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Hi Ashley,
Graph f(x) = 2x + 4
:
f(x)=y on the coordinate system:
y=2x+4
Let x=0 and solve for y
y=2(0)+4
y=0+4
y=4, plot (0,4)
Now let y=0 and solve for x
0=2x+4
0-4=2x+4-4
-4=2x
-4/2=2x/2
-2=x Plot (-2,0)
Connect the points and you have this line:

Happy Calculating, Ashley!!!

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Hi Lyn,
E1) x - y = 5
E2) x + y = 3
:
For E1) let x=0 and solve for y:
0-y=5
-y=5
-1(-y)=-1(5)
y=-5 Plot (0,-5)
Now let y=0 and solve for x:
x-0=5
x=5 Plot (5,0)
Connect the points and you have this line:

For E2) let x=0 and solve for y:
0+y=3
y=3 Plot (0,3)
Now let y=0 and solve for x:
x+0=3
x=3 Plot (3,0)
Connect the points and you have a second line:

They intersect at: (4,-1)
Happy Calculating, Lyn!!!

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Hi Lyn,
I saw some questions by you about graphing inequalities. I can only graph equalities or I would have answered those also.
Can someone help me solve the system by graphing it for me?
I have to send it through the computer.
E1) x - 2y = 8
E2) x + y = -1
:
For E1, let x=0 and solve for y
0-2y=8
-2y/-2=8/-2
y=-4 Plot (0,-4)
Now let y=0 and solve for x:
x-2(0)=8
x-0=8
x=8 Plot (8,0)
Connect the points and you have a line:

For E2, let x=0 and solve for y:
0+y=-1
y=-1 Plot (0,-1)
Now let y=0 and solve for x:
x+(0)=-1
x=-1 Plot (-1,0)
Connect the points and you have a second line:

They intersect at (2,-3)
I think I did this one earlier today. Maybe it was for someone else.
Happy Calculating, Lyn!!!

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Here's one way to do it. I did this problem for someone else earlier today.
Graph f(x) = 3x + 2
f(x) is the same thing as y, so you graph this the same way as y=3x+2
Let x=0 and solve for y:
y=3(0)+2
y=0+2
y=2 Plot (0,2)
Let x=1 and solve for y
y=3(1)+2
y=3+2
y=5 Plot (1,5)
Connect the points and you have a line.

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Could you help?
Write 5^3=125 in logarithmic form.
Rule:==>>
log5(125)=3 The 5 should be smaller and a little lower.
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Evaluate log5(3125). I am not sure how to make the 5 small just below the g on log.
To evaluate this you have to use the cahnge of base formula and a scientific calculator.
Change of base formula is:or log(b)/log(a)
log5(3125)=ln(3125)/ln(5)=8.047189562/1.609437912=5
:
If you knew that 3125=5^5 then
log5(3125)=log5(5^5)=5
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Write the expression logb(x-1)+3logb(x-2)-2logb(x+3) as a single logarithm. Assume that the variables represent positive numbers.
Rules we'll use:
1.
2.
3.
:

rule 1
rule 2

:
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I'm not sure whether you meant 2 to be the base of the log or the coefficient of x. I'm going to solve this as a common log with 2 as the coeffiecient of x. If you want it to be the base just make 2 the base of all the logs and remove it as the coefficient of x.
:
Express the expression in terms of logarithm of x, y, and z.
:
Rules I'm using:
1.
2.
3.
:
rule 1&2. This might be all you need
rule 3
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Calculate log 4235 to four decimal places.
This is a scientific calculator problem, so I can't show you the work.
log 4235=3.626853415
log 4235=3.6269
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Ninety-five percent of cars are parked in one space in the parking lot. If 8 cars are taking two spaces, how many cars are parked in one space?
:
I am not sure if this is the easiest way to do this, but here's one way to do this.
If 95% parked in 1 space, then 100%-95%=5% parked in two spaces.
Let the total number of cars be x:
then
.05x=8
.50x/.05=8/.05
x=160
Once you find that then, 160-8=152 parked in one space.
You can also say, .95(160)=152 parked in one space.
:
Here's another way to set this up. Set up a proportion of 95% to 5% equal to x to 8:



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The sum of the perimeters of two squares is 40 inches. the sum of their areas is 58 square inches. What are the dimensions of the squares?
:
Let the sides of one square be: x
Let the sides of the other square be:y
:
The perimeter of a square is: , p=perimeter, s=side
E1) Therefore the sum of the perimeters is 40 is:
:
The area of a square is: , A=area, s=side
E2) Therefore the sunm of their area is 58 is:
:
Therefore you have two equations and two unknowns. Solve E1 for either variable, I'm going with y.
4x+4y=40
-4x+4x+4y=-4x+40
4y=-4x+40

y=-x+10
Substitute that into E2 for y and solve for x:







Factor
(x-3)(x-7)=0 set each parentheses = to 0
x-3=0 and x-7=0
x-3+3=0+3 and x-7+7=0+7
x=3 and x=7
If you were to substitute either x into E1 you'd get the other x
4(3)+4y=40
12+4y=40
4y=28
4y/4=28/4
y=7 You can check 7 for yourself, you'll get 3.
One square is 3 in x 3 in
the other is 7 in x 7 in
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Hi Lyn,
Lane invested $14,000, part at 15% and part at 2%. If the total interest at the end of the year is $1,060, how much did she invest at 15%?

(A) $8,000 (B) $7,000 $6,000 (D) $5,000
:
Let the amount at 15% be: x
Then the rest of the 14,000 is invested at 2%: 14,000-x
The formula for simple interest is , I=interest, P=principle, r=rate, and t=time (in years)
:
The interest earned at 15% is: (15/100)x=.15
The interest earned at 2% is (2/100)(14,000-x)=.02(14,000-x)
The total interest whe you add them together is: 1,060
:
Problem to solve:
.15x+.02(14,000-x)=1,060
(100).15x+(100).02(14,000-x)=(100)1,060
15x+2(14,000-x)=106,000
15x+28,000-2x=106,000
13x+28,000=106,000
13x+28,000-28,000=106,000-28,000
13x=78,000
13x/13=78,000/13
x=6,000
The amount invested at 15% is: x=$6,000
:
Now for fun, find out how much was invested at 2%.
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Hi Lyn,
Graph f(x) = 3x + 2
f(x) is the same thing as y, so you graph this the same way as y=3x+2
Let x=0 and solve for y:
y=3(0)+2
y=0+2
y=2 Plot (0,2)
Let x=1 and solve for y
y=3(1)+2
y=3+2
y=5 Plot (1,5)
Connect the points and you have a line.

Happy Calculating, Lyn!!!

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Factor the numerator and denominator
Cancel the matching numerator and denominators.


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f(x) is read "f of x."
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Page 42, Question #82: Evaluate each expression; 6-(-8)^2 over -3-(-1).
Is this what you mean?

You treat the numerator and denominator as if they were parentheses. Simplify them completely and then divide if possible.
Exponent
Add/subtract
divide
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Page 61, Question #38: Use distributive properties to remove parentheses; b(a+w)
Multiply b by everything in the parentheses.
b(a+w)
b(a)+b(w)
I usually put my variables in alphabetical order once I multiply them.
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Factor out the GCF
x(3x-7)=0 Set each part = to 0 and solve for x
x=0 and 3x-7=0
x=0 and 3x-7+7=0+7
x=0 and 3x=7
x=0 and 3x/3=7/3
x=0 and x=7/3
:
Set the problem = to 0



Factor
(x-11)(x-3)=0 Set each parentheses = 0 and solve for x.
x-11=0 and x-3=0
x-11+11=0+11 and x-3+3=0+3
x=11 and x=3
:
use the square root property, take the square root of both sides.

