Ask question

Ask question

All categories

3 years ago

7

The equation y = −2x + 3 is the boundary line for the inequality y ≤ −2x + 3. Which sentence describes the graph of the inequali

ty?
A. The region shaded above a dashed boundary line.

B. The region shaded above a solid boundary line.

C. The region shaded below a solid boundary line.

D. The region shaded below a dashed boundary line.

2 answers:

bulgar [2K]3 years ago

8 0

Answer:

C. The region shaded below a solid boundary line.

Step-by-step explanation:

The given inequality is

$y\le-2x+3$

The boundary line for this inequality is $y=-2x+3$ .

Since the inequality involve $\le$ , we use a solid boundary line.

After graphing the boundary line; we test the origin to determine which half -plane to be shaded. This is because the boundary lie is not passing through the origin.

Testing the origin yields $0\le-2(0)+3$ .

This implies that; $0\le3$ . This statement is true.

Hence we shade the lower half-plane of the solid boundary line.

The correct choice is C.

See graph

lukranit [14]3 years ago

6 0

Answer: Option C

Step-by-step explanation:

The point-slope form of the equation of the line is:

$y=mx+b$

Where m is the slope and b is the intersection with the y-axis.

In the line $y=-2x + 3$ , you can identify that:

$m=-2\\b=3$

The symbol of the inequality " $\leq$ " indicates that you must shade the region below the boundary line and for the symbols of inequalities " $\leq$ " and " $\geq$ " the line must be solid (Observe the graph attached).

Then the answer is the option C.

You might be interested in

When is x - y = 4x - 4y

Setler79 [48]

The answer is
When x = 4
Y = 4
Maybe the answer is correct

3 0

3 years ago

Given f(x) = 364-27, what is the value of f(16)

vekshin1

Answer:

f(16)=337

Step-by-step explanation:

4 0

3 years ago

Mona had some colored papers. The teacher gave her 12 more papers. she counted all the

timama [110]

Answer:

24

Step-by-step explanation:

really need more information about the subject, but im assuming its just basic addition.

36-12=24

8 0

3 years ago

The length l, width w, and height h of a box change with time. At a certain instant the dimensions are l = 3 m and w = h = 6 m,

Gemiola [76]

Answer:

a) The rate of change associated with the volume of the box is 54 cubic meters per second, b) The rate of change associated with the surface area of the box is 18 square meters per second, c) The rate of change of the length of the diagonal is -1 meters per second.

Step-by-step explanation:

a) Given that box is a parallelepiped, the volume of the parallelepiped, measured in cubic meters, is represented by this formula:

$V = w \cdot h \cdot l$

Where:

$w$ - Width, measured in meters.

$h$ - Height, measured in meters.

$l$ - Length, measured in meters.

The rate of change in the volume of the box, measured in cubic meters per second, is deducted by deriving the volume function in terms of time:

$\dot V = h\cdot l \cdot \dot w + w\cdot l \cdot \dot h + w\cdot h \cdot \dot l$

Where $\dot w$ , $\dot h$ and $\dot l$ are the rates of change related to the width, height and length, measured in meters per second.

Given that $w = 6\,m$ , $h = 6\,m$ , $l = 3\,m$ , $\dot w =3\,\frac{m}{s}$ , $\dot h = -6\,\frac{m}{s}$ and $\dot l = 3\,\frac{m}{s}$ , the rate of change in the volume of the box is:

$\dot V = (6\,m)\cdot (3\,m)\cdot \left(3\,\frac{m}{s} \right)+(6\,m)\cdot (3\,m)\cdot \left(-6\,\frac{m}{s} \right)+(6\,m)\cdot (6\,m)\cdot \left(3\,\frac{m}{s}\right)$

$\dot V = 54\,\frac{m^{3}}{s}$

The rate of change associated with the volume of the box is 54 cubic meters per second.

b) The surface area of the parallelepiped, measured in square meters, is represented by this model:

$A_{s} = 2\cdot (w\cdot l + l\cdot h + w\cdot h)$

The rate of change in the surface area of the box, measured in square meters per second, is deducted by deriving the surface area function in terms of time:

$\dot A_{s} = 2\cdot (l+h)\cdot \dot w + 2\cdot (w+h)\cdot \dot l + 2\cdot (w+l)\cdot \dot h$

Given that $w = 6\,m$ , $h = 6\,m$ , $l = 3\,m$ , $\dot w =3\,\frac{m}{s}$ , $\dot h = -6\,\frac{m}{s}$ and $\dot l = 3\,\frac{m}{s}$ , the rate of change in the surface area of the box is:

$\dot A_{s} = 2\cdot (6\,m + 3\,m)\cdot \left(3\,\frac{m}{s} \right) + 2\cdot (6\,m+6\,m)\cdot \left(3\,\frac{m}{s} \right) + 2\cdot (6\,m + 3\,m)\cdot \left(-6\,\frac{m}{s} \right)$

$\dot A_{s} = 18\,\frac{m^{2}}{s}$

The rate of change associated with the surface area of the box is 18 square meters per second.

c) The length of the diagonal, measured in meters, is represented by the following Pythagorean identity:

$r^{2} = w^{2}+h^{2}+l^{2}$

The rate of change in the surface area of the box, measured in square meters per second, is deducted by deriving the surface area function in terms of time before simplification:

$2\cdot r \cdot \dot r = 2\cdot w \cdot \dot w + 2\cdot h \cdot \dot h + 2\cdot l \cdot \dot l$

$r\cdot \dot r = w\cdot \dot w + h\cdot \dot h + l\cdot \dot l$

$\dot r = \frac{w\cdot \dot w + h \cdot \dot h + l \cdot \dot l}{\sqrt{w^{2}+h^{2}+l^{2}}}$

Given that $w = 6\,m$ , $h = 6\,m$ , $l = 3\,m$ , $\dot w =3\,\frac{m}{s}$ , $\dot h = -6\,\frac{m}{s}$ and $\dot l = 3\,\frac{m}{s}$ , the rate of change in the length of the diagonal of the box is:

$\dot r = \frac{(6\,m)\cdot \left(3\,\frac{m}{s} \right)+(6\,m)\cdot \left(-6\,\frac{m}{s} \right)+(3\,m)\cdot \left(3\,\frac{m}{s} \right)}{\sqrt{(6\,m)^{2}+(6\,m)^{2}+(3\,m)^{2}}}$

$\dot r = -1\,\frac{m}{s}$

The rate of change of the length of the diagonal is -1 meters per second.

6 0

3 years ago

ANSWER ASAP <br> Write an equation of a line that passes through the points (2,3) and (2,-6).

Agata [3.3K]

1st you need to fine the slope using

S = y2-y1/x2-x1

S = -6 - 3/2-2

S = -9/0

S = Undefined

when we have undefined slope the equation would be a vertical lines.

Thus the equation would be the x value of the point

Thus the equation is x = 2

6 0

3 years ago