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You are correct!! Here is the graph:


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You have two right triangles, in which the two poles are the vertical legs of the triangles, and the length of the wire is the sum of the two hypotenuses (or would that be hypotenii???). Since the distance between the poles is 30 meters, let x= distance from first pole to the point where the wire touches the ground, and 30-x = distance from this point on the ground to the base of the second pole.

By Theorem of Pythagoras, the length of the wire from the top of the first pole to the ground is , and the distance from the top of the second pole to the ground is . The total length of the wire, is the sum of these radicals


It doesn't simplify much:

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I'm confused too!! You have three different quadratic equations, and I don't see how any of them relate to changing 5.5 to a fraction.

However, the first equation is
, which becomes
, which factors into

or
or .

This works very well by factoring, so you don't need the quadratic formula, unless you specifically wanted to do it by quadratic formula. In this case, algebra.com has a "pluggable solver" that looks like this:

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=169 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4, -0.333333333333333. Here's your graph:

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You can't solve for x unless they give you the value of R. If you are to graph it, then it is a VERY steep graph with the y intercept (actually the R intercept) of 0, and a slope of 50 over 1. Like this:

Look closely at this graph. The graph is so steep you can hardly see it!!

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A rational number can always be changed to either a repeating or a terminal decimal.

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It may be helpful to find a way to eliminate the p, and then eliminate the q, and write two equations, one for p and one for q.

First, if you add the two equations together, you can eliminate the p, and get
x=2+p-2q
y=3-p+3q
x+y = 5 + q, so q = x+y-5

Second, to eliminate the q, multiply both sides of the first equation by 3, and the second equation by 2:
3(x)=3(2+p-2q)
2(y)=2(3-p+3q)

3x= 6 +3p-6q
2y = 6-2p+6q

3x+2y = 12 +p, so p=3x+2y - 12

There you have it:
p=3x+2y-12
q=x+y-5

I have no idea how to check this, unless you solve for x and y to see if you come back with the same equations that you started with. It looks like Linear Algebra to me. Hey, I gotta go to work this morning!!

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Let L = number of loaves of bread.
C = total cost of the loaves.
Machine cost:
C = 199 + .79L

Store cost:
C = 1.59L

199 +.79L = 1.59L

Subtract .79L from each side:
199+.79L -.79L = 1.59L - .79L
199=.8L

Divide both sides by .8:



Answer: On the 160th loaf of bread, the machine becomes the lesser cost.

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Factor the common factor of ax:
ax(x+8) = 0
ax = 0 or x+8 = 0
x=0 or x=-8

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You are probably talking about a cube root, fourth root, etc.

For example, is a cube root. It means "what number can you raise to the third power and get 27?" Of course, the answer is 3, because .

As another example, is a fourth root. It means "what number can you raise to the fourth power and get 16?" Of course, the answer is 2, because .

I have a complete explanation of this as a Lesson Plan in algebra.com under "Square-cubic-other-roots." Also, see my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com, then go to Basic Algebra, the look for "Samples from Basic Algebra: One Step at a Time", then Chapter 5, which is a complete explanation of radicals.

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They are both negative!

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The way to find an inverse function, you begin with an xy equation:.

There are two steps:
1. Interchange the x and y; and
2. Solve for y.

Given:

Step 1:

Step 2: Solve for y.
Add +3 to each side:

Divide by 7:

Take the 5th root of each side or raise both sides of the equation to the power


It looks like e) is the correct answer!

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Given: {(–8, 7), (–5, –4), (–3, 3), (–3, 6)}

First, the Domain is the set of all x values, which are the first numbers in each pair: {-8,-5,-3}.

Second, the Range is the set of all y values, which are the second numbers in each pair: {7,-4,3,6}

Third, it is NOT a function, since two points have the same x coordinate: (-3,3) and (-3,6).

Now,
a. Domain: {7, –4, 3, 6}; Range: {–8, –5, –3}
Domain and range are backwards. False

b. Domain: {–8, –5, –3}; Range: {7, –4,3, 6}
Both are correct!! True

c. Domain: {–8, –5, –3}; Range: 11
Domain is correct, but range is wrong. False
d. The relation is not a function.
This is true.

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Since you have a product of x times y equal to a positive number, this means that either x and y are both positive (Quadrant I) or they are both negative (Quadrant III). Therefore all the points are in Q I and III, so there are NO points in Q II and IV. Final answer is e).

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No! The x value is -5, which is NOT between -3 and 12. The value of y is 3, which is between -6 and 15, but the x value is not, so it will not be in the viewing window.

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This is a parabola that opens upward, and the axis of symmetry for such a graph in the form of will always be .

In the case of , the axis of symmetry will be

The graph looks like this, using a graphing calculator, or this fantastic "algebra.com" calculator:


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Anytime you have a fraction equal to a fraction, like this:, remember that

means that

means that

Now, 5x-25 =6x - 9

Subtract 5x from each side to get all the x terms on the right side:
5x-5x -25= 6x-5x-9
-25 = x-9

Next, add +9 to each side:
-25+9 = x-9+9
-16=x

Check by substituting back into the original equation:



It checks!!

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You need to state the problem. Most of the tutors are not going to have a copy of your book.

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The ln of a product is the SUM of the logs, so use the positive. The negative is still outside the parentheses.

I have ln (x/square root of yz) =
ln x - 1/2 (ln y + ln z).

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Could this be ?
if so, then do this by the laws of logarithms:





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You are almost right. You made a couple of very small errors, which I have corrected below for you.

I have done slope -1 and (2, -1).
form f(x) =ax+b
a= -1
f(x) = -1
Since f(2)=-1
f(2)= -1(2)+b
-1=-2+b
-1+2=b
1=b
f(t) = -1t+1

Now, check it! The slope is indeed -1.
f(2)= -1(2) + 1 = -2 +1 = -1, as it should be.

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Notice that there are five buttons across the top of the calculator. The first one is "y=" and the last one is "GRAPH". Start with the "y=" button. This opens up a whole screen full of y1=, y2=, y3=, etc. Next, you need to find the x-variable button, which is the second button down in the second column. This button actually says something that looks like "x,t,0,n". Press this button to get "x". To get the "squared" you can either press the x^2 button in the first column, or you can press the "^2" buttons. Then finish typing in the equation with a "minus 11 x + 18".

After you get that all typed in, press the last button across the top that says "GRAPH", and it should graph a parabola. See my handout on my website, since you may want to adjust the window to see it better.

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You need to see my handout on the TI 84 graphing calculator. It's on my website, which you can find by clicking on my tutor name "rapaljer" anywhere in algebra.com. Then look for the page on "Calculator Handouts and Websites". My handout was so large I had to place it in three sections, and you will need the second of these three for graphing. It's really too much to do right here. Let me know if you need help with this. I won't have access to my office Email until Tuesday.

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g(x) = 1/(1 - x)
h(x) = 1/(1 + x)


(g o h)(x) = g[ f(x) ]
g[ f(x) ] =

This looks a LOT worse than it really is!! It's a complex fraction, and I have a LOT of these worked out on my Math in Living Color pages of my website! I'm more comfortable in that format, and they are in "Living Color"!

Multiply both numerator and denominator by the LCD which is (1+x).
g[ f(x) ] =
g[ f(x) ] =
g[ f(x) ] =
g[ f(x) ] = , which is the f) answer.

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Let x = first number
and y = second number

Now, you need to write two equations since there are two unknowns.
The sum of two numbers is 130.
x+y = 130

One number is 46 times more than 1/2 the other number.
x= 1/2*y+46
If you don't like this equation because of the fraction, just multiply both sides by 2:
2x = y + 92 or 2x-y = 92

There, now it's not a word problem any more. It's solving two equations with two unknowns!!
x+ y = 130
2x -y = 92

Just add the two equations together:
3x= 222
x=74

Now, x + y = 130
so, 74 + y = 130
y=56

Check in the second equation:
x=1/2*y +46
74=1/2*56 + 46
74=28 + 46
It checks!!

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This is a fractional equation. Start by factoring the denominators so you can find the LCD for the problem.


The LCD = 6x(x-3), so multiply both sides of the equation by the LCD. It's ugly at first, but in the first step all the fractions divide out!



After all the denominator factors divide out, this is what is left:




One more step: Check each denominator, and make sure that x= 6 doesn't make any denominators zero. Also, you can check the answer by substituting x= 6 into the original equation (if you want to go to some trouble).

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Any equation that is in the form of a number times x plus or minus a number times y equal to a number term will ALWAYS be a straight line. This form Ax+By=C is called the standard form of a line.

Also, any equation in the form of y = mx + b (called the slope-intercept form of a line) is also a straight line.

It's when you get x^2 or y^2 or division by x or y, like y = 12/x, etc. Then this is NOT a straight line.

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Given log 4 = .6021, notice that 1/16 is actually .

So, log 1/16
= log 4^-2
= -2* log 4
=-2(.6021)
=-1.2042

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Set the equation equal to zero:
8k^2+5k=2k^2+4
8k^2 -2k^2 + 5k -4 = 2k^2 + 4 - 2k^2- 4
6k^2 + 5k - 4 = 0

Factoring this trinomial is the hard part!! Try this combination:
6k^2 + 5k - 4 = 0
(3k + 4 )(2k - 1)= 0
3k = -4 or 2k = 1
k= -4/3 or k = 1/2

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This is factoring by grouping. Group the first two and last two terms together.




Notice that there is a common factor of (x-1):

or

Are you solving with complex numbers or real numbers only? If real numbers only, then the only answer you have to worry about is x=1. End of problem, since real numbers squared cannot equal a negative.

However, if complex numbers are allowed, then
gives two solutions:
,
, in addition to .

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This is factoring by grouping. Group the first two and last two terms together.




Notice that there is a common factor of (x-1):

or

Are you solving with complex numbers or real numbers only? If real numbers only, then the only answer you have to worry about is x=1. End of problem, since real numbers squared cannot equal a negative.

However, if complex numbers are allowed, then
gives two solutions:
,
, in addition to .

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In the equation y=mx+b, the coefficient of x is the slope and the constant term or the number term is the y-intercept. m=slope, b= y-intercept.
y = 4x -3
slope m= 4
y-intercept = b = -3

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