gwenspooner85

The formula for the number of terms is (last term-first term)/common difference +1. For 3, 7, 11, ..., 407, the number of terms are:

(407-3)/4+1

=404/4+1

=101+1

=102

For 2, 9, 16, .. 709 the number of terms are:

(709-2)/7+1

=707/7+1

=101+1

=102

Both of them have 102 terms.

We are given two angles in each triangle. We can solve for the missing angles. In the upright triangle, the missing angle is 180-50-60=180-110=70. In the upside down one, the missing angle, x, is 180-50-70=180-120=60. Notice than 70 degrees, x, and y form a straight line which is 180. Then y is 180-70-60=180-130=50.

\(\large{-4p+(-2)+2p+3}−4p+(−2)+2p+3\\ =-4p-2+2p+3-4p-2+2p+3\\ =-2p-2p+1+1\\ =-4p+2\)

The area of the shaded area is the large rectangle minus the small rectangle. So we have

(3x+8)(2x+6)-(x+6)(x-3)

=6x^2+34x+48-(x^2+3x-18)

=5x^2+31x+66

Let x be a unit. Then we form an equation for the sum of the triangle's angles:

3x+4x+7x=180

18x=180

x=10

Then 3x=30, 4x=40, and 7x=70.

What do you mean??? There is an AMC 8 class on aops.

1.

-16+5n=-7(-6+8n)+3

-16+5n=42-56n+3

61n=61

n=1

2.

-4k+2(5k-6)=-3k-39

-4k+10k-12=-3k-39

9k=-27

k=-3

Because 7 ate/eight 9. :)))

There's no problem, it always says waiting for moderation for a bit after a question with a picture is posted.