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Completing the square:

Start with the given equation.


Subtract 12 from both sides.



Now let's complete the square for the left side.


Start with the given expression.


Factor out the coefficient . This step is very important: the coefficient must be equal to 1.


Take half of the coefficient to get . In other words, .


Now square to get . In other words,


Now add and subtract inside the parenthesis. Make sure to place this after the "m" term. Notice how . So the expression is not changed.


Group the first three terms.


Factor to get .


Combine like terms.


Distribute.


Multiply.


So after completing the square, transforms to . So .


So is equivalent to .


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Now let's solve


Start with the given equation.


Add to both sides.


Combine like terms.


Divide both sides by .


Reduce.


Take the square root of both sides.


or Break up the "plus/minus" to form two equations.


or Take the square root of to get .


or Subtract from both sides.


or Combine like terms.


--------------------------------------


Answer:


So the solutions are or .



===========================================================

Factoring:

Start with the given equation.


Subtract 12 from both sides.


Now let's factor:





Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .


Now multiply the first coefficient by the last term to get .


Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?


To find these two numbers, we need to list all of the factors of (the previous product).


Factors of :
1,2,3,4,6,8,12,24
-1,-2,-3,-4,-6,-8,-12,-24


Note: list the negative of each factor. This will allow us to find all possible combinations.


These factors pair up and multiply to .
1*(-24) = -24
2*(-12) = -24
3*(-8) = -24
4*(-6) = -24
(-1)*(24) = -24
(-2)*(12) = -24
(-3)*(8) = -24
(-4)*(6) = -24

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First Number	Second Number	Sum
1	-24	1+(-24)=-23
2	-12	2+(-12)=-10
3	-8	3+(-8)=-5
4	-6	4+(-6)=-2
-1	24	-1+24=23
-2	12	-2+12=10
-3	8	-3+8=5
-4	6	-4+6=2

From the table, we can see that the two numbers and add to (the middle coefficient).


So the two numbers and both multiply to and add to


Now replace the middle term with . Remember, and add to . So this shows us that .


Replace the second term with .


Group the terms into two pairs.


Factor out the GCF from the first group.


Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.


Combine like terms. Or factor out the common term


So factors to .


In other words, .



So turns into


Start with the given equation


or Use the zero product property


or Solve for 'm' in each equation.


So the solutions are or (which are the same as the ones above)

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So

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So when

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So where

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Start with the given equation.


Subtract 4 from both sides.


Notice that the quadratic is in the form of where , , and


Let's use the quadratic formula to solve for "k":


Start with the quadratic formula


Plug in , , and


Square to get .


Multiply to get


Rewrite as


Add to to get


Multiply and to get .


or Break up the expression.


So the solutions are or

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Hint: The vertex of is (h,k). To find the x-intercepts, plug in f(x)=0 and solve for x.

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Start with the given expression.


Rewrite as . Rewrite as .


Now factor by using the difference of cubes formula.


Remember the difference of cubes formula is


Multiply

-----------------------------------
Answer:
So factors to .

In other words,

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Notice that 8*3 = 24

So 8*30 = 240

Add 8 more, and you'll get 8*31 = 248

So

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Since variance = standard deviation squared, this means that

variance =

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Start with the given equation.


Notice that the quadratic is in the form of where , , and


Let's use the quadratic formula to solve for "x":


Start with the quadratic formula


Plug in , , and


Square to get .


Multiply to get


Subtract from to get


Multiply and to get .


or Break up the expression.


So the solutions are or


These solutions approximate to or

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Start with the given equation.


Notice that the quadratic is in the form of where , , and


Let's use the quadratic formula to solve for "x":


Start with the quadratic formula


Plug in , , and


Square to get .


Multiply to get


Rewrite as


Add to to get


Multiply and to get .


Take the square root of to get .


or Break up the expression.


or Combine like terms.


or Simplify.


So the solutions are or

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You are correct. Good job.

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f(x)= x/(x^2+7)


f(-x)= -x/((-x)^2+7)


f(-x)= -x/(x^2+7)

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(6*3)/(4+10-5) = (18)/(9) = 2

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In this case, a = 1, b = 3, and c = -2

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If a parallelogram has one right angle, then the other angles are right angles (since the opposite angle is equal and the adjacent angles are supplementary).

So there are 4 right angles. Since we have 4 right angles and 4 congruent sides, we have a square.

So...

A parallelogram is a square if and only if it has at least one right angle and four congruent sides

making the answer choice B.

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Start with the compound interest formula


Plug in (the amount invested), (the decimal equivalent of 5.5%), (since interest is compounded semiannually) and (18 years).


Evaluate } to get


Add to to get


Multiply and to get .


Evaluate to get .


Multiply and to get .


Round to the nearest hundredth (ie to the nearest penny).


So there will be $531.10 in the account.

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Start with the given equation.


Add to both sides.


Subtract from both sides.


Combine like terms on the left side.


Combine like terms on the right side.


Divide both sides by to isolate .


Reduce.


----------------------------------------------------------------------

Answer:

So the solution is

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Start with the given equation.


Distribute.


Subtract from both sides.


Subtract from both sides.


Combine like terms on the left side.


Combine like terms on the right side.


Divide both sides by to isolate .


Reduce.


----------------------------------------------------------------------

Answer:

So the solution is

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Start with the given equation.


Subtract from both sides.


Subtract from both sides.


Combine like terms on the left side.


Combine like terms on the right side.


Divide both sides by to isolate .


Reduce.


----------------------------------------------------------------------

Answer:

So the solution is

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Note: there is no vertex as this is not a parabola.


Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is


Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point




Now since the slope is comprised of the "rise" over the "run" this means


Also, because the slope is , this means:




which shows us that the rise is -3 and the run is 4. This means that to go from point to point, we can go down 3 and over 4



So starting at , go down 3 units


and to the right 4 units to get to the next point



Now draw a line through these points to graph

So this is the graph of through the points and

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Start with the given equation.


Combine like terms on the right side.


Add to both sides.


Subtract from both sides.


Combine like terms on the left side.


Combine like terms on the right side.


Divide both sides by to isolate .


Reduce.


----------------------------------------------------------------------

Answer:

So the solution is

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There are symbols missing. Please repost.

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Start with the given equation.


Subtract from both sides.


Subtract from both sides.


Combine like terms on the left side.


Combine like terms on the right side.


Divide both sides by to isolate .


Reduce.


----------------------------------------------------------------------

Answer:

So the solution is

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Start with the given equation.


Combine like terms on the left side.


Combine like terms on the right side.


Subtract from both sides.


Subtract from both sides.


Combine like terms on the left side.


Combine like terms on the right side.


Simplify.


Since this equation is NEVER true for any x value, this means that there are no solutions.

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When multiplying exponential expressions with the same base, just add the exponents:


So

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I'm going to use a table to solve this problem. Tables are usually given at the back of the book.

Standard Normal Probability Table:
The table shows the area to the left of a z-score (area shown in red)


Now use the table to find the area to the left of -2.18 (it's shown in green and red below)

z	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
-3.4	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0002
-3.3	0.0005	0.0005	0.0005	0.0004	0.0004	0.0004	0.0004	0.0004	0.0004	0.0003
-3.2	0.0007	0.0007	0.0006	0.0006	0.0006	0.0006	0.0006	0.0005	0.0005	0.0005
-3.1	0.0010	0.0009	0.0009	0.0009	0.0008	0.0008	0.0008	0.0008	0.0007	0.0007
-3.0	0.0013	0.0013	0.0013	0.0012	0.0012	0.0011	0.0011	0.0011	0.0010	0.0010
-2.9	0.0019	0.0018	0.0018	0.0017	0.0016	0.0016	0.0015	0.0015	0.0014	0.0014
-2.8	0.0026	0.0025	0.0024	0.0023	0.0023	0.0022	0.0021	0.0021	0.0020	0.0019
-2.7	0.0035	0.0034	0.0033	0.0032	0.0031	0.0030	0.0029	0.0028	0.0027	0.0026
-2.6	0.0047	0.0045	0.0044	0.0043	0.0041	0.0040	0.0039	0.0038	0.0037	0.0036
-2.5	0.0062	0.0060	0.0059	0.0057	0.0055	0.0054	0.0052	0.0051	0.0049	0.0048
-2.4	0.0082	0.0080	0.0078	0.0075	0.0073	0.0071	0.0069	0.0068	0.0066	0.0064
-2.3	0.0107	0.0104	0.0102	0.0099	0.0096	0.0094	0.0091	0.0089	0.0087	0.0084
-2.2	0.0139	0.0136	0.0132	0.0129	0.0125	0.0122	0.0119	0.0116	0.0113	0.0110
-2.1	0.0179	0.0174	0.0170	0.0166	0.0162	0.0158	0.0154	0.0150	0.0146	0.0143
-2.0	0.0228	0.0222	0.0217	0.0212	0.0207	0.0202	0.0197	0.0192	0.0188	0.0183
-1.9	0.0287	0.0281	0.0274	0.0268	0.0262	0.0256	0.0250	0.0244	0.0239	0.0233
-1.8	0.0359	0.0351	0.0344	0.0336	0.0329	0.0322	0.0314	0.0307	0.0301	0.0294
-1.7	0.0446	0.0436	0.0427	0.0418	0.0409	0.0401	0.0392	0.0384	0.0375	0.0367
-1.6	0.0548	0.0537	0.0526	0.0516	0.0505	0.0495	0.0485	0.0475	0.0465	0.0455
-1.5	0.0668	0.0655	0.0643	0.0630	0.0618	0.0606	0.0594	0.0582	0.0571	0.0559
-1.4	0.0808	0.0793	0.0778	0.0764	0.0749	0.0735	0.0721	0.0708	0.0694	0.0681
-1.3	0.0968	0.0951	0.0934	0.0918	0.0901	0.0885	0.0869	0.0853	0.0838	0.0823
-1.2	0.1151	0.1131	0.1112	0.1093	0.1075	0.1056	0.1038	0.1020	0.1003	0.0985
-1.1	0.1357	0.1335	0.1314	0.1292	0.1271	0.1251	0.1230	0.1210	0.1190	0.1170
-1.0	0.1587	0.1562	0.1539	0.1515	0.1492	0.1469	0.1446	0.1423	0.1401	0.1379
-0.9	0.1841	0.1814	0.1788	0.1762	0.1736	0.1711	0.1685	0.1660	0.1635	0.1611
-0.8	0.2119	0.2090	0.2061	0.2033	0.2005	0.1977	0.1949	0.1922	0.1894	0.1867
-0.7	0.2420	0.2389	0.2358	0.2327	0.2296	0.2266	0.2236	0.2206	0.2177	0.2148
-0.6	0.2743	0.2709	0.2676	0.2643	0.2611	0.2578	0.2546	0.2514	0.2483	0.2451
-0.5	0.3085	0.3050	0.3015	0.2981	0.2946	0.2912	0.2877	0.2843	0.2810	0.2776
-0.4	0.3446	0.3409	0.3372	0.3336	0.3300	0.3264	0.3228	0.3192	0.3156	0.3121
-0.3	0.3821	0.3783	0.3745	0.3707	0.3669	0.3632	0.3594	0.3557	0.3520	0.3483
-0.2	0.4207	0.4168	0.4129	0.4090	0.4052	0.4013	0.3974	0.3936	0.3897	0.3859
-0.1	0.4602	0.4562	0.4522	0.4483	0.4443	0.4404	0.4364	0.4325	0.4286	0.4247
0.0	0.5000	0.4960	0.4920	0.4880	0.4840	0.4801	0.4761	0.4721	0.4681	0.4641

From the table, we see that the area to the left of z = -2.18 is 0.0146


So P(z< -2.18) = 0.0146