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Chapter 3: Q. 8 (page 174)

Solve $x^{2} - 10 x + 24 \geq 0$

Short Answer

Expert verified

The solution of inequality is $\{x x \leq 4 or x \geq 6\}$ or in interval notation $(- \infty, 4] or [6, \infty)$ .

Step by step solution

01

Step 1. Given information.

Solve the given quadratic inequality.

$x^{2} - 10 x + 24 \geq 0$

02

Step 2. Graph the function.

Graph the function $f (x) = x^{2} - 10 x + 24$ .

03

Step 3. Find intercept.

y- intercept: $f (0) = 0^{2} - 10 (0) + 24 = 24$

x- intercept: Solve $f (x) = 0$

$x^{2} - 10 x + 24 = 0 x^{2} - 4 x - 6 x + 24 = 0 x (x - 4) - 6 (x - 4) = 0 (x - 4) (x - 6) = 0 x = 4, x = 6$

So, the x-intercept are $x_{1} = 4 and x_{2} = 6$ .

The solution set is $\{x x \leq 4 or x \geq 6\}$ and in interval notation $(- \infty, 4] or [6, \infty)$ .

04

Step 4. Conclusion

The solution set of inequality is $\{x x \leq 4 or x \geq 6\}$ or in interval notation $(- \infty, 4] or [6, \infty)$ .

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Most popular questions from this chapter

The John Deere company has found

that the revenue, in dollars, from sales of riding mowers is a function of the unit price p, in dollars, that it charges. If the revenue R is $R (p) = - \frac{1}{2} p^{2} + 1900 p$

what unit price p should be charged to maximize revenue? What is the maximum revenue?

Determine the quadratic function whose graph is given.

State the circumstances that cause the graph of a quadratic function $f (x) = a x^{2} + b x + c$ to have no x-intercepts.

The daily revenue R achieved by selling x boxes of candy is figured to be $R (x) = 9.5 x - 0.04 x^{2}$ The daily cost C of selling x boxes of candy is $C (x) = 1.25 x + 250$ .

(a) How many boxes of candy must the firm sell to maximize revenue? What is the maximum revenue?

(b) Profit is given as P(x) = R(x) - C(x). What is the profit function?

(c) How many boxes of candy must the firm sell to maximize profit? What is the maximum profit?

(d) Provide a reasonable explanation as to why the answers found in parts (a) and (c) differ. Explain why a quadratic function is a reasonable model for revenue.

Find the average rate of change of $f (x) = 3 x^{2} - 2$ from 2 to 4.

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