lokiisnotdead

Hey there, guest!

Since they mentioned that BE is congruent to BC, that means that triangle BCE is isosceles. And since it is isosceles, angle C is equal to angle E. So, angle E = 35 degrees.

From here, everything is much easier. Since we know angle DFB is 102, that means angle DFE is 180-102=78 degrees (since EB is a straight line).

We also know angle EDF is 180-35-78=67 degrees (using the triangle theorem). 

Now, I think I've done enough for you. I think you can solve the rest on your own!

You got this!

:)

thanks Melody! :)

Hi guest!

First off, we can start by subtracting 7 from both sides. We then get \(-2|7-9c|=-22\)

Then, we can divide both sides by -2. Now, we have \(|7-9c|=11\).

Since there are the absolute value brackets, there are 2 different scenarios:

\(7-9c=11\), AND \(7-9c=-11\). Now we just solve for both equations.

\(7-9c=11\)

\(-9c=4\)

\(c=-\frac{4}{9}\)

AND

\(7-9c=-11\)

\(-9c=-18\)

\(c=2\)

So, the final answer is \(\boxed{c=2 \text{ AND } c=-\frac{4}{9}}\)

I hope this helped you, guest!

If you have any questions, don't hesitate to ask!

:)

The solution it gives me is:

There are \({10 \choose 2} =45\) ways to choose two of the points to connect with a segment, so there are \(\boxed{45}\) segments drawn.

wow! that's right! thanks Melody!

Isn't the answer just \(52+160=212^{\circ}\)? I feel like that's wrong though... it seems too easy....

I'm glad it did :)

Hi guest!

To find the volume of the cylinder, we have to multiply the area of the base by the height.

The base has a radius of 10/2=5. 5^2*pi=25pi. 

Now let's find the height. Even though the cylinder is slanted, the height is still the same. So, the height is 11.

25pi*11= 275pi. Rounding this to the nearest hundredth would be \(\boxed{863.94\text{ ft}^3}\)

I hope this helped you, guest!

Please let me know if I did something wrong!

:)

that doesn't seem to be right... but thanks for helping :)

Hi guest!

To find the area of the shaded region, we can first find the area of the pizza slice looking thing (sorry I forgot what it's called), and then subtract the triangle from it.

Since we know that the radius is 3, the area of the whole circle is 3^2*pi= 9pi. The pizza slice shape thing is 60 degrees, which is 1/6 of the whole circle (360/60=6). So the pizza slice shape thing is \(9\pi*\frac{1}{6}=\frac{3}{2}\pi\). This is equal to \(\approx 4.712\)

Now, let's find the area of the equilateral triangle (we know it's equilateral since the 2 sides are equal to 3, which means the other 2 angles are also 60 degrees). The formula for the area of an equilateral triangle is \(\frac{\sqrt{3}}{4}a^2\). So, the area of the triangle is \(\approx 3.897\)

Now, we just have to subtract \(4.712\) and \(3.987\).

\(4.712-3.987=0.725\) which is closest to \(\boxed{0.8\text{u}^2}\)

I'm not sure this is the correct answer, so please let me know if it's right!

:)