Jennifer bought a pair of shoes on sale for 40% off the original price. After she used a $15 gift card, her total was $74.82. Wh
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Answer:
p = 2
n = 14
m = 3
Step-by-step explanation:
In order to be able combine (either add or subtract) rational expressions we need to write them with a common (similar) denominator. For that reason we first find the Least Common Denominator of both fractions, that way understanding how to express the two fractions using equivalent fractions with like denominator that can be combined.
We see that the denominator of the first fraction contains the factor "x", therefore "x" has to be a factor of that least common denominator.
We also see that the second fraction contains "2" as a factor, therefore 2 has to be a factor as well for our Least Common Denominator (LCD)
So the LCD we need is the product: 2*x which we write as 2x.
Now we write the first fraction as an equivalent one but with denominator "2x" by multiplying top and bottom by 2 (and thus not changing the actual value of the fraction):
Next we do the same with the second fraction, this time multiplying top and bottom by the factor "x":
Now that both fractions are written showing the same denominator , we can combine them as indicated:
This expression gives as then the values for the requested coefficients.
p = 2
n = 14
m = 3
Answer: (A)
(B) Length varies between 1 and 150
(C) Largest area is 22500ft²
Step-by-step explanation: Suppose length is l and width is w.
The rectangular garden has perimeter of 600ft, which is mathematically represented as
Area of a rectangle is calculated as
Now, we have a system of equations:
Isolate w, so we have l:
w = 300 - l
Substitute in the area equation:
A = l(300 - l)
A = 300l - l²
(A) <u>Function of area in terms of length is given by </u><u>A = 300l - l²</u>
(B) The practical domain for this function is values between 1 and 150.
(C) For the largest area, we need to determine the largest garden possible. For that, we take first derivative of the function:
A' = 300 - 2l
Find the values of l when A'=0:
300 - 2l = 0
2l = 300
l = 150
Replace l in the equation:
w = 300 - 150
w = 150
Now, calculate the largest area:
A = 150*150
A = 22500
<u>The largest area the fence can enclose is </u><u>22500ft².</u>
<span>3x + y = 9 (I)
</span><span>y = –4x + 10 (II)
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</span>
Pass the incognito "4x" to the first term, changing the signal when changing sides.
<span>-------------------------
simplify by (-1)
</span>
<span>
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</span>
<span>
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</span>
<span>
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</span>
<span><span>
</span></span><span>Substitute in equation (I) to find the value of "Y".
</span>3x + y = 9 (I)
3*(1) + y = 9
3 + y = 9
y = 9 - 3
Answer:
</span><span>y = –4x + 10 (II)
------------------------
</span>
Pass the incognito "4x" to the first term, changing the signal when changing sides.
<span>-------------------------
simplify by (-1)
</span>
-------------------------
</span>
<span>
-------------------------
</span>
-----------
</span>
</span></span><span>Substitute in equation (I) to find the value of "Y".
</span>3x + y = 9 (I)
3*(1) + y = 9
3 + y = 9
y = 9 - 3
Answer: