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I've done this one earlier today. I put that one in slope intercept form, for you I'm going to put it in standard form, since you didn't specify a preference.
Write the equation of the line that passes through the points (3,5) and (-1,10)
First we need to find the slope between the two points because in order to find the equation of a line, we need one point and a slope.
The slope formula:
(x1,y1)=(3,5) and (x2,y2)=(-1,10)


Now, use the point slope formula:, where m=slope and (x1,y1) is a given point. For this problem, m=-5/4 and (x1,y1)=(3,5)








<---standard form of a line
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write the equation of the line that passes through (3,2) and is perpendicular to the line 5x+4y=11
First, we need to find the slope of the line they gave us. To do this we need to put the equation in slope intercept form , where m=slope, and (0,b)=y-intercept.





the slope of this line is -5/4.
We need a line perpendicular to this line so our slope needs to be 4/5. (Flip the slope and change the sign.)
Now we use the point slope formula , where m=slope and (x1,y1)=the given point. Our m=4/5 and our point is (x1,y1)=(3,2)








<--slope intercept form of a line
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20. Write the equation of the line with x-intercept (–1, 0) and undefined slope.
A) y = –1
B) x = –1
C) y = –x
D) x = 0
Vertical lines have undefined slopes. They are special cases, the equation of the vertical line going through (-1,0) is
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18. Write the equation of the line passing through (–3, –7) and (–3, –6).
A) x = –3
B) y = –3
C) y = x – 3
D) y = x
Notice that both of the points have the same x. If you were to plot the points and connect the dots you would have a vertical line (|). That is a special case the equation of a vertical line going through those points is:
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Write the equation of the line that passes through the points (x1,y1)=(3,5) and (x2,y2)=(-1,10)
:
We need a slope (m) and a point to make the equation of a line:
If we have two points, (x1,y1) and (x2,y2) we can find the slope with the slope formula:


:
Now that we have a slope to go with a point we can use the point-slope formula , where m=slope and (x1,y1) is a given point, to make an equation of a line:









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write an equation in the point-slope form and the slope-intercept form.
slope=-5, passing through (-4, -2)
:
The point-slope formula is where m=slope and (x1,y1) is the given point:

<--Point-slope form
:
The slope intercept form is , where m=slope and (0,b)=y-intercept. We take the point-slope form and solve it for y.



<---slope-intercept form
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write an equation in slope intercept form for graph.
(4,3) (7,-2)
We need a slope and a point to make the equation of a line. The formula for finding the slope (m) when given two points is:

(x1,y1)=(4,3) and (x2,y2)=(7,-2)

m=-5/3
Now we use one of the points (x1,y1)=(4,3) and the slope m=-5/3 in the point slope formula: .









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Rules expressed as common logs:
1.
2.
Express as a single logarithm:

Rule 1
Rule 2
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74. An open box is to be made from a square piece of cardboard of dimensions 30 inches by 30 inches by cutting out squares of area x^2 from each corner.
a. Express the volume V of the box as a function of x.
b. State the domain of V.
Each side of the square would look like x--------x, if the length started out as 30 inches, then each side would be 30-2x.
V=L*W*H
The height is x.
Length and width are the same because it has a square base.
a.

b.Each dimension has to be greater than 0.
x>0 and 30-2x>0
30-2x>0
-30+30-2x>0-30
-2x>-30
-2x/-2<-30/-2
x<15in
Therefore
is the domain.
Interval notation: (0,15in)
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Find the Inverse of the following function:
:

Switch the x and y and solve for y.


Take the log of both sides:

Note the common log of 10=1



Replace y with f^-1(x)

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Write each of the following phrases, using symbols.
The sum of m and n, divided by the difference of m and n.
sum=+
divided=/
differenc=-
The sum of m and n: m+n
The difference of m and n: m-n
The sum of m and n, divided by the difference of m and n:
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write an equation in slope intercept form for the line that satisfies each set of conditions.
passes through (7,1) and (7,8)
This is a trick question, because you can't wriet this equation in slope intercept form. It's slope is undefined and it doesn't have a y-intercept.
The formula for slope when given two points is:
your (x1,y1)=(7,1) and your (x2,y2)=(7,8)

When 0 is the denominator of a fraction, the fraction is undefined.
Lines with undefined slopes are special cases, they are vertical lines.
The equation of a vertical line going through those two points is:
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Jeans are on sale at the local department store for 25% off. If the jeans originally cost $55 find the sale price. (Round to nearest cent)
The original price=$55
The discount is=(25/100)($55)=.25(55)=$13.75
Then the sale price is (=)the original price ($55)- the discount ($13.75)
The sale price= $55-$13.75=$41.25
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write an equation in slope intercept form for the line that satisfies each set of conditions.
passes through (4,6) parallel to the graph of Y=2/3x+5
The line you're given is in slope intercept form: where m=slope and (0,b)=y-intercept.
it's slope m=2/3.
Parallel lines have the same slope, so you need and equation of a line with a slope m=2/3 going through (x1,y1)=(4,6)
When you have a point and a slope and need the equation of a line you use the point slope formula: , where m=slope and (x1,y1) is the point you're going through.
your m=2/3 and (x1,y1)=(4,6)









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Write me back with your directions and problem and I'll try to help you. I don't have your book.

