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Determine whether the lines are parallel, perpendicular, or neither.
1) and
2)
First, put your equations into the slope-intercept form: y = mx + b
1) and
2)
Notice that the slope (m) in equation 1) is 3 and the slope (m) in equation 2 is -1/3
Recall that perpendicular lines have slopes that are the negative reciprocal of each other.
So, equation 1) has a slope of 3 while equation 2) has a slope of -1/3 which is the negative reciprocal of 3. The lines are, therefore, perpendicular.

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First, you know that the perimeter is given as P = 400 ft. and you have the formula for the perimeter of a rectangle: P = 2L + 2W, so you can write:
Solve this for L
Divide both sides by 2.
You also know that the area of a rectangle is given by:
Now substitute the L=200-W from above into this equation and solve for W.
Simplify this.
You can rewrite this as:

Ok, now you have a quadratic equation which, when graphed, will show a parabola that opens downward (because of the negative coefficient).
This means that the vertex of this parabola will be a maximum and it represents the maximum value of A, the area. This is exactly what you are looking for, right?
So, let's find the value of W that will give us the maximum value of A.
Using the relationship: where: W is the width, as it was defined above. The a is the coefficient of the term, that's (-1), and the b is the coefficient of the term, and that's 200, so:


Now, when W = 100, then L = 200-100 = 100
So, to obtain the maximum area from the given perimeter of 400 ft, the width must be 100 ft and the length must be 100 ft.
In othe words, the patio will be a 100 by 100 ft square.
When you graph the quadratic equation, you will see the following parabola:

This shows you the relationship between the width, W, (the horizontal axis) and the area, A, (the vertical axis).

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Solve for x:
Apply the quotient rule for logarithms to the left side:
Now, if then A = B, so...
Multiply both sides by 3.
Subtract x from both sides.
Add 9 to both sides.
Divide both sides by 2.

Check: Substitute x = 7 into the original equation.

Using your calculator to find the natural logs:
= 1.3863 and...

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Factor completely:
1)

2)
First, factor a 3.
Now, can you see that the parentheses contain the difference of two squares?:.
The difference of two squares can be factored thus:
Applying this to your problem, you will get:
...and there it is!

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Convert:
to:
from.
Use the process known as "completing the square"
You want to make the constant term here equal to the square of half the x-coefficient (that's the -6).

So you must add a 1 to the 8 to make the required 9. But to keep the same equation, you must also subtract 1 to compensate for the added 1.
Now rearrange this as follows:
Factor the parentheses.
...and there you have it! Compare with:

Here: a = 1, h = 5, and k = -1

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Calculate F for C = -10, 0, 15, 100
Just substitute the given numbers for C in the formula and solve for F.
C = -10




So, If C = -10 then F = 14.
C = 0



So, if C = 0 then F = 32
Now do exactly the same for C = 15 and for C = 100

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It appears as though you have multiplied instead of dividing.
= =

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Solve for x:
Apply the law of exponents for logarithms to the left-hand side.
Subtract from both sides.
Rewrite the this in exponential form.

Solution:
x = 10

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Solve for a:
Multiply both sides by a.
Multiply both sides by 2.
Subtract 2 from both sides.
Factor this quadratic equation.
Apply the zero product principle.
and/or
The roots are:

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The area of a circle is given by:

As you probably know,the formula for the area of a circle is:

Set these two equal to each other:
Divide both sides by
Now factor the right-hand side.
Take the square root of both sides.

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Factor:
=

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Solve by substitution:
1) 8x-4y = 16
2) y = 2x-4 Substitute this for the y in equation 1) and solve for x.
1a) 8x-4(2x-4) = 16 Simplify and solve for x.
1a) 8x-8x+16 = 16
1a) 16 = 16
The two equations represent the same line and any value of x will satisfy the equations.

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Solve for x:
Subtract 5 from both sides.
Divide both sides by -3...remember to reverse the inequality sign (> to <).

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Let n be the required number. The opposite of n is -n. From the problem description, you can write:
-3n-5 = -2n-25 Simplify and solve for n. Add 3n to both sides.
-5 = n-25 Addd 25 to both sides.
20 = n
The number is 20

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Factor:
Do you see this as the difference of two cubes?

The difference of two cubes can be factored thus:
Applying this to your problem, where A = x and b = 5, we get:

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Factor:
Do you recognise this as the sum of two cubes?

You can factor the sum of two cubes as follows:
Applying this to your problem, where A = 10x and B = 1, you get:
Simplify.

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The standard form is: ax + by = c
y = 4x-11 Add 11 to both sides.
y+11 = 4x Now subtract y from both sides.
11 = 4x+y Rewrite as:
4x+y = 11 This is now in standard form.
Multiply everything by 3 to clear the fractions.
Now add x to both sides.
This is now in standard form.

