You can put this solution on YOUR website!
They basically are asking you to factor the polynomial. "Linear factors" mean they want the factors all with degree of 1.
.
p(x)=x^3-x^2-9x+9
group terms:
p(x)=(x^3-x^2)-(9x-9)
p(x)=x^2(x-1)-9(x-1)
p(x)=(x-1)(x^2-9)
p(x)=(x-1)(x^2-3^2)
p(x)=(x-1)(x-3)(x+3)

You can put this solution on YOUR website!
WHAT PERCENT IS 4 OF 9?
4/9 * 100
0.444 * 100
44.4%

You can put this solution on YOUR website!
What am I supposed to do if a question is like this. A school bus with capacity for 42 passengers. How many school buses are needed to transport a total of 180
passengers on a trip to the state legislature?
.
Just divide:
180/42 = 4.29
the math says you need 4.29 buses
Since, you can't have a "partial" bus the answer is
you will need 5 buses

You can put this solution on YOUR website!
How do we solve a problem that looks like this:
Log base 3 10= 2.1
Log base 3 11= 2.2
Log base 3 8= 1.9
Find Log base 3 330
Log base 3 330=?
.
Log base 3 330
Log base 3 33*10
Log base 3 3*11*10
Log base 3(3) + Log base 3(11) + Log base 3(10)
Log base 3(3^1) + Log base 3(11) + Log base 3(10)
1 + Log base 3(11) + Log base 3(10)
1 + 2.2 + Log base 3(10)
1 + 2.2 + 2.1
3.2 + 2.1
5.3

You can put this solution on YOUR website!
A jar contains quarters and dimes whose value totals $4.40. It has three times as many dimes as quarters. How many dimes is in the jar.
.
Let d = number of dimes
then
d/3 = number of quarters
.
.10d + .25(d/3) = 4.40
.30d + .25d = 13.20
.55d = 13.20
d = 13.20/.55
d = 24 (number of dimes)

You can put this solution on YOUR website!
I'm assuming they're asking you to simplify:
2logx-3log(x+1)
logx^2-3log(x+1)
logx^2-log(x+1)^3
log(x^2/(x+1)^3)

You can put this solution on YOUR website!
How can I translate this word problem into an equation? Jim is 5 years older than Joe. If the sum of their ages is 55, how old are they?
.
Let x = age of Joe
then
x+5 = age of Jim
.
x + x+5 = 55
2x + 5 = 55
2x = 50
x = 25 years old (Joe)
.
Jim:
x+5 = 25+5 = 30 years old

You can put this solution on YOUR website!
Let f(x)=x^2 +3x+9 and g(x)=(2x+3)/(x-2) Find f(-1)-g(0)
.
first, find f(1):
f(x)=x^2 +3x+9
f(1)=(1)^2 +3(1)+9
f(1)=1+3+9
f(1)=13
.
then, find g(0):
g(x)=(2x+3)/(x-2)
g(x)=(2(0)+3)/(0-2)
g(x)=(3)/(-2)
g(x)= -3/2
.
finally:
f(-1)-g(0)
13-(-3/2)
13 + 3/2
26/2 + 3/2
(26+3)/2
29/2 (answer)

You can put this solution on YOUR website!
Bob throws a ball vertically upward from the top of the cliff, the height of the ball above the base of the cliff is approximated by the model h = 65 + 10t- 5t ^2 where h is the height in metres and t is the time in seconds.
a) How high is the cliff?
h = 65 + 10t- 5t ^2
set t to zero to find height of cliff:
h = 65 + 10(0)- 5(0)^2
h = 65 metres
.
b) How long does it take the ball to reach a height of 50 metres above the cliff?
set h to 50 and solve for t
h = 65 + 10t- 5t ^2
50 = 65 + 10t- 5t^2
0 = 15 + 10t- 5t^2
0 = -5t^2+10t+15
0 = 5t^2-10t-15
0 = t^2-2t-3
0 = (t+1)(t-3)
t = {-1, 3}
throw out the negative solution leaving:
t = 3 seconds
.
c) After how many seconds does the ball hit the ground?
set h to 0 and solve for t:
h = 65 + 10t- 5t ^2
0 = 65 + 10t- 5t^2
0 = -5t^2+10t+65
0 = 5t^2-10t-65
0 = t^2-2t-13
solve using the "quadratic equation" to get
t = {4.74, -2.74}
throw out the negative solution leaving:
t = 4.74 seconds
.
Details of quadratic equation follows:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=56 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4.74165738677394, -2.74165738677394. Here's your graph:

