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To solve this you use the Pythagorean theorem, which says;
+=
So we just plug into the equation the values given;
+=
49+=625
subtract 49 from each side;
=625-49
=576
Now to get rid of the square you are going to find the sqroot;
=
b=24
Hope you understand
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It is in slope-intercept form,
slope =
y-intercept=-3
So plot the point (0,-3) on a graph, and with the slope of , plot your next point. you should actually do at least three points.
So your going to sttart at the point (0,-3), go p 5 units and to the right 1. That is your next point, then from that point go up 5 units and to the right 1. That is point 3 and you connect those with a straight line and that is your graph!

hope you understand
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First you need to find the slope;
m=
m=
m=
Now that we have slope we can plug in the points given to get the y-intercept;
Y-Y1=m(X-X1)
y-2=(x-5)
y=x-5+2
y=x-3
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Doesn't the equation actually read;
+6x+8
If so you can not add + 6x, they are not like terms;
You would factor;
(x+4)(x+2)
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I would be glad to help when I can. You can e-mail me anytime, I just can't guarantee when and how often I will be available. You can also just keep posting questions on this site and they should be answered.
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Try this sight;
www.hotmath.com, when you enter go into the Algebra tap, and at the bottom of that page is hotmath algebra, click on that.
It looks like you divided 4 by 2 which you should do is add 2x to both sides.
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Sorry we did not get to your problem til today, hope this helps!
For each eqution you are going make a table choosing values for x and solving the eqution for y;
1)3x-y=6
x|y
----
1|
2|
0|
So when x=1;
3(1)-y=6
3-y=6
-y=6-3
-y=3
y=-3
One solution; (1,-3)
When x=2;
3(2)-y=6
6-y=6
-y=6-6
y=0
2nd solution; (2,0)
When x=0;
3(0)-y=6
o-y=6
-y=6-0
-y=6
y=-6
3rd so;ution;(0,-6)
Now see if you can do the next one; for the next problems ,you will do the same thing, but then you graph them;
y=x
x|y
---
1|
2|
0|
when x=1;
y=(1)
First point (1,1)
when x=2;
y=(2)
2nd point; (2,2)
when x=0;
y=(0)
3rd point (0,0)
Now graph;

Now see if you can graph the others, if you have problems let me know
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15First you need to put the equation in slope-intercept form;
y=mx+b
4x+5y=15
5y=15-4x
5y=-4x+15
y=-x+15
So now y-intercept = 15, and slope is -
So on the graph you will plot the point (0,15), and from there and with the slope of -, you will plot your next point.
From point (0,15) you will go down 4 units and to the left 5.
When you have 3 points you connect those with a line.

Hope you understand
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Let x = the first integer
x+1 = second integer
x+2 = third integer
x+(x+1)+(x+2)=-33
3x+3=-33
3x=-36
x=-12
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Let x = the first integer
let x+2 = the second integer
x+(x+2)=96
2x+2=96
2x=94
x=47
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=
Multiply each side by 7;
(7)=(7)
=x
5}=x
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4p<-2
First divide 4 from each side;
<
p<
2+p>-5
Subtract 2 from each side;
2+p-2>-5-2
p>-7
Hope you understand
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THese are already in slope-intercept form, so you ould graph them;
eq.1;
y-intercept=-1
slope =
eq.2;
y-intercepr=1
slope =
So on the graph you will make a your first point at (0,-1)
From that point you will go up 2 units and to the right 1;
Your next point should be (1,1);
Then from there go up 2 units and right 1;
3rd point (2,3);
Eq.2;
You will start at point (0,1);
Fom that point go up 1 unit and to th right 1, your second point should be (1,2);
From that point go up 1 unit and to the right, 3rd point (2,3), lets do 1 more point;
so from point (2,3) go up 1 unit and to the right 1 (3,4)
Where those lines intersect, that point will be the solution for both eq.

Hope you understand
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Formula for perimeter of regtangle;
p=2l+2w;
With the values given solve the equation;
p=120
l=3w
120=2(3w)+2w
120=6w+2w
120=8w
15=w
So the width = 2(15)
w=30
l=3w=3(15)=45
check;
120=2(45)+2(15)
120=90+30
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This can be solved different ways;
we will solve it be substitution;
We will take eq.2 x=6-2y
and substitute that for x in eq.1;
2(6-2y)-2y=18
12-4y-2y=18
12-6y=18
-6y=18-12
-6y=6
y=-1
Now lets plug that into eq.2 for y;
x=6-2(-1)
x=6+2
x=8
Hope you understand
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Formula for a perimeter;
p=2l+2w
Now fill in the equation with the given values;
p= 82cm
l=w+5
82=2(w+5)+2w
82=2w+10+2w
82=4+10
72=2w
18=w
So the width =
the length = +5
l=
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5x+30y
Factor out GCF;
5(x+6y)
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There are diferent ways to solve this, and yes one is by graphing;
You make a table choosing values for x and then solving the equation for y;
So lets pick values for x;
when x=1
-x+y=2
-(1)+y=2
y=2+1
Y=3
So one point would be(1,3);
And if you plugeg that into the equation;
x+y=4
(1)+(3)=4
Now see if you can get two more points and graph the equation
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First distribute the -5 and the 4;
-20x+20+20x+20=x-10
40=x-10
40+10=x
50=x
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3x-7=2x+8
subtract 2x from both sides;
3x-7-2x=2x+8-2x
x-7=8
Now add 7 to both sides;
x-7+7=8+7
x=15
Hope you understand
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+=2
The LCD=21, so you multiply the first equation by 7, the second equation by 3;
+=2
+=2
=2
=2
Now multiply each side by 21;
10x+13=42
10x=42-13
10x=29
x=2.9
Hope this helps
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Let x be the =first integer
x+1 = the second intger
4x+8(x+1)=68
4x+8x+8=68
12x+8=68
12X=60
X=5
The first integer = 5 and the second integer;
x+1=5+1=6
Hope you understand
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3ax+6ay
factor out 3a;
3a(x+2y)
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this is actually the cube root of 8, not 3(squareroot 0f 8);
=4
Hope you understand
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For this equation you make a table choosing values for x and solving the equation for y;
x|y
---
-1|
3|
-3|
So when x=-1;
7(-1)+2y=5
-7+2y=5
2y=5+7
2y=12
y=6
X=-1, y=6
7(3)+2y=5
21+2y=5
2y=5-21
2y=-16
y=-8
So when x=3, y=-8
7(-3)+2y=5
-21+2y=5
2y=5+21
2y=26
y=13
When x=-3, y=13
Hope you understand
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Let x be the amount he invested at 5%,
10,000-x=amount invested at 4%
so we have;
5%x+(10,000-x)4%=470
5%x+400-4%x=470
400+1%x=470
1%x=70
x=7000
So if $7,000 was invested at 5%;
then $7,000-10,000=$3,000
$3,000 wasinvested at 4%
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Let x=pencils that cost .15
so; x+7=pencils that cost .35
.15x+.35(x+7)=3.45
.15x+.35x+2.45=3.45
.50x+2.45=3.45
.50x=1
x=2
So there were 2 pencils at .15;
and there were 9 pencils at .35.
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Let x=ribbons that cost .15
then x=ribbons that cost .20
so we have;
.15x+.20=1.20
.15x+.15x=1.20
.30x=1.20
x=4
So the ribbons that cost .15 is 4;
and the ribbons that cost .20= (4)=3
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(9 - 5)2 + 5 + 4² =
You would follow Order Of Operations to solve this (PEMDAS)
Parenthsis first;
(9-5)2+5+=
(4)2+5+=
8+5+=
Exponents;
8+5+16=
then add;
13+16=29
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-x-5y=30
2x-7y=25
We will solve this by elimination, that means you want to eliminate one variable so you can solve the equation for the other, you need to add the equations together to be able to eliminate a variable;
Before we do this you need to make one of the variables exact opposites of each other so they cancel out;
So we will multiply 2 to eq.1;
(2)-x-5y=30
-2x-10y=60
Now we can add the equtions together;
-2x-10y=60
2x-7y=25
----------
-17y=85
Now that one variable was eliminated, solve for y;
-17y=85
y=-5
Now plug the answer you got for y into one of the equaitons and solve for x;
-x-5(-5)=30
-x+25=30
-x=5
x=-5
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Add 3 to both sides;
m-3+3<-17+3
m<-14
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