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This is the first time that you've made a mistake!!!

The height for the original part is  10 cm

Never mind that the solid is standing at the angle of 60 degrees.

If you cut the bottom of the solid at the angle of 30 degrees, and put that part on the top of the solid, 

the height is going to be exactly 10 cm.

So, we have...      V = (10 * 4 * 3) / 8 

                      or     V = 5 * 2 * 1.5  

As follows:  \(\frac{x}{y}+\frac{4}{3}+\frac{9}{2}=\frac{x}{y}+\frac{35}{6}\\ \frac{x}{y} \times \frac{4}{3} \times \frac{9}{2}=6\frac{x}{y}\\ \text{from which it follows that }5\frac{x}{y}=\frac{35}{6}\\ \text{or }\frac{x}{y}=\frac{7}{6}\)

The intersection refers to those elements that are common to both sets, so \(A\cap B={2, 7}\) 

As follows:

I'll leave you to do the number crunching.

Steps as follows:

You do not need a formula. You just need to understand.

And it would be nice if you answered my questions.

Let PQRS be a square with side length 10.
The points X and Y lie outside the square such that XQ = 6, XP = 8, YS = 6, and YR = 8.
Find \(XY^2\).

\(\begin{array}{|rcll|} \hline XY^2 &=& (6+8)^2 + (6+8)^2 \\ XY^2 &=& 2(6+8)^2 \\ XY^2 &=& 2(14)^2 \\ \mathbf{XY^2} &=& \mathbf{392} \\ \hline \end{array}\)

V = pi * h ( R^2 - r^2 )

i think i founf it melody!

Let B, A, and D be three consecutive vertices of a regular 18-gon.
A regular heptagon is constructed on \(\overline{AB}\), with a vertex C next to A.
Find \(\angle BCD\), in degrees.

The inscribed \(\angle BCD\) is half of the central \(\angle BAD\)

\(\begin{array}{|rcll|} \hline \angle BCD &=& \dfrac{\angle BAD}{2} \\ && \boxed{\angle BAD = \dfrac{16*180^\circ}{18}\\ \angle BAD =160^\circ } \\ \angle BCD &=& \dfrac{160^\circ}{2} \\ \mathbf{\angle BCD} &=& \mathbf{80^\circ } \\ \hline \end{array}\)

The surface area of anything is the area of all the individual surfaces all added together.

Think about your triangular prism.

How many sides does it have?

What shapes are they?

Are any of the sides the same?

Find the are of each side then add them all together.

I can't' give you are formula unless you tell me the numerals (letters) that you want to use. (and what they stand for)

Good to see that you are having a go but it is not correct.

Look at my first answer and try again.

noooooooooo the formula!

Second part:

Draw a vector from the origin to the point (3, -1). That is vector a. Then draw a vector from the origin to the point (2, 2). That is vector b. Then complete the parallelogram from these two sides. The diagonal of the parallogram that goes from the origin to the opposite corner is the vector a + b

From the origin, go right 3 units and down 1 unit. Draw a vector from the origin to this point. That is vector a.

From that point, go left 1 unit and down 4 units. Draw a vector from the point (3, -1) to this point. That is vector b.

The red vector is the vector a + b

5

After that you can always put a pack of 4 into the cart and take out a pack of 3 resulting in the addition of 1 tennis ball OR (if there are no packs of 3 left in the cart) take out two packs of 4 and put in 3 packs of 3 resulting in the addition of 1 tennis ball.

nice explanation

To find the angle, we need to do:

arctan( -648 sqrt(3) / -648 ) = pi / 3

But our point is in the third quadrant, so we need to add pi to that angle to get it into the third quadrant.

pi/3 + pi = 4pi / 3

nice explanation

Angle BCD is 74 degrees.

XY^2 = 288.

Let  x  be the number of pennies they each had to start with.

A month later, Kenny has 2 + 3x pennies while Linny has 4x - 7 pennies.

4x - 7 = 8 + (2 + 3x)

4x - 7 = 10 + 3x

x = 17

Randy rate   1 job  20 minutes   = 1/20

Sandy = 1/30

1/30  + 1/20 = 1/x     x is the minutes for both of them to complete the job

                                       solve for 'x'    then you answer is   sandy time - x    = 30 - x