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3 years ago

In the piece-wise function graphed below, which is the correct equation for when -2 ≤ x ≤ 0

Mathematics

1 answer:

Finger [1]3 years ago

3 0

Answer:

y = 3x + 5

Step-by-step explanation:

In the interval - 2 ≤ x ≤ 0 the graph is a straight line.

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, - 1) and (x₂, y₂ ) = (0, 5) ← 2 points on the line

m = $\frac{5+1}{0+2}$ = $\frac{6}{2}$ = 3

The line intercepts the y- axis at (0, 5) ⇒ c = 5

y = 3x + 5 ← equation for - 2 ≤ x ≤ 0

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Mrs. Robinson, an insurance agent, earns a salary of $4,800 per year plus a 3% commission on her sales. The average price of a p

kap26 [50]

Answer:

$4800+183x\geq 8000$

She must sell at least 18 policies to make an annual income of at least $8,000

Step-by-step explanation:

Let $x$ be the number of policies Mrs. Robinson must sell

We know that Mrs. Robins makes 3% on commission for each policy sold. We also know that the average price of a policy is $6,100, so she makes 3% of $6,100 per policy sold. To find the 3% of $6,100 we just need to multiply 3% and $6,100; then dive the result by 100%:

$\frac{3*6,100}{100} =183$

Now we know that she makes $183 per policy sold. Since $x$ is the number of policies sold, $183x$ is her total commission for selling $x$ policies.

We also know that She makes $4,800 per year, so her total annual income is her salary plus her commissions, in other words:

$4800+183x$

Finally, we know that she wants to make at least $8,000, so her salary plus her commissions must be greater or equal than $8,000:

$4800+183x\geq 8000$

Let's solve the inequality:

1. Subtract 4800 from both sides

$4800-4800+183x\geq 8000-4800$

$183x\geq 3200$

2. Divide both sides by 183

$\frac{183x}{183} \geq \frac{3200}{183}$

$x\geq 17.48$

Since she can't sell a fraction of a policy, we must round the result to the next integer:

$x\geq 18$

We can conclude that she must sell 18 policies to make an annual income of at least $8,000.

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a coach asked two players how much water they drank before practice. Ashley said she drank 1/2 pint and Claire said she drank 0.

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1. The problem gives the following information: Ashley said she drank 1/2 pints and Claire said she drank 0.7 pints.

2. Therefore, to solve this problem you must follow the proccedure that is shown below:

3. You must sum the amount of water that Ashley and Claire drank before the practice. Then, you have:

1/2 pints=0.5 pints (Ashley)
0.7 pints (Claire)

x=0.5 pints+0.7 pints
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How many pints of water did Ashley and Claire drink combined?

The answer is: 1.2 pints or 1 1/5 pints

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