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5(x+2)=40
x+2=40/5
x+2=8
x=8-2
x=6

The number is 6.

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Let the number be x.
5x=x-52
4x = -52
x = -52/4
x = -13

Check:
5(-13)=-65
and
-13 -52 = -65

So yes, both sides match. x=-13

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1. Let x = the number, the other number would be x-19
x + x-19 = 65
2x-19=65
2x=84
x=84/2
x=42
The other number is 42-19=23. So the two numbers are 42 and 23.
2. Similar to the last one...

x+x-7 = 39
2x-7=39
2x=46
x=46/2
x=23
The other number is 16.

I don't understand the 3rd question, sorry.

Hope that helps for the first two!

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A square has 4 equal sides, so the perimter is:
P = 4+4+4+4
P = 16 cm

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There is a very convenient formula for solving these types of problems. It is D=ST, where D=distance, S=Speed, and T=Time.

You are given that S= 5 mph and T = 3 hours.

D=ST
D=5*3
D=15

You can travel 15 miles.

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You will need to use the equation D=vt for this question, where D=distance, v=velocity (or speed) and t=time.

Let's isolate for time:

t = D/v

and list everything we know (where b stands for boat, w stands for water, d stands for downstream and u stands for upstream):
Vb= 15 mph
Dd = 8 miles
Du = 4 miles
Vd = 15+Vw
Vu = 15-Vw

Note that when you're travelling downstream with the current, you add the boat and water speed together. When you're travelling upstream against the current, you subtract.

We know that t=D/v, and we know that tu = td, so:

Dd/Vd = Du/Vu
8/(15+Vw) = 4/(15-Vw)

Cross-multiply to solve for Vw:

8(15-Vw) = 4(15+Vw)
120-8Vw = 60+4Vw
60 = 12Vw
Vw = 60/12
Vw = 5

The speed of the water is 5 mph.

Hope that helps!

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2a+5=a+9
Think of an algebraic equation like a balance or a teeter totter. Any operation you do to one side, you must do to the other side. Let's try to get a on the left side, and all the numbers on the right side:

2a+5=a+9
2a-a+5 = a - a + 9
a+5 = 0+9
a+5 = 9
a = 9 - 5
a = 4

Let's check it to see if it's right:
2a+5=a+9
2(4) + 5 = 4 + 9
8+5 = 4+ 9
13 = 13

Yes, it's correct. a=4

Hope that helps!

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We know that the formula for the perimeter of a rectangle is:
P = 2L + 2W

In this question, we are given the values for perimeter, P, and the width, W. We can substitute these values into the equation and solve for L:

P = 2L + 2W
49 = 2L + 2(6.5)
49 = 2L + 13
49 - 13 = 2L
36 = 2L
36/2 = L
L = 18

The length of the porch is 18 feet. Hope this helps!

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V=P(1+r/n)^nt

Let's write down what we are given:

P = 10000
r = 0.051
t = 10 years
n = 12 (because it is compounded monthly, or 12 times per year)

V=P(1+r/n)^nt
V = 10000(1+0.051/12)^(12*10)
V = 16634.93

So he will have $16,634.93 after ten years.

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Let x = the larger number
Let y = the smaller number

You have two variables, so you need two equations:

Equation 1: x-y=16
Equation 2: 5y=2x-8

You can now use elimination or substitution to solve. I will use substitution:

x-y=16
x=16+y

Substitute this into the second equation:

5y=2x-8
5y=2(16+y)-8
5y=32+2y-8
5y=24+2y
3y=24
y=8

Now find x:
x=16+y
x=16+8
x=24

So the two numbers are 8 and 24.

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L=w+2

Area = Lw
35 = (w+2)w
35 = w^2 +2w
0 = w^2 + 2w -35
Factor (or use the quadratic formula):
0=(w+7)(w-5)
w=-7, w=5
The width can't be a negative number, so we can't choose w=-7. The width must be 5.

We know that the length is 2 more than the width, so the length must be 7.

Dimensions:
L=7
w=5

Area = 7x5=35

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Just to clarify, is this your question?



If so, here's how you do it:


First, get rid of the brackets by distributing the 6:

Next, subtract 5p from both sides, so that the right side is zero:

Rearrange so that it is in standard form:


To solve this, you can either factor it (which is a pain!) or use the Quadratic Formula.

If you factor it, you will end up with:
(2p-3)(3p+2) = 0
p=3/2 or p=-2/3

If you use the Quadratic Formula:


p=3/2 or p=-2/3

So as you can see, you get the same answer whether you factor it or use the quadratic formula.

Check out this link for a graph of the function: http://www.wolframalpha.com/input/?i=6p^2-5p-6%3D0

Hope this helps!

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The relationship between Distance, Speed and Time is found in this formula:

D=ST

You have D at T, and you're looking for S. First, let's change T from 30 minutes to 0.5 hours, so that our speeed will be in km/h.

D=ST
21 = S(0.5)
S = 21/0.5
S = 42 km/h

So the average speed is 42 km/h.

