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Solved Algebra Problems

Some of the most common algebra problems solved.… read more

The ritz carlton hotel used a customer opinion questionare to obtain performing data about its dining and entertainment services. Customers were asked to rate six factors: Welcome, Service, food, menu, appeal, atmosphere and overall experience. Data were recorded for each factor 1 for fair 2 for average and 3 for good and 4 for excellent a) The customers response provided data for six variables. Are the variables quantative or qualitative? b) What measurement of scale if used?

Solution:

  1. A quantitative variable is a phenomenon measured in amounts, that is, numerical units. For example, a numerical score is a quantitative variable.
  2. The measurement is based on a scale of 1 to 4.
… read more

2x-5y=9 and 3x+4y=25. Solve by the method of elimination.

Solution:

1.    3x + 4y=25
2.    2x – 5y=9

We could rewrite these as follows by multiplying the first equation by 5 and the second by 4:

1.    15x + 20y = 125
2.    8x  – 20y = 36

If we add the above two equations, we can eliminate y:

23x = 161

So x =3D 7, and plugging this into the first equation we can figure out
y:  21 + 4y =3D 25,

so y = 1… read more

I need help with solving systems by graphing. this is one of the problems y=5x-2 y=x+6

Solution:

First write down the two equations and then pick several values of x and use those values to calculate the corresponding values of y. You can use the  x,y pairs to then plot each line. You will see that the two lines intersect at 2,8 =i.e. x=2 and y=8).

… read more

Find the domain of the function. f(x)= 2x^2+5x+3/2x^2-5x-3

Solution:

First, let’s plot  f(x) =

Here’s what the graph looks like:

Now, the definition of “domain of a function” as follows: The domain of a given function is the set of “input” values for which the function is defined.” For instance, the domain of cosine would be all real numbers, while the domain of the square root would be only numbers greater than or equal to 0 (ignoring complex numbers in both bases).

As you can see from the above graph, the function is valid for all “real” values of x, except for 0. The set of “real numbers”, as you may know, can be thought of as points on an infinitely long number line. The shorthand way of saying “all real numbers except for x” is as follows:

… read more

Cara made some cookies for her math club bake sale. She sold 3/5 of them in the morning and 1/4 of the remaining cookies in the afternoon. If she sold 200 more cookies in the morning than in the afternoon, how many cookies did she make?

Solution:

1. Let’s call the number of cookies Cara made “x”
2. First she sold three fifths of x(.6x)
3. The remaining amount is two fifths of x(.4x)
4. Then she one fourth of x;two fifths of “x” (.25*.4x = .1x)
5. .6x=.1x+200
6. .5x=200
7. x= 400… read more

Find three consecutive odd integers such that the sum of the largest and twice the smallest is 25. If x represents the smallest integer, then which equation could be used to solve the problem?

Solution:

X is the smallest number

y=x+2

z=x+4

z+2x=25

x+4+2x=25

3x=21

X=7

Y=9

Z=11

The equation that we used to solve the problem is x+4+2x=25, which can be simplified to = x=21.… read more

If a line passes through the points (3, 5) and (1, 2), its slope is =______.

The slope is defined as the change in Y divided by the change in X.

In this case, this would equal
(5-2)/(3-1)
= 3/2
= 1.5… read more

Find the descriminant of x^2-7x+2=0 and describe the natural roots

Solution:

  1. When you have an equation in the form of ax2 + =x + c = 0, the solution is x = where  D = b2 – 4ac
  2. D stands for discriminant, and values of x are the natural roots
  • If D > 0, then the values of x are real and distinct.
  • If D = 0, then the values of x are real and equal
  • If D < 0, then the values of x are unreal
  1. In your question, x2 – 7x + 2 = 0, so the values of a, b and c are as follows:
  • a = 1
  • b = -7
  • c = 2
  1. D = b2 – 4ac = 49 – 8 = 41 (this is the value of the discriminant)
  2. Since D > 0, then the values of x (the natural roots) are real and distinct
… read more

Factor the following expression: x^2-9

Solution:

First recognize that this is in the form of (x2-a2), which can always be factored as (x+a)(x-a). If you multiply these two terms, you get x2-ax+ax-a2, which is equal to x2-a2.

So in this case, we can see that a=3,

so  x2-9

=  x2-32

= (x+3)(x-3)… read more

Simplify : 12 – ( x + 3 ) +10

Solution:

You can simply 12 – ( x + 3 ) +10 by rearranging the terms:

  1. 12 –x -3 +10
  2. 19-x
… read more

If 2(x-5)=-11, then x=?

Solution:

  • 2(x – 5) = -11
  • 2x – 10 = -11
  • 2x = -1
  • x = -0.5
… read more

2sqrt(45)

Solution:

To calculate 2 times the square root of 45 (2sqrt(45)), you just need to calculate the square root of 45 and then multiply it by two:

Step1: 2 x sqrt (45)

Step 2: 2 x 6.708

Step 3: 13.416

We used a calculator to get obtain the square root of 45. Are you allowed to use a calculator? If not, we can show you how to calculate this manually.… read more