Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:
y > −4x − 1
y is less than 3 over 2 times x minus 1
Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area. (6 points)
Part B: Is the point (−1, −1) included in the solution area for the system? Justify your answer mathematically. (4 points)
Answer:
Part A: The solution area is to the left of x=-2, over the right line y=2x+3 and below the right line y=-(3/2)x-4.
Part B: No, the point (-4,6) is not included in the solution area for the system.
Step-by-step explanation:
System of inequalities:
(1) y > 2x + 3
(2) y < -(3/2)x - 4
Part A
1) The first inequality represents the region over the line:
y=2x+3
This is a linear equation and its graph is a right line. We must graph the right line, and then shadow the area above this right line. To graph this right line we need two points, because through two points only goes one right line. Giving two arbitrary values to x, for example:
x=0→y=2(0)+3→y=0+3→y=3; Point=(x,y)→Point=(0,3)
x=1→y=2(1)+3→y=2+3→y=5; Point=(x,y)→Point=(1,5)
1) The second inequality represents the region below the line:
y= -(3/2)x - 4
This is a linear equation and its graph isaright line. We must graph the right line, and then shadow the area below this right line. To graph this right line we need two points, because through two points only goes one right line. Giving two arbitrary values to x, for example:
x=0→y=-(3/2)(0)-4→y=0-4→y=-4; Point=(x,y)→Point=(0,-4)
x=2→y=-(3/2)(2)-4→y=-3-4→y=-7; Point=(x,y)→Point=(2,-7)
The two lines intersect at the point (-2,-1). The solution area is to the left of x=-2, over the right line y=2x+3 and below the right line y=-(3/2)x-4.
Part B
No, the point (-4,6) is not included in the solution area for the system, because this point is not below the right line y=-(3/2)x-4
Part A: The purple region in the graph attached below is the solution to the given inequalities.
Part B: (-1,-1) is not included in the solution area for the system of inequalities.
In mathematics, inequalities specify the connection between two non-equal expressions.
Given the following information:
1) y > −4x − 1
2) y is less than 3 over 2 times x minus 1, this can be expressed in inequality as follows:
[tex]y < \dfrac{3}{2}x-1[/tex]
Part A:
Attaching image to describe the graph of the system with shaded area.
The red colored region corresponds to the solution of inequality of line 1)
The blue colored region corresponds to the solution of inequality of line 2)
Thus, purple colored region corresponds to the common region due to the 2 lines.
Part B:
To check whether (-1,-1) is included in the solution area for the system:
Plot the point(-1,-1) of it falls in the purple shaded region then it wll be the solution. From the graph, it is clear that point lie outside the shaded region. Thus, (-1,-1) is not the solution.Mathematical justification:
Substituting (-1,-1) in eq1)
-1>-4(-1)-1
-1>3
This is false as -1 is less than 3.
Substituting (-1,-1) in eq2)
-1<3(-1)/2-1
-1<-3/2-1
-1<-5/2
-1<-2.5
This is also false as -1 is greater than -2.5
Thus, it is justified that (-1,-1) is not included in the solution.
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how long would it take to travel 200 meters at 5 m/s
To travel 200 meters at 5 m/s, it would take 40 seconds.
To travel 200 meters at 5 m/s, we can use the formula for speed:
speed = distance / time
5 m/s = 200 meters / time
time = 200 meters / 5 m/s = 40 seconds
Sarah buys 2 gallons of milk. There are approximately 3.875 liters in a gallon. How many milliliters of milk did Sarah buy?
To calculate the volume in milliliters, we first convert gallons to liters (2 gallons * 3.875 liters/gallon = 7.75 liters), then convert liters to milliliters (7.75 liters * 1000 ml/liter = 7750 milliliters). So, Sarah purchased 7750 milliliters of milk.
Explanation:Sarah purchased 2 gallons of milk, with each gallon approximately 3.875 liters. To convert liters to milliliters (ml), we should remember that 1 liter equals 1000 milliliters. So, to find the total amount in milliliters, we first convert gallons to liters (2 gallons * 3.875 liters/gallon = 7.75 liters), then convert liters to milliliters (7.75 liters * 1000 ml/liter = 7750 milliliters). Therefore, Sarah bought 7750 milliliters of milk.