You can put this solution on YOUR website!
A man salary is 1850 dollars per month.Out of this 20 percent goes to his rent,690 dollars goes to foodand 940 dollars on other expenses.What percentage has he over spent?
.
Total expenditure:
.20(1850) + 690 + 940
370 + 690 + 940
1060 + 940
2000
.
amount overspent:
2000-1850 = 150
.
percentage over spent:
150/1850 * 100
0.08 * 100
8%

You can put this solution on YOUR website!
Solve this application using logarithms. Refer to the examples above.
How much principal, to the nearest dollar, should you invest at 4% in order to have $3,000 for a vacation to Europe in 3 years?
.
Assuming simple interest then:
a = pe^(rt)
3000 = pe^(.04*3)
3000 = pe^(.12)
3000/e^(.12) = p
2660.76 = p
nearest dollar:
$2661 = p

You can put this solution on YOUR website!
My son can clean the attic in 4 hours and I can do it in 2 hours. How long would it take if we worked together.
.
Let x = time (hours) for both
then
x(1/4 + 1/2) = 1
x(1/4 + 2/4) = 1
x(3/4) = 1
x(3) = 4
x = 4/3 hours
or
x = 1 hour and 20 minutes

You can put this solution on YOUR website!
The difference between the measure of an angle and it's suplementary is 36 find the measure of the two angles
.
Let x = measure of angle
then
180-x = supplement of angle
.
x - (180-x) = 36
x - 180+x = 36
2x - 180 = 36
2x = 216
x = 108 degrees
.
supplement:
180-x = 180-108 = 72 degrees
.
measure of the two angles: 108 and 72 degrees

You can put this solution on YOUR website!
if 8 is added to twice a number and this sum is multiplied by 4 the result is the same as if the number is multiplied by 4 and 8 is added to the product
.
Let n = the number
then
4(2n+8) = 4n+8
8n+32 = 4n+8
4n+32 = 8
4n = 24
n = 6
.
The number is 6

You can put this solution on YOUR website!
Completing the square
2x^2+7x-4
group x terms:
(2x^2+7x)-4
factor out the 2:
2(x^2+7/2x) - 4
2(x^2+7/2x+49/4) - 4 - (2)(49/4)
2(x^2+7/2x+49/4) - 4 - (49/2)
2(x^2+7/2x+49/4) - 8/2- (49/2)
2(x^2+7/2x+49/4) - 57/2
2(x+7/2)^2 - 57/2

You can put this solution on YOUR website!
10^(x-3)+11=1210
10^(x-3) = 1199
(x-3) = log(1199)
x = log(1199) + 3
x = 6.08

You can put this solution on YOUR website!
A rectangular room is 20 feet long and 10 feet wide. If you paint a red rectangle on the floor that is 8 feet long and 3 feet wide, what is the area of the floor in the room that will NOT be red? please help!
"area of room" - "red area"
(20*10) - (8*3)
(200) - (24)
176 square feet

You can put this solution on YOUR website!
y-2=1/2(x-4)
y-2= (1/2)x-2
y = (1/2)x-2+2
y = (1/2)x+0
y = (1/2)x (this is what they're looking for)
where
slope is 1/2
y-intercept is at 0

You can put this solution on YOUR website!
The legs of a right triangle are 15 meters and 9 meters. Find the length of the hypotenuse?
applying the Pythagorean theorem:
h^2 = 15^2 + 9^2
h^2 = 225 + 81
h^2 = 306
h = 17.49 meters

You can put this solution on YOUR website!
how long would it take to double an investment of 1000 at 9 percent compounded quarterly?
.
Use:
A = P(1+i/n)^(nt)
where
A is amount after time t (2P)
P is the principal (P)
i is the interest per year (.09)
n is the times compounded during the year (4)
t is number of years (what we're looking for)
.
A = P(1+i/n)^(t/n)
2P = P(1+.09/4)^(4t)
2 = (1+.09/4)^(4t)
2 = (1.0225)^(4t)
= 4t
= t
7.79 years = t

