In two or more complete sentences write and solve an equation for the situation and explain how you will solve the equation. Aft
1 answer:
Answer:
Grace weighed 167 pounds before she started her exercise program.
Step-by-step explanation:
Given,
Weight lost by Grace = 45 pounds
Weight of Grace after exercise weeks = 122 pounds
Let,
x represents the weight of Grace before she started the exercise program.
Loss means subtraction, therefore,
We will subtract the lost weight from original weight.
Original weight - Weight lost = Weight after exercise weeks
Adding 45 on both sides
Grace weighed 167 pounds before she started her exercise program.
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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.
Answer: The answer is: " 72 words per minute. "
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Step-by-step explanation:
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This is a "unit rate" problem.
We want to solve for/ find the number of words PER single minute.
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Given 48 words per (2/3) minute;
How many words per (one) minute?
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The answer is {48 ÷ (2/3) } words per minute:
Note: dividing by a number is the same as multiplying by the reciprocal (inverse) of that particular number:
Hence:
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The answer is {48 * (3/2) } words per minute:
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Write as:
" " ;
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The "48" can be changed to "24" ; and the "2" can be changed to "1" ;
→ {Since: "48 ÷ 2 = 24 "} ;
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And we have:
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" " ;
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The answer is: " 72 words per minute ."
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Hope this is helpful to you!
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