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You have the correct answer...and so does your book!
Multiply both sides by 2.
Subtract 3 from both sides.
Finally, divide both sides by 2.
or

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Find the axis of symmetry: The axis of symmetry is the line that divides the curve represented by this equation, into two mirror-halves.
Since your equation is already in the standard form of:
you can find the axis of symmetry which is given by:
In this case, a = -1 and b = 6

The axis of symmetry is the line represented by the equation x = 3.
If you graph this, it would be a vertical line passing through the point (3, 0)
For creating the table of points, you select a value for the independent variable (that's x), substitute this into your equation and solve for the corresponding value of y. This will give you the (x, y) of one point. Do this several times to get several points for your table.
Then you plot these points on a piece of coordinate graph paper on which you have previously drawn the x-axis and the y-axis.
Here's an example of how you would generate one of these ponts:
Pick a value for x: x = 0 and substitute this into your equation and solve for y.
Set x = 0

For x = 0, y = -2
So, for one of the points, you have (0, -2)
Do this for a few more points then plot them on graph paper and sketch the graph. The graph should look like this:

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Find the x-intercepts:
Since the x-intercepts occur at y = 0, set the equation to zero and solve for the x's.
This can be factored.
, so
x = 2 and x = -3

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What kind of help would you like?
What do you have to do with these two trinomial expressions?
Please clarify and re-post.

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Simplify:
Remove the parentheses and change all of the signs inside the parentheses.
This usually be written:

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Simplify:
This trinomial can be factored.
The factors will take the form: (x+m)(x+n) where m and n must meet the follwing restrictions:
m*n = -80 and
m+n = 2
How do we know this?
Well, when you multiply the two factors, you should get back the original trinomial, right? Right!...so, usinf FOIL:
= and if you compare this with the original trinomial, you can see that:
m+n = 2 and
m*n = -80
Since the sum of m and n is quite small (2), this would indicate that the absolute values of m and n are are very close to each other.
A wise choice would be:
m = 10 and n = -8 or
m = -10 and n = 8
because both of their products are -80.
Select the pair whose sum is 2, that has to be m = 10 and n = -8.
So, now you can write:

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By "solve" I expect you "simplify"
Simplify:

Now multiply the exponents inside the parenthese by the ones outside the parentheses.

Combine like-factors:

Remember that you can change the sign of the exponents by moving the factor down or up as the case maybe.
To simplify this expression, you want all the exponents to be positive.

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First, you can indicate an exponent by using the caret (^) following the variable or number, thus:
(r^4)^4
It will look even better if you use three opening curly brackets before the expression or equation and three closing curly brackets after the expression or equation:
Is this what you intended?
If so, then using the laws of exponenets, you would multiply the two exponents to get:

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Problem A:
If the mandated slope is not to exceed (rise over run) and the steps (rise) are 2 feet high, you can write the proportion:
Simplify and solve for x ft.
feet.
The base of the ramp has to be 24 feet from the building.
Since the allowable slope is and the run is 1 foot or 12 inches, then the allowable rise would be 1 inch.

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The way you solve these problems is just replace the x in the function with the number given.
a) If f(x) = 5x-2, find:
f(4)-f(3)
First, to find out what f(4) is, you replace x with 4 in the function f(x) = 5x-2, so:
f(4) = 5(4)-2
f(4) = 20-2
f(4) = 18
Similarly for f(3)
f(3) = 5(3)-2
f(3) = 15-2
f(3) = 13
Now, f(4)-f(3) = 18-13 = 5
b) For f(9)-f(8)
f(9) = 5(9)-2
f(9) = 45-2
f(9) = 43
Similiarly for f(8)
f(8) = 5(8)-2
f(8) = 40-2
f(8) = 38
Now, f(9)-f(8) = 43-38 = 5
You should get the picture by now.
d) The given function can be written as an equation in the slope-intercept form: y = mx+b where m is the slope and b is the y-intercept.
Your function can be similarly written:
y = 5x-2 where the slope m = 5 and the y-intercept, b = -2
So you can see that the slope of the given function is the same as the the differences given by:
f(x)-f(x-1)

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1) The solution to is (5, -2).
What is the value of c?
Since you have been given the solution of (5, -2) you can substitute x = 5 and y = -2 into the given equation and solve for c.
Simplify.
Subtract 10 from both sides of the equation.
Finally, divide both sides by 2.

2) If g(x) = 2x+3 find g(9) Substitute 9 for x in the function.
g(9) = 2(9)+3
g(9) = 18+3
g(9) = 21
3)If , find h(4) Substitute 4 for x in the function.



If y varies directly as x, you can write: y = kx where k is the constant of proportionality. To find the value of k, susbstitute the given x = 3/2 and y = 1/4
Multiply both sides by

Now you have:
Substitute x = 54.

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Well, Silly Sally ought to ask her math teacher for help on this before she decides.
If she accepts the $25.00-offer, she will, of course, have $25.00 at the end of the two-week period.
If, however, after consulting with her math teacher, she decides to accept the second offer, she would soon see that this is the better offer because, after 14 days, she would get a total of pennies. This equals $163.83:

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A linear equation represents a straight line on a graph.
A system of linear equations would be more than one line.
Let's say the system of linear equations represents two straight lins on a graph.
To solve such a system of linear equatins means to find the point (x, y) at which these two lines intersect.
If the two lines do indeed intersect, then you can find the point of intersection algebraically or by graphing the two lines and inspecting the graph to find the point of intersection. This is called a "consistent system".
If the two lines do not intersect, then there are two posibilities:
1) They are parallel, in which case, there is no point of intersection and thus, no solution to this system of equations. This is called an "inconsistent system".
2) The two lines are collinear (one lies on top of the other), in which case, there is an infinite number of solutions because any point that lies on one of the lines will also lie on the other line. This is a "consistent system" and the equations are "dependent equations">

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Solve for y:
Add the fractions on the left side. The common denominator is 4y
Multiply both sides by 4y
Subtract 3y from both sides.
Finally, divide both sides by 33.
or y = 0.8484...