which ordered pairs are in the solution set of the system of linear inequalities? y > -1/3x+2 -y <2x+3A. (2,2), (3,1) (4,2)B. (2,2) (3,-1) (4,1)C. (2,2) (1,-2) (0,2)D. (2,2) (1,2) (2,0)

which ordered pairs are in the solution set of the system of linear inequalities?
y > -1/3x+2
-
y <2x+3

A. (2,2), (3,1) (4,2)
B. (2,2) (3,-1) (4,1)
C. (2,2) (1,-2) (0,2)
D. (2,2) (1,2) (2,0)

Answers

Answer 1

Answer: Choice A. (2,2), (3,1), (4,2)

==========================================================

Explanation:

The graph of [tex]y \ge -\frac{1}{3}x+2[/tex] has the boundary y = (-1/3)x+2 which is a solid line. This line goes through (0,2) and (3,1). We shade above the boundary because of the "greater than" sign.

The graph of y < 2x+3 has a dashed boundary line of y = 2x+3, and we shade below the boundary because of the "less than" sign.

The two regions overlap in the upper right corner where it's shaded in the darkest color. The points (2,2), (3,1) and (4,2) are in this upper right corner region. If we plug the coordinates of each point into each inequality, then we'll get true statements.

For instance, let's try (x,y) = (2,2) into the first inequality

[tex]y \ge -\frac{1}{3}x+2\\\\2 \ge -\frac{1}{3}(2)+2\\\\2 \ge -\frac{2}{3}+2\\\\2 \ge -\frac{2}{3}+\frac{6}{3}\\\\2 \ge \frac{-2+6}{3}\\\\2 \ge \frac{4}{3}\\\\2 \ge 1.33\\\\[/tex]

Which is true since 2 is indeed larger than 1.33, so that confirms (2,2) is in the shaded region for [tex]y \ge -\frac{1}{3}x+2\\\\[/tex]

Let's check the other inequality as well

[tex]y < 2x+3\\\\2 < 2(2)+3\\\\2 < 4+3\\\\2 < 7\\\\[/tex]

That works too. So (2,2) is in BOTH shaded regions at the same time; hence, it's a solution to the system. You should find that (3,1) and (4,2) work for both inequalities also. This will confirm choice A is the answer.

--------------------------------

Extra info (optional section)

A point like (3,-1) does not work for the first inequality as shown below

[tex]y \ge -\frac{1}{3}x+2\\\\-1 \ge -\frac{1}{3}(3)+2\\\\-1 \ge -1+2\\\\-1 \ge 1\\\\[/tex]

Since -1 is neither equal to 1, nor is -1 larger than 1 either. The false statement at the end indicates (3,-1) is not a solution to that inequality.

Based on the graph, the point (3,-1) is not above the blue solid boundary line. All of this means we can rule out choice B.

You should find that (1,-2) is a similar story, so we can rule out choice C. Choice D can be ruled out because (2,0) is not a solution to the first inequality.

Related Questions

Write this quadratic equation in standard form.

Answers

Answer:

-[tex]x^{2} + 3x -8 = 0[/tex]

Step-by-step explanation:

[tex]x^{2} + x -8 - 2x = 0[/tex] [tex]x^{2} + 3x -8 = 0[/tex]

find area of a square garden having a length 45m

Answers

Answer:

A = 2025 ft^2

Step-by-step explanation:

The area of a square is given by

A = s^2 where s is the side length

A = 45^2

A = 2025 ft^2

Answer:

Step-by-step explanation:

The area of any square is s^2

s in this case is 45

Area = s^2

Area = 45 * 45

Area = 2025 m^2

(-1)×(-1)×(-1)×(2m+1) times where m is a natural number,is equal to?
1. 1
2.-1
3.1 or-1
4.None

Answers

Answer:

(2). -1

Step-by-step explanation:

The given parameter can be represented as:

[tex](-1)^{2m + 1}[/tex]

See comment for correct question

Required

The end result

From the question, we understand that m is a natural number

This means that:

[tex]2m + 1 \to[/tex] odd number

So:

[tex](-1)^{2m + 1} = -1[/tex] --- i.e. -1 to the power of an odd number will give -1

Hence; (2) is correct

what is the value of x

Answers

Answer:

c 112⁰

Step-by-step explanation:

cuz the triangle is the same and x is on a straight line so get 180 - 68 = 112

Answer:

the angle opposite to x is 61 degree (being alternate angle)

x+ 61 = 180(being linear pair)

or, x = 180 - 61

so, x = 119

the answer is 119(d).

An automobile went 84 miles on 6.5 gallons of gasoline. At this rate, how many gallons would be needed to travel 126 miles

Answers

Answer:

10 gallons

Step-by-step explanation:

84 ÷ 6.5 =12.9(The unit rate.)

Seeing as one gallon can get you 12.9 miles;

126÷12.9=9.7

So the answers 9.7 gallons, but if you need to round, then 10 to get a whole number.

Answer:

9.75

Step-by-step explanation:

We can write a ratio to solve

84 miles 126 miles

-------------- = -------------------

6.5 gallons x gallons

Using cross products

84 x = 6.5 * 126

84x=819

84x/84 = 819/84

x = 9.75

What are the zeros of this function?

Answers

Answer:

The zeros of this function would be: x = 4 and x = 6, assuming that option got caught off while you were taking a picture.

Step-by-step explanation:

When they're asking for the zeros of this type of function, where is forms this kind of U-shape or also known as a quadratic equation, they're asking what the x-value is when y = 0, or when the line of the function touches the x-axis. Notice that it happens when x = 4 and when x = 6.

Answer:

45 percent

Step-by-step explanation:

20-11=9

9 divided by 20= 0.45

0.45 x 100= 45%

A car dealership is advertising a car for $16,299.99. If the sales tax rate is 6.5 percent, what
is the total tax paid for the car?
A. S993 34
B. $1.000.00
CS1.059 50
DS1.359.19

Answers

Answer:

C. 1059.50

Step-by-step explanation:

Sales price x sales tax rate = sales tax

16299.99 x .065 (6.5%) = 1059.50

Find the midpoint of the line segment defined by the points: (5, 4) and (−2, 1) (2.5, 1.5) (3.5, 2.5) (1.5, 2.5) (3.5, 1.5)

Answers

Answer:

[tex]\boxed {\boxed {\sf (1.5 , 2.5)}}[/tex]

Step-by-step explanation:

The midpoint is the point that bisects a line segment or divides it into 2 equal halves. The formula is essentially finding the average of the 2 points.

[tex](\frac {x_1+x_2}{2}, \frac {y_1+ y_2}{2})[/tex]

In this formula, (x₁, y₁) and (x₂, y₂) are the 2 endpoints of the line segment. For this problem, these are (5,4 ) and (-2, 1).

x₁= 5 y₁= 4 x₂= -2 y₂= 1

Substitute these values into the formula.

[tex]( \frac {5+ -2}{2}, \frac {4+1}{2})[/tex]

Solve the numerators.

5+ -2 = 5-2 = 3 4+1 = 5

[tex]( \frac {3}{2}, \frac{5}{2})[/tex]

Convert the fractions to decimals.

[tex](1.5, 2.5)[/tex]

The midpoint of the line segment is (1.5 , 2.5)

How does sample size affect determinations of statistical significance? The smaller the sample size, the more confident one can be in one's decision to reject or retain the null hypothesis. The smaller the sample size, the greater the probability that the variable has an effect. The larger the sample size, the more accurate the estimation of the true population value. The larger the sample size, the greater the probability that the variable has an effect.

Answers

Answer:

The larger the sample size, the more accurate the estimation of the true population value.

Step-by-step explanation:

As large will be the sample size more data will be shown and more are the c c changes of it being an estimate of a true population. The sample size can be determined on the basis of use of experience, target variance, confidence level, and target for power.

33. The population of Canada, y (in millions), can be approximated by the relation y=
0.146x + 31, where x represents the number of years since 2000.
a. Approximate the population of Canada in the year 2006.
b. In what year did the population of Canada reach approximately 32,752,000?

Answers

Answer:x=6573/500,x=13(73/500

Step-by-step explanation:

It will takes 12 years to reach approximately 32,752,000.

What is Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

y = 0.146x + 31

where x represents the number of years since 2000.

a) The population of Canada in the year 2006

x= 6

y= 0.146 x 6 + 31

y = 31.876

b) The population of Canada reach approximately 32,752,000 in

y = 32.752

0.146x + 31= 32.752

0.146x = 1.752

x= 1.752/0.146

x= 12

Hence, it will takes 12 years to reach approximately 32,752,000.

Learn more about Equation here:

https://brainly.com/question/10413253

#SPJ2

Help im stuck! xoxo thanks! <3

Answers

Answer:

3. 60° is the correct answer.

