1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
KengaRu [80]
2 years ago
6

8) Choose the correct linear system of inequalities for the graph given.

Mathematics
1 answer:
ziro4ka [17]2 years ago
3 0

Answer:

To graph a linear inequality in two variables (say, x and y ), first get y alone on one side. Then consider the related equation obtained by changing the inequality sign to an equality sign. The graph of this equation is a line.

If the inequality is strict ( < or > ), graph a dashed line. If the inequality is not strict ( ≤ or ≥ ), graph a solid line.

Finally, pick one point that is not on either line ( (0,0) is usually the easiest) and decide whether these coordinates satisfy the inequality or not. If they do, shade the half-plane containing that point. If they don't, shade the other half-plane.

Graph each of the inequalities in the system in a similar way. The solution of the system of inequalities is the intersection region of all the solutions in the system.

Example 1:

Solve the system of inequalities by graphing:

y≤x−2y>−3x+5

First, graph the inequality y≤x−2 . The related equation is y=x−2 .

Since the inequality is ≤ , not a strict one, the border line is solid.

Graph the straight line.

Consider a point that is not on the line - say, (0,0) - and substitute in the inequality y≤x−2 .

0≤0−20≤−2

This is false. So, the solution does not contain the point (0,0) . Shade the lower half of the line.

Similarly, draw a dashed line for the related equation of the second inequality y>−3x+5 which has a strict inequality. The point (0,0) does not satisfy the inequality, so shade the half that does not contain the point (0,0) .

The solution of the system of inequalities is the intersection region of the solutions of the two inequalities.

Example 2:

Solve the system of inequalities by graphing:

2x+3y≥128x−4y>1x<4

Rewrite the first two inequalities with y alone on one side.

3y≥−2x+12y≥−23x+4−4y>−8x+1y<2x−14

Now, graph the inequality y≥−23x+4 . The related equation is y=−23x+4 .

Since the inequality is ≥ , not a strict one, the border line is solid.

Graph the straight line.

Consider a point that is not on the line - say, (0,0) - and substitute in the inequality.

0≥−23(0)+40≥4

This is false. So, the solution does not contain the point (0,0) . Shade upper half of the line.

Similarly, draw a dashed line of related equation of the second inequality y<2x−14 which has a strict inequality. The point (0,0) does not satisfy the inequality, so shade the half that does not contain the point (0,0) .

Draw a dashed vertical line x=4 which is the related equation of the third inequality.

Here point (0,0) satisfies the inequality, so shade the half that contains the point.

The solution of the system of inequalities is the intersection region of the solutions of the three inequalities.

Step-by-step explanation:

I got it right

You might be interested in
-18 = 9z - 9<br> z =___?
maw [93]

Answer:

z = - 1

Step-by-step explanation:

Given

- 18 = 9z - 9 ( add 9 to both sides )

- 9 = 9z ( divide both sides by 9 )

- 1 = z

6 0
3 years ago
Candace complete a 3.1 mile run in 22 1/2 minutes. At that pace, what is her unit rate, in minutes per mile? Round your answer t
Finger [1]

3.1 x 22 1/2 = 69.75 rounded is 70

7 0
2 years ago
Formula for the area of a circle in terms of its circumference
Usimov [2.4K]
\bf \textit{circumference of a circle}\\\\&#10;C=2\pi r\qquad \qquad \implies \cfrac{C}{2\pi }=\boxed{r}\\\\&#10;-------------------------------\\\\&#10;\textit{area of a circle}\\\\&#10;A=\pi r^2\qquad \qquad \implies A=\pi \left( \boxed{\cfrac{C}{2\pi }} \right)^2\implies A=\pi \left( \cfrac{C^2}{(2\pi )^2} \right)&#10;\\\\\\&#10;A=\cfrac{\pi  C^2}{2^2\pi^2}\implies A=\cfrac{C^2}{4\pi }
5 0
3 years ago
Quadrilateral A'B'C'D' is the image of quadrilateral ABC D under a dilation with a scale factor of 4. c What is the length of se
DENIUS [597]

a dilation with a scale factor of 4, is multiplication by 4 each side, so we need the measure of the side CD and then multiply by 4 to find C'D'

we can notice tht length of CD, is 3 squares,multiplying by 4 the new length is 3x4= 1 2 squares

4 0
11 months ago
I already know the answer to this but
irina [24]

Answer:

yes

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Other questions:
  • PLZZZ HELP I WILL GIVE BRAINLEST ON A TIMER
    15·2 answers
  • What is the simplified expression for 3 power 3 multiplied by 3 power 3 over 3 power 4
    8·2 answers
  • Passes through (1,9), slope = 2
    7·1 answer
  • What is 700,000 in scientific notation
    6·1 answer
  • What is the best next step in the construction of an equilateral triangle?
    11·2 answers
  • The point-slope equation of a line is y- Yo= m(x-xo), where m is the
    11·1 answer
  • A student is asked to calculate the value of 212 − 132 using the identity x2 − y2 = (x − y)(x + y). The student's steps are show
    6·1 answer
  • What is 6 cm as a fraction in meters
    7·2 answers
  • An envelope is 3. 1/3 inches long by 3. 1/2 inches wide what is that area of the envelop
    10·1 answer
  • PLS HELP ITS ALMOST DUE 3 MINUTES I GIVE BRAINLIEST!
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!