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32 to the power n =2 how to find n
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you take log base 32 of both sides:

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I think you meant:

If not, please write back.
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Solve for C:
A(B)=1+C(D)
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we could write it without the parentheses:
AB = 1+CD
then
subtracting 1 from both sides we get:
AB - 1 = CD
finally divide both sides by D to get:
(AB-1)/D = C

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The manager of a farmer's market has 250 lb of grain that costs $1.40 per pound. How many pounds of meal costing $0.80 per pound should be mixed with the 250 lb of grain to produce a mixture that costs $1.05 per pound?
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Let x = amount (lbs) of $0.80 per pound meal added
then
.80x + 1.40(250) = 1.05(250+x)
.80x + 350 = 262.50 + 1.05x
350 = 262.50 + 0.25x
87.5 = 0.25x
350 lbs = x

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jimmy is a partner in an internet based coffee supplier. The company offers gourmet coffee beans for $11 per pound and regular coffee beans for $7 per pound. Jummy is creating a medium price product that will sell for $9 per pound. The first thing to go into the mixing bin was 10 pounds of the gourmet beans. how many pounds of the less expensive regular beans should be added?
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Let x = amount (pounds) of lest expensive beans ($7 per pound)
then
10-x = amount (pounds) of $11 per pound beans
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7x + 11(10-x) = 9(10)
7x + 110-11x = 90
110-4x = 90
-4x = -20
x = 5 pounds

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What is the value of f(2) for the function f(x) = 5x + 3?
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Simply substitute x with 2:
f(x) = 5x + 3
f(2) = 5(2) + 3
f(2) = 10 + 3
f(2) = 13
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Answer: 13

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a rhombus has a perimeter of 84 cm and an area of 252 cm square.find the lenght of the altitude
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Since all sides are equal, the length of one side is:
84/4 = 21 cm
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area = (1/2)ba
252 = (1/2)(21)a
504 = (21)a
504/21 = a
24 cm = a (altitude)

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take log base 2 of both sides:

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For my homework I need to use the distributive property to write 7x^2-11x in equivalent form as a product of two linear factors. Basically I don't have any idea what any of this means. Please explain the distributive property, and linear factors.
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They're asking you to "factor" the expression.
"Linear factors" are polynomials of degree 1.
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So, if we start with:
7x^2-11x
common to both terms is x, so "factor" it out:
x(7x-11) (this is what they want)

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(-5)^-2
1/(-5)^2
1/25

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To go over a tree, a golfer uses a 7-iron to hit the ball with an initial upward velocity of 80 feet per second.
a. Write a quadratic function that gives the height of the ball t seconds after it is hit.
I think that a. is h(t)= 80t-16t^2 but I'm not sure... (YES!)
b. Graph the function you found in part (a). (you can only give me the T chart.)
c. After how many seconds will the ball be at its maximum height?
t = -b/(2a)
t = -80/(2(-16))
t = -80/(-32)
t = 2.5 seconds
d. What is the approximate maximum height the ball will reach?
plug t=2.5 from b into original equation:
h(2.5)= 80(2.5)-16(2.5)^2
h(2.5)= 98.4 feet

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a medivac helicopter travels 78 km due south of its base to pick up a patient the helicopter then travels 93 km due north to a hospital the entire trips take 1.22h what is the avarage speed and the average velocity.
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total distance traveled = 78+93 = 171 km
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average speed = 171/1.22 = 140.2 km/hr

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a ball is thrown vertically upward from the ground. its distance in feet from the ground in t seconds is s=-16t^2+96t. after how many seconds will the ball be 128 feet from the ground
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Set s to 128 and solve for t:
s=-16t^2+96t
128=-16t^2+96t
dividing both sides by -16:
-8 = t^2-6t
0 = t^2-6t+8
factoring:
0 = (t-2)(t-4)
t = {2,4}
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answer:
the ball is 128 feet from the ground at
2 seconds and again at 4 seconds

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Working together it takes two computers 12 minutes to send out a company's email. If it takes the slower computer 30 minutes to do this job on its own, how long will it take the faster computer to do this job on its own?
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Let x = time (minutes) it takes for the faster computer to do the job alone
then
12(1/30 + 1/x) = 1
multiplying both sides by 30x:
12(x + 30) = 30x
12x + 360 = 30x
360 = 18x
20 minutes = x

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If I have 405 points out of 585 points. What is my grade?
405/585 * 100
0.69 * 100
69%
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Your grade would then depend on whether the instructor is grading on a "curve" or on an "absolute" scale.
On an "absolute" scale, you would be getting a D.
So, let's hope your instructor is grading on a "curve". In this case, your grade would depend on how well the rest of the class did.

