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find the number of real number solutions for the equation
x^2-13x+42=0
factoring:
(x-6)(x-7) = 0
x = {6, 7}

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Starting with:

then, applying "log rules":

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what is 83 out of 96 percentage?
83/96 * 100
0.865 * 100
87%

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The height of a soccer ball that is kicked from the ground can be approximated by the function:
y = -16x^2 + 80x
where y is the height of the soccer ball in feet x seconds after it is kicked.
.
Find the time it takes the soccer ball to reach its maximum height: seconds
Vertex of parabola is the max.
Time when it hits the max is at the "axis of symmetry":
x = -b/(2a)
x = -80/(2(-16))
x = -40/(-16)
x = 40/16
x = 2.5 seconds
.
What is the soccer ball’s maximum height: feet
plug the value of x found above back into the original equation:
y = -16x^2 + 80x
y = -16(2.5)^2 + 80(2.5)
y = 100 feet
.
Find the time it takes from the moment the soccer ball is kicked until it returns to the ground: seconds
set y to zero and solve for x:
y = -16x^2 + 80x
0 = -16x^2 + 80x
0 = -16x(x - 5)
x = {0, 5}
0 is when it was first kicked
so the answer is
x = 5 seconds

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F(x)= -2/(x - 1) (find domain)
.
The domain specifies all valid values that 'x' can take.
The ONLY restriction is if the denominator is zero (can't divide by zero).
.
setting denominator to zero and solve for x:
x - 1 = 0
x = 1 (this is the ONLY number x can't be)
.
Therefore, the domain is all real numbers except 1
Or, interval notation:
(-oo, 1) U (1, +oo)
where oo stands for infinity

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Store gives a discount to 4 of every 10 shoppers. What percent of the shoppers would receive a discount?
4/10 * 100
.4 * 100
40%

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solve

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The difference when a number z is subtracted from sixteen is two.
.
Let z = a number
then
16 - z = 2

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What must be the next point to have a slope of 3/4 if the first point is (4,5)?
.
Remember, slope is rise/run
So, for a slope of
3/4
identical slope is also:
(-3)/(-4)
.
Considering 3/4 as the slope:
if you started at an arbitrary point (x,y)
the next point would be (x+4, y+3).
if you started at (4,5)
the next point would be:
(4+4,5+3)
(8,8)
.
Considering (-3)/(-4) as the slope:
if you started at an arbitrary point (x,y)
the next point would be (x-4, y-3).
So, given that (x,y) is (4,5)
the next point would be:
(4-4,5-3)
(0,2)

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If QRST is a rectangle with QT = 50 and RS = 4x + 8, find x.
.
QT = RS (opposite sides of a rectangle are equal)
50 = 4x + 8
42 = 4x
10.5 = x

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35=1/3b(5) solve for b v=1/3bh
.
35=1/3b(5)
dividing both sides by 5:
7=1/3b
multiplying both sides by 3:
21 = b

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Your answer is correct:
(3x^2+4)(2x^2+3)
I can rewrite the above as:
(2x^2+3)(3x^2+4) (multiplication is commutative)
(3+2x^2)(4+3x^2) (addition is commutative)
this gives you what the book had.

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The letters of the word HONESTY are written on slips of paper, and are placed in a box. A slip of paper is chosen at random. What is the probability that:
.
total number of letters = 7
.
a. the letter is a vowel?
vowels are E, O and Y
probability = 3/7
.
b. the letter is a consonant?
consonants are H, N, S, and T
probability = 4/7
.
c. the letter is H?
probability = 1/7
.

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The line is a "horizontal line":
y = 8

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x^2-11x+30=0
x^2-11x = -30
take 1/2 'b', square it and add to both sides:
x^2-11x+(11/2)^2= -30+(11/2)^2
x^2-11x+121/4= -30+121/4
(x-11/2)^2 = -120/4+121/4
(x-11/2)^2 = 1/4
take square root of both sides:
x-11/2 = +-1/2
x = +-1/2 + 11/2
x = {10/2, 12/2}
x = {5, 6}

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I took a test of 50 questions and got 42 correct what is my percentile on this test?
42/50 * 100
0.84 * 100
84%

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I have to write an equation for a line that goes through 0,5 and is parallel to y=5/2x+3
slope of y=5/2x+3 is 5/2
plug the slope (5/2) and the given point (0,5) into the "point-slope" form:
y - y1 = m(x - x1)
y - 5 = (5/2)(x - 0)
y - 5 = (5/2)x
y = (5/2)x + 5 (this is what they're looking for in "slope-intercept" form
.
And another one is how to graph an inequality -4x-3y ≥ -7
put into "slope-intercept" form:
-4x-3y ≥ -7
-3y ≥ 4x -7
3y <= -4x +7
y <= -(4/3)x + 7/3
.
Begin by drawing a solid line:
y = -(4/3)x + 7/3
And, then because it is <= (less than or equal) to the line, shade the area BELOW the line.

