You can put this solution on YOUR website!
I will answer your first question. If you have more than one, you should post them separately.
If we call the length L and the width W, then remember that perimeter is:

We have that the length is 15 more than twice the width, so we can represent length by 2W+15. Thus we have:





So the width is 15 feet. Thus the length would be 2(15)+15=45 feet.

You can put this solution on YOUR website!
I assume the directions are to multiply out since there is no equal sign. We would use the FOIL (first, outside, inside, last) method to multiply this out.

You can put this solution on YOUR website!
Remember that the area of a triangle is:

where b is the base and h is the height. We are told in this problem that A=77 and that b is 3 more than h. So we can represent b with h+3. Thus we have the equation:




So we have that h=-14 or h=11. Since we can't have negative measurements, h must be 11. This means that b is 14 (since b is 3 more than h).

You can put this solution on YOUR website!
Let's call the length L and the width W. Then since the length is five times the width, we have that L = 5W. Now, remembering that the perimeter of a rectangle is 2L+2W, we have
2L+2W=108
Now using the fact that L=5W we have:
2(5W)+2W=108
10W+2W=108
12W=108
W=9
So the width is 9m, which makes the length 9*5=45m.

You can put this solution on YOUR website!
Remember that the diagonal of a square splits the square into 2 right triangles. So we can use Pythagorean's theorem. Remember that

where c is the hypotenuse. So the diagonal is the hypotenuse here, and thus c = 10. Now, since we are dealing with a square, all the sides are the same length, so a = b. So we have:

You can put this solution on YOUR website!
Since both the Mazda and Honda depend on the Nissan, let's name a variable for the Nissan's weight, N. Since the Mazda weighs 20 pounds more, then it weighs N+20. Since the Honda weighs 70 pounds more, it weighs N+70. So since all together they weigh 10,050, we have that
Nissan + Mazda + Honda = 10,050
N + (N+20) + (N+70) = 10,050
3N + 90 = 10,050
3N = 9,960
N = 3,320
So the Nissan weighs 3,320 lbs. Since the Mazda is 20 more, the Mazda weighs 3,340 lbs, and since the Honda is 70 lbs more, the Honda weighs 3,390 lbs.

You can put this solution on YOUR website!
The first thing we need to determine here is the slope of the line. Remember that if you have two points (x1,y1) and (x2,y2), the slope is:

So here, (x1,y1) is (6,-4) and (x2,y2) is (3,2), so the slope is:

Now, remember that if you have a point (x1,y1) and a slope m, the equation of the line is:
y-y1 = m(x-x1)
So we have
y-(-4) = -2(x-6)
y+4 = -2x+12
y = -2x + 8

You can put this solution on YOUR website!
Let's start by naming variables. Let's call the length L and the width W. Then the first sentence tell us that:
L = 2W - 2
Remember that the perimeter of a rectangle is P = 2L + 2W. So the second sentence tells us:
2L + 2W = 32
Now, in order to solve these two equations, notice that we can use the first equation to replace L with 2W - 2. This gives us:
2(2W - 2) + 2W = 32
4W - 4 + 2W = 32
6W - 4 = 32
6W = 36
W = 6
So the width is 6 cm. To finish the problem, we need to find the length, so let's substitute 6 in for W in the first equation:
L = 2(6) - 2
L = 12 - 2
L = 10
So the dimensions of the rectangle are 10 cm by 6 cm.

You can put this solution on YOUR website!
If our two numbers are x and y, to do this problem we just take it one sentence at a time.
"the sum of two numbers is 13"
This tells us that when you add our two numbers you get 13. So we have:
x+y=13
"two times the first number minus three times the second number is 1"
Two times the first number would be represented by 2x and three times the second number is represented by 3y. So we have:
2x-3y=1
So we have a system of equations:


Let's use the addition method to solve this system. If we multiply the first equation by 3 we will be able to eliminate the y's.


Now we add:


And using our first equation we have that y must be 5. So our two numbers are 8 and 5.

You can put this solution on YOUR website!
Remember that if you have a slope m and a point (x1,y1), the equation for the line is:
y-y1=m(x-x1)
So for the first problem we have m=2 and (x1,y1)=(2,4). So we have:
y-4=2(x-2)
y-4=2x-4
y=2x
The next two are similar, so this should help you complete that. For the question about slope, if you have two points (x1,y1) and (x2,y2) the slope is:

You can put this solution on YOUR website!


When solving a system of equations, you can either solve by substitution or adding. Most students prefer adding, so I will go with that method. The first step is to get both of the equations in the same form. I will do this by adding 6x to both sides in the first equation:


Next, we need to manipulate one or both of the equations in order to be able to get rid of a variable when adding. Notice that if we multiply the first equation by -1, the x's will be removed when added.


