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Can someone help me with this please. If the measure of an angle is 23 degrees 17' 18", what is the measure of its supplement?
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Two angles are "supplementary" if the sum of the two angles equals 180.
.
180 00' 00"
23 17' 18"
.
Borrowing from the 180 and then subtracting we have:
179 59' 60"
23 17' 18"
-----------
156 42' 42"
.
That is,
156 degrees 42 minutes and 42 seconds

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Where is "cuts the y-axis" is equivalent to the y-intercept.
.
To find it, set x = 0 and solve for y:
3x+12y=24
3(0)+12y=24
0+12y=24
12y=24
y = 2
.
Therefore, it "cuts the y-axis" at (0, 2)

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Standard equation of a circle is:
(x - h)^2 + (y - k)^2 = r^2
.
We "complete the square" to put our equation into the standard form:
x^2+y^2-2x-2y+2=0
x^2+y^2-2x-2y = -2
(x^2-2x)+(y^2-2y) = -2
(x^2-2x+1)+(y^2-2y+1) = -2+1+1
(x-1)^2+(y-1)^2 = 0
.
Radius = 0

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If Y= f(x)= 5-x-3x^2
Find
a) the Y-intercept
y = -3x^2 - x + 5
Set x = 0 and solve for y:
y = -3(0)^2 - 0 + 5
y = -0 - 0 + 5
y = 5
So, y-intercept is at (0, 5)
.
b) the X-intercept
Set y = 0 and solve for x:
y = -3x^2 - x + 5
0 = -3x^2 - x + 5
Since we can't factor, we must use the quadratic equation.
Doing so yields:
x = {-1.468, 1.135}
Note: details at the end
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c) the vertex
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vertex form:
y= a(x-h)^2+k
.
Starting with:
y = -3x^2 - x + 5
y = -3(x^2 + (1/3)x) + 5
y = -3(x^2 + (1/3)x + 1/36) + 5 + 1/13
y = -3(x + 1/6)^2 + 66/13
y = -3(x - (-1/6))^2 + 66/13
.
Therefore, vertex is at (-1/6, 66/13)
.
.
.
Details of solving the quadratic for part b 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=61 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -1.46837494598444, 1.13504161265111. Here's your graph:

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Let x = first of three consecutive numbers
x+1 = second of three consecutive numbers
x+3 = third of three consecutive numbers
.
3x = 2(x+1) + 4
3x = 2x + 2 + 4
3x = 2x + 6
x = 6
.
Our three consecutive numbers are:
6, 7, and 8

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Let x = length
width is given as 15 cm
.
Perimeter = 2(width + length)
.
72 < 2(15+x)
dividing both sides by 2:
36 < 15+x
subtracting both sides by 15:
21 < x
.
This says that the length has to be "greater than" 21 cm.

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8x-7=5x+2
Add 7 to both sides:
8x-7+7=5x+2+7
8x=5x+9
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Subtract 5x from both sides:
8x=5x+9
8x-5x=5x+9-5x
3x=9
.
Divide both sides by 3:
(3x)/3=9/3
x=3

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Let x = distance Woody above ground
then
hypotenuse = 17-x
.
From Pythagorean:
x^2 + 10^2 = (17-x)^2
x^2 + 100 = 289 - 34x + x^2
100 = 289 - 34x
-189 = -34x
-189/-34 = x
5.559m = x

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Draw a graph of the line passing through the points(-6,-7) and(-3,-5).Does the
point (3,-1)also lie on this line?
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Algebraically:
slope m = (-5+7)/(-3+6) = 2/3
.
y - y1 = m(x - x1)
y - (-5) = (2/3)(x - (-3))
y + 5 = (2/3)x + 2
y = (2/3)x - 3 (this is the equation of the line)
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Testing the point:(3,-1)
y = (2/3)x - 3
-1 = (2/3)3 - 3
-1 = 2 - 3
-1 = -1
.
So, YES, the point does lie on the line.
.

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The equilibrium point is when supply and demand are equal.
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Supply: p= (q+10)^2 , Demand: p=388-16q-q^2
.
Notice BOTH equation defines 'p'. Set them equal to each other then solve for 'q':
(q+10)^2 = 388-16q-q^2
Expanding the left side with FOIL:
(q+10)^2 = 388-16q-q^2
(q+10)(q+10) = 388-16q-q^2
q^2 + 20q + 100 = 388-16q-q^2
Move all terms to the left:
2q^2 + 20q + 100 = 388-16q
2q^2 + 36q + 100 = 388
2q^2 + 36q - 288 = 0
Divide both sides by 2:
q^2 + 18q - 144 = 0
Factoring the left:
(q+24)(q-6) = 0
.
q = {-24, 6}
A negative solution does not make sense so:
q = 6

