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27-y^2=0


+/-
+/-
+/-
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You're right is a third degree polynomial, however the degree is the highest of the combined exponents of a term in the polynomial.
:
For instance } is a 6 degree polynomial because the first term has a combined exponent value of 4+2=6.
:
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Geometry. Refer to the triangle in the figure. Find an expression that represents its perimeter.
One side is 3/4x
2nd side is 5/ x^2
Bottom side is 1/x^2
To find the perimeter, you add the sides together:



The LCD is 4x^2, whatever you multiply the denominator by you also must multiply the numerator by.



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Bob scored 48 points last season. this is 6 fewer than twice the number Gene scored. How many points did Gene score? Please show how you solved it.
Let the number of points Gene scored be: x
twice means 2*
6 fewer means: -6
is means: =
Therefore,
48=2x-6
48+6=2x-6+6
54=2x
54/2=2x/2
27=x
Gene scored 27 points.
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Add or subtract as indicated. Express your result in simplest form
3/ x^2 + 4x +3 – 1/ x^2 – 9


The LCD is (x+1)(x+3)(x-3) whatever you multiply the bottom by you have to multiply the top by.




or
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Add or subtract as indicated. Express your results in simplest form
x^2/ x -3 – 9/ x -3





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I'm guessing as to where your fractions begin and end. It helps us if you put the whole numerator in parentheses and the whole denominator in parentheses.
If I misinterpretted you, please let me know.
Add or subtract as indicated. Express your results in simplest form
5a – 12/ a^2 – 8a + 15 – 3a – 2/ a^2 – 8a + 15







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Suppose a baseball is shot up from the ground straight up with an initial velocity of 32 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0
• 16 represents ½g, the gravitational pull due to gravity (measured in feet per second 2).
• v0 is the initial velocity (how hard do you throw the object, measured in feet per second).
• s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.
a) What is the function that describes this problem?
v0=32 ft/s; s0=0 ft
s=-16t^2+32t+0
s=-16t^2+32t
:
b) The ball will be how high above the ground after 1 second?
s=-16(1)^2+32(1)
s=-16(1)+32
s=-16+32
s=16 ft.
:
c) How long will it take to hit the ground?
0=-16t^2+32t
0=-16t(t-2)
-16t=0 or t-2=0
-16t/-16=0/-16 or t-2+2=0+2
t=0 or t=2
When t=0 the ball is shot up, the ball lands at t=2 s.
:
d) What is the maximum height of the ball?
The ball reaches its maximum height at the vertex of the parabola represented by the quadratic equation. There are a couple of ways of finding that. This is just one way.
You can use the formual , to find the value of t and then substitute that value into the equation to find the height s.
a=-16 and b=32


t=1 s
We found the height at t=1 s for b.
The maximum height is s=16 ft.
:
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simplifying complex fractions:
x-xy -¹ / 1 + x/y

Multiply the top and bottom by the LCD y


or
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One leg of a right triangle is 2 inches smaller than the hypotenuse. The other leg is 5 inches long. What are the lengths of the unknown leg and hypotenuse?
The Pythagorean theorem says the hypotenuse squared = leg squared + other leg squared c^2=a^2+b^2
Let the hypotenuse be: x
Then the leg that is two inches smaller than the hypotenuse is: x-2
The other leg is: 5









The hypotenuse is x=7.25 in
The missing leg is x-2=7.25-2=5.25 in
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what is 30% of 85?




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simplify each expression. Use positive exponents. (4xy^2)^4(2y)^-3





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Please explain how the graph of y=(1/2)^x + 1 can be obtained from the graph
y=2^x. Thank you.
The graph of y=2^x is found by plotting some points like this:
x=-2, y=2^(-2)=1/4, (-2,1/4)
x=-1, y=2^(-1)=1/2, (-1,1/2)
x=0, y=2^0=1, (0,1)
x=1, y=2^1=2, (1,2)
x=2, y=2^2=4, (1,4)

y=(1/2)^x+1 can be written as:
y=2^(-x)+1
So your graph of y=2^x will be reflected about the y-axis because of the -x
It will also be shifted up vertically because of the +1.
Ultimately, it looks like this:

If you multiply all the x's you plotted for the first graph by -1 and then added 1 to all their corresponding y's you'll have points to plot for this graph.
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log base 5^(x-4) + log base 5^(x+1)=3. Use the product rule for logs.
log base 5^ (x-4)(x+1)=3 Rewrite as an exponential eqaution.

Rememeber that even when you solve this, you need to check your solutions and make sure they aren't extraneous.
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Are you supposed to be factoring or solving for x?
16x^2-36=?
This is the difference of perfect squares the rule for that is .

:
9x^2+81=?
This is the sum of perfect squares and is prime. It can't be factored or solved unless you have started using the complex number system.
:
If you have started using complex numbers or need these solved for x let me know.
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Can you please help me in simplifying this complex fraction?
x-3/x+3 + x+3/x-3
___________________
x-3/x+3 - x+3/x-3
Multiply the top and bottom by the LCD: (x-3)(x+3)







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use the following sets: U = (2,4,6,8,10,12,14)
A = (4,6,8), B = (2,6,10,12), C = (2,8,14)
Find A U B
A. (4,6,8,2,6,10,12)
B. (6)
C. Null Set
. (2,4,6,8,10,12) It has everything in A and everything in B
Find A U C '
. (4,6,8,10,12) It has everything in A and everything not in C
B. (4,6)
C. (2,4,6,8,14)
D. (8)

Find A' U (B n C)
A. (2)
. (2,10,12,14)It has everything not in A and what's everything that's in common between B and C.
C. (2,4,6,8)
D. U = Universal Set
Find n(B' n C)
A. (8,14)
B. (2)
. 2 The number of elements that aren't in B and also in C are 2.
D. 4
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Find the solutions of the following equations. Check for extraneous solutions.
(x-5)^1/4+3=2



There is no even root that results in a negative outcome, so you can stop here and say there's no solution. However, if your teacher wants you to keep going:




However this is extraneous, because:



Not true.
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PG. 483
Find the solution to each system of equations by the substitution method. Check your answers. Place your solution in the form (x,y), (a,b), (p,q), or (s,t).
(2.) x = 4 - 4y
-x + 2y = 2
Substitute x=4-4y in the second equation and solve for y:
-(4-4y)+2y=2
-4+4y+2y=2
-4+6y=2
4-4+6y=2+4
6y=6
6y/6=6/6
y=1
Now substitute y=1 in the first equation and solve for x.
x=4-4(1)
x=4-4
x=0
The solution is (x,y)=(0,1)
You check by substituting x=0 and y=1 into both equations and see if they balance:
0=4-4(1)
0=4-4
0=0 the first one checks
-(0)+2(1)=2
0+2=2
2=2 The second one checks as well, so you're right.
:
(6.) 4x + 2y = 4
3x + y = 4
Solve the second equation for y.
3x-3x+y=4-3x
y=4-3x
Now substitute y=4-3x into the first equation and solve for x.
4x+2(4-3x)=4
4x+8-6x=4
-2x+8=4
-2x+8-8=4-8
-2x=-4
-2x/-2=-4/-2
x=2
Now substitute x=2 into the second equation and solve for y.
3(2)+y=4
6+y=4
6-6+y=4-6
y=-2
The solution is (x,y)=(2,-2)
Check by substituting x=2 and y=-2 in both equations and see if they balance.
4(2)+2(-2)=4
8-4=4
4=4 First equation checks out.
3(2)+(-2)=4
6-2=4
4=4 This one checks too.
:
Find the solution by the addition method. Check your answers.
(6.) -x + y = 2 Add the two equations together and the x's are eliminated
x + y = 4
--------------
0+2y=6 solve for y
2y=6
2y/2=6/2
y=3
Substitute y=3 into either equation and solve for x.
x+(3)=4
x+3-3=4-3
x=1
The solution is (x,y)=(1,3) I'll leave the rest for you to check.

