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Answer:
a. 4x^2 +16x -48 = 4x^2 +16x -48
b. -3x^2 +12x +36 = -3x^2 +12x +36
c. x^2 +12x +35 = x^2 +12x +35
Step-by-step explanation:
In general, you would prove this by transforming one of the expressions into the other. The easiest would be to transform the factored form into the vertex form, perhaps, as this would spare you trying to explain the magic of factoring.
Alternatively, you can transform both expressions into the same (standard) form. I believe that will be the easiest of all.
The product of two binomials is ...
(x +a)(x +b) = x(x +b) +a(x +b) = x^2 +bx +ax +ab
(x +a)(x +b) = x^2 +(a+b)x +ab . . . . after collecting terms
The square of a binomial is the same thing, but with b=a, so ...
(x +a)^2 = x^2 +2a +a^2
Using these forms, we can avoid showing all of the intermediate "work" of making the desired transformations.
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a. 4(x -2)(x +6) = 4(x +2)^2 -64
4(x^2 +4x -12) = 4(x^2 +4x +4) -64 . . . . . expanding the products
4x^2 +16x -48 = 4x^2 +16x +16 -64 . . . . using the distributive property
4x^2 +16x -48 = 4x^2 +16x -48 . . . . . collect terms; expressions are equal
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b. -3(x +2)(x -6) = -3(x -2)^2 +48
-3(x^2 -4x -12) = -3(x^2 -4x +4) +48
-3x^2 +12x +36 = -3x^2 +12x -12 +48
-3x^2 +12x +36 = -3x^2 +12x +36
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c. (x +5)(x +7) = (x +6)^2 -1
x^2 +12x +35 = x^2 +12x +36 -1
x^2 +12x +35 = x^2 +12x +35
Ok, it's all pretty much like the "$50 coat is on sale for $35".
<span>If the regular price of the coat is $50 and now it is on sale for $35, then it will cost you $15 less, like this: </span>
<span>$50 - $35 = $15 </span>
<span>You could also say the coat was discounted by $15, or the coat was reduced by $15, or you'll save $15 if you buy that coat ($50 - $15 = 35). </span>
<span>You could also put it in terms of percentages. If the discount is $15, you can figure that $15 is what percent of the regular price, like this: </span>
<span>$15 = X% of $50 </span>
<span>$15 = X% x $50 (divide both sides by 50 to isolate X) </span>
<span>15/50 = X% </span>
<span>.30 = X% (multiply by 100 to convert to a non-decimal) </span>
<span>30% = X </span>
<span>So, you can say all of the following and they all mean the same thing: </span>
<span>1. the $50 coat is on sale for $35 </span>
<span>2. the $50 coat is discounted by $15 </span>
<span>3. the $50 coat is reduced by $15 </span>
<span>4. you'll save $15 if you buy this coat </span>
<span>5. the $50 coat is on sale for 30% off </span>
<span>6. the $50 coat is discounted by 30% </span>
<span>7. you'll save 30% if you buy this coat </span>
<span>8. 30% savings! </span>
<span>9. Save 30%! </span>
<span>So, how does that apply to the $18,000 a year? Ok, if Shelby earns $18,000 this year and then earns $19,500 next year, then she gets an additional $1,500 ($19,500 - $18,000 = $1,500). In the coat problem, everything was discounted, on sale, going down. In this problem, everything is going up, increasing. </span>
<span>You know the dollar increase is $1,500. To figure the percent increase, you need to figure out that $1,500 is what % of $18,000. Remember, it's not the $19,500 that was increased; it was an increase on the $18,000: </span>
<span>$1,500 = X% of $18,000 </span>
<span>1,500/18,000 = X% </span>
<span>.083333 = X% </span>
<span>8.3333% = X </span>
<span>One more: If Shelby get a 10% increase in her salary at the end of one year, that's the same as saying that Shelby gets her salary plus she gets 10% more, like this: </span>
<span>$18,000 + (10% of $18,000) = </span>
<span>$18,000 + $1,800 = </span>
<span>$19,800 end of first year </span>
<span>For the second year, her salary begins at $19,800 and increases 10%, like this: </span>
<span>$19,800 + (10% x $19,800) = </span>
<span>$19,800 + $1,980 = </span>
<span>$21,780 end of second year </span>
<span>You can do it from here.</span>
Answer:
f(3)=5
f(0)= -7
Step-by-step explanation:
replace
4(3)-7
f(3)=5
f(0)=4(0)-7
f(0)=0-7
f(0)= -7
It means nothing. Example: <span>3 – 3 means start at 3 and go down 3.
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