Hope this helps!

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Recall the general form for a quadratic equation:
ax^2 + bx + c

-2x^2 + 13x - 21

We will use the Decomposition Method for factoring.
First, multiply a*c = (-2)(-21) = 42

So you need to find two numbers that multiply to 42 and add up to the b term, +13. This is pretty easy: the numbers are 7 and 6.

Now the hard part is to decompose the b term, +13, into these two factors. Notice that I list 6x first, so that it pairs with the 2x^2, and the 7x second, so that it pairs with the 21 at the end.

-2x^2 + 13x - 21
-2x^2 + 6x + 7x - 21

Next, factor out the -2x and 7 from each. Note that you are left with identical terms, (x-3) for each.

-2x(x-3) + 7(x-3)

Combine the -2x and 7 into one bracket:

(-2x + 7)(x-3)
This leaves you with two answers, which you can find by setting each bracket to zero, and solving for x:
-2x+7 =0
7=2x
x=7/2

x-3=0
x=3

Hope this helps! Let me know if you're confused by anything.

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Recall the equation of a line, y=mx+b. We will be using a similar equation, but with snow, S, and time, t instead of y and x.

The rate of inches per hour represents the slope of the graph, m.
The y-variable would be the amount of snow, S.
The x-variable would be the time, t, in hours.

The function has three pieces:

i) S = t (slope = 1)
ii) S = 2t (slope = 2)
iii) S = t (slope = 1)

For the first piece, i), t=2, so the amount of snow is 2 inches.
For the second piece, ii) t=6, so the amount of snow is 12 inches.
For the third piece, iii) t=1, so the amount of snow is 1 inch.

In total, it snowed 15 inches.

Hopefully this makes sense. The graph is just three lines. The first and third pieces are identical, while the middle piece is a bit steeper, with a slope of 2.

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x+y=5
2x+y=6

Let`s isolate for x in equation 1:

x = 5-y

Now let`s substitute this value into 2x+y=6:

2(5-y) + y = 6
10 - 2y + y = 6
10 - y = 6
10 - 6 = y
y = 4

Now find x:

x=5-y
x=5-4
x=1

So the answer, as an ordered pair is: (1,4)

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Let x = number of $11.50 discs you bought
let y = number of $7.50 discs you bought

Two equations:
x+y=12 (because there are 12 disks bought in total)
11.50x + 7.50y = 110 (because the total cost is $110)

Use substitution or elimination to solve. I will use substitution.

y = 12-x

11.50x +7.50(12-x) = 110
11.50x + 90 -7.5x = 110
4x = 20
x = 5

So there were five $11.50 disks bought. This means there must have been seven $7.50 disks bought.

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The sine graph will look like this: http://www.wolframalpha.com/input/?i=y%3D2+sin(x/2)
(Copy and paste the URL if you can't click it.)

In any sine curve, the general equation is:

y=a*sinb(x-c) + d

Where a=amplitude, b=compression (determines period), c=phase shift (left or right shift), and d=vertical displacement (up/down shift)

In your question, a=2, b=1/2, and c=0, d=0.

So the amplitude is 2. This means that the curve goes up to a max of y=2 and a min of y=-2.

You can find the period by using this simple formula:
P = 2Pi /b
Your value of b is 1/2, so the period is:

P = 2Pi / (1/2)
P = 4Pi

So the period of this function is 4Pi, which you should be able to see from the graph on the link. In essence, this means that the curve was stretched out in the x-direction by double. If b=2, it would be compressed to a period of 1Pi.

Hope this helps!

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The difference of squares rule is this:

a^2 - b^2 = (a+b)(a-b)

In your case, a^2=36x^2 and b^2=9y^2, therefore:

36x^2 - 9y^2 = (6x+3y)(6x-3y)

That's it. It's factored!

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Let w = width
Let L = length

Length is 2 less than 7 times the width:
L = 7w - 2

Formula for area of a rectangle is A = w*L, and we know that A = 57

Substitute the formula for L into the equation, and solve for w:

A= w*L
57 = w(7w-2)
57 = 7w^2 - 2w
0 = 7w^2 - 2w -57

Use the quadratic equation (or WolframAlpha.com) to solve.

You should find that w=3
This means that L is:

L=7w-2
L=7(3)-2
L=21-2
L=19

So the dimensions are w=3, L=19.

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It appears as if you have three variables, but if you keep reading the question, you'll see you can actually express the three lengths in terms of the first.

We know the 3 lengths add up to 40.

Let's let x = the first length

We also know the second length is 4 times the first, so the second length is 4x. That means the third length must be 3x. Putting it all together:

x + 4x + 3x = 40
8x = 40
x = 40/8
x = 5

So the first length is 5 inches.

The second length is 5*4 = 20 inches
The third length is 3*5 = 15 inches.

Check that the three lengths add up to 40:

5+15+20 = 40

Yes, it works! Good job you're done.

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You have two variables, so you need to make two equations.

