College Algebra Help!!!?

Question

1) In triangle ABC, the angle C is six times as large as angle A. The measure of angle B is 52 greater than that of angle A. Find the measure of the angles.

2) A 11 in by 14 in rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is 270 in 2 (this last 2 is squared).

Solve the equation
3) 5 over x+9 + 11 over x+2 =9 over x squared + 11x + 18

4) 4 with a radical over x= radical over 9x+9

Solve the equation by the zero-factor property.

5) 14 x squared + 57x + 28 = 0

6) 2 x squared = 9x -9

Answer 1

1) Write an equation. a triangle's angles always sum up to 180 degrees.

180=a+b+c
a=a
b=6a
c=a+52

so..
180=a+6a+a+52
180=8a+52
-52 -52
128=8a
divide both sides by 8
and..
16=a

now you have a, plug it in

a=16
b=6(16)
b=96
c=16+52
c=68

plug it in now

180= 16+96+68
180=180

there you have your answer, a=16 b=96 and c=68

Sorry, i couldn't help you with the other ones. i'm only in eighth grade you know!

Answer 2

#1

A+B+C=180,
so A+(52+A)+(6*A)=180
Subtract 52 from both sides
A+A+6A=180-52=128
8A=128
Divide both sides by 8
A=16

Now you can find the measures of B and C

B=52+16=68
C=6*16=96

You can check your work by adding 16+68+96=180

#2

I figured this out by trial and error. First I tried a 1 in wide path, which would have been 13*16 or 208 in squared. Then I tried a 2 in wide path, which would have been 15*18 or 270 in squared. Sorry, I don't know the "right" way to do it, but the answer's 2 in.

I'll let someone else take the rest, but I hope this helps!

Answer 3

3

Answer 4

1) Rather than guess as someone has suggested, try this:
All angles of a triangle add up to 180, so
A+B+C=180
Substituting for C
A+B+6A=180 so 7A+B=180
Substituting for B
7A+A+52=180 so 8A+52=180
A=(180-52)/8 = 16
so
B=68
C=96

Answer 5

number one is a=16 degrees, b=68 degrees, & c=96 degrees. i did this by guess & check.