You can put this solution on YOUR website!
if h(r)= 2/3r-6, what is the value of h(-9)?
.
substitute -9 for r and solve:
h(r)= 2/3r-6
h(-9)= 2/3(-9)-6
h(-9)= 2(-3)-6
h(-9)= (-6)-6
h(-9)= -12

You can put this solution on YOUR website!
log(x+3)=2+log(x)
log(x+3) - log(x) = 2
log[(x+3)/(x)] = 2
(x+3)/(x) = 10^2
(x+3)/(x) = 100
(x+3) = 100x
3 = 99x
3/99 = x
1/33 = x

You can put this solution on YOUR website!
The measure of an angle is 5 times the measure of its supplement. Find the measures of the two angles
.
Let x = measure of angle
then
180-x = supplement of angle
.
x = 5(180-x)
x = 900-5x
6x = 900
x = 150 degrees (measure of angle)
.
supplement:
180-x = 180-150 = 30 degrees

You can put this solution on YOUR website!

Start with:
F = 9/5C+32
subtract 32 from both sides:
F - 32 = 9/5C
multiply both sides by 5:
5F - 160 = 9C
divide both sides by 9:
(5F - 160)/9 = C

You can put this solution on YOUR website!
Try this site -- it was featured on 60 Minutes:
http://www.khanacademy.org/
Use the "Watch" pull-down menu...

You can put this solution on YOUR website!
fx=x^2-6x-2
you could "complete the square":
fx=(x^2-6x)-2
fx=(x^2-6x+9)-2-9
fx=(x^2-6x+9)-11
fx=(x-3)^2+(-11)
so, vertex is at (3, -11)

You can put this solution on YOUR website!
Write an equation for the parabola with the vertex (1,3) that passes through (-2,-15)
.
Vertex form of a parabola is
y = a(x-h)^2 + k
where
(h,k) is the vertex
.
Since the problem gives you the vertex we can plug it in:
y = a(x-1)^2 + 3
Now, we plug in the given point and solve for a:
-15 = a(-2-1)^2 + 3
-15 = a(-3)^2 + 3
-15 = a(9) + 3
-18 = a(9)
-2 = a
.
So, our equation is now:
y = -2(x-1)^2 + 3

You can put this solution on YOUR website!
The dimensions of a brick, in inches, are 2 by 4 by 8. How many such bricks are needed to have a total volume of exactly 1 cubic foot?
Since they give you the dimensions of the brick in INCHES -- we begin by converting 1 cubic foot into cubic inches:
12*12*12 = 1728 cubic inches
.
You already found that the volume of a brick is 64 cubic inches
.
to find how many bricks are needed to make 1 cubic foot:
1728/64 = 27 bricks

You can put this solution on YOUR website!
If log(base 3)(5) = x, find log(base 3) (25/27) in terms of x
.
log(base 3)(25/27)
log(base 3)(25) - log(base 3)(27)
log(base 3)(25) - log(base 3)(3^3)
log(base 3)(25) - 3
log(base 3)(5*5) - 3
log(base 3)(5)+log(base 3)(5) - 3
x+x - 3
2x-3

You can put this solution on YOUR website!
2log(base e)(x) + log(base e)(7) = 1
log(base e)(x^2) + log(base e)(7) = 1
log(base e)(7x^2) = 1
(7x^2) = e^1
x^2 = e/7
x = .6232

You can put this solution on YOUR website!
2log(base9)x = 1/2 + log(base9)(5x + 18)
log(base9)x^2 = 1/2 + log(base9)(5x + 18)
log(base9)x^2 - log(base9)(5x + 18) = 1/2
log(base9)x^2/(5x + 18) = 1/2
x^2/(5x + 18) = 9^(1/2)
x^2/(5x + 18) = 3
x^2 = 3(5x + 18)
x^2 = 15x + 46
x^2-15X = 46
x^2-15X-46 = 0
Applying the "quadratic formula" yields:
x = {17.61, -2.61}
throw out the negative solution (extraneous) leaving:
x = 17.61
.
details of quadratic follows:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=409 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 17.6118742080783, -2.61187420807834. Here's your graph: