Rime: A number with exactly two factors; one and itself. What does this mean? This means that for us to call a number prime, only two whole numbers can divide into it without a remainder. Here are a few examples: 2, 3, 5, 7, 11<span>, </span>13<span>, </span>17<span>, </span>19<span>, </span>23<span>, and so on.</span>
Answer:
x = 2
Step-by-step explanation:
These equations are solved easily using a graphing calculator. The attachment shows the one solution is x=2.
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<h3>Squaring</h3>
The usual way to solve these algebraically is to isolate radicals and square the equation until the radicals go away. Then solve the resulting polynomial. Here, that results in a quadratic with two solutions. One of those is extraneous, as is often the case when this solution method is used.

The solutions to this equation are the values of x that make the factors zero: x=2 and x=-1. When we check these in the original equation, we find that x=-1 does not work. It is an extraneous solution.
x = -1: √(-1+2) +1 = √(3(-1)+3) ⇒ 1+1 = 0 . . . . not true
x = 2: √(2+2) +1 = √(3(2) +3) ⇒ 2 +1 = 3 . . . . true . . . x = 2 is the solution
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<h3>Substitution</h3>
Another way to solve this is using substitution for one of the radicals. We choose ...

Solutions to this equation are ...
u = 2, u = -1 . . . . . . the above restriction on u mean u=-1 is not a solution
The value of x is ...
x = u² -2 = 2² -2
x = 2 . . . . the solution to the equation
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<em>Additional comment</em>
Using substitution may be a little more work, as you have to solve for x in terms of the substituted variable. It still requires two squarings: one to find the value of x in terms of u, and another to eliminate the remaining radical. The advantage seems to be that the extraneous solution is made more obvious by the restriction on the value of u.
Let the two numbers be x and y.
Let m = the fraction (or percentage) for increasing the numbers.
Increase x by 5, multiply (x+5) by (1+m), and set it qual to 36.
(x + 5)*(1 + m) = 36
Increase y by 5, multiply (y+5) by (1+m), and set it equal to 36.
(y+5)*(1+m) = 36
Therefore
(x+5)*(1+m) = (y+5)*(1+m)
x + 5 = y + 5
x = y
x - y = 0
Answer: 0.
The difference between the two numbers is zero.
Answer:
<u>The correct answer is C. 600 shares worth $16.67 each </u>
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Number of old shares Jim owns in Gamma Vision Inc = 400
Value of each share = $ 25
Ratio of new shares : old shares after the split = 3:2
2. How many shares will he have after the split and how much will each be worth? Select the best answer from the choices provided.
A. Let's use the ratio provided to calculate the number of new shares Jim will own, this way:
New shares = 400 * 3/2 = 1,200/2 = 600
B. Let's calculate the price of the new share, this way:
The total value of the new shares should be the same than the total value of the old shares, then:
400 * 25 = 600 * x
10,000 = 600x
x = 10,000/600 = 16.67
<u>The correct answer is C. 600 shares worth $16.67 each </u>
Answer:
55,050
Step-by-step explanation: