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3 years ago

What is the solution to the given inequality?

Mathematics

1 answer:

SashulF [63]3 years ago

5 0

1/2 - 1/4x ≥ -1/4

Combine 1/4x to get x/4:

1/2 - x/4 ≥ -1/4

Subtract 1/2 from both sides:

-x/4 ≥ -1/4 - 1/2

Simplify:

-x/4 ≥ -3/4

Multiply both sides by 4:

-x ≥ -3/4 * 4

-x ≥ -3

Multiply each side by -1 ( and since you are multiplying by -1, you also need to reverse the inequality sign)

Answer: x ≤ 3

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Answer:

$x=-3\:or\:x=\frac{3}{2}$

Step-by-step explanation:

The given parabola has equation

$2x^2+5x-9=2x$

We rewrite in standard form to obtain:

$2x^2+5x-2x-9=0$

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Split the middle terms to get:

$2x^2+6x-3x-9=0$

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Write an equation in slope-intercept form for the following line:<br><br> (-14,1) and (13,-2)

alex41 [277]

Answer:

$\large \boxed{y = - \frac{1}{9} x - \frac{5}{9} }$

Step-by-step explanation:

In order to find an equation of a line with two given ordered pairs. We have to find a slope first which we can do by using the formula below.

$\large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }$

m-term is defined as slope in y = mx+b form which is slope-intercept form.

Now we substitute these ordered pairs (x, y) in the formula.

$\large{m = \frac{1 - ( - 2)}{ -14 - 13} } \\ \large{m = \frac{1 + 2}{ - 27} } \\ \large{m = \frac{3}{ - 27} = - \frac{1}{9} }$

After we calculate for slope, we substitute m-value in slope-intercept form. The slope-intercept form is

$\large \boxed{y = mx + b}$

We already know m-value as we substitute it.

$\large{y = - \frac{1}{9} x + b}$

We are not done yet because we need to find the b-term which is our y-intercept. (Note that m-term is slope while b-term is y-intercept)

We can find the y-intercept by substituting either (-14,1) or (13,-2) in the equation. I will be using (13,-2) to substitute in the equation.

$\large{y = - \frac{1}{9} x + b} \\ \large{ - 2 = - \frac{1}{9} (13) + b} \\ \large{ - 2 = - \frac{13}{9} + b} \\ \large{ - 2 + \frac{13}{9} = b} \\ \large{ - \frac{5}{9} = b}$

Finally, we know b-value. Then we substitute it in our equation.

$\large{y = - \frac{1}{9} x + b} \\ \large{y = - \frac{1}{9} x - \frac{5}{9} }$

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