GYanggg

Hey bigguy1989!

To solve for A and B, we plug in our two values for x and y to set up the systems of equations. 

When x = 1 and y = 3: (1,3), we get: 3A = B + 1

When x = 5 and y = 13: (5,13), we get: 13A = 5B + 1

We obtain the systems: 

3A = B + 1

13A = 5B + 1

To solve the systems, we multiply the top one by 5, and we get:

3A = B + 1 \(\Rightarrow\) 15A = 5B + 5

Now we can subtract first equation from second equation so the B's cancel out. 

15A - 13A = 5B - 5B + 5 - 1

2A = 4

A = 2 \(\Rightarrow\) B = 5

The line becomes 2y = 5x + 1

In standard form: 2y - 5x = 1

In slope-intercept: y = 2.5x + 0.5

I hope this helped,

Gavin

Hey Guest!

We use the formula:

\(A=\pi{r}^2\), to find the area of the circle,

Where A is the area, r is the radius, and π is the ratio of the circumference to the diameter, or just 3.1415...

Since π is a constant, all we need to do, is find the radius of the circle to get the area. 

Since the radius is half of the diameter, it is equal to \(11\div2=5.5\)

We plug our values into the formula to get:

\(30.25\pi\)

I hope this helped,

Gavin

A. 

10 people choose 3 person committee. 

\(\binom{10}{3}=120\)

B. 

Since Fred is already included, all we need to do is form a two person committee. 

\(\binom{9}{2}=36\)

C. 

If Fred does not want to be chosen, he can be taken out of the pool.

Now it is just a nine person choosing. 

\(\binom{9}{3}=84\)

The relantionship between the three answers is the sum of the answers to B and C is the answer to A.

This is because it is either Fred is on the team or not on the team. There is no other option. 

Therefore, the sum of the possible committees where Fred is on and not on the team, is equal to the total amount of possible committees. 

I hope this helped,

gavin

Hey rohitaop!

Here is my solution:

We can consider the cases:

If A is the first letter, we have B-Z possibilities, or 25 letters. 

If B is the first letter, we have C-Z possibilities, or 24 letters. 

.

.

.

If Y is the first letter, we have Z possibilities, or 1 letter. 

We have the sum:

1 + 2 + 3 + 4 ... + 24 + 25, we use the arithmetic sum formula where the difference is 1. 

25 * (25+1) / 2 = 325.

I hope this helped,

Gavin

Hey Oscar!

Once again, we use the formula:

\(S_{abc}=AB\sin{c}\)

Where A and B are the adjacent sides to the angle c. 

We could apply the formula in this problem:

\(\text{area}=8\cdot7\sin{28}\)

After solving the right side, you got the area. 

I hope this helped,

Gavin 

We use the formula:

\(A=\frac12ab\sin{C}\)

Therefore, the area of the triangle is:

\(\frac12\cdot14.2\cdot8\cdot\sin{99}\)

I hope this helped,

Gavin

Hey NSN!

Find \(\csc{\frac{5\pi}{4}}\)

\(\csc{\frac{5\pi}{4}}\) = \(\frac{1}{\sin{\frac{5\pi}{4}}}\)

\(\sin{\frac{5\pi}{4}}=\sin({\frac{\pi}{4}+\pi})=-\frac{\sin{\pi}}{4}=-\frac{\sqrt{2}}{2}\)

\(\boxed{-\sqrt{2}}\)

I hope this helped,

Gavin

42. Assuming s is the major arc, here is the solution:

π here is 180 degrees, so 5π/3 is also 5 * 180 / 3 = 300

That angle is 300 degrees. 

The circumference is 2r * π, where r is the radius and π is 3.1415...

The circumference is 18π. 

Since the major arc is 300/360 or 5/6 of the circumference, it is 

5/6 * 18π = 15π long. 

This in decimal is 15 • 3.141...=47.124...

A. 

I hope this helped,

Gavin

41. Here is the solution:

Imagine the unit circle: 

We know that 300 degrees is in the fourth quadrant, where cosine is positive.

300 degrees has a reference angle of 60 degrees, since it is 60 degrees away from the x-axis

Since \(\cos{60º}=\frac12, \cos{300º}=\frac12\)

I hope this helped,

Gavin

Hey RB!

I'm not that good at number theory but here is what I have:

Multiplying both sides of the congruence:

\(2x\equiv y+5\pmod 9 \)

by 5 gives:

\(10x \equiv 5y+25\pmod 9,\)

then reducing both sides modulo 9 gives

\( x\equiv 5y+7\pmod 9. \)

Thus, the product of the blanks is \(5\cdot 7=\boxed{35}.\)

I hope this helped,

Gavin