Determine the solution to the system of equations graphed below and explain your reasoning in complete sentences.

Mathematics

1 answer:

Anarel [89]3 years ago

3 0

Answer:

(0, -3)

Step-by-step explanation:

The solution to the system of equations is the point at which they intersect. The problem statement tells you that point is (x, y) = (0, -3).

Often, for a system defined using functional notation, we don't care about the value of the function. We only care about the value of x where the functions have the same value. That is ...

the solution to f(x) = g(x) is x = 0.

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One supplementary angle is 15 degrees less than twice the other. Find the measure of the two supplementary angles.

o-na [289]

Hey there!

To find our answer, we need to set up a system of equations. Remember, supplementary angles equal 180 degrees when combined. We will call one of our angles A and the other one B. Let's set it up below! :)

A=2B-15 (one angle is 15 degrees less than twice the other)

A+B=180

We need to find one of our variables. To do this, we only put one variable in the equation. But how, there are two variables in both equations! Well, as you can see, we see the A is equal to 2B-15, so we can take 2B-15 and put it into the second equation in place of A because it is equal to A, and then we will only have Bs and we can solve for it. This method is known as solving systems of equations with substitution.

Let's solve with substitution!

2B-15+B=180

3B-15=180 We combine our Bs.

3B=195 We add 15 to both sides.

B= 65 We divide both sides by three.

Now, we need to find what A is, but this will be really easy to do! If you remember, our angles are supplementary, so when you combine them, we will get 180, as you can see in our second equation in our first system of equations. So, we simply subtract 65 from 180.

180-65=115

Our two angles are 65° and 115°.

We can also check this with the original problem.

If you double 65, we have 130. Then, if we subtract 15, we have 115. Systems of equations are a pretty awesome way to figure this out!

I hope this helps! Have a great day!

5 0

2 years ago

The distance from Neptune to Mars is 4.272\times 10^{9}4.272×10 9 kilometers. How long would it take a rocket, traveling at 4.8\

just olya [345]

The time taken is $8.9 * 10^4hrs


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