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Point P is not in the center.  Therefore diagonal AC does not go through P.  In other words, APC is not a straight line. 

I already know that's wrong.

The area of trapezoid PQRS is 120.

Because PA=3 and PC=7, the diagonal AC=10. Since ABCD is a rectangle, it is also a parallelogram. Since ABCD is a parallelogram, segment AB ≅ segment DC because opposite sides of a parallelogram are congruent. Therefore PB=10-PD= 10-6=4. 

The answer is 4.

1. First let's find the missing angle of the triangle on the right which has the measurements 100° and 30°.

180°-(100°+30°)=180°-130°=50°.

(The opposite side of the 50° angle will also equal 50°)

2. Now we know the triangle on the left has the angle measurements of 50° and 50°. Let's find the missing angle.

180°-(50°+50°)=180°-100°=80°.

3. Since there's a straight 180° line on the bottom, and we know that one measurement is 80°, while the other measurement is 35°, we have to subtract 80°+35° from 180° to find the value of x. 180°-(80°+35°)=180°-115°=65°.

Answer: x=65° 

Not exactly, but nice try! Adding on to what guest said, all you have to do is see on the graph how many times the y is at -1. There is 4.

Also, even though the picture is pixalated, it is still very disturbing, and NOT a surprise at all. Can you edit your post to get rid of it? Thanks!

:)

There are 2 values of c such that f(c) = -1.

angle x = 180 - 115

The perimeter of the new polygon is 27.

There are 1005 possibe lengths for AX.

The probability is 5/338.

You should try graphing it: https://www.desmos.com/calculator/bliuxjinip (answer is 1)

Anyways, this can also be done without graphing. 

We first need to know where the parabola is facing. This picture can come in handy:

 (If you cant see picture, got to this link: https://www.conceptmathhelp.com/vertex-of-a-paraboladomain-and-range-of-parabola/)

Once you have figured that out, find the vertex using the vertex formula. Since the parabola is opening left, and our vertex has a 0 for the x, it means we have only have 1 y intercept.

:)

There are 24 committees.

(a-1)(b-2)(c-3)(d+2019)=2020

a = 2

b =3

c =4

d =1

(2 - 1)(3 - 2)(4 - 3)(1 + 2019) = 2020

1*1*1*2020 = 2020

a = 2

b = 1

c = 2

d = 1

(2 - 1)(1 - 2)(2 - 3)(1 + 2019) = 2020

1*(-1)*(-1)*2020 = 2020

I found 2 such numbers:

2121,  2341 

Find the solutions to 16^x - 25*4^x + 24 = 0.

Let  u = 4^x, so the equation becomes:

u^2 -25u +24 = 0 This factorises as  (u - 24)(u - 1) = 0  so u = 24 and u = 1

Hence we have 4^x = 24    and  4^x = 1

Can you take it from here?   (Think about taking logs of both sides)

Here are the two things we need to find: slope and y intercept. So:

slope=-3-2/-4--8=-5/4 (learn more here: https://www.wikihow.com/Find-the-Slope-of-a-Line)

y intercept=-3-y/-4-0=-5/4:y=-8 (learn more here: https://www.wikihow.com/Find-the-Y-Intercept)

Therefore, the equation is y=-5/4x-8

:)

99 = F + 18D..............................(1)
19/2 * [2F + 18D] = 99................(2), solve for F, D

F = - 1683 / 19 - This is the first term
D =  198 / 19 - This is the common difference

20th term = - 1683 / 19 + [(198 / 19)*19]
20th term =2079 / 19

For this one, we need to set up a system of equations. Let cow be c, and goat be g. So:

4c+9g=50150

9c+4g=91900

So, what can we do here? Well, if we add them two together, we get:

13c+13g=141050

Divide by 13:

c+ g = 10850

Now, what can we do? Well we subtract the two equations:

-5c + 5g = -40750

Divide by -5:

c - g = 8150

Now, add the two equations that we made together:

2c=19000

c=9500

please correct me if I'm wrong.

:)

Thank you for the hint. I am actually looking for a inversion solution but I am going to try coordinate bashing. Is there any special things I should do to do this like having a certain point as the origin or using a certain theorem? Thanks!

Remember, 0 also works!

Please just post one question per post.

Question 1

I've started it for you.

Now just use angle sum of triangles to find the angles at P and T

Hint:

A radius and a tangent meet at right angles.

Just look at the term 5(x - 1/2)^2  (x-1)^2   

What happens to this term if you plug in x = 1/2?

What happens to it if you plug in x = 1?