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determine whether the following pairs of lines are perpendicular or not perpendicular
y=-x+4
y=x-3
:
These lines are in slope intercept form , where m=slope and (0,b)=y-intercept.
Perpendicular lines have slopes that are negative reciprocals of each other, that means they are opposite signs and upside down, because of this quality, if we multiply their slopes we get -1 .
y=-x+4 -->> m=-1
y=x-3 -->> m=1
:
If you multiply their slopes -1*1=-1, therefore the lines are perpendicular.
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5^3(5a^4)^3 Is this what you meant?





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what is
L1) 2x-3y=12
L2) x=4y+1
substituion form
:
Substitute the right side of L2 into L1 for x and solve for y
2(4y+1)-3y=12
8y+2-3y=12
5y+2=12
5y+2-2=12-2
5y=10
5y/5=10/5
y=2
:
Substitute 2 in for y in L2 and solve for x
x=4(2)+1
x=8+1
x=9
The solution (x,y)=(9,2)
This is the point that both equations share. Garphically, its' the point of intersection of the two lines.
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Find the excluded values for :
Excluded values for m would be anything that causes the denominator to = 0 because that causes the fraction to be undefined.
m(m+1)=0
m=0 and m+1=0
m=0 and m+1-1=0-1
m= 0 and m=-1
The excluded values for m are 0 and -1.
That means that m cannot equal 0 or -1.
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here's a table.
x y
4 14
8 15.5
12 17
16 18.5
How would i find the value of y when x=120?? how about finding the value of x when y=50??
Your rate of change is the slope between various points. I checked this out and this is indeed a linear relation.
The formula to find the slope between two points is:

You can choose any two points to find the slope, so let's choose the ones without decimals to make it a little easier.
(x1,y1)=(4,14) and (x2,y2)=(12,17)


We can now find the equation of the line using the point-slope formula:, m=slope,(x1,y1)=any point on the line.
(x1,y1)=(4,14) and m=3/8









:
When x=120
3(120)-8y=-100
360-8y=-100
-360+360-8y=-360-100
-8y=-460
-8y/-8=-460/-8
y=115/2

:
When y=50
3x-8(50)=-100
3x-400=-100
3x-400+400=400-100
3x=300
3x/3=300/3

:
If I just blew your mind and you've never seen any of this before, another way you can do this is to plot the points on a graph and using graph paper and a ruler you can approximate the same thing.
:
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how would i write an equation in point slope form, when it only gives me the coordinates: (-4,-6)??
In order to make an equation of a line you're supposed to have a point AND a slope.
The point slope form is , where m=slope and (x1,y1) is the given point.
Since you were only given: (x1,y1)=(-4,-6) all you can do is:
y-(-6)=m(x-(-4))
y+6=m(x+4)
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if f(x) =2x+5 find the following.
:
f(-4) Substitute -4 in for x and simplify.
f(-4)=2(-4)+5
f(-4)=-8+5
f(-4)=-3
:
f(3)-5 Substitute 3 in for x subtract 5 and simplify.
f(3)-5=(2(3)+5)-5
f(3)-5=6+5-5
f(3)-5=6
:
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-8-t=-25
8-8-t=8-25
-t=-17
-(-t)=-(-17)

check by substituting 17 in for t and see if the sides are =.
-8-17=-25
-25=-25 We're right!!!
:
8=b-3+19
8=b+16
8-16=b+16-16
-8=b

Check:
8=(-8)-3+19
8=-11+19
8=8 We're right again!!!
:






Check:


Three for three!!!
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You have 20 stampes that have a total value of $6.62. Some of the stamps are worth $0.24 each and others are worth $0.37 each. How many stamps of each type do you have?
It's easier to deal with money in terms of cents to avoid decimals.
Let the number of 24 cent stamps be:x
then because there is 20 stamps all together the number of 37 cent stamps is:20-x
The total value is: 662 cents
:
24x+37(20-x)=662
24x+740-37x=662
-13x+740=662
-13x+740-740=662-740
-13x=-78
-13x/-13=-78/-13
x=6
The number of 24cent stamps: x=6
The number of 37 cent stamps:20-x=20-6=14
:
Check, if you had 6 $.24 stamps and 14 $.37 stamps would the value be $6.62?
6(.24)+14(.37)=6.62 ?
1.44+5.18=6.62 ?
6.62=6.62 !!! We're right!!!
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Because t is less than or equal to 9, put either a closed circle or a ] over 9 and shade to the left over the numbers less than 9.
<<=================]---->
-1,0,1,2,3,4,5,6,7,8,9,10
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Rule: loga (b*c)=(loga b)+(loga c)
Given log10 11=wand log10 5=x, find log10 55
log10 (11*5)
(log10 11)+(log10 5)

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Rule loga b=c ---> b=a^c
log3 x=2 I think you mean log base 3 of x =2. If so rewrite it as an exponential equation:


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Determine the number of solutions to the quadratic equation using the discriminant to determine if the answers are real or complex. (no need to find the roots, just the numer & solution type)
:
The discriminant of a quadratic equation written in standard form is Notice that this is just the inside of the square root in the quadratic equation.
If the discriminant is positive there are 2 real solutions.
If the discriminant is 0 there is one real solution.
If the discriminant is negative there are 2 complex solutions.
:
i. 2x^2+5x+5=0
a=2, b=5,c=5 The discriminant is


negative. There are 2 complex solutions.
:
ii. 3z^2+z-1=0
a=3, b=1,c=-1 The discriminant is


positive. There are two real solutions.
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namethree fraction whose decimal equivalent is 0.40.
This is read 40 one-hundredths, so start there.
40/100
4/10 reduce the top and bottom by 10
2/5 reduce the top and bottom by 2
There's an infinite number of possibilities!!!
400/1000
6/15
12/30
What can you come up with?
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y=3x-7
y=-x+1
We're looking for when their x=x and y=y, so set the problems equal to each other.
3x-7=-x+1
3x+x-7=x-x+1
4x-7=1
4x-7+7=1+7
4x=8
4x/4=8/4
x=2
Let x=2 and solve for y in one of the equations.
y=-(2)+1
y=-1
The solution is:(2,-1)
Graphically, it's their point of intersection:

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when x=2 and y= -4





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It helps to put parenthesese around the fractions so that we know where they begin and end. If this isn't what you meant, let me know and I'll redo it.
The LCD is 7*5=35, multiply both sides by 35 and clear your fractions.







:
Check by letting x=-5 and see if the sides actually equal.


we're right if I interpretted your problem correctly.
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I haven't found an easy way of indicating cubed roots either. I've used: \3/
Find the perfect cubes within the radical sign.
\3/
\3/ Take the perfect cubes out and leave the rest inside the radical sign.
-3x^5*y^2\3/
-3x^5y^2 the cubed root of 2.
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One-third X plus two-fifths X equals one-fifteenth
What is X?
This can be easier if we clear the fractions by multiplying everything by the LCD, 15:






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Find the domain of the rational function:

The domain of a simple rational function is all real numbers EXCEPT the numbers that make the denominator equal 0.




(x+5)(x-3)=0
x+5=0 and x-3=0
x=-5 and x=3 will make the denominator 0 and the fraction undefined.
Therefore the domain includes all real numbers except:-5, and 3.
set builder notation:{x|x not= -5,3}
interval notation:(-infinity,-5)U(-5,3)U(3,infinity)
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Please find derivative and simplify:
d/dx[ln(x)]=1/x
d/dx[cf(x)]=cf'(x)
d/dx[c]=0
Chain Rule: d/dx[f(g(x))]=f'(g(x))*g'(x)
:
y=ln((3x-5)^3/(5x+4)^4) Use properties of logs to simplify first.
y=ln((3x-5)^3)-ln((5x+4)^4)
y=3ln(3x-5)-4ln(5x+4) Now take the derivative using the chain rule:


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Given the following quadratic function: f(x) = x ^2 - 2x - 8,
(1) Rewrite the function in vertex form. Identify the vertex.
Vertex form is: , where (h,k)=vertex.
We need to create a perfect square trinomial by adding and subtracting the same number, so you are really only adding 0.
:
f(x)=x^2-2x-8
f(x)=(x^2-2x+__)-___-8 Fill the blanks with (1/2(-2))^2=(-1)^2=1


The vertex (h,k)=(1,-9)
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Use the discriminant to determine whether or not the quadratic 2x^2 + 3x + 2
is prime. If it is not prime, factor it.
The discriminant of a quadratic equation written in standard form: is , if this is negative there is no real number solution, if it's not a perfect square, it's not factorable.
:
a=2, b=3, and c=2
:


It's not factorable and has no real solution.
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Let

Factor as usual.

p-3=0 and p+2=0
p=3 and p=-2 But we want to know what X is, so let again.
and
and
and
Check by substitution:





27 checks out





-8 checks too
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Find the Derivatives of the following and simplify:
d/dx[cf(x)]=cf'(x)
d/dx[e^x]=e^x
d/dx[c]=0
The chain rule: d/dx[f(g(x)]=f'(g(x))g'(x)
:
Use the chain rule:


:
---->> Use the chain rule again:



:

There is no x, this is a constant even though it doesn't look like one. . The derivative of a constant is 0.

:
I'm not sure if I'm interpretting you right on this one, let me know if there's a misunderstanding!!!
-------->> --->> Use chain rule:


:
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This is an unusual request, I hope I'm understanding what you want with the radicals.
simplify, use only radicals in answer:

Find your perfect squares
Take them out

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We need to have you type in your problem and directions. We don't have your book. I noticed that you put this in the catagory of polynomials and rational expressions. If you need to raise something to a power: x^2 tells us "x squared". If you need to type a fraction: x/2+y, means (x divided by 2)+y. If you want the y to be part of the denominator type it this way:x/(2+y). Look forward to hearing from you.
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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:, where I=interest, P=principle, r=rate, t=time.
For this problem:
P=2500
t=1
I=275




If they ask for the answer in percentage multiply this by 100%.
%
r=11%
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A survey of 400 people found that 66 were left-handed. What percent of those surveyed were left-handed?
%
%
%
%
16.5%
:
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The electricity costs of a business decreased from $12,000 one year to $10,920 the next. What is the rate of decrease?



:
If you need this in percentage, multiply this by 100%
%
-9%
The negative indicates a 9% decrease. If you say decrease, you don't need to say it was negative.
:
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Rules we will be using:


:
notice that






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