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4 years ago

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Solve the inequality. q - 1/2 > 1/3

1 answer:

sergij07 [2.7K]4 years ago

5 0

Answer:

q>5/6

Step-by-step explanation:

We have to leave the variable alone on its side of inequality, one way of doing this is by summing the oppositer term to -1/2 to both sides

so q-1/2+1/2>1/3+1/2

This leaves us the following

q>1/2 + 1/3

Which is the same as the following inequality

q>5/6

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Which equation represents a graph with a vertex at (–3, 2)?

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<u>We will proceed to find the equations in the vertex form in each case</u>

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Group terms that contain the same variable, and move the constant to the opposite side of the equation

$y-38= 4x^{2}+24x$

Factor the leading coefficient

$y-38= 4(x^{2}+6x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$y-38+36= 4(x^{2}+6x+9)$

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$y= 4(x+3)^{2}+2$

<u>the vertex is the point $(-3,2)$ </u>

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Group terms that contain the same variable, and move the constant to the opposite side of the equation

$y-38= 4x^{2}-24x$

Factor the leading coefficient

$y-38= 4(x^{2}-6x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

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<u>Part c) </u> $y=4x^{2}+12x+2$

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Complete the square. Remember to balance the equation by adding the same constants to each side

$y-2+9= 4(x^{2}+3x+2.25)$

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<u>the vertex is the point $(-1.5,7)$ </u>

<u>Part d)</u> $y=4x^{2}+16x+13$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

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$y+3= 4(x+2)^{2}$

$y= 4(x+2)^{2}-3$

<u>the vertex is the point $(-2,-3)$ </u>

therefore

<u>the answer is </u>

$y= 4x^{2}+24x+38$

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