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
solong [7]
3 years ago
9

Determine whether the points (–3,–2) and (3,2) are in the solution set of the system of inequalities below. y ≤ ½x + 2 y < –2

x – 3
Mathematics
1 answer:
lana [24]3 years ago
7 0

Given:

The system of inequalities:

y\leq \dfrac{1}{2}x+2

y

To find:

Whether the points (–3,–2) and (3,2) are in the solution set of the given system of inequalities.

Solution:

A point is in the solution set of the given system of inequalities if it satisfies both inequalities.

Check for the point (-3,-2).

-2\leq \dfrac{1}{2}(-3)+2

-2\leq -1.5+2

-2\leq 0.5

This statement is true.

-2

-2

-2

This statement is also true.

Since the point (-3,-2) satisfies both inequalities, therefore (-3,-2) is in the solution set of the given system of inequalities.

Now, check for the point (3,2).

2

2

2

This statement is false because 2>-9.

Since the point (3,2) does not satisfy the second inequality, therefore (3,2) is not in the solution set of the given system of inequalities.

You might be interested in
The table represents the function 7 = 5x- Output ) Input (3) -2 -18 8 x 1 2 2 12 8 2 2. What is the input when the output is 12
notsponge [240]
y_{-2}=5\cdot(-2)-8=-10-8=-18y=5x-812=5x-812+8=5x20=5xx=\frac{20}{5}x=4

6 0
1 year ago
Find the slope of this line: (15,7) (3,-2)<br><br> Help
Oliga [24]

Answer:

m=\frac{3}{4}

Step-by-step explanation:

\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(15,\:7\right),\:\left(x_2,\:y_2\right)=\left(3,\:-2\right)

m=\frac{-2-7}{3-15}

\mathrm{Refine}

m=\frac{3}{4}

5 0
3 years ago
Farmer Ed has 8,000 meters of fencing &amp; wants to enclose a rectangular plot that borders a river. If farmer Ed does not fenc
attashe74 [19]

Answer:

largest area that can be enclosed = 8,000,000 m²

Step-by-step explanation:

Since it is a rectangle plot, the area is expressed as; A = xy, where x is length and y is width.

Because it is next to the river, he only needs to fence three sides, so amount of fencing; F = x + 2y.

Since we know the amount of fencing available is 8000m, we get:

8000 = x + 2y

solving for x, we have;

x = 8000 - 2y

substitute 8000 - 2y for x into the area equation to give;

A = (8000 - 2y)y distribute

A = -2y² + 8000y

Now, due to the negative sign next to 2, this will be a parabola which opens down, meaning that the point of maximum area will be at the vertex,

Thus; y = -b/2a = -8000/[2(-2)] = 2000

x = 8000 - 2(2000) = 4000

A = 4000(2000) = 8,000,000 m²

8 0
3 years ago
PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!!!!!!!!!!!!!!!PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!
snow_lady [41]
A= pi x r^2 x h
so pi x 16 x5

A= 80 pi or 251.3
5 0
3 years ago
Quick Math, 75% of 180?
sdas [7]
75% = 3/4
3/4 of 180 = 135
5 0
3 years ago
Other questions:
  • Find the derivative of <br>y = arcsin(x)​
    9·2 answers
  • Solve the following logarithm equation<br> log5(10 + x) = log5(3 + 4x)
    5·1 answer
  • This is the back side of the paper
    5·1 answer
  • How do you write a ratio ad a percent
    11·2 answers
  • The average retirement age for a certain country was reported to be years according to an international group dedicated to promo
    13·1 answer
  • A quart of paint covers about 85 square feet. About how many quarts would you need to cover a fence with an area of 3,817 square
    12·1 answer
  • What is 15% of 40?<br> 02<br> О 4<br> 05<br> 06
    15·2 answers
  • 2520=r(2r+18) This is a geometry problem
    10·1 answer
  • Select ALL the answers that apply.
    11·1 answer
  • The workers at a nursery plant 37 trees in each of 15 parks. They plant 42 trees in each of 23 parks.
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!