4. 8

Step-by-step explanation:

3. sum of all the sides of a quadrilateral is 360°

hence,

2h+2h+h+h=360°

6h=360°

h=360°/6

h=60°

4. Sum of interior angle of a polygon with n sides is 1080. N=8 (octagon)

Hope this helps you. Have a nice day.^_^

Answer:

3)60°

4)8 sides

Step-by-step explanation:

3) 2h+2h+h+h=360°

6h=360°

6h/6=360°/6

h=60°

4)(n-2)180=1080°

n-2=1080°/180

n-2=6

n=8

.........................................................

Answers

Answer:

..............................what this

Write an inequality for the shaded region shown in the figure.

Answers

Answer:

the equation of the circle is x^2 + y^2 < 36

NOT LESS OR EQUAL cause of the dotted lines

and the theory behind this is because the square root of 36 is +-6 so when the equation is less than +-6 the shade cannot go outside these point, if you know what i mean

hope that answers your question :)

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 5 small boxes has a total weight of 88 kilograms. A delivery of 12 large boxes and 2 small boxes has a total weight of 235 kilograms. How much does each type of box weigh?

Answers

Answer:

Step-by-step explanation:

We need a system of equations here. The first equation is that 3L boxes + 5s boxes (L = large and s = small) = 88 kg so

3L + 5s = 88

12L + 2s = 235 according to the other information given.

Solve the first equation for either L or s. I'll solve for L, just because:

3L = 88 - 5s and

L = [tex]\frac{88}{3}-\frac{5}{3}s[/tex] and sub that into the second equation for L:

[tex]12(\frac{88}{3}-\frac{5}{3}s)+2s=235[/tex] and if you distribute the 12 into the parenthesis you'll simplify it down a bit to

352 - 20s + 2s = 235 and combine like terms:

-18s= -117 so

s = 6.5 kg and plug that in to solve for L:

L = [tex]\frac{88}{3}-\frac{5}{3}(6.5)[/tex] and

L = 18.5 kg

PLEASE ANSWER ASAP THANK YOU!!! How much money will be in a bank account after 3 years if $9 is deposited at an interest rate of 5% compounded annually? Round to the nearest dollar.....

Answers

Answer:

10 bucks

Step-by-step explanation:

Money=9*(1+0.05)^3

Money=9*(1.05)^3=10.41≈10

lim(x-0) (sinx-1/x-1)

Answers

9514 1404 393

Answer:

as written: the limit does not existsin(x-1)/(x-1) has a limit of sin(1) ≈ 0.841 at x=0

Step-by-step explanation:

The expression written is interpreted according to the order of operations as ...

sin(x) -(1/x) -1

As x approaches 0 from the left, this approaches +∞. As x approaches 0 from the right, this approaches -∞. These values are different, so the limit does not exist.

Maybe you intend ...

sin(x -1)/(x -1)

This can be evaluated directly at x=0 to give sin(-1)/-1 = sin(1). The argument is interpreted to be radians, so sin(1) ≈ 0.84147098...

The limit is about 0.841 at x=0.

HELP URGENT !!!!!!

what happens if the lines that are being cut by the transversal are not parallel

Answers

The answer is c. Alcohol your welcome

A plane traveled 4425 miles with the wind in 7.5 hours and 3675 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind.

Answers

Answer:

540 and 50 respectively

Step-by-step explanation:

Let the speed of plane in still air be x and the speed of wind be y.

ATQ, (x+y)*7.5=4425 and (x-y)*7.5=3675. Solving it, we get x=540 and y=50

a road rises 16 feet for every 50 feet of horizontal distance covered. in percent what is the grade of the road?

Answers

Answer:

32%

t7y7y8 I am not going out for the

Other Questions

List 7 ways in which fights are started then list 7 methods that prevent fights. Need help fast will give brainliest Find the missing side of triangle Standish Company manufactures consumer products and provided the following information for the month of February: Units produced 131,000 Standard direct labor hours per unit 0.20 Standard fixed overhead rate (per direct labor hour) $2.50 Budgeted fixed overhead $65,000 Actual fixed overhead costs $68,300 Actual hours worked 26,350Required:a. Calculate the fixed overhead spending variance using the formula approach.b. Calculate the volume variance using the formula approach. Manatees can swim in water up to 20 feet deep. Write an expression that represents the depth d, that a manatee can swim Ellicott City Manufacturers, Inc., has sales of $6,344,210, and a gross profit margin of 67.3 percent. What is the firm's cost of goods sold? Round your final answer to the nearest dollar. 2. Answer any five questions:a. A few simple rules will keep you, not from all error, but from silly error. Bertrand Russiaforwards few rules in his essay. Keeping Errors at Bay. Do you agree with his deWhy?b. What does Chaudhary argue in "How Sane are We? Do you agree with herGive reasonsC. Why does the narrator of the short story Third Thought' close his monologue sayingBuying and selling are a perfectly straightforward matter between dealer and custome!Document and explain this statement.d. What are the most popular careers in your country? What career would you likechoose in future? Give reasons.e. 'Everyone is in sales. It doesn't matter what area you work in, you have clients and youneed to sell." Do you agree? Support your argument.f. Suppose, you were starting a new job in a new company. What benefits and faciliteswould you look for, apart from the salary? Explain.Textile Inc. usecompetitors. Cand bad relaticconsultant forthe company tb. The openingexperiment isas an effort toApply the foWhere the2. Answer the followa. Chekhov w Titanium is a metal often used as an alloying agent to provide materials that are strong, lightweight, and temperature-resistant Which of the following represents the correct ground-state configuration for a neutral atom of titanium? A) 1s 2s 2p 3s 3p 4830 B) 1s 2s 2p 3s 3p 4s3d C) 15*2s2p 3s 3p 4s D) 152s 2p 3s 3p 3d For his science project, Chip decided to test how well plants grew with fertilizer. He started off by planting seeds in three different pots and labeling each of the plants. Plant A had no fertilizer. Plant B had the recommended amount of fertilizer. Plant C had four times the recommended amount of fertilizer. For ten consecutive days he measured the height of each plant in centimeters. The follow ing table shows his results. Which plant grew the most from Day 7 to Day 9? What Internet access method would be suitable for a business requiring a high bandwidth connection where no cabled options exist? [tex]\sqrt{x - 5} - \sqrt{3 - 2.x} = 0[/tex] Which of these sentences correctly uses the comparative form of an adverb?A. The director gives better presentations than other team members.B. He gave the best presentation.C. The most best dancer will be given an award at the party.D. She paints so well it is almost better than the art teacher. Go where you may, search where you will, roam through all the monarchies and despotisms of the Old World, travel through South America, search out every abuse, and when you have found the last, lay your facts by the side of the everyday practices of this nation, and you will say with me, that, for revolting barbarity and shameless hypocrisy, America reigns without a rival.Which of the following best describes Douglasss word choice in this excerpt? A. pleasant B. clever C. casual D. lighthearted 4. A diver is 20 m underwater and they are startled by a shark. They are tempted to take a big breath of air, drop their gear, and swim to the surface while holding their breath. Explain why this is dangerous g Which scientist proposed the first atomic theory? 1. Costs that do not change with the change in the level of production for some time is classified as ________. a. variable costs. b. fixed costs. c. mixed costs.d. none of these choices are correct. 2. Under variable costing, the cost of goods manufactured consists of all except:_____.a. direct materials. b. direct labor. c. variable factory overhead. d. fixed factory overhead. 3. Costs that have characteristics of both a variable cost and a fixed cost are classified as ________. a. variable costs.b. fixed costs.c. mixed costs.d. none of these choices are correct. a - 6 - 6a = 4find the value of a Based on the excerpt, the Nazis were pursuing a policy of racial purity that developed ultimately into which event?O the bombing of BritainO the establishment of The Final SolutionO the invasion of Polandthe establishment of OThe Anti-Comintern Pact Write a function rule for tableIs it a, b, c or d? Identify the statement about Windows tasks that is FALSE.To launch an application, click the Windows icon, select "All Programs," and then click an application.The boot process is the process for powering off a computer.A common way to shut down the computers operating system is by using the Start menu.Users log into their accounts on the Welcome screen, before Windows is ready to use. The triangle below is equilateral. Find the length of side x in simplest radical formwith a rational denominator.12

which ordered pairs are in the solution set of the system of linear inequalities? y > -1/3x+2 - y <2x+3 A. (2,2), (3,1) (4,2) B. (2,2) (3,-1) (4,1) C. (2,2) (1,-2) (0,2) D. (2,2) (1,2) (2,0)

Answers

Related Questions

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

which ordered pairs are in the solution set of the system of linear inequalities?
y > -1/3x+2
-
y <2x+3

A. (2,2), (3,1) (4,2)
B. (2,2) (3,-1) (4,1)
C. (2,2) (1,-2) (0,2)
D. (2,2) (1,2) (2,0)