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The vertex form is:
y= a(x-h)^2+k
where
(h,k) is the vertex
.
For more info, see:
http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php
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For your problem:
y= x^2 + 18x - 4
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You must "complete the square":
y= (x^2 + 18x) - 4
Take half of 18 and square it:
y= (x^2 + 18x + 81) - 4 - 81
y= (x^2 + 18x + 81) - 85
y = (x+9)^2 - 85 (this is what they're looking for)

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Assuming you are expected to solve a system linear equations using the "elimination method":
.
2x + 2y = 8
4x - 6y = 36
.
multiply both sides of the top equation and add it to the second:
6x + 6y = 24
4x - 6y = 36
------------
10x = 60
Dividing both sides by 10:
x = 6
.
Now, we plug the value above into either equation to find y. Let's pick the top one:
2x + 2y = 8
2(6) + 2y = 8
12 + 2y = 8
2y = -4
y = -2
.
therefore:
(x,y) = (6, -2)

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cost of items = 9.55 + .95 = 10.5
tax on items = 10.5(.08) = 0.84
.
Total amount spent = 0.84 + 10.5 = 11.34
.
Amount left = 50 - 11.34 = 38.66
.
Percent left = 38.66/50 * 100 = 0.7732 * 100 = 77.32%

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9^X = 1/243
Take log9 (log base 9) of both sides:
X = log9(1/243)
X = log9(1) - log9(243)
X = log(1)/log(9) - log(243)/log(9)
X = 0/log(9) - log(243)/log(9)
X = -log(243)/log(9)
X = -2.5

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You can use the "addition method".
Starting with:
5x-2y = 22
x+2y = 2
.
Add the two equation together to get:
5x-2y = 22
x+2y = 2
----------
6x = 24
Dividing both sides by 6
x = 4

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A quadratic looks like:
y = ax^2 + bx + c
.
The problem gives you three points:
(1,-2),(2,-2),(3,-4)
Which relates to:
(1,-2)
-2 = a(1)^2 + b(1) + c
-2 = a + b + c
.
(2,-2)
-2 = a(2)^2 + b(2) + c
-2 = 4a + 2b + c
.
(3,-4)
-4 = a(3)^2 + b(3) + c
-4 = 9a + 3b + c
.
Now, you have basically a "system of equations":
-2 = a + b + c
-2 = 4a + 2b + c
-4 = 9a + 3b + c
.
Can you finish the problem from here?

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For:
2x^4+15x^2-8
you do not need to use grouping.
.
Factoring would give you:
(2x^2+1)(x^2-8)

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The HP Laser Jet 9000 works twice as fast as the Laser Jet 2300. If the machines work together, a university can produce all its staff manuals in 15hr. Find the time it would take each machine, working alone, to complete the same job?
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Let x = speed of Laser Jet 2300
then
2x = speed of Laser Jet 9000
.
15(x + 2x) = 1
15x + 30x = 1
45x = 1
x = 1/45
the above says, completes a job in 45 hours (speed of Laser Jet 2300)
.
Laser Jet 9000:
2x = 2(1/45) = 2/45 = 1/22.5
the above says, completes a job in 22.5 hours (speed of Laser Jet 9000)
.

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my teacher says we need the bottom equation to solve the top equation then to find the answer to the bottom equation after.
0.3x-0.2y = 0.5 (top equation)
x- 2y = -5 (bottom equation)
.
Taking the "bottom equation", let's solve for 'x':
x- 2y = -5
adding 2y to both sides we get:
x = 2y -5
.
Now, we take the above, and substitute it into the "top equation":
0.3x-0.2y = 0.5
0.3(2y -5)-0.2y = 0.5
distributing the 0.3 to terms inside the parenthesis:
0.6y-1.5 -0.2y = 0.5
combining y's:
0.4y-1.5 = 0.5
adding 1.5 to both sides:
0.4y = 2
y = 2/0.4
y = 5 (solution for y)
.
Finally, we take the above solution of y and plug it back into the bottom equation and solve for x:
x- 2y = -5
x- 2(5) = -5
x- 10 = -5
adding 10 to both sides:
x = 5 (solution for x)
.
Solution:
y=5
x=5
.
The above method is called the "substitution method".

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√2 x² - 4x – 7 √2 = 0
.
The coefficients are:
a = √2
b = -4
c = 7√2
.
The determinant (stuff under the radical in the quadratic equation):
b^2 - 4ac
= (-4)^2 - 4(√2)(7√2)
= 16 - 4(2)(7)
= 16 - (8)(7)
= 16 - 56
= -40
.
Since the determinant is negative, you will have two complex solutions.
.
See:
http://www.purplemath.com/modules/quadform3.htm
for additional information

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Tony put some money into a savings account and deposited no more into this account for one year. At the end of the year, there was $5885 in the account, including 7% of the original amount for interest. How much did he deposit originally?
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Let x = original amount deposited
then
x + .07x = 5885
x(1+.07) = 5885
x(1.07) = 5885
x = 5885/1.07
x = $5500.00
.
.
.

After a 15% discount, an item was sold for $61.20. What was the original price of the item?
Let x = original price
then
x - .15x = 61.20
x(1 - .15) = 61.20
x(.85) = 61.20
x = 61.20/(.85)
x = $72.00

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Let x = hours it takes for both:
then
x(1/4 + 1/6) = 1
x/4 + x/6 = 1
6x + 4x = 24
10x = 24
x = 2.4 hours
or
2 hours and 24 minutes

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.
If two angles are supplementary, their angles add up to 180.
If two angles are complementary, their angles add up to 90.
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Let x = measure of the angle
.
Supplement = 180-x
Complement = 90-x
.
Finally, from: "The supplement of an angle measures 37 degrees more than twice its complement." we get:
180-x = 2(90-x) + 37
180-x = 180-2x + 37
-x = -2x + 37
x = 37 degrees

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Suppose y varies directly as x, and y=-65 when x=-26. Write a direct variation equation that relates x and y.
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If "y varies directly as x" it is in the form of:
y = kx
where k is a constant
.
Using the values provided, you can find k.
y = kx
-65 = k(-26)
-65/(-26) = k
2.5 = k
.
So, our equation is:
y = 2.5x

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Wite the slope-intercept form of an equation for a line that passes through (-1,0) and is perpendicular to the graph of 3x-5y=20
.
First, determine the slope of
3x-5y=20
.
Do this by putting it into the "slope-intercept" form:
y = mx + b
where
m is slope
b is y-intercept
.
3x-5y=20
-5y = 3x + 20
y = (-3/5)x + (-3/5)20
y = (-3/5)x - 12
.
So, if we want to be "perpendicular" to the line above, the NEW slope must be the "negative reciprocal" of -3/5.
Let M = our new slope
M(-3/5) = -1
M = 5/3
.
The NEW line now has
slope of 5/3
passing through (-1,0)
.
Plug the above into the "point-slope" form:
y - y1 = m(x - x1)
y - 0 = (5/3)(x - (-1))
y = (5/3)(x + 1)
y = (5/3)x + 5/3 (this is what they're asking for)

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An 18-foot ladder is placed 6 feet from the wall. Approximately how high does the ladder reach?
.
Draw a diagram of the problem, it'll help you "see" the solution easier.
.
Basically, you have a right-triangle so you can apply Pythagorean theorem:
.
Let h = height the ladder reaches
then
h^2 + 6^2 = 18^2
h^2 = 18^2 - 6^2
h^2 = 324 - 36
h^2 = 288
h = sqrt(288)
h = 16.97 feet

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x+2y=-9
4x+2y=6
.
Multiply both sides of top equation by -1:
-x-2y=9
4x+2y=6
.
Now, add the two equation together:
-x-2y=9
4x+2y=6
-------
3x =18
x = 6 (solution for x)
.
Substitute the above back into the original top equation and solve for y:
x+2y=-9
6+2y=-9
2y=-15
y=-15/2 (solution for y)

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Find the slope of the line that passes through(-2,9.5) and (4,5).
.
m (slope) = (y2 - y1)/(x2 - x1)
.
Plugging in our values into:
m = (y2 - y1)/(x2 - x1)
m = (9.5 - 5)/(-2.9 - 4)
m = (9.5 - 5)/(-2 - 4)
m = (4.5)/(-6)
m = - 4.5/6
m = - 1.5/2
m = - (3/2)/2
m = - 3/4

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I have 28 coins in my pocket, they are all either nickels and dimes. There are eight more nickels than dimes. The value of these coins is 1.90. How many nickels? How many answers should I have?Define my variable, define in terms? Translate this information into an equation? Thank You guys you all are life savers in my class.
.
Let d = number of dimes
and n = number of nickels
.
Since we have two unknowns, we'll need two equations.
.
from "I have 28 coins in my pocket"
n+d = 28 (equation 1)
from "There are eight more nickels than dimes." we get:
n = d+8 (equation 2)
.
Solve equation 1 for 'd':
n+d = 28
d = 28-n
.
Substitute the above into equation 2 and solve for n:
n = d+8
n = 28-n+8
2n = 28+8
2n = 36
n = 18 (number of nickels)
.

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2x^2+19x+35
(2x + 5)(x + 7)

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You will need to apply "log rules".
Review them at:
http://www.purplemath.com/modules/logrules.htm
.
log3 + 2 = log x
log3 - log x = -2
log(3/x) = -2
3/x = 10^(-2)
3/x = 0.01
3 = 0.01x
3/0.01 = x
300 = x