Let x = number of books bought online
Let y = number of books bought in store

There were 250 books sold in total:

x+y = 250

Their sales totaled $4995:

15x + 22.50y = 4995

Use elimination or substitution with the two equations to solve for x and y. I will use elimination, by multiplying the first equation by 15, then subtracting.

15x + 22.50y = 4995
15x + 15y = 3750
-----------------
0 + 7.50y = 1245

y = 1245/7.50
y= 166

Now find x:
x+y=250
x+166=250
x=250-166
x=84

So there were 84 books sold online, and 166 sold in the store. Hope this helps! Let me know if you need any more help.

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You have two variables, number of chickens and number of pigs. This means you need to algebra equations.

Let c = number of chickens
Let p = number of pigs

We know that there are 13 heads in total, so that means that:

c + p = 13

(Because each chicken and pig has one head each!)

We also know that there are 36 feet. Chickens have 2 feet, while pigs have 4 feet:

2c + 4p = 36

Now you have your two equations. Solve them with elimination or substitution.

c+p=13
2c+4p=36

Multiply the first equation by 2, then subtract:
2c+2p=26
2c+4p=36
---------
0 - 2p = -10
p = 5

Now find c:
c = 13 - p
c= 13-5
c = 8

So there are 8 chickens and 5 pigs.

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Roger studied for x hours
Her sister studied for (x+5) hours.

Together, they studied for 30 hours in total. You need to set up an algebra equation to model this question:

x + (x+5) = 30

Now collect like terms:

2x + 5 = 30
2x = 30 -5
2x = 25
x = 12.5

So Roger studied for 12.5 hours. That means his sister must have studied for 12.5+5 = 17.5 hours.

Check your work. Does 12.5+17.5 = 30?

Yes, it does! So that means this must be correct.

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There's a formula to find the angle total of a polygon if you know n, the number of sides.

Angle Total = (n-2) * 180

For this question, you know the angle total is 5400, so solve for n:

5400 = (n-2) * 180
5400 / 180 = n-2
30 = n-2
n = 32

So the polygon has 32 sides. It is called an Icosidodecagon, and you can view it here:

http://mathworld.wolfram.com/Icosidodecagon.html

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x+4y=19
5x+y+0
Let's solve this one by elimination method. Multiply the second equation by 4, then subtract it from the first equation:

x+4y = 19
20x +4y = 0
-----------
-19x = 19

x= -1

Plug this value into either equation to find y:
5x+y = 0
5(-1) + y = 0
-5 + y = 0
y = 5

So the solution is (-1,5) or x=-1, y=5.

Second question is weird because it has no nice answers. Are you supposed to write your answers as fractions or as decimals? I did it with fractions:

a-b=25
3a+4b=4
Multiply the first equation by 3, then subtract.

3a - 3b = 75
3a + 4b = 4
--------------
0 - 7b = 71

b = -71/7

Plug this into either equation to find a:

3a - 3(-71/7) = 75
3a + 213/7 = 75
3a = 75- 213/7
3a = 312/7
a = 312/21
a = 104/7

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Let h = number of hundred dollar bills
Let t = number of twenty dollar bills
the equation is:

100h + 20t = 400

Image that h is like the y-variable, and t is like the x-variable.
The graph would look like this: http://www.wolframalpha.com/input/?i=100y+%2B+20x+%3D+400
(copy this link into your web browser)

Try plotting this graph yourself on graph paper, and you should see a variety of combinations that are possible. Anything that falls on the line is possible.

For instance, if h=3, then t=5.
This makes sense because 100(3) + 20(5) = 400

Another possibility is if h=2, then t=10.
100(2) + 20(10) = 400

I will leave it up to you to find the last combination. Hint... keep going down the line as I've done.

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2/3 of $1500 is $1000, so her take-home pay is $1000.

I found this by multiplying $1500 * (2/3)

She spends 1/4 of this take-home pay on car payments.

$1000 * (1/4) = $250

Her car payments are $250.

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x + 5y =5
x=3-5y

The second equation already has x isolated, so let's substitute that value of x into the first equation:

x+5y=5
(3-5y) + 5y = 5
3 -5y + 5y = 5
3 + 0 = 5
3 = 5

This is not true, so it means there is no solution. This is because these two lines have identical slopes. They are parallel lines, so they never intersect.

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Find 5 percent of 64:
64*0.05 = 3.2


So there would be 3.2 defective calculators per batch, on average. If you want a whole number answer, you could round it down to 3.

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N=4x^2 + 5x +1

So they're telling you that N=85 because it says N is in thousands. You need to solve for x. Whatever number you get for x, add that to 1990 and you will find the year.

N=4x^2 + 5x +1
85=4x^2 +5x + 1
0 = 4x^2 + 5x -84

You now have a quadratic equation. You can solve this using the quadratic formula.



Where a = 4, b = 5 and c = -84

After doing the algebra for the quadratic formula (or using an online solver), you will find that there are two answers:

x = -5.25 or x = 4

Choose the positive answer, x=4, because it wouldn't make sense to be negative.

That means that there were 85,000 computers in this city in 1994.

Hope this helps!