Now we add down the columns and obtain:

Now that we have found y, we substitute it back into one of the original equations in order to find x. I will use the second equation (it doesn't matter which one you use).




Thus the answer is (3,6).

You can put this solution on YOUR website!

To find the slope and y intercept, we need to solve this equation for y.



Remember now that in the equation y=mx+b, m is the slope and b is the y intercept. So here, the slope is 1/4 and the y intercept is -1/2.

You can put this solution on YOUR website!
Two lines are perpendicular if their slopes are opposite reciprocals of each other.
Example:
y=2x+9
y=(-1/2)x-3

You can put this solution on YOUR website!

The first step in writing this expression in standard form is to multiply both the numerator and denominator by the complex conjugate of the denominator. Remember that the complex conjugate of a+bi is a-bi. So here, we want to multiply the numerator and denominator by 3-9i.

This gives:

Now we combine like terms, remembering that i^2 = -1.

You can put this solution on YOUR website!

Our goal is to isolate z. The first step is to add 13 to both sides of the inequality.

Lastly, we divide both sides by 4:

You can put this solution on YOUR website!

The goal here is to isolate h. Our first step here is to distribute the 6 through on the right hand side.

Next, we subtract 21 from both sides of the inequality:

Now, subtract 6h from both sides:

Last, we divide both sides by -3, remembering that when you divide or multiply by a negative number you have to flip the inequality.

You can put this solution on YOUR website!

We want to isolate w, so the first step here would be to subtract 14 from both sides.

The last step in isolating w is to divide both sides by -6, remembering that you have to flip the inequality when multiplying or dividing by a negative number.

You can put this solution on YOUR website!
The volume of a pyramid with a square base is (1/3)(area of base)(height). Here, the area of the base is 6*6 = 36 and the height is 9. So the volume is (1/3)(36)(9) = 108 yd^3.

You can put this solution on YOUR website!
The mode of a set of numbers is the number that appears the most. In this case, it is 24.7.

You can put this solution on YOUR website!
Let's call the number x.
2x + 20 = -30

You can put this solution on YOUR website!
If you have slope, m, and a point (x1,y1), the equation is:
y - y1 = m(x - x1)
So we have
y - (-5) = -3(x - 4)
y + 5 = -3x + 12
y = -3x + 7

You can put this solution on YOUR website!
To determine the percentage of the total amount, all that is needed is division. For example, to find out what percent 68.31 is of 122.90, we divide 68.31/122.90 and get 0.5558. To turn this number into a percentage we multiply it by 100. So the percentage is 55.58%.

You can put this solution on YOUR website!
If you have two points (x1,y1) and (x2,y2), the midpoint is
((x1+x2)/2,(y1+y2)/2)
So we have:
((0+8)/2,(0+4)/2)
(4,2)

You can put this solution on YOUR website!
To solve this problem, you need to remember that the diagonal of a rectangle splits it into two right triangles. So to find the length of the diagonal we only need to use Pythagorean's theorem.

You can put this solution on YOUR website!

The problem here is that we have two logarithms. Our first step is too subtract log(x+1) from both sides.

Now, using one of the laws of logarithms (log(a) - log(b) = log(a/b)) we have:

Now we rewrite the problem in exponential form as:

Now multiply both sides by x+1 :





However, you cannot take the log of a negative number. Thus, this equation has no solution.

You can put this solution on YOUR website!
Let's call one number x and the other number y. Then from the first sentence we have

The second sentence tells us that

If we substitute 1.2y for x in the original equation we get



So one number is 90, and the other must be 108.

You can put this solution on YOUR website!

The first step here would be to distribute the 4 through the parentheses:


Now we combine like terms:

Add 4 to both sides:

Divide both sides by -5:

You can put this solution on YOUR website!
Area is length times width (or height), so here we have A = (2X)(x)

You can put this solution on YOUR website!
p = 2s + 2t

You can put this solution on YOUR website!
Remember that the equation for compound interest is:

Here, P = 1000, r = 0.05, A = 2000 (initial amount doubled) and n = 2. So we have:

Dividing both sides by 1000 gives

Now we take the log of both sides in order to get the exponent down:

Divide both sides by log(1.025):

Last, divide both sides by 2:

Using the calculator we have t = 14.04 years.

You can put this solution on YOUR website!
The first step in finding the equation is to determine the slope. Remember that the slope of the line passing through (x1, y1) and (x2, y2) is:

So in our case we have:

So our slope is m=2. Now, the equation for a line using the slope and one point is:
y - y1 = m(x - x1)
So using m=2 and (0, -1) we have
y - (-1) = 2(x - 0)
y + 1 = 2x
y = 2x-1