Item 5
1 answer:
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Answer:
1. =
2. =
3. =
4. =
Step-by-step explanation:
1.
Taking LCM of (x+3) and (x+5) which is: (x+3)(x+5)
Prove closure: The value of x≠-3 and x≠-5 because if there values are -3 and -5 then the denominator will be zero.
2.
Factors of x^2-16 = (x)^2 -(4)^2 = (x-4)(x+4)
Factors of x^2+5x+6 = x^2+3x+2x+6 = x(x+3)+2(x+3) =(x+2)(x+3)
Putting factors
Prove closure: The value of x≠-2 and x≠4 because if there values are -2 and 4 then the denominator will be zero.
3.
Factors of x^2-9 = (x)^2-(3)^2 = (x-3)(x+3)
Factors of x^2-5x+6 = x^2-2x-3x+6 = x(x-2)+3(x-2) =(x-2)(x+3)
Putting factors
Taking LCM of (x-3)(x+3) and (x-2)(x+3) we get (x-3)(x+3)(x-2)
Prove closure: The value of x≠3 and x≠-3 and x≠2 because if there values are -3,3 and 2 then the denominator will be zero.
4.
Factors of x^2-5x+6 = x^2-3x-2x+6 = x(x-3)-2(x-3) = (x-2)(x-3)
Factors of x^2-16 = (x)^2 -(4)^2 = (x-4)(x+4)
Converting ÷ sign into multiplication we will take reciprocal of the second term
Prove Closure: The value of x≠2 and x≠4 because if there values are 2 and 4 then the denominator will be zero.
<h2>Answer:</h2>
1. Between April 1 and May 1, Bob's price incrdased by <u>$0.50 or 15%</u>.
2. Between May 1 and June 1, Bob's price decreased by <u>$0.50 or 13%</u>.
3. Suppose that atgas station across the street, prices are always 20% higher than Bob's. In absolute dollar terms, the difference between Bob's prices and the prices across the street is <u>$0.1 more expensive</u> when gas costs $3.85 than when gas costs $3.35.
4. Suppose the Fed raises the target for the federal fundsb rate from 2% to 2.25%. This change of percentage points means that the Fed raised its target by approximately <u>0.25%</u>.
<h2>Step-by-step explanation:</h2><h3>1. Between April 1 and May 1, Bob's price incrdased by...</h3><em>Take the difference of the prices to find an absolute value:</em>
$3.85 - $3.35= $0.50.
<em>Use the following formula to find the relative value:</em>
C= |Original value - New value|/ Original value
=15%.
<em>Take the difference of the prices to find an absolute value:</em>
$3.85 - $3.35= $0.50.
<em>Use the following formula to find the relative value:</em>
C= |Original value - New value|/ Original value
=13%.
<em>In this question we are looking for the difference of a difference. </em>
<em>If the proces across the street are always 20% higher, to find how much the gallon costs just multiply the price by 1.20, to increase 0.2 or 20%:</em>
$3.85 * 1.20= $4.62.
<em>Now, to see how much expensive this price is compared to Bob's, take de difference between the prices:</em>
$4.62 - $3.85= $0.77.
<em>Do the same to find the difference between the gas prices when the price is $3.35.</em>
$3.35 * 1.20= $4.02.
$4.02 - $3.35= $0.67.
Now, find the difference of those differences:
$0.77 - $0.67= $0.1.
<h3>4. Suppose the Fed raises the target for the federal funds rate from 2% to 2.25%. This change of percentage points means that the Fed raised its target by approximately (blank).</h3><em>Find the difference between percentages:</em>
2.25% - 2%= 0.0225 - 0.02= 0.0025= 0.25%.
<em>Simpler method:</em>
2.25% - 2%= 0.25%.