x-3=+\-3
x-3+3=3+\-3
x=3-3 and x=3+3
x=0 and x=6
:
Square the left



Set = to 0

Factor, I'm using the ac, arch, or grouping method.


set each parentheses = to 0 and solve for x.
x-6=0 and 5x-6=0
x-6+6=0+6 and 5x-6+6=0+6
x=6 and 5x=6
x=6 and 5x/5=6/5
x=6 and x=6/5
:
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(Not necessary to find the roots - just determine the number & type of solution) use a discriminant to determine the number of solutions for the quadratic equasions - and if the solutions are real or complex.
:
The discriminant of a quadratic equation written in standard form is
If the discriminant is positive, there are two real solutions.
If the discriminant is 0, there is one real solution.
If the discriminant is negative, there are two complex solutions.
:
a. 2x^2+x-1=0 a=2, b=1, c=-1

= The discriminant is positive, there are two real solutions.
:
b. 4/3x^2-2x+3/4=0 a=4/3, b=-2, c=3/4

=


The discriminant is 0, there is one real solution.
:
c. m^2+m+1=0 a=1, b=1, c=1

=
= The discriminant is negative, there are two complex solutions.
:
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A line passes through (-4,2) and has the same y-intercept as 2x-y=3. Put this in standard form.
This is a thinker.
To find the y-intercept of the equation of a line you can let x=0 and solve for y.
2(0)-y=3
0-y=3
-y=3
-(y)=-(3)
y=-3 The y-intercept is (0,-3)
To find an equation of a line we need a slope and a point. We don't have a slope, but we do have two points. We can find the slope between two points with the slope formula:
(x1,y1)=(-4,2) and (x2,y2)=(0,-3)


Now we can use the slope, m=-5/4 and the y-intercept (0,b)=(0,-3) To make an equation of a line with the slope intercep formula , m=slope, and (0,b) is the y-intercept.

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Hi Jamie,
Solve the system by substitution
L1) x + y = 12
L2) y = 2x
Substitute 2x into L1 and solve for x:
x+(2x)=12
3x=12
3x/3=12/3
x=4
Substitute 4 into L2 and solve for y:
y=2(4)
y=8
The solution is (x,y)=(4,8)
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The goal is to get the r all by itself. To get rid of the things with it you do the inverse operation to it. (If it's multiplied-divide it and if it's squared-sqrare root it.) Whatever you do to one side of the equal sign, you must do to both sides.
solve for r.
because a/a=1

+/- because

You can ignore the +/-, because Volume is positive.

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Find the equation for this line (1,4)(5,6)
In order to find the equation for a line you need the slope and a point.
You don't have a slope, so we need to find it using the slope formula , m=slope, (x1,y1) and (x2,y2) are given points.
(x1,y1)=(1,4) and (x2,y2)=(5,6)



Now we can use the point slope formula ,m=slope, and (x1,y1) is a given point.
m=1/2 and (x1,y1)=(1,4)




Slope intercept form of the line.





Standard form of a line.
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Hi Lyn,
Can someone help me solve the system by graphing it for me?
I have to send it through the computer.
L1) x - 2y = 8
L2) x + y = -1
For L1, let y=0 and solve for x
x-2(0)=8
x-0=8
x=8 Plot (8,0)
Now let x=0 and solve for y:
0-2y=8
-2y/-2=8/-2
y=-4 plot (0,-4)
Connect the points and you have this line.

For L2), let y=0 and solve for x
x+0=-1
x=-1 Plot (-1,0)
Let x=0 and solve for y
0+y=-1
y=-1 Plot (0,-1)
Connect the points and you have a second line:

They intercect at (2,-3)
Happy Calculating, Lyn!!!

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Hi Ashley,
I think you left off a y. Otherwise, without another variable we could not rewrite the equation as a function of x.
I'm adding a y.
Rewrite 2x-3y=-6 as a function of x.
Solve the equation for y:
-2x+2x-3y=-2x-6
-3y=-2x-6


Now y is a function of x. Y depend on what x is.
Happy Calculating, Ashley!!!

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Hi Sher,
I saw your other questions on graphing inequalities. I don't think anyone can graph the inequalities. We can only graph the functions and tell you where we would shade if we could. If you want me to do those anyway, let me know. Otherwise, I'm leaving them for someone else in hopes that someone out there knows some computer commands that I don't.
:
Given , I need to find f(0).
:
For this you just substitute 0 in for x and simplify:



:
Did you know that f(0) is the y intercept of the graph? This graph crosses the y axis at (0,2).
:
Happy Calculating, Sher!!! One More Week :-)

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Here's a problem set I did for someone else a couple of days ago. The last few are composite functions.
:
Use the functions , , and to find each of the following.
(1) (f + g) (-1)





:
(2) (g - f) (x)



:
(3) (fh)(0)






:
(4) (g o f) (-1)=g(f(-1))
f(-1)=2(-1)+7
f(-1)=-2+7
f(-1)=5
g(f(-1))=g(5)
g(5)=(5)^2+3(5)
g(5)=25+15
g(5)=40

:
(5) (f o f) (0)=f(f(0))
f(0)=2(0)+7
f(0)=0+7
f(0)=7
f(f(0))=f(7)
f(7)=2(7)+7
f(7)=14+7
f(7)=21

:
(6) (g/f) (4)




:
(7) (g o h) (1/2)=g(h(1/2))




g(h(1/2))=g(-2/13)





:
(8) (f o g o h) (8)=(fog)(h(8))



(fog)(h(8))=(fog)(1)=f(g(1))



f(g(1))=f(4)
f(4)=2(4)+7
f(4)=8+7
f(4)=15

:
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Find the equation of the line through the two points (3,4) and (2,-1); write the equation in the slope intercept form and find the x and y intercept of the line.
:
In order to write the equation of a line, we need a point and a slope.
We don't have a slope, so we need to use the slope formula: , m=slope, (x1,y1) and (x2,y2) are given points.
(x1,y1)=(3,4) and (x2,y2)=(2,-1)



Now we can find the equation of the line using the point-slope formula to find the equation of the line. , m=slope, (x1,y1) is a point on the line.
m=5, (x1,y1)=(3,4)



This is in slope intercept form: , where m=slope and (0,b)=y-intercept.
The y-intercept is (0,-11)
To find the x-intercept, let y=0 and solve for x:






The y-intercept is (2.2,0)
In case you'd like to see the graph of the line for fun:

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First factor the denominators and look for the lowest common denominator (LCD).

The LCD is: (x+2)(x-2) Notice that if x=-2 or 2 there will be 0 in 1 or more denominators. If we get those answers they are extraneous, or false solutions. Multiply each term by the LCD.


5(x+2)-5=1(x-2)
5x+10-5=x-2
5x+5=x-2
-x+5x+5=-x+x-2
4x+5=-2
4x+5-5=-2-5
4x=-7
4x/4=-7/4

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Ms. Jordan has been given a loan of $2500 for 1 year. If the interest charged is $275, what is the interest rate on the loan?
:
The formula for simple interest is: , I=interest, P=principle, rate=rate (in decimal), and t=time (in years)
:
P=2500
t=1
I=275
r=r (we don't know this yet)
:




If you need the interest rate in percentage, multiply it by 100%
r=.11(100%)=11%
:
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During the basketball season,Pierre scored 25% more points than Jim. Pierre scored 220 points for the season. The number of points jim scored was
Let the amount of points that Jim scored be: x
Then 25% of x is: (25/100)x=.25x
"More than" means add:
x+.25x=220
1.25x=220
1.25x/1.25=220/1.25
x=176
:
Happy Calculating!!!