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2 years ago

Write an expression to represent the product of 6 and the square of a number plus 15.

Mathematics

1 answer:

inn [45]2 years ago

8 0

Answer:

6x² + 15

Step-by-step explanation:

Let the number be x.

"the square of a number"

x²

"the product of 6 and the square of a number"

6x²

"the product of 6 and the square of a number plus 15"

6x² + 15

The coefficient is the number that multiplies the variable, so it is 6.

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Which values are with in the range of the piecewise defined function?

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Answer:

y = -6; -3; 0

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

f(x) = 2x+2 , x < -3

f(x) = x, x = -3

f(x) = - x -2 , x > -3

From the graph, we can see that the values are

y = -6; -3; 0

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andrew-mc [135]

$\dfrac{ \dfrac{x+3}{4x^2-16} }{ \dfrac{2x^2+10x+12}{2x-4} }$

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Write the divide fraction horizontally:
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$= \dfrac{x+3}{4x^2-16} \div \dfrac{2x^2+10x+12}{2x-4}$

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Factorise the numerators and denominators when possible:
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$= \dfrac{x+3}{4(x+2)(x-2)} \div \dfrac{ 2(x + 3) (x + 2)}{2(x-2)}$

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Convert the divide fraction to multiplication fraction
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$= \dfrac{x+3}{4(x+2)(x-2)} \times \dfrac{2(x-2)}{2(x+3)(x+2)}$

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Cancel the factors
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$= \dfrac{1}{4(x+2)} \times \dfrac{1}{(x+2)}$

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Combine to single fraction
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$= \dfrac{1}{4(x+2)^2}$

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