Which graph represents the solution set of the system of inequalities?
{ y < -3x - 2
{ y ≤ x - 2
Answers
God bless!
The common shaded region of the given inequality is given by figure 3 with yellow color.
What is an inequality and how to graph it ?An inequality is a statement that compares two expressions we can solve an inequality by adding same number to both sides or by subtracting same number from both side.
To graph the inequality
Replace the sign of the inequality with equal to sign.Graph the equation made with equal to line.If the point (x, y) satisfies the inequality then check whether the inequality is satisfied on that point or not.Shade the region on that side of line where any point satisfies the equation if not shade the opposite side of region.if the sign of inequality is < ,> with equal to gin then make the line dotted for respective equality otherwise a solid line.Given inequalities are :
y < -3x -2
y ≤ x-2
For y < -3x-2 consider the equality y = -3x -2
Put x =0 ⇒ y = -2 , ( 0, -2)
Put y = 0 , x = -2/3, ( -2/3 , 0)
∴ y = -3x -2 is the line passing through the points ( 0, -2) and ( -2/3 , 0)
⇒ Put (0,0) in y<-3x-2 ⇒ 0 < -3(0) -2 ⇒0 < -2 which is false
Therefore , the inequality y<-3x-2 is the shaded region shown in figure 1
Similarly for inequality y ≤ x - 2 , Consider y = x - 2
Put x = 0 ⇒ y =-2, (0,-2)
Put y=0 ⇒ x =2 , (2,0), thus y = x - 2 is the line passing through (2,0) and (0,-2)
Put (0,0) in y ≤ x - 2⇒ 0 ≤ -2 , which is false
therefore the region of this inequality is as shown in figure 2.
The common shaded area is given by yellow color figure 3 .
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Related Questions
162 water bottles in 9 cases, write each ratio as a unit rate
Answers
I dont really see why ur answer was marked " no " because all u did was reduce the fraction instead of simply dividing 162 by 9.....but the way u did it resulted in the same answer....because ratios are basically just equivalent fractions
Hiiiii pleaseeeee helppppp pleaseeeee understanddddd this question.
Answers
It is #1: 0.348348348348348348348........
IF you look at #1, you can tell that the line on the number after 0., means that it goes forever.
A truck with a heavy load drove from Boston to New York at 45 mph. After unloading, it returned from New York to Boston at a speed of 65 mph. What was its average speed for the whole trip?
Answers
Answer:
Average speed: 585/11 or 53 2/11
Step-by-step explanation:
Let distance from New York to Boston, and vice-versa, be D
Then, time taken to travel from Boston to New York is: D/45
Also, time taken to travel from New York to Boston is: D/65
Total time taken for entire trip: D/45+D/65
Average speed: total distance/total time
Average speed: 2D/22D/585
Average speed: 53 2/11 or 585/11 mph
A recipe that yields 12 cups of soup calls for 28ounces of beef broth. How many ounces of beef broth do you need to make 18 cups of the soup?
Answers
Given the first information, we know that for 12 cups of soup, there are 28 oz of beef broth. This can be expressed as 28/12.
With the second information, we know that for 18 cups of soup, there is x amount of beef broth. This can be expressed as x/18
In this case, x stands for broth.
Because these are ratios, we know they will equal each other. We can set up this as an equation.
28/12=x/18
Solve for x
28/12=x/18
28/12 can be simplified to 7/4
7/4 • 18= x
126/4 = x
31.5= x
ANSWER:
31.5 oz of beef broth is needed to make 18 cups of soup
to make fruit punch you need 3 cups of grape juice for every 5 cups of apple juice if you have 15 more cups of apple juice how many cups do you have total how many cups do you have for each flavor use tape diagram to show your answer
Answers
what is the measure of xy
Answers
180 = 43 + m(arc)XY
m(arc)XY = 137
Answer is A.
