Match the solution set of each of the following inequalities with its graph.
Answers
The following inequalities with its graph are:
For graph 1: x≤-2,
For graph 2: x≥2,
For graph 3: x≥2,
For graph 4: -2<x
For graph 5: x<2
Inequality is defined as a relationship between two expressions or values that are not equal to each other.
A number line is a representation of real numbers in the form of a graduated straight line.
The solution for the first graph is x less than or equal to -2.
1. x≤-2
The solution to the second graph is x higher than or equal to 2
x≥2
In the third graph, the solution x is greater than or equal to 2
x≥2
The solution x in the fourth graph is greater than -2.
x>-2 or -2<x
The solution x in the fifth graph is smaller than 2.
x-2<0
x<2
As a result, the inequalities for the respective graphs are x-2, x2, x2, -2x, and x2.
Related Questions
7 indian and 4 chinese finish a job in 5 days. 7 japanese and 3 chinese finish the same job in 7 days. given that the efficiency of each person of a particular nationality is same but different from others.one chinese,one indian and one japanese will complete the work in
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20 7/12
The question is about work and efficiency and requires solving a system of equations to find the individual work rates of people from different nationalities. However, because we have insufficent data (two equations but three unknowns), we cannot find a unique solution and thus can't determine how long it would take for one Chinese, one Indian, and one Japanese to complete the work together.
The student's schoolwork question involves solving a problem related to work and efficiency, which is a part of mathematics, specifically related to rate and work problems.
First, let's find the rate of work done by individuals from each nationality. We can set up the equations based on the given information:
Let's denote the efficiency of one Indian as I, one Chinese as C, and one Japanese as J.According to the given information:7I + 4C = 1/5 (since 7 Indians and 4 Chinese finish the job in 5 days)7J + 3C = 1/7 (since 7 Japanese and 3 Chinese finish the job in 7 days)
We will need to solve this system of equations to find the individual efficiencies I, C, and J. However, we have two equations and three unknowns, so we cannot find unique solutions for I, C, and J unless we have one more equation or information.
Since we cannot determine the individual efficiencies with the given information, we cannot determine how long it would take one Chinese, one Indian, and one Japanese to complete the work.
kathi starts with a number. she adds 3 to her number, then doubles the result. finally, she subtracts 7. if she ended with 9 what number did ahe start with
Answers
2(x+3)-7=9
Distribute the 2
2(x)+2(3) -7=9
2x+6-7=9
Combine like terms
2x-1=9
Add one to both sides
2x-1+1=9+1
2x=10
Divide both sides by two to isolate the variable.
2x/2=10/2
x=m
5+3=8
8+8=16
16-7=9
i need help with this one!
Answers
The table below shows the number of marbles of different colors in a bag:
Marble Experiment
Color of
Marbles Number of
Marbles
Red
5
White
8
Black
2
Deja draws a marble from the bag randomly without looking. She then draws another marble from the bag without replacing the first one. Which expression shows the probability of drawing red marbles in both the trials? (5 points)
5 over 15 multiplied by 4 over 14
5 over 15 multiplied by 4 over 15
5 over 15 added to 4 over 14
5 over 15 added to 4 over 15
Answers
Favorable outcomes={5 Red}
1) P(drawing 1st Red) = 5/15
2) P(drawing ANOTHER RED) = 4/14 (because one Red already drawn and NOT replaced, so the remaining Red are now 4 and the new sample space is now 14, since 1 red already drawn), Hence
P( 1 Red AND another Red) = (5/15).(4/15) or:
"5 over 15 multiplied by 4 over 14"
The correct answer is: 5 over 15 multiplied by 4 over 14
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given this, Deja draws a marble from the bag randomly without looking.
The total number of marbles in the bag is:
5 + 8 + 2 = 15
Deja draws a marble from the bag randomly without looking. Therefore, the probability of drawing a red marble in the first trial is:
P(red on first draw) = 5/15
Deja draws another marble from the bag without replacing the first one. Therefore,
The probability of drawing a red marble in the second trial, given that she drew a red marble in the first trial, is:
P(red on second draw | red on first draw) = 4/14
We multiply these probabilities because the events are independent (i.e., the outcome of the first draw does not affect the outcome of the second draw).
Therefore, the expression that shows the probability of drawing red marbles in both trials is:
= P(red on the first draw) × P(red on second draw | red on the first draw)
= (5/15) × (4/14) = 4/63
So the correct answer is: 5 over 15 multiplied by 4 over 14.
Learn more about probability here:
https://brainly.com/question/30034780
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Which linear inequality is represented by the graph?
y < 2/3x + 3
y >3/2 x + 3
y >2/3 x + 3
y < 3/2x + 3
Answers
The linear equality represented by the graphis [tex]\boxed{{\mathbf{y > }}\frac{{\mathbf{2}}}{{\mathbf{3}}}{\mathbf{x + 3}}}[/tex] and it matches with [tex]\boxed{{\mathbf{OPTION C}}}[/tex].
Further explanation:
From given graph, theline passes through points [tex]\left({3,5}\right)[/tex] and [tex]\left({ - 3,1}\right)[/tex] as shown below in Figure 1.
The slope of a line passes through points [tex]\left({{x_1},{y_1}}\right)[/tex] and [tex]\left({{x_2},{y_2}}\right)[/tex] is calculated as follows:
[tex]m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}{\text{}}[/tex] ......(1)
Here, the slope of a line is denoted as and points are [tex]\left({{x_1},{y_1}}\right)[/tex] and [tex]\left({{x_2},{y_2}}\right)[/tex].
Substitute [tex]3[/tex] for [tex]{x_1}[/tex] , [tex]5[/tex] for [tex]{y_1}[/tex] , [tex]-3[/tex] for [tex]{x_2}[/tex] and [tex]1[/tex] for [tex]{y_2}[/tex] in equation (1) to obtain the slope of a line that passes through points [tex]\left( {3,5}\right)[/tex] and [tex]\left({ - 3,1}\right)[/tex].
[tex]\begin{aligned}m&=\frac{{1 - 5}}{{ - 3 - 3}}\\&=\frac{{ - 4}}{{ - 6}}\\&=\frac{2}{3}\\\end{aligned}[/tex]
Therefore, the slope is [tex]\frac{2}{3}[/tex].
The point-slope form of the equation of a line with slope passes through point is represented as follows:
[tex]y - {y_1} = m\left({x - {x_1}}\right){\text{}}[/tex] ......(2)
Substitute [tex]3[/tex] for [tex]{x_1}[/tex] , [tex]5[/tex] for [tex]{y_1}[/tex] and [tex]\frac{2}{3}[/tex] for [tex]m[/tex] in equation (2) to obtain the equation of line.
[tex]\begin{aligned}y - 5 = \frac{2}{3}\left({x - 3} \right)\\3\left( {y - 5} \right) = 2x - 6\\3y - 15 = 2x - 6\\3y = 2x - 6 + 15\\\end{aligned}[/tex]
Further simplify the above equation.
[tex]\begin{aligned}3y=2x + 9\\y=\frac{2}{3}x+\frac{9}{3}\\y=\frac{2}{3}x + 3\\\end{aligned}[/tex]
Therefore, the value of [tex]y[/tex] is [tex]\dfrac{2}{3}x + 3[/tex].
Since the shaded part in Figure 1 is above the equation of line [tex]y = \dfrac{2}{3}x + 3[/tex], therefore, greater than sign is used instead of is equal to
Therefore, the inequality is [tex]y > \dfrac{2}{3}x + 3[/tex].
Now, the four options are given below.
