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Flura [38]
3 years ago
7

The width of a rectangle is 5x+3, and the length of the

Mathematics
1 answer:
jok3333 [9.3K]3 years ago
5 0

Answer:

<em>Answer: 1/4</em>

Step-by-step explanation:

<u>Algebraic Operations</u>

The width of a rectangle is given as W=5x+3 and the length of the rectangle is given as L=20x+12.

It's required to determine the ratio of the width to the length, that is:

\displaystyle   \frac{W}{L}=\frac{ 5x+3}{20x+12}

This fraction can be simplified if we factor the expression in the denominator. The LCF of 20x and 12 is 4, thus:

\displaystyle   \frac{W}{L}=\frac{ 5x+3}{4(5x+3)}

Now note we have the exact same expression up and down, thus simplifying:

\displaystyle   \frac{W}{L}= \frac{1}{4}

Answer: 1/4

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3 years ago
If a rectangle has an area of x^2+x-20 and a width of x-4, what is the length?
Mrac [35]

Answer:

This (x - 5) represents the length of the rectangle.

Step-by-step explanation:

The formula for the area of a rectangle of length L and width W is A = L * W.

Here, the width is x - 4 and the area is x^2 + x - 20.  Dividing the width (x - 4) into the area results in an expression for the length:

x - 4  /   x^2 + x - 20

Let's use synthetic division here.  It's a little faster than long division.

If the divisor in long division is x - 4, we know immediately that the divisor in synthetic division is 4:

4   /   1    1    -20

              4     20

    --------------------

         1     5     0

This synthetic division results in a remainder of 0.  This tells us that 4 (or the corresponding (x - 4) is indeed a root of the polynomial x^2 + x - 20, and so *(x - 4) is a factor.  From the coefficients 1 and 5 we can construct the other factor:  (x - 5).  This (x - 5) represents the length of the rectangle.

4 0
2 years ago
Is this proportion true 12/15=47/50<br>16/36=12/27<br>15/20=24/26<br>or 4/16=2/14
jekas [21]
For <span>12/15=47/50, we multiply 12/15 by (1/3)/(1/3) to get 4/5. For 47/50, we multiply it by (1/10)/(1/10) to get the same denominator and 4/7/5. They are not equal.

For 16/36 and 12/27, we'll notice that 36 and 27 are both multiples of 9, so we need to get that as the denominator! Multiply 16/36 by (1/4)/(1/4) because 9 goes into 36 4 times and 12/27 by (1/3)/(1/3) due to that 27 goes into 9 3 times, we get 4/9=4/9 - these are equal!

I challenge you to get the rest of them on your own using my techniques!</span>
3 0
3 years ago
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