Solve...............

Mathematics

1 answer:

Vladimir [108]2 years ago

7 0

Answer:

To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. ... If the inequality is ≤ or ≥, graph the equation as a solid line. This line divides the xy- plane into two regions: a region that satisfies the inequality, and a region that does not. Next, pick a point not on the line.

Step-by-step explanation:

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On the grid, sketch a graph to represent

Greeley [361]

Answer:

Please find attached, the required graph created on MS Excel

Step-by-step explanation:

The distance between Sandy's house and the school = 200 m

The number of minutes Sandy talked to her friend for = 10 minutes

The time it took Sandy to return home to pick her homework = 5 minutes

Let <em>x </em>represent Sandy's location she stops to talk to her friend 10 minutes, we have;

The slope of the motion on the graph, m₁ = (x - 0)/(t - 0)

The slope of her motion running home to pick the up her homework, m₂ = (x - 0)/(5 - 0)

Given that t > 5, the slope on trip back home, m₁, is larger than are her initial slope, m₂

Therefore, where x = 125, we have;

The rate at which she returned home = m₂ = (125 m - 0)/(5 min - 0) = 25 m/min

Given that the same rate m₂ is what she used in heading back to school, we have;

The time it takes her to get to school = 200 m/(25 m/min) = 8 minutes

Therefore, whereby it took her 10 minutes to reach point <em>x</em>, we have the following coordinate points on the graph in a tabular form;

$\begin{array}{ccc} Time \ (minutes) \ x-axis&&Distance \ (meters) \ y-axis\\0&&0\\10&&25\\15&&0\\23&&200\end{array}$

The plot of the above point is completed using MS Excel as shown in the attached diagram.

7 0

2 years ago

Over what interval is the function in this graph increasing?

brilliants [131]

A function is increasing if it "points upwards".

Think that you have two inputs $x_1$ (think of them as being very close to each other). A function $f$ is increasing if

$f(x_1)$

So, smaller input, smaller output.

So:

In the first segment on the left, the function is decreasing: if you move with little steps rightwards, the output will get smaller and smaller (the function points to the right bottom)
In the second segment, the line is constant (it's horizontal). This means that even if you consider a larger input, the output reimains the same
In the third segment, the function is increasing: if you consider a larger input, the output will be larger as well: the function points to the top right.
In the fourth segment, the function is decreasing again (look at the first bullet point)

So, the function is increasing in the third segment, which is delimited by

$-2\leq x \leq 3$