You can put this solution on YOUR website!
form of horizontal hyperbola:
(x-h)^2/a^2 - (y-k)^2/b^2 = 1
.




a=
b=
8 + 20 = c^2
28 = c^2
= c
.
vertex:
(0,0)
.
foci:
(0,+-)
.
asymptotes:
y = +-(b/a)x
y = +-x
y = +-x

You can put this solution on YOUR website!
log(2x + 3)=log 7
2x + 3 = 7
2x = 4
x = 2

You can put this solution on YOUR website!
First problem:
4g^2-32g=0
factor out common factor of 4g:
(4g)(g-8)=0
setting each term to zero:
g = {0, 8}
.
Second problem:
3m^2=-6m
3m^2+6m = 0
factor out common factor of 3m:
(3m)(m+2) = 0
setting each term to zero:
m = {0, -2}

You can put this solution on YOUR website!
x^2-4y^2-2x-24y-39=0
reorder terms:
x^2-2x-4y^2-24y = 39
group terms:
(x^2-2x)-(4y^2+24y) = 39
(x^2-2x)-4(y^2+6y) = 39
complete squares:
(x^2-2x+1)-4(y^2+6y+9) = 39+1-36
(x-1)^2-4(y+3)^2 = 4
(x-1)^2 /4 - (y+3)^2 = 1
.
This is a horizontal hyperbola
(h,k) is (1,-3)
a is 2
b is 1

You can put this solution on YOUR website!
3 ( log 5 - log 3 ) - ( log 5 - 2 log 6 ) = 2 - log n , find n.
.
3 ( log 5 - log 3 ) - ( log 5 - 2 log 6 ) = 2 - log n
3log 5 - 3log 3 - ( log 5 - 2 log 6 ) = 2 - log n
log 5^3 - log 3^3 - ( log 5 - 2 log 6 ) = 2 - log n
log 125 - log 27 - ( log 5 - 2 log 6 ) = 2 - log n
log 125 - log 27 - ( log 5 - log 6^2 ) = 2 - log n
log 125 - log 27 - ( log 5 - log 36 ) = 2 - log n
log 125 - log 27 - log 5 + log 36 = 2 - log n
log 125/27 - log 5 + log 36 = 2 - log n
log 125/(27*5) + log 36 = 2 - log n
log (125*36)/(27*5) = 2 - log n
log (125*36)/(27*5) = 2 - log n
log (125*36)/(27*5) - 2 = -log n
-[log (125*36)/(27*5) - 2] = log n
10^(-[log (125*36)/(27*5) - 2]) = n
10^(-[log (4500)/(27*5) - 2]) = n
10^(-[log 900/27 - 2]) = n
10^(-[log 100/3 - 2]) = n
10^(-[1.52287874528 - 2]) = n
10^(0.4771212547196624372950) = n
3 = n

You can put this solution on YOUR website!
If y varies inversely as x, and y=18 when x=3, find y when x = 8.
y=____(simplify your answer.)
.
Inverse variation:
y = k/x
using:y=18 when x=3 we can find k:
18 = k/3
54 = k
.
our equation:
y = 54/x
now we can answer:find y when x = 8
y = 54/8
y = 6.75

You can put this solution on YOUR website!
If log[2](7) = a and log[2](5) = b express in terms of a and b the formulas
i)
log[2](35)
log[2](7*5)
log[2](7) + log[2](5)
a + b
ii)
log [2](2.8)
log [2](7 * .4)
log [2](7 * 4/10)
log [2](7) + log [2](4/10)
log [2](7) + log [2](4) - log [2](10)
log [2](7) + log [2](2^2) - log [2](5*2)
log [2](7) + log [2](2^2) - (log [2](5)+log [2](2))
log [2](7) + log [2](2^2) - (log [2](5)+log [2](2^1))
log [2](7) + log [2](2^2) - (b+1)
log [2](7) + log [2](2^2) -b-1
a + 2 -b-1
a-b+1

You can put this solution on YOUR website!
the max population that earth can sustain is 40 billion. if the current population is 4.2 billion, in how many years will the max population be reached? Assume that each year the population is 2% more than the previous year.
.
Exponential growth equation:
A = Pe^(rt)
the problem give us:
P is 4.2
A is 40
r is .02
.
40 = 4.2e^(.02t)
40/4.2 = e^(.02t)
ln(40/4.2) = .02t
ln(40/4.2)/.02 = t
112.69 = t
or
113 years = t

You can put this solution on YOUR website!
40% OF A HOUSE NUMBER IS 48 WHAT IS THE NUMBER OF THE HOUSE
.
Let x = the house number
then
.40x = 48
x = 48/.40
x = 120

You can put this solution on YOUR website!
Find the equation of the circle that is tangent to the x-axis and the circle is at (-7,4).
.
Plotting the center on graph, we can see that the distance between the center and the x-axis is 4. Therefore, the radius is 4.
.
Standard form of a circle is:
(x-h)^2 + (y-k)^2 = r^2
where
(h,k) is the center and r is the radius
.
plug in our data:
(x-(-7))^2 + (y-4)^2 = 4^2
(x+7)^2 + (y-4)^2 = 16

You can put this solution on YOUR website!
Log3 (2x+1)=2
(2x+1)= 3^2
2x+1 = 9
2x = 8
x = 4

You can put this solution on YOUR website!
-30m^3n^4-5m^4
factor out a -5:
-5(6m^3n^4+m^4)
factor out m^3:
-5m^3(6n^4+m)

You can put this solution on YOUR website!
Y=-0.04x^2+0.6x+2
.
Maximum is at vertex:
x-value of vertex is "axis of symmetry":
x = -b/(2a)
x = -0.6/(2*(-0.04))
x = -0.6/(-0.08)
x = 0.6/(0.08)
x = 7.5
Max height:
Y=-0.04(7.5)^2+0.6(7.5)+2
Y= 4.25 meters (max height)
.
Max distance, we set Y to zero and solve for x:
0=-0.04x^2+0.6x+2
0=0.04x^2-0.6x-2
0=0.02x^2-0.3x-1
applying the "quadratic formula" yields:
x = {17.81, -2.81}
throw out the negative solution (extraneous) leaving
x = 17.81 meters (max distance)
.
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=0.17 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 17.8077640640442, -2.80776406404415. Here's your graph:

You can put this solution on YOUR website!
2a^2-46a+254=0
first, divide both sides by 2:
a^2-23a+127=0
applying the "quadratic formula" yields:
a = {13.80, 9.21}
.
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=21 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 13.7912878474779, 9.20871215252208. Here's your graph:

You can put this solution on YOUR website!
if y varies directly as x, and y=9 when x=4, find y when x=16
.
When you see "direct variation" think:
y = kx
.
To find k, use "y=9 when x=4":
y = kx
9 = k(4)
9/4 = k
.
so, our equation is:
y = (9/4)x
.
now, we can answer:
find y when x=16
y = (9/4)x
y = (9/4)(16)
y = (9)(4)
y = 36

You can put this solution on YOUR website!
from pipe a it takes 4 hours to fill the tank.from pipe b it takes 8 hours empty the tank.if the both pipes are opened how many hours to fill the tank?
.
Let x = time (hours) to fill tank w/both pipes open
then
x(1/4 - 1/8) = 1
x(2/8 - 1/8) = 1
x(1/8) = 1
x/8 = 1
multiply both sides by 8:
x = 8 hours

You can put this solution on YOUR website!
logx-log2=3
log(x/2)=3
x/2 = 10^3
x/2 = 1000
x = 2000

You can put this solution on YOUR website!
log(x-3) + log(x+2) = log(4x)
adding two logs is equivalent to multiplication:
log(x-3)(x+2) = log(4x)
now, we can eliminate the logs from both sides:
(x-3)(x+2) = (4x)
x^2-x-6 = 4x
x^2-5x-6 = 0
(x+1)(x-6) = 0
x = {-1, 6}
we throw out the -1 (extraneous solution) leaving
x = 6

You can put this solution on YOUR website!
-2-6-18-54..., N=7
.
Nth term of geometric series:
an = a1*r^(n–1)
.
r = 3
n = 7
a1 = -2
.
a7 = (-2)*3^(7–1)
a7 = (-2)*3^6
a7 = (-2)*729
a7 = -1458
.
answer: -1458

