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kupik [55]
3 years ago
8

Determine what must be multiplied so that the expression below will have a common denominator. Use the backslash / to type in a

fraction.

Mathematics
1 answer:
Mashutka [201]3 years ago
7 0

Answer:

Multiply the first fraction by \frac{x+4}{x+4}

Multiply the second fraction by \frac{x-4}{x-4}

Step-by-step explanation:

Given

\frac{4}{x^2 - 16} + \frac{3}{x^2 + 8x + 16}

Required

Make the denominator equal

\frac{4}{x^2 - 16} + \frac{3}{x^2 + 8x + 16}

Factorize the denominator

\frac{4}{x^2 - 4^2} + \frac{3}{x^2 + 4x + 4x+ 16}

\frac{4}{(x - 4)(x + 4)} + \frac{3}{(x+ 4)(x + 4)}

Multiply the first fraction by \frac{x+4}{x+4}

Multiply the second fraction by \frac{x-4}{x-4}

\frac{x+4}{x+4} * \frac{4}{(x - 4)(x + 4)} + \frac{3}{(x+ 4)(x + 4)} * \frac{x-4}{x-4}

\frac{4(x + 4)}{(x - 4)(x + 4)(x + 4)} + \frac{3(x - 4)}{(x+ 4)(x + 4)(x - 4))}

\frac{4(x + 4)}{(x^2 - 16)(x + 4)} + \frac{3(x - 4)}{(x^2 - 16)(x + 4))}

<em>The expression now have the same denominator</em>

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Can you help me with my work
ira [324]

Answer

The vertex is at point (-3, -1)

The axis of symmetry is x = -3

Explanation

We are asked to find the vertex and axis of symmetry of the equation given.

f(x) = x² + 6x + 8

The vertex of a quadratic equation is the point where the graph of the quadratic equation changes from sloping negatively to sloping positively and vice-versa.

The axis of symmetry represents the straight line that divides the graph of the quadratic equation into two mirror parts that are similar to and are mirror images of each other. This axis of symmetry usually passes through the vertex.

To find the vertex, it is usually at the turning point where the first derivative of the quadratic equation is equal to 0.

(df/dx) = 0

f(x) = x² + 6x + 8

(df/dx) = 2x + 6

At the vertex

(df/dx) = 2x + 6 = 0

2x = -6

Divide both sides by 2

(2x/2) = (-6/2)

x = -3

We then insert this into the equation to get the corresponding f(x) value.

f(x) = x² + 6x + 8

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Hence, the vertex is at point (-3, -1)

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Hope this Helps!!!

3 0
1 year ago
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Arturiano [62]
7/8 is equal to 0.875. Have a good day!
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2 years ago
X:y = 9:7 Form an equation that links x and y
sleet_krkn [62]

Equations are expressions with equal values

The equation that links x and y is 7x = 9y

<h3>How to determine the equation</h3>

The ratio is given as:

x : y = 9 : 7

Express the ratio, as a fraction

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Cross multiply

7 *x = 9 * y

Evaluate the product

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Hence, the equation that links x and y is 7x = 9y

Read more about equations at:

brainly.com/question/7784687

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