(8.) 2x + y = 4
3x - 2y = -1
If you multiply the first equation by 2 the y's will be eliminated when you add the equations. 2(2x+y)=2(4)--->4x+2y=8
4x+2y=8
3x-2y=-1
--------
7x+0=7 solve for x
7x=7
7x/7=7/7
x=1
Substitute x=1 into either equation and solve for y.
2(1)+y=4
2+y=4
2-2+y=4-2
y=2
The solution is (x,y)=(1,2) Don't forget to check it.
:
(14.) 5x - 3y = 14
2x - y = 6
Multiply the second equation by -3 and the y's will be eliminated when you add the equations. -3(2x-y)=-3(6)---->-6x+3y=-18
5x-3y=14
-6x+3y=-18
----------
-x+0=-4
-x/-1=-4/-1
x=4
Substitute that into either equation:
2(4)-y=6
8-y=6
8-8-y=6-8
-y=-2
-y/-1=-2/-1
y=2
The solution is (x,y)=(4,2) Don't forget to check it.
:
PG. 504
Solve using two equations with two variables.
(4.) El Segundo High School put on their annual musical. The students sold 650 tickets for a value of $4375. If orchestra seats cost $7.50 and balcony seats cost $3.50, how many of each kind of seats were sold?
Let orchestra seats be: x
Let balcony seats be: y
Then the amount of tickets sold is represented by: x+y=650
The amount of money made on the tickets is: 7.50x+3.50y=4375
You can use either substitution or elimination to solve, I think in this case, substitution is easiest.
x+y=650
x-x+y=650-x
y=650-x substitute into the second equation.
7.50x+3.50(650-x)=4375
10(7.50x)+10(3.50)(650-x)=10(4375)
75x+35(650-x)=43750
75x+22750-35x=43750
40x+22750=43750
40x+22750-22750=43750-22750
40x=21000
40x/40=21000/40
x=525
Substitute that into the first equation
525+y=650
525-525+y=650-525
y=125
Orchestra seats x=525
Balcony seats y=125
:
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12. (2x-14)/ ( 3x^2-21x)



:
13. (x^2-1)/(2x^2+x-1)



:
14. (2x^2+12x+18)/(x^2-x-12)




:
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Between what two integers does the solution of 5^x=67 lie?
and
67 is between 25 and 125
Therefore the solution for x lies between 2 and 3, .
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what are all of the solutions of 2/3(x-3)^2=4







That means x=3+sqrt(6) or x=3-sqrt(6)
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3x=-3y-21;(0,1)
What you are usually asked to do is determine whether (0,1) is a solution to the given equation. To do this, realize that (0,1)=(x,y), therefore let x=0 and y=1 and see if both sides equal.
3(0)=-3(1)-21
0=-3-21
0=-24
They aren't equal therefore (0,1) is not a solution.
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x^2/3=1/16








:
Check:




We're right!!!!
:
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can you help me Factor the Quadratics
13. a^2 + 4ab - 3b^2
This is prime, there are no integers that multiply to give you the last coefficient, -3, but add to give you the middle coefficient, +4
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If Susie can paint a house in 4 hrs and John can paint a house in 6 hrs. How long will it take them to paint it together?
This is the way I was taught this, but I know there is another way to do this:
Susie can paint 1 house in 4 hrs, her work rate is:1/4
John can paint 1 house in 6 hrs, his work rate is: 1/6
They both can paint 1 house in x hrs, their combined work rate is:1/x
:
Problem to solve:



Cross multiply, or flip both sides over and you have:



x=12/5 hrs.
x=2 and 2/5 hrs there are 60 minutes in an hour
x=2 hrs and (2/5)(60)min
x=2 hrs and 24 mins.
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can you help me Factor the Quadratics
14. 9k^2 + 30kn + 25n^2
This is a perfect square trinomial:
a^2+2ab+b^2=(a+b)^2
9k^2+30kn+25n^2=(3k)^2+2(3k)(5n)+(5n)^2=
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Check to make sure this solution isn't extraneous by plugging it back into the original equation and see if both sides equal.




The solution is valid.
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can you please help me Factor the Following Quadratic:
7a^2 + 17a + 6
This is the arch, ac, or grouping method. I've heard it called all three things.
This is in ax^2+bx+c form. a=7, b=17, and c=6
We need to replace the b term with two numbers that multiply to give you a*c, but add to give you b. Then we factor by grouping.
a*c=7*6=42
42=14*3 and 17=14+3, so....
7a^2+14a+3a+6 factor the GCF out of the first two and last two terms:
7a(a+2)+3(a+2) factor out (a+2)

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Insert grouping symbols in the proper place so that the given value of the expression is obtained. The value of the expression should be 28.
:
I am assuming that x means multiply and is not the variable "x."
:
5 - 3 x 2 + 8 x 5 - 2 = 28

Proof:
2 x 2 + 8 x 3 = 28
4 + 24 = 28
28 = 28
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Simplify the complex fractions
w+3
---
4w
---
w-3
---
2w
There are two methods to do this. You can realize that this is the top fraction divided by the bottom.
divided by
Flip the second fraction over and multiply:




:
The second method involves multiplying the top and bottom by the LCD of both fractions, 4w:





Pick your favorite method.
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