10=45 \mathrm{ft}$

5 0

4 years ago

Simplify the polynomial by combining like terms. 3.63x2 - 4.54x + 7.96x2 +9.85 -3.12x

Brums [2.3K]

Answer:

11.59x² -7.66x + 9.85

Step-by-step explanation:

3.63x² - 4.54x + 7.96x² +9.85 -3.12x

11.59x² -7.66x + 9.85

7 0

3 years ago

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Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat

eimsori [14]

Answer:

There are NO real roots for this equation. The only roots have imaginary parts and therefore cannot be represented on the real x-axis.

Step-by-step explanation:

We notice that the expression on the left of the equation is a quadratic with leading term $2x^2$ , which means that its graph is that of a parabola with branches going up.

Therefore, there can be three different situations:

1) if its vertex is ON the x axis, there would be one unique real solution (root) to the equation.

2) if its vertex is below the x-axis, the parabola's branches are forced to cross it at two locations, giving then two real solutions (roots) to the equation.

3) if its vertex is above the x-axis, it will have NO real solutions (roots) but only non-real ones.

So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently.

We recall that the x-position of the vertex for a quadratic function of the form $f(x)=ax^2+bx+c$ is given by the expression:

$x_v=\frac{-b}{2a}$

Since in our case $a=2$ and $b=-3$ , we get that the x-position of the vertex is:

$x_v=\frac{-b}{2a}\\x_v=\frac{-(-3)}{2(2)}\\x_v=\frac{3}{4}$

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = 3/4:

$y_v=f(\frac{3}{4})=2( \frac{3}{4})^2-3(\frac{3}{4})+4\\f(\frac{3}{4})=2( \frac{9}{16})-\frac{9}{4}+4\\f(\frac{3}{4})=\frac{9}{8}-\frac{9}{4}+4\\f(\frac{3}{4})=\frac{9}{8}-\frac{18}{8}+\frac{32}{8}\\f(\frac{3}{4})=\frac{23}{8}$

This is a positive value for y, therefore we are in the situation where there is NO x-axis crossing of the parabola's graph, and therefore no real roots.

We can though estimate a few more points of the parabola's graph in order to complete the graph as requested in the problem. For such we select a couple of x-values to the right of the vertex, and a couple to the right so we can draw the branches. For example: x = 1, and x = 2 to the right; and x = 0 and x = -1 to the left of the vertex:

$f(-1) = 2(-1)^2-3(-1)+4= 2+3+4=9\\f(0)=2(0)^2-3(0)+4=0+0+4=4\\f(1)=2(1)^2-3(-1)+4=2-3+4=3\\f(2)=2(2)^2-3(2)+4=8-6+4=6$

See the graph produced in the attached image.

4 0

3 years ago

Marshall left home biking at a constant rate of 20 mph. One hour later, it looked like it may rain, so his friend, Brett, set ou

xxTIMURxx [149]

Answer:

First, we need to find how far ahead Marshall was. Since he had been biking at 20 mph for one hour, he had gone 20 miles.

Next, we need to find how long it will take Brett to catch up to Marshall. In order to do this, we need to find how much faster Brett is going than Marshall. We do this by subtracting Marshall's speed from Brett's speed.

60 - 20 = 40. So, Brett is catching up to Marshall at 40 mph. Now, we figure out how long it will take for someone going 40 miles per hour to go 20 miles. We find this by dividing 40 miles per hour by 20. This is equal to 1/2 hour. So, it will take Brett 0.5 hours to catch up to Marshall. This is the same as A, so A is the correct answer.

We can check our answer by seeing how far Marshall and Brett will have gone. Marshall will have been biking for 1.5 hours, so we multiply 20 * 1.5 = 30. Marshall went 30 miles.

Brett drove for .5 hours at 60 mph, so he went 30 miles. Since Brett and Marshall went the same distance, our answer is correct.

4 0

3 years ago

Jessica has four more hockey cards than one third the number of cards that David owns if Jessica has 12 hockey cards how many do

erica [24]

I believe the answer would be 24

work:

12-4=8 8x3=24

7 0

3 years ago

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