Find the area of the triangle on problem #7 and what statement in true for the triangle on #8

Step-by-step explanation:

Using the pythagorean theorem, a^2+b^2=c^2

32/2=16, 20 would be the hypotenuse, so it would be 20^2-16^2=a^2 because we want to find the middle line. 400-256=144. sqrt(144) = 12.

Then since it is an isosceles triangle, we can simply do 12*16=192

The answer for 7 is 192ft^2

For #8, the answer is short leg * sqrt(3) = long leg

On another note, you can find the hypotenuse of a 30-60-90 triangle by doubling the shortest leg

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

  or  

step-by-step explanation:

if the four friends split the cost, p, of the pizza evenly, then each friend pays one-fourth of the cost of the pizza.

the expression is   or