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state the slope & y intercept of the graph of each equation
2x-4y=10
First put the equation into slope intercept form , where m=slope and (0,b)=y-intercept:



(the fractions on the right reduce by a factor of 2)

The slope=m=1/2
The y-intercept=(0,b)=(0,-5/2)
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We want our x's preferably on the left side of the inequality because it makes it easier to graph. What ever you do to one side you have to do to the other.
-x<-4x+2
4x-x<4x-4x+2
3x<2
3x/3<2/3
x<2/3
2/3 is more than halfway from 0 to 1. When the variable is on the left we can shade our numberline in the direction of the arrow. It's not < or= so we use an open circle or a parenthesis over 2/3.
<<=======)-------------->
-2,-1,0,2/3,1,2,3,4,5,6
or
<<=======o-------------->
-2,-1,0,2/3,1,2,3,4,5,6
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Hi Sher,
Celsius temperature readings can be converted to Fahrenheit readings using the formula F= 9/5C + 32. What is the Fahrenheit temperature that corresponds to each of the following Celsius temperatures: 0 , 15, and 100?
For 0, substitute 0 in for C and solve for F:


F=32 degrees F
For 15, substitute 15 in for C and solve for F:



F=59 degrees F
For 100, substitute 100 in for C and solve for F:



F=212 degrees F.
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Hi Sher,
3x + 4y = 12
pair 1 is= (,3/4)
pair 2 is= (,0)
First substitute 3/4 in for y and solve for x.
3x+4(3/4)=12
3x+12/4=12
3x+3=12
3x+3-3=12-3
3x=9
3x/3=9/3
x=3
So the first ordered pair is(3, 3/4).
:
Second substitute 0 in for y and solve for x:
3x+4(0)=12
3x+0=12
3x=12
3x/3=12/3
x=4
So the second ordered pair is (4,0)
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What percentage of Europe's population was in the age 0-14 group in 1950?
:
Age 0-14 143,175 in 1950
:
Total 547,318 in 1950
To find the pecentage, put the *100%
*100%
*100%
26.159% Round off where your teacher tells you to.
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Write the equation of the line slope-intercept form ( where m=slope and (0,b)=y-intercept.) if the slope is 2/3 and (9,3) is a point on the line.
The formula you use when given a point and a slope and asked for the equation of the line is the point-slope formula: Where m=slope and the point you're given is (x1,y1).
Your slope is m=2/3 and your point (x1,y1)=(9,3)





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The rules we're going to use are:
1.
2. =>
3.
solve the equation ln(x+5)- ln(3)= ln (x-3)


Rule 1
Rule 2
Rule 3









:
Check by subtituting 7 in for x's in the original equation and see if both sides equal once you simplify:


Rule 1
We're right!!!
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Hi Sher,
The formula for simple interest is: where I=interest, P=principle, R=rate, and T=time.
You want to solve for rate, so solve your formula for R:




A principal of $5,000 was invested in a savings account for 4 years. If the interest earned for the period was $400, what was the interest rate?
P=5000, T=4, I=400



If you need this expressed as a percentage, r=.02*100%=2%
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I don't have your book, but I can tell you the order of operations until you send me your problem:
Parenthesis (Work them from the innermost to the outermost parenthesis.)
Exponents
Multiplication and Division (left to right)
Addition and Subtraction (left to right until you get comfortable.)
Some people use the pnumonic devise (PEMDAS) or (Please Excuse My Dear Aunt Sally) to help them remember.
The only other thing I can think of is that if you have rational expression, you treat the numerator as if its in parenthesis and the denominator as if its in parenthesis.
Also, if you have an absolute value, you treat that as if its in parenthesis.
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Find the least value of and the corresponding value of x
:
Graphically, this is a parabola and it's least value would correspond to it's vertex.
The formula for finding the x value of the vertex of a parabola written in standard form is.
Your a=2, your b=-4, and your c=3
So the x value of the vertex is:



Substitute that in for x and simplify to find the least value:




Here's what it looks like graphically, to illustrate my point:

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14. Find the slope and the y-intercept.
y = 7x – 7
This line is in slope intercept form: , where m=slope and (o,b) is your y-intercept.
Your slope is 7.
Your y-intercept is (0,-7)
:
15. Find the slope and y-intercept.
x = 1
A) Slope: 0; y-intercept: (0, 1)
B) Slope: undefined; y-intercept: (0, 1)
C) Slope: 0; y-intercept: none
D) Slope: undefined; y-intercept: none
Notice that the equation only has an x and no y. x=1 is a special case, it is a vertical line {|}in which x is always 1. Vertical lines have slopes that are undefined and don't cross the y-axis (they can be the y-axis, but they can't cross the y-axis). Therefore the answer is
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Take the natural log of both sides.
Because
Because






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What is the slope of the line whose equation is 2y=5x+4?
We need to put this equation in slope intercept form: , where m=slope and (0,b)=y-intercept. Hence, the name, "slope intercept form."


The coefficient of x=slope(m).

The slope is 5/2.
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Hi Lyn,
graph the solution set of x > -7
x is bigger than -7, but not = to -7, so there should be an open circle or a parenthesis over the -7 and the number line should be shaded to the right over the numbers bigger than -7.
<------(========================>>>
-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2
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The figure shows the graph of y=(x-3)(x-5)(x-a). Determine the value of a.
:
I don't have your book, but I'll tell you how to figure this out.
:
Your graph should be going through the x axis three times: once at 3, once at 5, and once at "a". (3,5, and "a" cause y=0.)
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Rules used:
The s is an exponent.









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