[tex]\begin{aligned}{\text{OPTION A}}\to y < \frac{2}{3}x + 3 \hfill \\{\text{OPTION B}} \to y > \frac{3}{2}x + 3 \hfill \\{\text{OPTION C}} \to y > \frac{2}{3}x + 3 \hfill \\{\text{OPTION D}}\to y < \frac{3}{2}x + 3 \hfill\\\end{aligned}[/tex]
Since OPTION C matches the obtained equation that is [tex]y > \dfrac{2}{3}x + 3[/tex].
Thus, the linear equality represented by the graph is [tex]\boxed{{\mathbf{y > }}\frac{{\mathbf{2}}}{{\mathbf{3}}}{\mathbf{x + 3}}}[/tex]and it matches with [tex]\boxed{{\mathbf{OPTION C}}}[/tex]
Learn more:
1. Which classification best describes the following system of equations? https://brainly.com/question/9045597
2. What is the value of in the equation when ? https://brainly.com/question/3965451
3. What are the values of x?https://brainly.com/question/2093003
Answer Details:
Grade: Junior High School
Subject: Mathematics
Chapter: Coordinate Geometry
Keywords: Coordinate Geometry, linear equation, system of linear equations in two variables, variables, mathematics,equation of line, line, passes through point, inequality
Simplify this expression
Answers
Let's put these into simpler terms:
-7s + 3s + 2s
10 - 8 - 7
-7s + 3s = -4s
-4s + 2s = 2s
10 - 8 = 2
2 - 7 = -5
We are now left with:
2s - 5, which is your simplified expression.
I hope this helps!
Which expression is equivalent to 2−35?
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-33
A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?
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What is a complex fraction?
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-------
6
a set of data can have no mode true or false
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True, A set of data can indeed have no mode. In statistics, the mode represents the value(s) that appear most frequently in a dataset.
However, there are scenarios where no value occurs more frequently than others, resulting in a lack of a mode. This can happen in several situations. For example, in a uniform distribution where all values occur with equal frequency, or in a dataset with no repetition of values (each value occurs only once). Additionally, if the data is continuous and does not have distinct categories or intervals, it may not have a mode. In summary, while a mode is a common descriptive statistic, it's not a requirement for every dataset, and some datasets do indeed have no mode.
Ryan has a shelf that is 64 over 3 inches wide. How many magazines can Ryan arrange on the shelf if each magazine is 4 over 3 inches thick?
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Find 3 consecutive integers whose sum is 180
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4x + 6 = 180
4x = 174
x = cannot be an even integer
If they were consecutive even integers,
x + (x+2) + (x+4) + (x+6) = 180
4x + 12 = 180
4x = 168
x = 42, 44, 46, 48
ken had a number of colored marbles in a bag. 1/4 of the marbles were red, 2/3 of the marbles were blue, and the rest were yellow. Given that there were 120 red and yellow marbles all together, how many marbles were there in the bag
Answers
Blue = 2/3
Yellow= ?
First you will need to find how much of the fraction is yellow so:
RED= 1/4 = 3/12
BLUE= 2/3 = 8/12
YELLOW= add 3/12 with 8/12= 11/12
12/12 - 11/12= 1/12
so the yellow marbles are 1/12
yellow + red = 120
1/12 + 3/12= 120
4/12= 120
so 4/12 of the marbles are 120
how much is 8/12?
120 x 2= 240
now:
red + yellow = 120
blue= 240
how many are in the bag? 120 + 240 = 360
answer: 360
I don't know if this is correct. but I tried. hope this helped:)
I need help with this question please
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A company manufactures 295 toy cars each day how many toy cars does the company manufacture and 34 days
Answers
Factor 4x^2+8x-21 completely
Answers
(2x - 3)(2x + 7) <==
4x^2-6x+14x-21
2x(2x-3)+7(2x-3)
(2x+7)(2x-3)
the lengths of the sides of a triangle are three consecutive odd integers. The perimeter of the triangle is 45in. What is the length of the shortest side of the triangle?
Answers
.. 45/3 -1 = 14
Which sets of values can be the measures of the exterior angles of a triangle? Click all that apply.
120°, 110°, 130°
35°, 103°, 122°
123°, 87°, 220°
120°, 120°, 120°
123°, 157°, 90°
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120°, 110°, 130°
120°, 120°, 120°
The angles are within the range of angles are 120°, 110°, 130° and 120°, 120°, 120°
The exterior angle of a triangle is the sum of its exterior angles. The exterior angle of a triangle is obtuse in nature and obtuse angles are angles that are greater than 90 but less than 180 degrees.]Hence the set of angles required must fall within the range [tex]90^0<\theta<180^0[/tex]From the given options, the angles are within the range of angles are 120°, 110°, 130° and 120°, 120°, 120°
Learn more on exterior angles here: https://brainly.com/question/24231058
Best Answer Gets Brainliest
The double box-and-whisker plot represents the runs scored per game by two softball teams during a 32-game season. a. Which team is more consistent at scoring runs? Explain. b. In how many games did Team 2 score 6 runs or less? c. Team 1 played Team 2 once during the season. Which team do you think won? Explain. d. Which team do you think has the greater mean? Explain
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B. 4 games
C. Team 2 because they have the higher batting average.
D. Team 1 has the greater mean because team 1 has a mean of 9 and team 2 has a mean of 5.
Answer its, C and standard deviation, lowest
Step-by-step explanation:
3x - 13 = 7(x+2) - 4(x-7)
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What number makes the the number sentence true 420,008 - 9,569 =n
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You can just type your problem into a calculator-- you're just finding out what 420,008-9,569 is. :)
Answer: its 410439
(all u need to do is subtract!)
PLEASE HELP!!! I WILL RATE BRAINLIEST TO THE FASTEST AND CORRECT ANSWER!!!
Answers
- 4 < x^4 + 4x^2 ---> 0 < x^4+4x^2+4 = (x^2+2)^2, so it is always positive. Always satisfied. Curious ...
Now the other one:
x^4+4x^2<21 --> x^4+4x^2-21 < 0 --> (x^2+2)^2 - 25 < 0
(x^2+2)^2<25 ->>> x^2+2 < 5 ---> x^2 <3,
So -sqrt(3)<x<sqrt(3) is the answer! Brainliest?
SOMEONE, PLEASE HELP URGENTLY <3
What shape is generated when rectangle ABCD is rotated around the horizontal line through D and A?
A. Prism
B. Pyramid
C. Cone
D. Cylinder
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D. cylinder.
What is the slope of the line represented by the equation y = – 2/3- 5x?
A. -5
B. -2/3
C.2/3
D. 5
PLS HELP TY
Answers
Answer:
Option A The slope of the line is [tex]-5[/tex]
Step-by-step explanation:
we know that
The equation of the line into slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
we have
[tex]y=-\frac{2}{3}-5x[/tex]
Rewrite
[tex]y=-5x-\frac{2}{3}[/tex]
therefore
[tex]b=-\frac{2}{3}[/tex] -----> the y-intercept
[tex]m=-5[/tex] ------> slope
After 4 months of living in her dorm room, Molly had 5 fish. Eight months later, Molly still had 5 fish. Which of the graphs below models Molly's fish population?
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21/99 simplified in fraction
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Gavin bought 4 packages of cheese. Each package weighed 1.08 kilograms. How many kilograms of cheese did Gavin buy?
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=4.32kg
Gavin bought 4.32kg of cheese.
Hope this helps! A thanks/brainiest answer would be appreciated :)
4*1.08=4.32
A box of 21 holiday cards sells for $3.99. What is the unit price per card?
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(I really need help!!!)
x + 14 + (-x)
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what does coplanar mean
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What does coplanar mean?
Coplaner is a term used in geometry referring as points which rest on the very same plane; typically orbiting the same way. The point can be rested as 3 or several points in the same plane.
Hope I helped :D