A circle is a curve sketched out by a point moving in a plane. The correct option is A, 137°.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
In the given figure since W is the midpoint of ZY, therefore, the measure of arc ZV and arc VY will be equal; and ZX and XY will be equal. Also, it is given that the measure of arc ZV is 43°. Therefore, we can write,
mZV + mVY + mXY + mXZ = 360°
43° + 43° + mXY + mXY = 360°
2(mXY) = 360° - 43° - 43°
mXY = 274/2
mXY = 137°
Hence, the measure of arc XY is 137°.
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WHICH ANSWER GOES WHERE ON THE NUMBER LINE ? I will give 11 points and brainliest!!!
Answers
2^-1 goes in the middle of 0 and 1 since it is approximately 1.41
the square root of 4 goes on 2 since its value is exactly 2
π goes slightly in front of 3 since it is approximately 3.14
1.5^3 is past π but a little less than 3 and a half
At the sixth grade school dance there are 132 boys,89 girls,and 14 adults
Answers
Of the students at Milton Middle School, 153 are girls. If 45% of the students are girls, how many total students are there at Milton Middle school?
Answers
Solving for x, x = 153/0.45 = 340 students (total)
A teacher let her students grade their math quizzes. •Jon wrote 13 out of 18 •Jim wrote .7 (repeated .7) •Joe reduced his to 5/6 who had the higher grade?
Answers
Answer:
Joe
Step-by-step explanation:
Jon wrote 13 out of 18
Dividing 13 by 18 we get, decimal form
[tex]\frac{13}{18}=0.722........[/tex]
Jim wrote .7 (repeated .7)
0.777..........
Joe reduced his to 5/6
Dividing 5 by 6 we get, decimal form
[tex]\frac{5}{6}=0.833........[/tex]
These numbers are irrational numbers
0.833......>0.777........>0.722......
So, Joe had the higher grade.
The level of a lake was 8 inches below normal. It decreased 1 1/4 inches in June and 2 3/8 inches more in July. What was the new level with respect to the normal level?
Answers
It would be: 8 - (1 1/4 + 2 3/8)
8 - (5/4 + 19/8)
8-29/8
64-29/8
35/8 inches OR 4.375 is your answer
if wrong . im sorry about that
A sport store pays $45 for a baseball glove and sells it for $75. What is the mark up?
Answers
Or 45/75 gives you 0.6 or a 60% mark up.
PL has endpoints P(4, −6) and L(−2, 1). The segment is translated using the mapping (x, y) → (x + 5, y). What are the coordinates of P’ and L’? P’(9, -6), L’(-2, 1) P’(4, -6), L’(3, 1) P’(9, -6), L’(3, 1) P’(9, -1), L’(3, 6)
Answers
Answer: C P’(9,-6), L’(3,1)
The coordinates of P' and L' after the translation are (9, -6) and (3, 1) respectively.
Explanation:A translation rule in mathematics describes the process of moving a geometric figure from one location to another without changing its shape or orientation. It involves shifting the figure horizontally or vertically by a certain distance. Translation rules are essential in geometry and are used to analyze and manipulate shapes on a coordinate plane.
The segment PL has endpoints P(4, -6) and L(-2, 1). To find the coordinates of P' and L' after being translated using the mapping (x, y) → (x + 5, y), we simply add 5 to the x-coordinates of P and L. Therefore, the coordinates of P' are (4 + 5, -6) which is equal to (9, -6), and the coordinates of L' are (-2 + 5, 1) which is equal to (3, 1).
If f(x) = x2 – 25 and g(x) = x – 5, what is the domain of mc006-1.jpg?
all real values of x
all real values of x except x = 5
all real values of x except x = –5
all real values of x except x = 5 and x = –5
Answers
Answer:
b. all real values of x except x = 5
Step-by-step explanation:
Do you guys know what is 6y-3(4/3y-2)
Answers
6y-3 (4/3y-2)
6y-4y+6 (use the distributive property and multiply all the numbers inside the parentheses by -3)
2y+6 (add like terms)
That's pretty much it
Multiply everything in the parenthesis by -3.
