I dont get how to do this?

Question

members of the fire department lean a 30-foot ladder against a building. The side of the building is a perpendicular to the level ground so that the base of the ladder is 10 feet away from the base of the building. To the nearest foot , how far up the building does ladder reach?

please help me thank you

and this problem

the larger of two numbers exceeds twice the smaller number by 8. The sum of twice the larger and 3 times the smaller number is 65. If x is the smaller number, which equation below determines the correct value of x?

F. 3(2x+8) + 2x= 65

G. 3(2x-8) + 2x=65

H. (4x +8) + 3x =65

J. 2(2x+8) +3x=65

K. 2(2x - 8x) + 3x =65

thank you so much if you help me

Answer 1

ok  :)

The first problem is just a Pythagorean Theorem problem.  It really helps to draw a picture

        

........../.|

...30../...|

......./.....|    x                (sorry, not the best triangle)

....../......|

...../____|

........10

So, by the equation, a^2+b^2=c^2, we can determine that x=√c^2-a^2  (ALWAYS a useful thing to memorize, that)

or,

x=√30^2-10^2

x=√900-100

x=√800

x= 28.2842712

oh, and to the nearest foot, so just round it, down, which is nearer.  

x=28

For the next one, take it in small bits.  "The larger of two numbers exceeds twice the smaller number by 8"  Ok.  This means that we make the smaller number x.  The first sentence means that the second variable = 2x+8, twice the smaller number plus 8.  Not as hard as they make it sound.  

So, the next part.  Now we have the two 'numbers':  x and 2x+8.  So we fill in the blanks as we go.  Little bits, right?  twice the larger  2(2x+8) and three times the smaller  (3x)...the sum of them, equals 65.  

so, we get 2(2x+8) + 3x = 65  

The answer is J.

I really hope my math is right, lol.  If it is, I'm happy to explain it to you.