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4 years ago

14

The linear equation y=-2x+4 is represented on the graph below. A second linear equation is represented by the data in the table.

x y –4 –3 0 –1 2 0 6 2 What is the solution to the system of equations? (2, 0) (0, 4) (0, –1) (4, –4)

2 answers:

Solnce55 [7]4 years ago

8 0

Answer:

A.

Step-by-step explanation:

atroni [7]4 years ago

4 0

Answer:

The solution of the system of equations is (2,0)

Step-by-step explanation:

step 1

Find the equation of the second line

we have

y=-2x+4 ----> First equation

Find the second linear equation

we have

(-4,-3), (0,-1),(2,0),(6,2)

Find the slope m

Points (0,-1),(2,0) ---> y-intercept and x-intercept of the second equation

m=(0+1)/(2-0)

m=1/2

The equation of the line into slope intercept form is equal to

y=(1/2)x-1

step 2

Solve the system of equations

we have

y=-2x+4 ----> First equation

y=(1/2)x-1 ----> Second equation

Solve by graphing

The intersection point is (2,0)

therefore

The solution of the system of equations is (2,0)

see the attached figure

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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

Which expression is equivalent to: n (5-x)

emmasim [6.3K]

The answer is
c) 5n-nx

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3 years ago

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Pavlova-9 [17]

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2) t=4 1/2+ 4 1/2
t=9
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3 years ago

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Licemer1 [7]

Check the picture below.

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3 years ago

The circumference of Circle K is pi. The circumference of Circle L is 4xpi.

dmitriy555 [2]

Answer:

Ratio of circumferences: $\displaystyle\frac{1}{4}$

Ratio of radii: $\displaystyle\frac{1}{4}$

Ratio of areas: $\displaystyle\frac{1}{16}$

Step-by-step explanation:

Hi there!

We are given:

- The circumference of Circle K is $\pi$

- The circumference of Circle L is $4\pi$

Therefore, the ratio of their circumferences would be:

$\displaystyle\frac{\pi}{4\pi}$ ⇒ $\displaystyle\frac{1}{4}$ when simplified

The formula for circumference is $C=2\pi r$ , where <em>r</em> is the radius. To find the ratio of the circles' radii, we must identify their radii through their given circumferences.

If the circumference of Circle K is $\pi$ , or $1\pi$ , then its radius is $\displaystyle\frac{1}{2}$ .

If the circumference of Circle L is $4\pi$ , then its radius is $\displaystyle\frac{4}{2}$ , which is 2.

Therefore the ratio their radii would be:

$\displaystyle\frac{\frac{1}{2}}{{2}}$ ⇒ $\displaystyle\frac{1}{2}*\frac{1}{2}$ ⇒ $\displaystyle\frac{1}{4}$ when simplified

The formula for area is:

$A=\pi r^2$

First, let's find the area of Circle K:

$A=\pi (\displaystyle\frac{1}{2})^2\\\\A=\displaystyle\frac{1}{4}\pi$

Now, let's find the area of Circle L:

$A=\pi (2)^2\\A = 4\pi$

Therefore, the ratio of their areas would be:

$\displaystyle\frac{\frac{1}{4}\pi}{4\pi}$ ⇒ $\displaystyle\frac{\frac{1}{4}}{4}$ ⇒ $\displaystyle\frac{1}{4} * \frac{1}{4}$ ⇒ $\displaystyle\frac{1}{16}$ when simplified

I hope this helps!

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2 years ago