Frustration. Please help me out.?

Question

Really now...what is this?

Find the value of x: (2x) / 7 = (x - 1) / 3


And could i get some help with these?

Given Triangle RST is similar to Triangle DEF. If m Ang E = 38, m Ang R = 43, and m Ang T = 7x + 8, then x = ?



In Figure 8, if GI = 3, IH = 8, JK = 10, what is JI (if it is longer than IK)?



What is the volume of a right cone with radius 3 and height 4?


AND! For those people that are super good at math. Any suggestions to help me understand and more importantly MEMORIZE my math?


figure 8:::
http://i20.photobucket.com/albums/b231/Catalainya/geom_365.c.jpg

Answer 1

1. Multiply both sides with 21 and you get:
6x = 7x - 7 => x=7

2. If two triangles are similar, i believe that the corespondent angles are equal.
Since RST is similar to DEF =>
m R = m D, m S = m E, m T = m F
Also, the sum of all angles in a triangle is 180 degrees. Thusly R+S+T = 180 => R+E+T = 180 => 38+43+7x+8 = 180 => 7x = 91 => x=13

3. I honestly couldn't say. There must be a formula for this that i don't know

4. V = pi*R^2*h/3 = 3.14*9*4/3=3.14*12 = 37.68

5. Practice, practice, practice
Sorry about #3 tho, but even the figure seems wrong to me. Guess i don't know as much as i hoped =/

Answer 2

(1) Find the value: (2x) / 7 = (x - 1) / 3

cross multiply:
(2x) * (3) = (7) * (x-1)
6x = 7x - 7

Combine like terms:
6x - 6x = 7x - 6x - 7
0 = x - 7
7 = x

plug in:
2(7)/ 7 = (7-1)/ 3
14/ 7 = 6/ 3
2 = 2

so, x= 7!!

(2) Given Triangle RST is similar to Triangle DEF. If m Ang E = 38, m Ang R = 43, and m Ang T = 7x + 8, then x = ?

A triangle's inner angles will always add up to 180 degrees
38 + 43 + 7x + 8 =180
Once again, solve for x

89 + 7x = 180
89 - 89 + 7x = 180 - 89
7x = 91
7x/ 7= 91/ 7

x=13

check:
38 + 43 + 7(13) + 8 =180
180 = 180

so, x= 13

............I will come back and help for the rest....

Answer 3

(2x) / 7 = (x - 1) / 3 Just cross multipl and get:
7(x-1)= 2x(3)
7x-7 =6x
x = 7

7x+8 = 180 -38-43=99
7x= 91
x = 13

8*3 = x(10-x)
24 = 10x - x^2
x^2-10x +24 = 0
(x-4)(x-6) = 0
x = 4 and 6, so JI = 6

1/3pi r^2h = 1/3*pi*3^2*4 = 12pi units cubed

Practice a lot.

Answer 4

first question....

cross multiply.....

3(2x)=7(x-1)
6x=7x-7
6x-7x=-7
-x=-7
x=7

second question....

the sum of all interior angles in any triangle = 180 degrees

therefore,

38+43+(7x+8)=180
38+43+7x+8=180
7x=180-38-43-8
7x=91
x=91/7
x=13