You can put this solution on YOUR website!
Find an equation of the line that passes through (4, 2); perpendicular to 2x-3y=2
.
find slope of:
2x-3y=2
2x=3y+2
2x-2=3y
(2/3)x-2/3=y
slope is 2/3
a line perpendicular must have a slope that is the "negative reciprocal": -3/2
.
plug slope (-3/2) and point (4,2) into the "point-slope form"
y - y1 = m(x - x1)
y - 2 = (-3/2)(x - 4)
y - 2 = (-3/2)x - (-3/2)4
y - 2 = (-3/2)x - (-6)
y - 2 = (-3/2)x + 6
y = (-3/2)x + 8 (answer)

You can put this solution on YOUR website!
5.) A chemist mixes liquid that's 87% gas. Together with another liquid that's 93% gas, to obtain 6 gallons that has a blend of 88% gas. How much of the 93% did the chemist use?
A.) 1
B.) 3
C.) 5
D.) 6
.
Let x = amount (gallons) of 93% gas
then
6-x = amount (gallons) of 87% gas
.
.93x + .87(6-x) = .88(6)
.93x + 5.22-.87x = 5.28
.06x + 5.22 = 5.28
.06x = .06
x = 1
.
Answer: A

You can put this solution on YOUR website!
log(base 3)√45 - log(base 3)√5
log(base 3)√45/√5
log(base 3)√(45/5)
log(base 3)√9
log(base 3)3
log(base 3)3^1
1 (answer)

You can put this solution on YOUR website!
Ln(x-1) + ln (x^2-3) - 1/2ln (y+1)
Ln(x-1) + ln (x^2-3) - ln (y+1)^(1/2)
ln(x-1)(x^2-3) - ln (y+1)^(1/2)
ln(x-1)(x^2-3)/(y+1)^(1/2)

You can put this solution on YOUR website!
Put in "standard form" of a circle:
(x-h)^2 + (y-k)^2 = r^2
.
x^2 + y^2 + 5x − y + 2 = 0
x^2 + y^2 + 5x − y = -2
x^2 + 5x + y^2 − y = -2
(x^2 + 5x) + (y^2 − y) = -2
(x^2 + 5x+ 25/4) + (y^2 − y + 1/4) = -2 +25/4+1/4
(x^2 + 5/2)^2 + (y^2 − 1/2)^2 = -8/4 +25/4+1/4
(x^2 + 5/2)^2 + (y^2 − 1/2)^2 = (-8+25+1)/4
(x^2 + 5/2)^2 + (y^2 − 1/2)^2 = 18/4
(x^2 + 5/2)^2 + (y^2 − 1/2)^2 = (3sqrt(2)/2)^2
.
center: (-5/2, 1/2)
radius: 3sqrt(2)/2

You can put this solution on YOUR website!
I can help you. Email your questions directly to me at nerdybill@gmail.com and I can help you through the semester.
.
The issue currently is solutions to a system?
Using graphs, the "intersection" is the solution (although not very accurate).

You can put this solution on YOUR website!
h= -16t^2+80t+6 (is correct)
.
when the ball is on the ground, h is zero. So, set h to zero and solve for t:
0 = -16t^2+80t+6
0 = 16t^2-80t-6
0 = 8t^2-40t-3
solve using the "quadratic formula" yields:
x = {5.07, -0.07}
throw out the negative value (extraneous) leaving
x = 5.07 seconds
.
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=1696 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 5.07390753524675, -0.0739075352467502. Here's your graph:

You can put this solution on YOUR website!
I'm assuming you meant:
ln(2) + ln(x) =5
ln(2x) =5
2x = e^5
x = (e^5)/2
x = 74.21

You can put this solution on YOUR website!
In the equation y=ab^(x-h)+k, how does the value of k affect the graph?
.
The 'k' is the "vertical shift".
If positive, moves graph up k units.
If negative, moves graph down k units.

You can put this solution on YOUR website!
What is the average arithmetic mean of (4x+3), (-8x+-2) and (7x+8)
.
"sum" divided by 3:
[(4x+3)+(-8x+-2)+(7x+8)]/3
[4x+3-8x-2+7x+8]/3
[3-4x-2+7x+8]/3
[1-4x+7x+8]/3
[1+3x+8]/3
[3x+9]/3
x+3

You can put this solution on YOUR website!

take log base 5 of both sides:

apply "change of base":

You can put this solution on YOUR website!
what is the measure of each interior angle of a 40 sided polygon
.
Interior Angle = 180° - 360°/n
Interior Angle = 180 - 360/40
Interior Angle = 180 - 9
Interior Angle = 171°