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It would be undefined if the denominator is zero, so:
m^2-49 = 0
m^2 = 49
m = +- 7
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So, it is undefined if
m = -7
or
m = 7

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A ball is released 6 feet above the ground and thrown vertically into the air. The equation h=-16t^+112t+6 gives the height of the ball if the initial is 112 feet per second.
1. Write the equation of the axis of symmetry and find the coordinates of the vertex of the graph of the equation.
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axis of symmetry:
x = -b/(2a)
x = -112/(2(-16))
x = -112/(-32)
x = 3.5 (vertical line crossing at x=3.5)
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find, y-value when x=3.5:
-16t^+112t+6
-16(3.5)^+112(3.5)+6
202
So, vertex is at (3.5, 202)
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2. What is the maximum height above the ground that the ball reaches?
202 feet
3. How many seconds is the ball in the air?
set h=0 and solve for t:
h=-16t^+112t+6
0=-16t^+112t+6
applying the "quadratic formula" gives us:
x {-0.1, 7.1}
we can throw out the negative solution (extraneous) leaving
x = 7.1 seconds
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Details of quadratic formula 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=12928 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -0.0531676008879738, 7.05316760088797. Here's your graph:

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You are correct.
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You can check yourself... apply FOIL on
(c + 2)(c + 2)
and will get your original expression

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Your answer is correct. However, I'm not sure I followed how you got there.
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slope of (-4,1) and (-1,4):
m = (y2-y1)/(x2-x1)
m = (4-1)/(-1-(-4))
m = (4-1)/(-1+4)
m = 3/3
m = 1
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plug slope (above) and one point (-4,1) into "point-slope" form:
y - y1 = m(x - x1)
y - 1 = 1(x - (-4))
y - 1 = 1(x + 4)
y - 1 = x + 4
y = x + 5

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A guy wire attached to the top of a
30-foot-long pole is anchored 10 feet from the base
of the pole, as illustrated in the figure. Find the
length of the guy wire to the nearest tenth of a foot
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Apply Pythagorean Theorem:
Let x = length (feet) of wire
then
x^2 = 10^2 + 30^2
x^2 = 100 + 900
x^2 = 1000
x = 31.623
rounded to nearest tenth:
x = 31.6 feet

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I'll assume you meant log base 8:
log8(2x-1)=0
(2x-1)=8^0
2x-1=1
2x=2
x = 1

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Rewrite the quadratic equation in standard form by completing the square.
f(x)=x^2+8x+14
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f(x)=x^2+8x+14
f(x)=(x^2+8x)+14
f(x)=(x^2+8x+16)+14-16
f(x)=(x+4)(x+4)-2
f(x)=(x+4)^2-2 (this is the standard form)

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log[4](x)+ log[4](6x-7)=log[4]5
log[4](x)(6x-7)=log[4]5
(x)(6x-7)=5
6x^2 - 7x = 5
6x^2 - 7x - 5 = 0
6x^2 - 10x + 3x - 5 = 0
(6x^2 - 10x) + (3x - 5) = 0
2x(3x - 5) + (3x - 5) = 0
(3x - 5)(2x+1) = 0
x = {5/3, -1/2}
Since you can't take the log of a negative number, you can throw out -1/2 (extraneous) leaving:
x = 5/3

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On Thursday September 8, 2011 Arkansas State Senator Bruce Holland was convicted of fleeing a police officer. He was reportedly going 110 miles per hour during a 17 mile chase. Rounding to the nearest minute, how long did the chase last?
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Assuming he was traveling at 110 mph the entire time of the 17 mile chase (which, I'm sure he wasn't) then:
17/110 = .155 hours
or, about 9 minutes

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y= -6.25x²+ 150x + 7200
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The x-value of the vertex is at:
x = -b/(2a) (from the "quadratic formula" w/o the radical)
x = -150/(2(-6.25)
x = -150/(-12.5)
x = 150/12.5
x = 12
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To find the y-value, plug the above back into the equation:
y= -6.25x²+ 150x + 7200
y= -6.25(12)²+ 150(12) + 7200
y= 8100

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how do i find the x and y intercepts and slope of the equation 3x = -2
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3x = -2
x = -2/3
This is simply a vertical line that crosses the x-axis at -2/3
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x-intercept is at (0,-2/3)
y-intercept (none) runs parallel to the y-axis
slope is undefined since it is a vertical line

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Simplify by removing factors of 1
48v^10x^4/18v^4x^2
(6*8)v^10x^4/(6*3)v^4x^2
8v^10x^4/3v^4x^2
8v^4v^6x^4/3v^4x^2
8v^6x^4/3x^2
8v^6x^2x^2/3x^2
8v^6x^2/3

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f(x)= 3(x^2+5) Find f^-1(x), f^-1(27)
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Find f^-1(x):
y = 3(x^2+5)
switch the variables and solve for y:
x = 3(y^2+5)
x/3 = y^2+5
x/3 - 5 = y^2
sqrt(x/3 - 5) = y
or

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finding f^-1(27):




(that's plus or minus 2)

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Two cars leave town at the sime time traveling in opposite dirrections. One travels 70 mi/h and the other 55 mi/h. In how many hours will they be 250 miles apart?
apply the distance formula of d=rt
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Let x = time (hours) traveled
then
70x + 55x = 250
125x = 250
x = 250/125
x = 2 hours

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Classify the polynomial as constant, linear, quadratic, cubic, or quartic, and determine the leading term, the leading coefficient, and the degree of the polynomial.
f(x)=14-x^2
Ordered in highest to lowest degree:
f(x) = -x^2+14
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It is a "quadratic".
Leading term: -x^2
Leading coefficient: -1
Degree: 2

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State the domain of the rational function.
g(x)= x-8/(x+3)
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The "domain" specifies all possible values of x.
In this case, you just want to make sure the denominator is not zero because dividing by zero is undefined.
So, we set the denominator to zero to find the value x can't take:
x+3=0
x = -3
So, the domain is all real numbers except -3. Or, you can state it like:
(-oo, -3) U (-3, +oo)
where
oo stands for infinity