<u>Answer:</u>
-348
<u>Step-by-step explanation:</u>
We are given the following arithmetic sequence and we are to find the sum of its first 12 terms:
1, -4, -9, -14, . . .
For that, we will use the formula for the sum of the arithmetic mean:

We know the value of the first term (
) but we need to find the value of
. So we will use the following formula:



Substituting these values in the sum formula to get:

-348
Answer:
716in³
Step-by-step explanation:
The first step is to split the full prism into two, separate prisms. That means, we now have to find the volume of the half-a-cylinder, and the other base prism.
For the volume of the half-cylinder, we use the formula πr²h. That means, we do π·5·5·6, which is equal to around 471.24 cubic inches. However, we need to find the volume of half that cylinder, so we divide that answer by two. That should be about <u><em>235.62 cubic inches.</em></u>
For the volume of the other prism, we simply have to do length <em>times</em> height <em>times </em>width, or 6·8·10. That is equal to <em><u>480 cubic inches</u></em>, which is the volume of that prism.
To find the volume of the whole composite figure, you simple have to add the two underlined volumes above.
235.62+480= 715.62in³, or about <em><u>716in</u></em><em>³.</em>
<u><em>Hope this helps.</em></u>
Answer: Option B, Option C, Option E
Step-by-step explanation:
The options written correctly, are:

For this exercise you need to use the following Inverse Trigonometric Functions:

When you have a Right triangle (a triangle that has an angle that measures 90 degrees) and you know that lenght of two sides, you can use the Inverse Trigonometric Functions to find the measure of an angle
:

Therefore, the conclusion is that the angles "x" and "y" can be found with these equations:

Answer:
77.12 feets
Step-by-step explanation:
In a 33' by 69.7' room, what is the diagonal length from corner to corner along the floor?
Step one:
given data
Length of the room= 33 feets
width of the room = 69.7 feets
Required
The diagonal of the room
Step two:
from Pythagoras theorem
z^2= x^2+y^2
substitute
z^2= 33^2+ 69.7^2
z^2=1089+4858.09
z^2=5947.09
z=√5947.09
z=77.12 feets