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laiz [17]
3 years ago
14

The PTA at Newberg High School is having its annual dinner and auction to raise money for music and art programs. Last year, the

event raised $84,240. This year, it raised $54,756. What is the percent of decrease in the amount raised?
Mathematics
1 answer:
Zinaida [17]3 years ago
8 0
Percent of change = absolute value of the original amount minus new amount divided by the original amount.

The answer is a 35% decrease
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Which of these is the standard form of the following function?
Nady [450]

Answer:

A

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Given

f(x) = - 9(x + 5)² + 4 ← expand parenthesis using FOIL

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What is the first step in solving the equation x2 – 16/25 = 0?
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Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 

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Step by step solution :<span>Step  1  :</span> 16 Simplify —— 25 <span>Equation at the end of step  1  :</span><span><span> 16 (x2) - —— = 0 25 </span><span> Step  2  :</span></span>Rewriting the whole as an Equivalent Fraction :

<span> 2.1 </span>  Subtracting a fraction from a whole 

Rewrite the whole as a fraction using <span> 25 </span> as the denominator :

<span> x2 x2 • 25 x2 = —— = ——————— 1 25 </span>

<span>Equivalent fraction : </span>The fraction thus generated looks different but has the same value as the whole 

<span>Common denominator : </span>The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

<span> 2.2 </span>      Adding up the two equivalent fractions 
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

<span> x2 • 25 - (16) 25x2 - 16 —————————————— = ————————— 25 25 </span>Trying to factor as a Difference of Squares :

<span> 2.3 </span>     Factoring: <span> 25x2 - 16</span> 

Theory : A difference of two perfect squares, <span> A2 - B2  </span>can be factored into <span> (A+B) • (A-B)

</span>Proof :<span>  (A+B) • (A-B) =
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</span>Note : <span> <span>AB = BA </span></span>is the commutative property of multiplication. 

Note : <span> <span>- AB + AB </span></span>equals zero and is therefore eliminated from the expression.

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Factorization is :       (5x + 4)  •  (5x - 4) 

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Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the <span>denominator, </span>Tiger multiplys both sides of the equation by the denominator.

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Now, on the left hand side, the <span> 25 </span> cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
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Theory - Roots of a product :

<span> 3.2 </span>   A product of several terms equals zero.<span> 

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Solving a Single Variable Equation :

<span> 3.3 </span>     Solve  :    5x+4 = 0<span> 

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<span> 3.4 </span>     Solve  :    5x-4 = 0<span> 

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<span><span> x = 4/5 = 0.800
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