the sum of the square of a positive number and the square of 5 more than the number is 157. what is the number?
Let n = the positive number
then
from: "the sum of the square of a positive number and the square of 5 more than the number is 157" we get
n^2 + (n+5)...

Homer and Mike were replacing on mikes old deck. Mike can do the job in one hour less than Homer. they worked together for three hours until Homer had to go home. Mike finished the job working by himself for an additional 4 hours. How long would it have taken Homer to finish the deck by himself
Let...

log(x-5) + log(x-2) = 1
log((x-5)(x-2)) = 1
(x-5)(x-2) = 10^1
(x-5)(x-2) = 10
x^2-7x+10 = 10
x^2-7x = 0
x(x-7) = 0
x = {0, 7}
0 is an "extraneous" solution because you cannot plug it back into the original equation.
Solution: x = 7
...

Walmart company estimates that the computer they plan to buy in 18 months will cost $4,200. How much money should be deposited now into an account paying 5.75 % interest, compounded monthly so there will be enough money to pay cash for the computer in 18 months?
Compound interest formula:
A...

My teacher bought 20books from sale , she spent total $110 , some books are of $3 & some are of $8 , howmany books are of $8 if the no. of books price $3 is x
Because she bought a total of 20 books:
20-x = number of $8 books purchased
then because she spent $110:
3x + 8(20-x)...

(y^3 z^6)/(y^5 z^6)
since there are more y's in the denominator, we move the y's from the numerator to the denominator:
(z^6)/(y^5 y^(-3)z^6)
(z^6)/(y^(5-3)z^6)
(z^6)/(y^2z^6)
the z's all cancel leaving:
1/y^2

the length of a rectangle is 3 centimeters less than five times its width. its area is 14 centimeters. what are the dimensions of the rectangle?
Let w = width
then
5w-3 = length
w(5w-3) = 14
5w^2-3w = 14
5w^2-3w-14=0
(5w+7)(w-2) = 0
w = {-7/5, 2}
throw out...

Given:
h= -16t^2+64t+512
Set h to 0 and solve for t:
0 = -16t^2+64t+512
multiplying both sides by 1:
0 = 16t^2-64t-512
dividing both sides by 16:
0 = t^2-4t-32
factoring:
0 = (t+4)(t-8)
t = {-4, 8}
throw out the negative solution (extraneous)...

I presume they are asking you to derive the equation of the line that has:
slope of 6 and a y intercept of -3
Method 1:
"Slope-intercept" of a line:
y = mx + b
where m is the slope and b is the y-intercept
plug in the given data and you're done:
y = 6x +...

Find x if the slope between (7,-9) and (x,-13) is -1/3
slope between two points:
slope = (y2 - y1)/(x2 - x1)
plug the given data from the problem and solve for x:
-1/3 = (-13 - (-9))/(x - 7)
-1/3 = (-13 + 9)/(x - 7)
-1/3 = (-4)/(x - 7)
cross -multiplying:
3(-4)...

Solving for x:
1/3(x + 9) = 12
multiply both sides by 3 to remove the denominator:
(3)(1/3(x + 9)) = (3)12
(x + 9) = 36
subtracting 9 from both sides:
x + 9 - 9 = 36 - 9
x = 27

From Pythagorean identities:
1 + tan^2 x = sec^2 x
and
tan^2 x = sin^2 x/cos^2 x
So, now instead of
2 tan x / (1 + tan^2 x)
we have:
2(sin^2 x/cos^2 x) / sec^2 x
but 1/cos^2 x = sec^2 x
2(sin^2 x *sec^2 x) / sec^2 x
2(sin^2 x)
...

a. computer capacity is often measured in bits and bytes. a bit is the smallest unit, which is 1 or 0, in the computer's memory. a bytes is 2^3 bits. a megabyte (mb) is 2^20 bytes. how many bits are in a megabytes?
2^20 * 2^3 = 2^(20+3) = 2^23
b. a gigabyte (gb) is 2^30 bytes. how many...

Smile more and make it a point to say hello to people. You break the ice first.
Start/participate in study groups.
Be active in school -- participant in student government, join service clubs, clubs pertaining to your interest, or join sports program, etc.
Good luck...

A cylinder has the SA of 308 cm^2. The height is two times greater than the radius. What is the height of the cylinder?
Volume of cylinder = (area of base)(height)
Volume of cylinder = ((pi)r^2)(height)
Let h = height
then
h/2 = radius
substitute above into:
Volume...

Starting with:
[9m^2-1]/[3m+3]
factoring the denominator:
[9m^2-1]/[3(m+1)]
rewriting the numerator as:
[(3m)^2-1^2]/[3(m+1)] "difference of squares" -- special case factoring
[(3m-1)(3m+1)]/[3(m+1)]
canceling like-terms:
(3m-1)/3
or
m...

(TanX)-1)/(Tan(X)+1) = (1-cot(X))/(1+cot(X))
Let's make the "right side" of the equation look like the left:
(1-cot(X))/(1+cot(X))
since cot(x) = 1/tan(x) we can rewrite as:
(1-1/tan(x))/(1+1/tan(x))
(1-1/tan(x))/(1+1/tan(x)) * tan(x)/tan(x)
(tax(x)-1)/(tan(x)+1) ...

Isolate the unknown to one side of the inequality:
6x-5>4x-1
subtracting 4x from both sides:
2x-5 > -1
adding 5 to both sides:
2x > 4
dividing both sides by 2:
x > 2
To graph on a number line:
place an OPEN dot at 2
solid line from the dot and...

3(x+2)-2(y+1) if x=2 and y =2
substitute x for 2 and substitute y for 2:
3(2+2)-2(2+1)
apply "order of operations" -- parentheses first:
3(4)-2(3)
multiplication next:
12-6
6

2x+1-y+2 if x=1 and y=2
start with:
2x+1-y+2
substitute x for a 1 and substitute y for a 2:
2(1)+1-2+2
2+1-2+2
3-2+2
1+2
3