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3 years ago

Explain how the following inequality can be used to find the number of toys you can afford to buy. 150≤ 11x + 10 ≤ 450

Mathematics

1 answer:

irakobra [83]3 years ago

8 0

Answer:

The maximum number of toys you can afford to buy is 40

Step-by-step explanation:

Let

x -----> the number of toys

we have the compound inequality

$150\leq 11x+10\leq 450$

Divide into two inequalities

$150\leq 11x+10$ -----> inequality A

$11x+10\leq 450$ ----> inequality B

<em>Solve the inequality A</em>

$150-10\leq 11x$

$140\leq 11x$

Divide by 11 both sides

$12.7\leq x$

Rewrite

$x\geq 12.7$

<em>Solve the inequality B</em>

$11x\leq 450-10$

$11x\leq 440$

Divide by 11 both sides

$x\leq 40$

The solution for x is the interval ----> [13,40}

Remember that the number of toys must be a whole number

The domain is all whole numbers greater than or equal to 13 toys and less than or equal to 40 toys

therefore

The maximum number of toys you can afford to buy is 40

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2 years ago

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2 years ago

If the parent function is fx) = x^3 which transformed function is shown in the graph?

34kurt

Answer:

g(x) = (x-3)³ is the transformed function.

Step-by-step explanation:

Horizontal shift:

If f(x) is the parent function.

Then horizontal shift can be expressed as:

, will shift left units.

$y = f(x - c)$ , will shift $f(x)$ right c units.

Given the parent function

f(x) = x³

From the graph, it is clear that the transformed function is indicating that the parent function has been horizontally shifted right 3 units.

Therefore, according to the rule, $y = f(x - c)$ :

g(x) = (x-3)³ is the transformed function.

From the graph,

The Red graph indicates the parent function i.e. f(x) = x³

The Blue graph indicates the transformed function i.e. g(x) = (x-3)³

It is clear that the blue graph is obtained when the parent function has been horizontally shifted right 3 units.

Therefore, g(x) = (x-3)³ is the transformed function.

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