6y - 12/3y + 6 = 0
Simplify.
6y - 4y + 6 = 0
Combine like terms.
2y + 6 = 0
Subtract 6 from both sides.
2y = -6
Divide 2 on both sides.
y = -3
Hope this helps!
Jeff uses the expression 2(3b + 1) to determine how many books (b) he needs to order for his store. If b = 12, how many books should Jeff order?
Answers
So, Jeff should order 111 books
Replace b with 12.
2(3x12 + 1)
2(36 + 1)
2(37)
74.
Hope that helped!
Mark filled 48 glasses with orange juice for a camp breakfast. If each glass holds 1 cup of juice. How many quarts of orange juice did Mark use?
A) 6 quarts
B) 12 quarts
C) 24 quarts
D) 192 quarts
Answers
First of all, Mark used 48 cups of orange juice.
But wait. That isn't an answer choice!
Well then, it problably can be simplified to other units.
Since all the answer choices are in quarts, you can see that you should probably simplify it to quarts.
Since there are 4 cups in each quart, 48 cups is equal to 48/4=12 quarts.
Mark used B)12 quarts of orange juice.
Hope this helps!
Multiply 7 x 462 using place value and expanded form. Choose the number from the box to complete the expression
Answers
To multiply 7 x 462 using place value and expanded form, we first write 462 as the sum of the products of its digits and their place values (400 + 60 + 2). We then multiply each component by 7 and add the results to get 3234.
Explanation:
To multiply 7 x 462 using place value and expanded form, you first need to break down the number 462 into expanded form. This means you write it as the sum of the products of its digits and their place values. We start at the right and move to the left: 2 (units), 60 (tens), and 400 (hundreds). So 462 in expanded form is 400 + 60 + 2.
The next step is to multiply each component by 7: 7 x 400 = 2800, 7 x 60 = 420, and 7 x 2 = 14. You add those results together to get your final answer: 2800 + 420 + 14 = 3234. So, 7 x 462 = 3234.
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suppose an object is moving 66 feet per second. how fast would you have to drive in your car, in miles per hour, in order to keep up with this object?
Answers
66/5280=
.0125 m/h
You would need to drive at around 96.67 miles per hour to keep up with the object.
Explanation:To determine how fast you would have to drive in your car to keep up with an object moving at 66 feet per second, we need to convert the unit from feet per second to miles per hour. There are 5280 feet in a mile and 3600 seconds in an hour. Therefore, the conversion factor is 5280/3600 = 1.4667. Multiplying 66 by this conversion factor gives us approximately 96.67 miles per hour. So, you would need to drive at around 96.67 miles per hour to keep up with the object.
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Which expression is equivalent to 2x - 17?
A) -17 + 2x
B) -2x + 17
C) -2x - 17
D) 17 + 2x
Answers
In two or more complete sentences, describe how you would draw the graph of the solution set for the following inequality.
-3m+18 < 30
Answers
A nonlinear function that can be written on the standard form
ax2+bx+c,wherea≠0ax2+bx+c,wherea≠0is called a quadratic function.
All quadratic functions has a U-shaped graph called a parabola. The parent quadratic function is
y=x2y=x2The lowest or the highest point on a parabola is called the vertex. The vertex has the x-coordinate
x=−b2ax=−b2aThe y-coordinate of the vertex is the maximum or minimum value of the function.
a > 0 parabola opens up minimum value
a < 0 parabola opens down maximum value
A rule of thumb reminds us that when we have a positive symbol before x2we get a happy expression on the graph and a negative symbol renders a sad expression.
The vertical line that passes through the vertex and divides the parabola in two is called the axis of symmetry. The axis of symmetry has the equation
x=−b2ax=−b2aThe y-intercept of the equation is c.