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Find the nth term, the fifth term, and the eighth term of the geometric sequence..
For a geometric sequence, if A is the first term, and R is the ratio
of any two adjacent terms, then the nth term is given by the formula
.
A*R^(n-1)
.
64, 16, 4, 1 ......
R (ratio) is 1/4
A is 64
.
.
So, for:
an= 64(1/4)^(n-1)
.
a8= 64(1/4)^(8-1)
a8= 64(1/4)^7
a8= 4^3/4^7
a8= 1/4^4
a8= 1/256

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Use the remainder theorem to find f(c).
f(x)=2x^3-x^2+8x-4; c=2
.
Using synthetic division:
.
2.|.2..-1...8..-4
........4...6..28
------------------
....2...3..14..24
.
Since the remainder is 24
f(2) = 24

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If I have 176 problems, and answer 31 correctly, what is the percentage?
.
31/176 * 100
0.176 * 100
17.6%

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I would like to know the beginning amount if 2% of the beginning amount equals $500.00.
.
Let x = "the beginning amount"
then
.02x = 500
x = 500/.02
x = $25,000

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answer: 7a^2

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ln x - ln (x-4) = ln 5
ln x/(x-4) = ln 5
x/(x-4) = 5
x = 5(x-4)
x = 5x-20
0 = 4x-20
20 = 4x
5 = x

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Thirty gallons of a 14% acid solution mixed with 60 gallons of a 20% acid solution yield 90 gallons of an x% acid solution. What is the value of x?
.
.14(30) + .20(60) = (x/100)(90)
4.2 + 12 = 9x/10
16.2 = 9x/10
162 = 9x
18 = x

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(-2x) to the 4th power. How do you solve this equation?

this is equivalent to:

an even number of negative numbers multiplies to be positive:

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Speed of sound through water caries by temperature
s=-0.0276t^2 + 9.1558t + 4354.7 (between freezing and boiling)
s= speed in feet/second, t= temperature Fahrenheit
I dropped a loud waterproof buzzer in the ocean. My friend who was 4700 feet away heard it 1 second later. What is the temperature of the water? (nearest degree fahrenheit)
.
Set s to 4700/1 and solve for t:
4700 = -0.0276t^2 + 9.1558t + 4354.7
0 = -0.0276t^2 + 9.1558t - 345.3
Using the "quadratic equation" we get:
x = {43.4, 288.3}
Throw out the 288 because it is outside the boiling point leaving:
x = 43 degrees
.
Details of quadratic formula:

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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=45.70755364 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 43.3888373932807, 288.34304666469. Here's your graph:

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Working together, two people can complete a task in 8 hours. Working alone, one person takes 2 hours longer than the other to complete the task. How long would it take for each person to complete the task? (Round your answers to one decimal place.)
.
Let x = time (hours) it takes one person
then
x+2 = time (hours) it takes second person
.
8(1/x + 1/(x+2)) = 1
multiplying both sides by x(x+2):
8(x+2 + x) = x(x+2)
8(2x+2) = x^2+2x
16x+16 = x^2+2x
16 = x^2-14x
0 = x^2-14x-16
since we can't factor we
apply "quadratic formula" to get:
x = {15.1, -1.1}
throw out the -1.1 (extraneous) leaving:
x = 15.1 hours (one person's time)
.
second person's time:
x+2 = 15.1+2 = 17.1 hours
.
Answer: 15.1 hours and 17.1 hours
.
details of quadratic formula:

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=260 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 15.0622577482985, -1.06225774829855. Here's your graph:

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Hospitals use radioactive substance iodine-131 in their researches.A hospital purchased 40 grams of the substance.Eight days later,when a doctor wanted to use some of the iodine-131,he found out that only 20 grams remained.Predict the amount remaining two weeks after purchase.
A = Pe^(kt)
determine exponential decay constant k:
20 = 40e^(k*8)
.5 = e^(k*8)
ln(.5) = k*8
ln(.5)/8 = k
.
Our equation is now:
A = 40e^(t*ln(.5)/8)
.
Now we can answer:Predict the amount remaining two weeks after purchase.
two weeks is equivalent to 14 days:
thus t =14
A = 40e^(t*ln(.5)/8)
A = 40e^(14*ln(.5)/8)
A = 40e^(-1.213)
A = 11.89 grams

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The unit's digit of a two-digit number is twice the ten's digit. Twice the original number is 12 more than number in reversed order. What is the original number?
.
Let t = value of ten's digit
then
2t = value of unit's digit
.
from:"Twice the original number is 12 more than number in reversed order." we get
2(10t + 2t) = 10(2t) + t + 12
2(12t) = 20t + t + 12
24t = 21t + 12
3t = 12
t = 4 (value of ten's digit)
.
value of unit's digit:
2t = 2(4) = 8
.
Answer: 48

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37*150 = 5550 tiles

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What is the sixth term of (x + y)8?
(x + y)^8
8C5 x^(8-5)y^5
8C5 x^3y^5
8!/5!(8-5)! x^3y^5
(6*7*8)/(3)! x^3y^5
(6*7*8)/(3*2*1) x^3y^5
(6*7*8)/(6) x^3y^5
(7*8) x^3y^5
56 x^3y^5