Answer the question

Hey there!

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ANGLES

We see that the angle measure of angle VBC is 23 degrees. If you add this with the 90 degree angle of angle VCB, we can see that the measure of angle BVC is 67 degrees because sum of the interior angles of a triangle is 180 degrees.

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SOLVING FOR BC

Let's solve for some sides to to help us to to AC. We have that VC is 30 cm and is a leg of the triangle VCB. We see that the angle VBC is 23 degrees. Let's solve for CB. From the angle VBC, VC is the opposite side and CB is the adjacent. So, we see that the tangent of 23 is equal to 30 divided by whatever CB is. We can rearrange this problem to plug into our calculators.

If you use your calculator, you see that CB is equal to about 71 cm.

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SOLVING FOR AC

Now, let's look at the triangle BCA. We see that the angle BAC is 30 degrees. The side AC is the adjacent, and CB, 71 cm, is opposite. Tangent is opposite over adjacent, so we will use this.

We plug this in and we get about 123 cm.

Therefore, the answer is A. 123 cm.

I hope that this helps! Have a wonderful day!

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let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1