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3 years ago

Solve the following system of equation graphically 2x+y=-1 and x+2y=4

1 answer:

4 0

As 2x + y = -1

Then,

y = - 1 - 2x

We can to replace on the bellow equation.

x + 2y = 4

x + 2.( -1 -2x) = 4

Doing the distributive

x + 2.(-1) + 2.(-2x) = 4

x -2 -4x = 4

-3x -2 = 4

-3x = 4 + 2

-3x = 6

x = 6/-3

x = -2
________________

Then, the value of y will be:

y = -1 -2x

y = -1 -2.(-2)

y = -1 + 4

y = 3

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What is the advantage of using exponential notation?

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3 years ago

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A construction crew must build 4 miles of road in one week. On Monday, they build 12 mile of road. On Tuesday, they build 13 mil

Julli [10]

$\frac{19}{6}$ many more miles of road are left to build .

<u>Step-by-step explanation:</u>

Here we have , A construction crew must build 4 miles of road in one week. On Monday, they build 1/2 mile of road. On Tuesday, they build 1/3 mile of road. We need to find that How many more miles of road are left to build . Let's find out:

On Monday, they build 1/2 mile of road.
On Tuesday, they build 1/3 mile of road.

Let Miles of road left to build is x So,

⇒ $\frac{1}{2} +\frac{1}{3} +x = 4$

⇒ $x = 4 - (\frac{1}{2} +\frac{1}{3})$

⇒ $x = 4 - (\frac{1(3)+1(2)}{6} )$

⇒ $x = 4 - (\frac{5}{6} )$

⇒ $x = (\frac{4(6)-5}{6} )$

⇒ $x = \frac{24-5}{6}$

⇒ $x = \frac{19}{6}$

Therefore, $\frac{19}{6}$ many more miles of road are left to build .

5 0

3 years ago

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The position function of a particle in rectilinear motion is given by s(t) = 2t3 – 21t2 + 60t + 3 for t ≥ 0 with t measured in s

Norma-Jean [14]

The positions when the particle reverses direction are:

$s(t_1)=55ft\\\\s(t_2)=28ft$

The acceleraton of the paticle when reverses direction is:

$a(t_1)=-18\frac{ft}{s^{2}}\\ \\a(t_2)=a(5s)=18\frac{ft}{s^{2}}$

Why?

To solve the problem, we need to remember that if we derivate the position function, we will get the velocity function, and if we derivate the velocity function, we will get the acceleration function. So, we will need to derivate two times.

Also, when the particle reverses its direction, the velocity is equal to 0.

We are given the following function:

$s(t)=2t^{3}-21t^{2}+60t+3$

So,

- Derivating to get the velocity function, we have:

$v(t)=\frac{ds}{dt}=(2t^{3}-21t^{2}+60t+3)\\\\v(t)=3*2t^{2}-2*21t+60*1+0\\\\v(t)=6t^{2}-42t+60$

Now, making the function equal to 0, to find the times when the particle reversed its direction, we have:

$v(t)=6t^{2}-42t+60\\\\0=6t^{2}-42t+60\\\\0=t^{2}-7t+10\\(t-5)*(t-2)=0\\\\t_{1}=5s\\t_{2}=2s$

We know that the particle reversed its direction two times.

- Derivating the velocity function to find the acceleration function, we have:

$a(t)=\frac{dv}{dt}=6t^{2}-42t+60\\\\a(t)=12t-42$

Now, substituting the times to calculate the accelerations, we have:

$a(t_1)=a(2s)=12*2-42=-18\frac{ft}{s^{2}}\\ \\a(t_2)=a(5s)=12*5-42=18\frac{ft}{s^{2}}$

Now, substitutitng the times to calculate the positions, we have:

$s(t_1)=2*(2)^{3}-21*(2)^{2}+60*2+3=16-84+120+3=55ft\\\\s(t_2)=2*(5)^{3}-21*(5)^{2}+60*5+3=250-525+300+3=28ft$

Have a nice day!

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3 years ago

Food bill before tax $62 Sales tax: 8% Tip: 15%<br> What is the tax?

professor190 [17]

<h3>Answer: $4.96</h3>

Work Shown:

8% = 8/100 = 0.08

8% of 62 = 0.08*62 = 4.96

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3 years ago

an office supply company is shipping a case of paper to a school.There are 10 reams of paper in the case.If each ream of paper w

AnnZ [28]

If there are 10 reams, and each ream is 32 ounces, then there is 320 ounces total im the case! Then, if you know that there are 16 ounces in a pound, then you can do 320/16, and get a total of 20 pounds in the case!

Hope this helped!

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3 years ago

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