When you want to graph a quadratic function you begin by making a table of values for some values of your function and then plot those values in a coordinate plane and draw a smooth curve through the points.
what is 5/9-2/3×5/2=
Answers
5/9-5/3=
-10/9
Answer:
5/9-2/3×5/2=
5/9-5/3=
-10/9
Step-by-step explanation:
Which of the following inequality statements best represent the verbal expression? a number is at least 2
Answers
Answer:
it is the answer that the other person picked. i just got it right
Step-by-step explanation:
Inductive reasoning involves developing a general rule from specific situations. True or false
Answers
The answer is true
Hope it helped!
Answer:
The answer is true
Step-by-step explanation:
Inductive reasoning is a principle in mathematical and philosophical logic where general conclusions are derived from specific situations. Its contrary is deductive reasoning where we use a general rule to explain particular situations, reasoning commonly used in mathermatics. Example: all right angles measure 90 degrees, AB is right angle so AB measure 90 degrees,
In inductive reasoning we use the opposite logic that can take to incorrect general principles due to a bias. Example, my friend is tall and a good basket player, Joe is tall and also plays good basketball so All tall people are good basket players is a biased conclusion.
adam spent $3.42 on orange juice. orange juice costs $0.12 per ounce. how many ounces of ornage juice did adam buy?
Answers
The amount of ounces of orange juice is A = 28.5 ounces
What is an 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.
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 data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the number of ounces of orange juices be A
Now , the amount spent on orange juice = $ 3.42
The cost per ounce of juice = $ 0.12
So , the number of ounces A = amount spent on orange juice / cost per ounce of juice
On simplifying the equation , we get
The number of ounces A = 3.42 / 0.12
The number of ounces A = 28.5 ounces
Hence , the equation is A = 28.5 ounces
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Use the vertical line test to determine if the relation {(-6, -2), (-2, 6), (o, 3), (3, 5)} is a function. Explain your response.
Answers
Using the vertical line test, it is found that the relation is a function.
In the definition of a function, it has that for each input, there can only be one respective output, and the same is true for a relation, and the test of the number of outputs for each input is the vertical line test.
The relation is: {(-6, -2), (-2, 6), (0,3), (3,5)}
No repeated inputs, thus it passes the vertical line test and is a function.
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a company uses two vans to transport workers from a free parking lot to the work place between 7:00 and 9:00 am one van has 6 more seats than the other. the smaller van makes two trips every morning while the larger one only takes one trip. the two vans can transport 57 people, maximum. how many seats does the large van have?
Answers
So since it makes two trips,
2x
And since the other van can hold six more people,
2x + x + 6
And 57 people are transported:
3x + 6 = 57
We can then solve.
3x = 57 - 6
3x = 51
x = 17
So since we now know a small can hold 17 people, and we know that the larger van has 6 more seats, we can just say
17 + 6 = 23
So the large van has 23 seats.
I REALLY NEED YOU PEOPLE'S HELP! Divide. 6 2/3 ÷ 1/5 Express your answer as a mixed number in simplest form, & I'll give you free points if you answer my next questions coming up. 20-50
Answers
62/15=60 2/15
60 2/15 is your answer.
Hoped I helped!
62/15 = 4 2/15
What is the value of the expression [(29+18)+(17-8)] divided by 8
Answers
17-8= 9
47+9= 56
56 divided by 8 = 7.
The answer is 7.
Your class hopes to collect at least 325 cans of food for the annual food drive. There were 135 cans donated the first week and 89 more the second week.
A. write an inequality that describes this situation. let c represent the number of cans of food that must be collected by the end of the third week for your class to meet or surpass its goal.
B. how many cans are needed to meet or surpass the goal.
Answers
C=101 or greater
hope this helps (the underscore sign is under the inequality sign ;) )
Answer:
132+146+c>325;c>47
Step-by-step explanation: