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3 years ago

1. How can you tell that a point on the graph is a maximum or minimum?

Mathematics

1 answer:

nekit [7.7K]3 years ago

4 0

9514 1404 393

Answer:

there are no points higher than a maximum; no points lower than a minimum
average rate of change is the slope of a straight line connecting the points of interest.

Step-by-step explanation:

1. A point on a graph is a maximum if there are no points on the graph that are higher.

A point on a graph is a minimum if there are no points on the graph that are lower.

Sometimes you're interested in a "local" maximum or minimum. In that case, the "no points higher/lower" rule refers to points in the immediate vicinity of the one of interest.

Sometimes you're interested in a maximum or minimum on an interval. In that case, the rule applies to points contained within the interval. (The maximum or minimum may be at the end of the interval.)

2. Average rate of change is defined over some interval. That is, you are given the end points of the interval of interest. The average rate of change is the slope of a straight line between those end points. The slope formula applies:

$m=\dfrac{y_2-y_1}{x_2-x_1} \quad\text{where the end points of the interval are $(x_1,y_1)$ and $(x_2,y_2)$}$

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On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everyth

crimeas [40]

The inequality described can be written as:

y < 3x + 2.

<h3>How to get the inequality?</h3>

First, we know that we have a dashed line, and the region to the left of that line is shaded, then we will have:

y < line.

The linear equation is of the form:

y = a*x + b

Where a is the slope and b is the y-intercept.

Remember that if a line passes through the points (x₁, y₁) and (x₂, y₂), then the slope is:

$a = \frac{y_2 - y_1}{x_2 - x_1}$

Here we know that the line passes through (-3, -7) and (0, 2), so the slope is:

$a = \frac{2 - (-7)}{0 - (-3)} = 9/3 = 3$

And because the line passes through (0, 2), the y-intercept is 2, then the inequality is:

y < 3x + 2.

If you want to learn more about inequalities:

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2 years ago

Please help! Billy just received $10 for his birthday and immediately spent $2.50 on a pack of baseball cards. He then wants to

Oduvanchick [21]

Answer:

1.5x = 7.5 (a)

Step-by-step explanation:

If Billy has $7.50 remaining, then he can buy x no. of boxes.

Each box costs $1.50

So, 1.5x = 7.5

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2 years ago

Terry bought 2 1/2 dozen chocolate chip cookies. She paid $15 for her purchase. If there are 12 cookies in each dozen, what is t

Kruka [31]

Answer:

you have to divide 12 by 15

Step-by-step explanation:

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3 years ago

The student council at Livingston High School is making T-shirts to sell for a fundraiser, at a price of $16 apiece. The costs,

Allushta [10]

Answer:

5 shirts must be sold.

Step-by-step explanation:

First, set up the equation. Each shirt (x) is sold for $16:

For every amount (y) for x: (y)(x) = (16)(y)

The cost is $4, with the setup fee as $60.

(16)(y) = (4)(y) + 60

16y = 4y + 60

Isolate the variable (y). Note the equal sign, what you do to one side, you do to the other. First, subtract 4y from both sides.

16y (-4y) = 4y (-4y) + 60

16y - 4y = 60

12y = 60

Next, isolate the variable (y). Divide 12 from both sides.

(12y)/12 = (60)/12

y = 60/12

y = 5

5 shirts must be sold.

To check, plug in 5 for y in the equation:

16y = 4y + 60

16(5) = 4(5) + 60

Simplify.

16(5) = 4(5) + 60

80 = 4(5) + 60

80 = 20 + 60

80 = 80 (True).

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3 years ago

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aliya0001 [1]

Answer:

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Step-by-step explanation:

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3 years ago

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