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this ten frame show 5+8 draw to make ten then write the new fact
Drag the numbers to order them from greatest to least, with the greatest at the top.
√ 8/3
π
3.01245...
√ 17
Answer: Our numbers are: [tex]\sqrt{8/3}[/tex], π, 3.01245 and [tex]\sqrt{17}[/tex]. Let's analyze them:
1) [tex]\sqrt{8/3}= \sqrt{16/6} =4/\sqrt{6}[/tex] and [tex]\sqrt{6} \geq\sqrt{4}= 2[/tex], so [tex]4/\sqrt{6} \leq4/2 = 2[/tex]
So [tex]\sqrt{8/3}\leq2[/tex]
2) the number pi is 3.14159265
3) this number is 3.01245, doesn't require more analyzing-
4) [tex]\sqrt{17}[/tex], we know that [tex]\sqrt{16} = 4[/tex], then [tex]\sqrt{17} \geq 4[/tex]
So the correct order from greatest to lowest is:
[tex]\sqrt{17}[/tex], π , 3.01245, [tex]\sqrt{8/3}[/tex]
You also can check it with a calculator, but it isn't the idea of the problem.
A book store was selling 5 books for $27.25.Online you could buy 6 books for $32.16. Which place has a lower unit price
A 7-foot tall stop sign creates a shadow that is 2 feet long. At the same time, a utility pole creates a shadow that is 11 feet long. How tall, in feet, is the utility pole?
Answer:
The height of the pole is 38.5 m.
Step-by-step explanation:
Given information:
The height of stop sign is [tex]h=7\rm \; ft[/tex]
Length of shadow of stop sign is [tex]l=2\rm \; ft[/tex].
The length of shadow of pole is [tex]L=11\rm \; ft[/tex].
Now, the shadow is measured at the same time for both the cases. So, the triangles formed by stop sign and its shadow, and pole and its shadow will be similar.
For similar triangles, the sides are always in same proportion.
Solve for the length of pole as,
[tex]\dfrac{H}{h}=\dfrac{L}{l}\\\dfrac{H}{7}=\dfrac{11}{2}\\H=7\times 5.5\\H=38.5[/tex]
Therefore, the height of the pole is 38.5 m.
Refer the diagram for more clarity.
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christiano ronaldo has a messy house. the function that represents the total cost christiano spends have his house cleaned is c(v)=125v when v represents the number of visits. HOW MUCH DOES CRISTIANO RONALDO SPEND PER VISIT AND DEFINE THE INPUT AND OUTPUT IN THE GIVEN SCENARIO.
Identify the slope of the line shown in the graph below:
Graph of a vertical line with an x intercept of 3
the ratio of the amount of money Jason had to the amount of money Wilson had was 12:13. After Wilson spent $63, Jason had 3 times as much money as Wilson. How much money did Jason have? How much money did they have altogether in the end?
The ratio of the amount of money Jason had to the amount of money Wilson had was 12:13, then Jason had $12x and Wilson had $13x.
Wilson spent $63, then in the end he had $(13x-63). Since in the end Jason had 3 times as much money as Wilson, then
[tex]\dfrac{12x}{13x-63}=3.[/tex]
Solve it:
[tex]12x=3(13x-63),\\ \\12x=39x-189,\\ \\27x=189,\\ \\x=7.[/tex]
In the beginning Jason had $12·7=$84 and Wilson had $13·7=$91. In the end Jason had $84 and Wilson had $91-$63=$28.
Answer: Jason had $84, in the end altogether they had $84+$28=$112.
Answer:
I need help with this problem.
Theo ran a 3K in 9.6 minutes, Esteban ran a 5K in 13.5 minutes, and Tetsuo ran a 10K in 31.9 minutes. Who ran the fastest? Round to the nearest ten thousandth. Explain your reasoning.
PLEASE HELP!
Q1. A carpenter has 16 1/2 m of wood. He cuts the wood into pieces that are each 2 3/4 m long.
How many pieces of wood does the carpenter cut?
Q2. Divide.
3/5 ÷ 1 1/4
1. 1/4
2.12/25
3. 3/4
4. 2 2/5
Which is a simplified form of the expression 5c – 7(2c – 4)? A. 9c + 28 B. -9c + 28 C. 9c - 28 D. -9c – 28
Answer:
b
Step-by-step explanation:
What's 4.002 in word form?
When expressing the given number 4.002 in word form, describe it as "four and two thousandths."
The given number is 4.002.
To express the number 4.002 in word form, we break it down into its individual place values and assign corresponding words to each place. Here's the breakdown:
4.002:
The digit 4 is in the whole number place.The digit 0 in the tenths place.The digit 0 in the hundredths place.The digit 2 in the thousandths place.Now, let's express each place value in word form:
4.002 is spelled as "four and two thousandths."
Thus, when expressing 4.002 in word form, we describe it as "four and two thousandths."
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Brandon has 7 ten-dollars bills 8 one dollar bills.joshua has 3 fewer ten dollar bills fewer one dollar bills than Brandon . What is the value of Joshua’s money
A collector's model racecar is scaled so that 1 inch on the model equals 6 feet on the actual car. If the model is 0.75 inches high, how many feet high is the actual car? Enter your answer as a decimal.
Biff’s candy tax is working great for him. When any other student buys candy from the student store, Biff takes two pieces for himself for every five pieces the student buys. If George bought 35 pieces of candy, how many pieces will go to Biff? Show your work or explain your answer.
sometimes, people have a pet house mouse. If a mouse could travel at top speed, running 20.25 miles in 2.5 hours, how far could it travel in an hour
Final answer:
By dividing the total distance (20.25 miles) by the total time (2.5 hours), we find that the mouse has a top speed of 8.1 mph and could therefore travel 8.1 miles in one hour if it maintained this speed.
Explanation:
To find out how far a mouse can travel in an hour at its top speed, we can use the information provided that the mouse ran 20.25 miles in 2.5 hours. This question is essentially asking us to calculate the speed of the mouse in miles per hour (mph), which is a common way to express speed. We'll use a simple division to solve this problem.
First, we divide the total distance traveled by the total time taken to find the speed:
Total Distance = 20.25 milesTotal Time = 2.5 hoursSpeed = Total Distance ÷ Total Time = 20.25 miles ÷ 2.5 hoursPerforming the division:
Speed = 8.1 mph
Therefore, if the mouse continued to run at its top speed, it would be able to travel 8.1 miles in one hour.
Jeremy’s sister Susie, borrowed money from their mom to pay her order. Their mother has agreed to deduct an equal amount of money from Susie’s allowance each week for the next five weeks to repay the loan. What is the weekly change in Susie’s allowance?
Final answer:
The question requires dividing the total amount borrowed by Susie by the number of weeks to obtain the weekly change in her allowance.
Explanation:
The question pertains to a simple mathematical calculation of equal division of a loan amount across a specified number of weeks to determine the weekly change in Susie's allowance. Although the exact loan amount isn't provided, the process would involve dividing the total sum borrowed by the number of weeks (5 weeks, as mentioned) to find out how much Susie's allowance will reduce each week.
For instance, if Susie borrowed $100, her weekly allowance would be reduced by $100 / 5 = $20 per week.
Final answer:
The weekly change in Susie's allowance is $20.
Explanation:
The weekly change in Susie's allowance can be calculated by dividing the total amount borrowed by the number of weeks she has to repay the loan. In this case, if Susie borrowed $100 and has five weeks to repay it, the weekly change in her allowance would be $100/5 = $20. Therefore, her allowance would decrease by $20 every week for the next five weeks.
Please Help ASAP and Explain Please :)
A teacher promised a movie day to the class that did better, on average, on their test. The box plot shows the results of the test:
Which class should get the reward, and why?
A. The 2nd period class should get the reward. They have the highest score, a perfect 100.
B. The 2nd period class should get the reward. They have a higher median.
C. The 4th period class should get the reward. Though the medians are the same, the first and third quartiles are higher, so the students did better on average than in the 2nd period class.
D. The 4th period class should get the reward. Their lowest score is an outlier, and should be thrown out.
What is 7√11√ in simplest radical form?
Enter your answer in the box.
Answer:
√[tex]\frac{77}{11}[/tex]
The answer in the simplest radical form is [tex]\frac{\sqrt{77}}{11}[/tex].
What is a radical expression?A radical expression is an expression consisting of a square root or nth root.
The given expression is √7/√11.
Simplify the expression as follows:
√7/√11 × √11 / √11
√77 / 11
Hence, the answer in the simplest radical form is [tex]\frac{\sqrt{77}}{11}[/tex].
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The correct question is?
What is √7/√11 in the simplest radical form?
How do I solve this using elimination?
80x + 45y = 645
x + y = 12
Felix found the sum of two prime and one compostie number to be 45. The difference between the greatest and the least number is 4. Which one could be the three numbers?
A.13,17,15
B.18,14,13
C.15,14,16
D.11,19,12
Which is the MOST reasonable estimate of the y-intercept for this linear graph?
A) -1.7
B) -0.6
C) 0.6
D) 1.7
The MOST reasonable estimate of the y-intercept for this linear graph is 0.6
Option C
The y-intercept of a linear graph is the point where the line intersects the graph on the y-axis
The slope-intercept form of the equation of a line is:
y = mx + c
where m is the slope
and c is the y-intercept
Considering the graph shown, the line intersects the y-axis on the point y = 0.6
Since the line intersects the y-axis on the point y = 0.6, the most reasonable estimate of the y-intercept of the linear graph is 0.6
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How is interest similar to sales tax and markups? How is it different?
Interest, sales tax, and markups are all additional charges added to the original amount, but they differ in how they are calculated and when they are charged.
Explanation:Interest is similar to sales tax and markups in that they all involve additional charges or fees that are added to the original amount.
Interest is the extra amount paid for borrowing money, while sales tax is the extra amount paid on the purchase of goods or services, and markups are the extra amount added to the cost price to determine the selling price. They all increase the total cost or price of the transaction.
The main difference is that interest and markups are calculated as a percentage of the original amount, while sales tax is calculated as a percentage of the purchase price. Additionally, interest and markups are typically charged over a period of time or for a specific duration, while sales tax is a one-time charge at the point of sale.
The floor of a canyon has an elevation of −14.5−14.5 feet. Erosion causes the elevation to change by −1.5−1.5 feet per year. How many years will it take for the canyon floor to have an elevation of −31−31 feet?
Explain how to estimate 524÷9.
To estimate 524÷9, round 524 to 540 (a multiple of 9) and divide by 9. The estimate is 60.
Explanation:To estimate 524÷9, you can use rounding. Round 524 to the nearest multiple of 9, which is 540. Then, divide 540 by 9, which equals 60. Therefore, the estimate for 524÷9 is 60.
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The circumference of a circle of radius r is given by the polynomial 2 pi r2πr, where piπ is an irrational number. For an approximation of piπ, use 3.14. Find the circumference of a circle with radius 18 cm18 cm.
What is the distance between points (10,7) and (2,7) on a coordinate plane?
please help me
The distance between points (10,7) and (2,7) on a coordinate plane will be 8 units.
What is a distance formula?It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.
The distance formula can be given as:
[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
It is given that, the points on the coordinate planes are (10,7) and (2,7).
(x₁,y₁) = (10,7)
(x₂,y₂) = (2,7)
The distance between points (10,7) and (2,7) on a coordinate plane is found as,
(d) = √(x₂ - x₁)² + (y₂-y₁)²
Substitute the given values as,
(d) = √(2 - 10)² + (7 - 7)²
=√(-8)² + (0)²
=√64
=8 units
Thus, the distance between points (10,7) and (2,7) on a coordinate plane will be 8 units.
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solve for x , 2x-11 -9+ x