All categories

2 years ago

Which system of linear inequalities is represented by the graph?

Mathematics

2 answers:

masha68 [24]2 years ago

6 0

For the red line, we have:

gradient ( $m$ ) = 1/3
y-intercept = 3

Equation of straight line is given by $y=mx+c$ , where $m$ is the gradient and $c$ is where the line intercept the y-axis

So we have, $y= \frac{1}{3}x+3$

The shaded part is above the line, hence the first inequality is
$y \geq \frac{1}{3}x+3$

The black line, we have
gradient, $(m)$ = 3
y-intercept = -2

$y=mx+c$
$y=3x-2$ , rearranging gives
$3x-y=2$

The shaded region is to the right of the line, hence the inequality is
$3x-y\ \textgreater \ 2$

Note: The first option should be the correct answer but the inequality sign for y > 1/3x + 3 should be $\geq$

Lelu [443]2 years ago

4 0

I JUST TOOK THE TEST AND THE ANSWER IS B

You might be interested in

you roll a six sided number cube and flip a coin what is the probability of rolling a number greater than 5 and flipping heads?

Whitepunk [10]

Answer:

0.08333... or 8.333...%

Step-by-step explanation:

1/6 * 1/2 = 1/12

5 0

2 years ago

Read 2 more answers

Line segment AB has endpoints A(-1.5, 0) and B(4.5 8). Point C is on line segment AB located at (0, 2)

Pie

Answer:

The ratio of AC/CB=1/3

Step-by-step explanation:

We use the section formula:

$(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

We substitute the point A(-1.5,0) and B(4.5,8).

We plug in the points to get:

$(\frac{4.5m - 1.5n}{m+n},\frac{8m+n \times 0}{m+n})$

This is supposed to be equal to: (0,2).

$(\frac{4.5m - 1.5n}{m+n},\frac{8m+n \times 0}{m+n}) = (0,2)$

We can equate, corresponding coordinates to find m and n.

$\frac{4.5m - 1.5n}{m + n} = 0$

This implies that:

$4.5m - 1.5n = 0$

$4.5m = 1.5n$

$\frac{m}{n} = \frac{1.5}{4.5}$

$\frac{m}{n} = \frac{1}{3}$

Therefore the ratio is m:n=1:3

4 0

2 years ago

The answer to the question “On average, how many pages are in a novel?” would be measured by which scale?

Juli2301 [7.4K]

In the days of the typewriter, a double-spaced page with 1-inch margins would hold an average of 250 words. So you could assume that since 4 pages = 1000 words

8 0

3 years ago

Find the midpoint of the line using the midpoint formula. Midpoint of AB:______

dimaraw [331]

Answer: MP=(1,1)

Step-by-step explanation:

$MP= (\frac{x_1+x_2}{2})(\frac{y_1+y_2}{2})$

$MP= (\frac{-2+4}{2})(\frac{-3+5}{2})$ -2+4=2 -3+5=2

$MP= (\frac{2}{2})(\frac{2}{2})$ 2/2=1

$MP= (1,1)$

8 0

2 years ago

For the scenarios presented in Problems 9–17, identify a problem worth studying and list the variables that affect the behavior

Nastasia [14]

Answer:

Problem: A company with a fleet of trucks faces increasing maintenance costs as the age and mileage of the trucks increase

Identify a problem worth studying : Yes, this problem is worth studying as it illustrate the classical optimization problem where to either minimize or maximize the outcome given some constraints. In this problem we need to maximize our profit by minimizing our maintenance cost give the age of trucks.

List the variables that affect the behavior you have identified: Lease expense, license, taxes, insurance, number of trucks, number of mechanics, type of fuel, maintenance and repair, labor, number of breakdowns, wait time to repair, loss of revenue and delay penalties, drivers retention and attrition, and number of customer reviews (negative and positive) the service.

Which variables would be neglected completely: Unless there are plans to relocate to different state with different regulations, the following variables can neglected completely: Lease expense, licenses and permits, taxes, insurance, number of trucks, number of mechanics, type of fuel.

Which might be considered as constants initially: Assuming that our mechanics are full time employees, the labor cost can be considered constant. However, the parts and materials associated with the labor are not constant. And any one time cosmetic fixes can be considered constants such as a small paint job or seat cleaning.

Can you identify any sub models you would want to study in detail?: The sub model that I want to study in more detail is as follow:

Truck ownership cost=truck depreciation+truck Return on Investment (ROI)

As the truck depreciation is constant, the main focus will be on truck Return on Investment (ROI).

Truck Return on Investment (ROI)=(the gain from the truck−Cost of investment)/cost of investment.

Hence the detailed subsystem can be as follow:

Cost of investment=(Fuel cost +maintenance cost +breakdown cost+wait cost).

Identify any data you would want collected: The data you would want collected is maintenance cost and type of maintenance and specifically the tracks and truck parts that break down the most. The wait time needed to fix and maintain the trucks. And finally customer reviews. In other words, I would collect any data that directly or indirectly impact revenues. With the collected data, I would well informed about the best time to decide replacing trucks that are performing very poorly and negatively impacting the bottom-line of the company.

Step-by-step explanation:

The specific problem is selected above and it is worth analyzing and studying because is is similar to a classical optimization problem. This is because the desired output can be either maximized or minimized by adjusting the values of certain constraints such as maintenance cost, trucks parts and other necessary parameters.

8 0

2 years ago