Alicia will construct a rectangle that has a height of 4 units and an area of up to 48 square units. Which inequality represents
1 answer:
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<em>Answer:</em>
<em /><em />
<em>Step-by-step explanation:</em>
<em>We can use a property I like to call SEi-F. (Subtract Exponents in a Fraction)</em>
<em>But first, there is an exponent outside of the parentheses in both places. We can use the Power of Parentheses to simplify and then use the SEi-F.</em>
<em>We will start with the x in the numerator.</em>
<em>3*4 = 12</em>
<em>Now for the y in the numerator.</em>
<em>4*4 = 16</em>
<em>Our new numerator is </em><em />
<em>We do need to simplify the numerator one more time to get rid of the 4 outside the parentheses.</em>
<em>We will start with x's coefficient.</em>
<em>2*4 = 8</em>
<em>Now for y's coefficient.</em>
<em>1**4 = 4</em>
<em>*y seems to have no coefficient, but if so, it has a coefficient of 1. This applies to other variables.</em>
<em>Our final simplified numerator is </em><em>.</em>
<em>Repeat with the denominator.</em>
<em>Try it yourself!</em>
<em>Make sure that when you finish, you finish the fraction.</em>
<em>After completing the denominator, your completed fraction should be:</em>
<em /><em />
<em>Now we can use the SEi-F to complete the problem.</em>
<em>Start with x.</em>
<em>8x - 4x = 4x</em>
<em>12 - 6 = 6</em>
<em>The first term is </em><em>.</em>
<em>Now for y.</em>
<em>4y - 2y = 2y</em>
<em>16 - 18 = -2</em>
<em>The second term is </em><em />
<em>The complete, simplified equation is </em><em>.</em>
<em>I could be wrong on the answer, but the work should be correct.</em>
<em>Hope this helps. Have a nice day. Oh, and one more thing. Surprised I'm not stealing points?</em>
First, we simplify 6x+2y=36 into 3x+y=18 by dividing by 2. This means that y=-3x+18.
The sum
can be written as: 
,
<span>
from the binomial expansion formula: </span>
.
<span>
Thus, substituting </span>y=-3x+18 and simplifying we have<span>
</span>
.
This is a parabola which opens upwards (the coefficient of x^2 is positive), so its minimum is at the vertex. To find x, we apply the formula -b/2a. Substituting b=-108, a=10, we find that x is 108/20=5.4.
At x=5.4, the expression
, which is equivalent to , takes it smallest value.
Substituting, we would find
=32.4 This is the smallest value of the expression.
For x=5.4, y=-3x+18=-3(5.4)+18=1.8.
Answer: (5.4, 1.8)
The sum
<span>
from the binomial expansion formula: </span>
<span>
Thus, substituting </span>y=-3x+18 and simplifying we have<span>
</span>
This is a parabola which opens upwards (the coefficient of x^2 is positive), so its minimum is at the vertex. To find x, we apply the formula -b/2a. Substituting b=-108, a=10, we find that x is 108/20=5.4.
At x=5.4, the expression
Substituting, we would find
For x=5.4, y=-3x+18=-3(5.4)+18=1.8.
Answer: (5.4, 1.8)