What value of x satisfies this equation (5x + 20) = 2
1 answer:
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I'm assuming the function is f(x) = (2x+8)/(x^2+5x+6). If so, make sure to use parenthesis to indicate that you're dividing all of "2x+8" over all of "x^2+5x+6" as one big fraction. Otherwise, things are ambiguous and it leads to confusion.
Side Note: x^2 means "x squared"
Factor the numerator: 2x+8 = 2(x+4)
Factor the denominator: x^2+5x+6 = (x+2)(x+3)
There are no common factors between the numerator and denominator. So there is nothing to cancel out.
Recall that you cannot divide by zero. Something like 1/0 is undefined.
We need to find the x values that cause the denominator to be zero.
Set the denominator equal to zero and solve for x
x^2+5x+6 = 0
(x+2)(x+3) = 0
x+2 = 0 or x+3 = 0
x = -2 or x = -3
The x values x = -2 or x = -3 will lead to the denominator being zero. This means that the vertical asymptotes are x = -2 or x = -3 as shown by the blue dashed vertical lines in the attached image.
Side Note: x^2 means "x squared"
Factor the numerator: 2x+8 = 2(x+4)
Factor the denominator: x^2+5x+6 = (x+2)(x+3)
There are no common factors between the numerator and denominator. So there is nothing to cancel out.
Recall that you cannot divide by zero. Something like 1/0 is undefined.
We need to find the x values that cause the denominator to be zero.
Set the denominator equal to zero and solve for x
x^2+5x+6 = 0
(x+2)(x+3) = 0
x+2 = 0 or x+3 = 0
x = -2 or x = -3
The x values x = -2 or x = -3 will lead to the denominator being zero. This means that the vertical asymptotes are x = -2 or x = -3 as shown by the blue dashed vertical lines in the attached image.
<h3><u>Question:</u></h3>
The rectangle below has an Área of x^2 + 11x + 28 square meters and a length of x+7 meters. What expression represents the width of the rectangle?
<h3><u>Answer:</u></h3>The expression representing width of rectangle is (x + 4) meters
<h3><u>Solution:</u></h3>Given that rectangle has an area x^2 + 11x + 28 square meters and a length of x + 7 meters
To find: width of the rectangle
<em><u>The area of rectangle is given as:</u></em>
Here area = x^2 + 11x + 28 square meters
length = x + 7 meters
<em><u>Substituting the values in given formula,</u></em>
Cancelling (x + 7) on numerator and denominator,
Thus expression representing width of rectangle is (x + 4) meters