Which graph represents the solution set of the system of inequalities?
−3x+y>1
y≥x−1
Answers
Answer:
Option D is the correct choice.
Step-by-step explanation:
We have been given a system of inequalities. We are asked to choose the graph that represents solution set of the given system.
[tex]-3x+y>1[/tex]
[tex]y\geq x-1[/tex]
The boundary line of [tex]-3x+y>1[/tex] will be a dotted line as it has a [tex]>[/tex] sign. The boundary line of this inequality will cross y-axis at point (0,1) and will have a slope of 3.
The boundary line of [tex]y\geq x-1[/tex] will be a solid line as it has a [tex]\geq[/tex] sign. The boundary line of this inequality will cross y-axis at point (0,-1) and will have a slope of 1.
Now, we will check point (0,0) in both inequalities to find the shaded region.
[tex]y\geq x-1[/tex]
[tex]0\geq 0-1[/tex]
[tex]0\geq -1[/tex]
Point (0,0) satisfies inequality [tex]y\geq x-1[/tex], so shaded region will be area including point (0,0)
[tex]-3(0)+0>1[/tex]
[tex]0+0>1[/tex]
[tex]0>1[/tex]
Point (0,0) doesn't satisfy inequality [tex]-3x+y>1[/tex], so shaded region will be area excluding point (0,0).
The solution set of given system of inequalities will be area of included in both inequalities.
We can see that last option is the correct choice as it has one dotted line (y-intercept 1) and one solid line (y-intercept -1).
Therefore, option D is the correct choice.
Answer:
The bottom choice one the right is correct
Step-by-step explanation:
Hope this helps :)
Related Questions
Danielle earns a 7.25% commission on everything she sells at the electronic store where she works,.she also earns a base salary of $750 per week .how mcuh did she earn last week if she sold 4,000 in electronics merchandice?
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($4,000 × 0.0725 + $4,000 ) + $750
Now, all you have to do is solve it. You would start in the parenthesis using the order of operation (PEMDAS).
($4,000 × 0.0725 + $4,000 ) + $750
$4290 + $750 = $5,040
Danielle made $5,040 last week.
I hope this helps!
How do I write this number in scientific notation 0.0072
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Hope this helps
If its not too much trouble it would mean a lot if I could have brainliest because I have a BIG unit test coming up and I really need points so I can ask questions. :)
find a perimeter of a rectangle with a length of 665 feet and width of 421 feet. Draw your model and solve.
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w=width
l=length
So it is 2(665)+2(421)=2172
Alan had 2 mirrors installed in his house.The first mirror was 2 yards and 2 3rds yards wide the second mirror was 2 yards tall and 3 2 halfs wide. Is the area of the first mirror greater than or less than 2 square yards?Explain
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8 - 1/3x = 16
PLEASE ANSWER ITS DUE TOMORROW
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An architect is designing a house in which a 104 square foot room and a 130 square foot room share a wall what is the greatest possible integer length of the shared wall -- THIS QUESTION WAS ASKED AND ANSWERED. BUT ANSWERED INCORRECTLY. NOTE THE ANSWER GIVEN CHANGED THE DIMENSIONS TO 140 FROM 104. AND THIS WEBSITE WILL NOT ALLOW ME TO REPORT THAT.
Answers
Then, the area of both squares have x as common factor.
So, x is the greatest common factor of 104 and 130.
You should know how to calculate the greatest common factor of two integers.
Just find the prime factors and choose the common factors raised to the lowest exponent.
104 = (2^3) (13)
130 = (2) (5)(13)
=> the greatest common factor is 2 * 13 = 26, and that is the greatest possible integer length of the shared wall.
Answer: 26
math question answer a b and c hurry answer each one
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so we have Δd/Δt=8.8min
Δd= 8.8Δt
d=∫8.8Δt-------(1)
b. d should be positive because the diver is ascending at a positive rate relative to depth
c. d=rt
t=d/r = 32.12/8.8 min
t= 3.65min
c) About 3 minutes and 39 seconds = 3.65 minutes
what is the value of y in the something to the system of equations
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May I have some help?
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What is the answer????
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I think thats the answer but im not sure
Given the following linear function sketch the graph of the function and find the domain and range f (x) =-5x+4
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Both the domain and range of this function are all real numbers.
The two things that typically limit a domain are dividing by zero and taking the square root of a negative. Since this function does not have a square root or a denominator, then you must be able to use all real numbers.
Which of the following best describes the US government?
A. Executive rule
B. Representative democracy
C. Direct democracy
D. Dictatorship
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joe is playing a game with a regular die.If the number that turns up is even he will gain 5 times the number that comes up.If its odd,he will lose 10 times the number that comes up.He tosses a 3 express results as an integer
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3 - 30 = -27
what is the unit rate for 9 pages in 3 hours
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3 pages in 1 hour is the answer.
Hope this helps!
Recipe A makes 5 dinner rolls using 1 c of flour. Recipe C makes 45 rolls using 10 c of flour. Which recipe requires the most flour per roll?
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When calculating how much flour is used per roll in each recipe, recipe C (at 0.22 cups per roll) uses more flour per roll than recipe A (at 0.2 cups per roll).
Explanation:To determine which recipe uses the most flour per roll, we first need to calculate the flour-per-roll for each recipe. For recipe A, it makes 5 dinner rolls using 1 cup of flour. So, the flour-per-roll for recipe A is
1 cup of flour ÷ 5 rolls = 0.2 cups per roll
. For recipe C, it makes 45 rolls using 10 cups of flour. So, the flour-per-roll for recipe C is
10 cups of flour ÷ 45 rolls = 0.22 cups per roll
. Comparative analysis shows that recipe C requires more flour per roll than recipe A.
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What is the difference between congruent and similar images
Answers
In a similar triangle, they have to be proportional
hope this helps
Pls Answer!!!!!
The following graph shows the number of soccer games a team won in each of their first three seasons. Explain how you could redraw the graph so that the change in wins between the three Seasons does not seem so great.
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In the gragh that is shown, the scale used is 1 grid unit to represent 1 goal, if we may change the scale to something like 1 grid unit to represent 2 goals or 1 grid unit to represent 3 goal, then the change in wins between the three seasons will not seem so great
When would you use a drawing of comparison bars for word problem
Answers
Answer: Comparison bars are a display tool for solving the scenario in which two elements are compared with the difference is either known or unknown.
There are three kinds of use of comparison bars in word problem such as 1) If difference is unknown then A-B=Difference[where A -bigger quantity, B-smaller quantity]. 2) If bigger quantity is unknown then A=Difference-B 3) If smaller quantity is unknown then B=Difference-A.
A drawing of comparison bars, also known as a bar graph, can be used in word problems when there is a need to compare different entities or categories. It is particularly useful in situations where quantitative data needs to be visually represented and compared. For example, if you are given data about the sales of different types of fruits in a grocery store, you can use a bar graph to compare the sales of each fruit.
Explanation:A drawing of comparison bars, also known as a bar graph, can be used in word problems when there is a need to compare different entities or categories. It is particularly useful in situations where quantitative data needs to be visually represented and compared. For example, if you are given data about the sales of different types of fruits in a grocery store, you can use a bar graph to compare the sales of each fruit.
Here are the steps to create a drawing of comparison bars for a word problem:
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what is 6 to the negative 1 times (-2) to the third power times (-4) to the negative 2
Answers
____________________________________________
Explanation:
____________________________________________
We have: " 6⁻¹ * (-2)³ * (-4)⁻² = ? " ;
_______________________________________
Note: "6⁻¹ = [tex] \frac{1}{6^1} [/tex] = [tex] \frac{1}{6}[/tex] " .
Note the following property of exponents:
____________________________________
a⁻ˣ = [tex] \frac{1}{x^a} [/tex] ; {x ≠ 0}.
____________________________________________
Note: (-2)³ = (-2)*(-2)*(-2) = 4*(-2) = -8 .
_______________________________________
Note: (-4)⁻² = [tex] \frac{1}{(-4)^2} [/tex] ;
= [tex] \frac{1}{(-4)*(-4)} [/tex] ;
= [tex] \frac{1}{16} [/tex] ;
____________________________________
So; we have:
_____________________________________
6⁻¹ * (-2)³ * (-4)⁻² ;
= [tex] \frac{(1*8*1)}{(6*16)} [/tex] ;
→ Cancel out the "8" in the "numerator" (to a "1") ; and the "16" in the number (and change to a "2"); since: {"16÷8 = 2" ; and since: "{8÷8=1"} ;
→and we have:
[tex] \frac{(1*1*1)}{(6*2)} [/tex] ;
= [tex] \frac{1}{12} [/tex] .
_____________________________________
→ The answer is: [tex] \frac{1}{12} [/tex] .
_____________________________________
2 more than k is greater than -3 as an inequality
Answers
the inequality "2 more than k is greater than -3" can be represented as:[tex]\[ k + 2 > -3 \][/tex]
To translate the phrase "2 more than k is greater than -3" into an inequality, we can follow these steps:
1. Identify the expression "2 more than k."
2. Write the expression as an inequality where it is greater than -3.
Step 1: "2 more than k" translates to (k + 2).
Step 2: Since "2 more than k" is greater than -3, we write the inequality:
[tex]\[ k + 2 > -3 \][/tex]
So, the inequality "2 more than k is greater than -3" can be represented as:[tex]\[ k + 2 > -3 \][/tex]
The number z and −1.9 are additive inverses.
Drag and drop −1.9 and z to their correct positions on the number line.
Drag and drop the label “Sum” to the sum of −1.9 and z.
Answers
For z and -1.9 to be additive inverses, they must sum up to zero. Consequently, z should be 1.9, and both -1.9 and z (=1.9) placed on a number line would reflect their locations relative to zero. The sum of -1.9 and 1.9 would equal zero.
Explanation:In Mathematics, additive inverses are two numbers that add up to give zero. If the numbers z and -1.9 are additive inverses, this means that when added together, they produce the sum of zero. Therefore, z should be the opposite of -1.9, 1.9 on the number line.
The number -1.9 would appear on the left-hand side of the zero because it is a negative number. The number z (=1.9) would appear on the right-hand side of the zero because it's positive. According to the definition of additive inverses, the sum of these two numbers (-1.9 and 1.9) would be zero. So, 'Sum' would also be zero on the number line.
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he graph of the function f(x) = –(x + 6)(x + 2) is shown below.
Answers
Answer:
Which statement about the function is true?
⇒ The function is increasing for all real values of x where
x < –4.
12.75 is 25% of what number
Answers
The number that would have 12. 75 being 25 percent of it would be 51.
How to find the number ?To find the number of which 12. 75 is 25 %, you can set up a proportion and solve for the unknown number ( let's call it " x ").
You can write the proportion as:
( 25 / 100 ) * x = 12. 75
Now, simplify the left side of the equation:
( 1 / 4 ) * x = 12.75
To solve for x, multiply both sides by 4 to isolate x:
x = 12. 75 * 4
x = 51
So, 12. 75 is 25% of the number 51.
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Three fourths of w plus 5 is one half of a increased by nine. I neeed to turn into an equation!
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Help me please please
Answers
Hope this helps!
Your football team gained 4 yards on first down and 2 yards on second down during its last possession. Which number is the additive inverse of the yards gained?
Answers
Final answer:
The additive inverse of 6 yards (4 yards on first down and 2 yards on second down) is -6 yards. A yard is a unit of length equal to 3 feet and is an SI Base Unit standard used in football.
Explanation:
The student is asking about the additive inverse of the yards gained in a football game. The additive inverse of a number is a number that, when added to the original number, will result in zero. In this case, the football team gained 4 yards on first down and 2 yards on second down, making a total of 4 + 2 = 6 yards. Therefore, the additive inverse of 6 yards is -6 yards because 6 + (-6) equals zero.
When considering SI Base Units, a yard is a unit of length equal to 3 feet. This is a predefined standard used internationally, and especially relevant in football, where moving the ball 10 yards results in a first down. This standardization ensures clarity and uniformity in the game, regardless of the location.
Simplify 29-4.37+(5.68)
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Hope this helps!
the monthly fees for single rooms at 5 colleges are $370, $310, $380, $340, and $310 respectively. what is the mean if these monthly fees?
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The mean value of the data $370, $310, $380, $340, and $310 will be $342.
What is Mean?The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean.
The monthly fees for single rooms at 5 colleges are $370, $310, $380, $340, and $310 respectively.
The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.
The mean is given as,
Mean = (Sum of the observation) / (Total number of the observation)
The sum of the observation will be
Sum of the observation = $370 + $310 + $380 + $340 + $310
Sum of the observation = $1,710
The total number of the observation will be
Total number of the observation = 5
Then the mean of the data will be
Mean = $1,710 / 5
Mean = $342
Thus, the mean value of the data $370, $310, $380, $340, and $310 will be $342.
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Nissa reads 1 pages in 1 minute. How many pages can Nissa read in 5.2 minutes? a.1.75
b. 3.45
c. 5.2
d.9.1
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a group of 4 students are selling candy bars to raise money for a field trip. the group needs to sell 53 candy bars. if each student sells an equal amount, how many candy bars do they get in all? interpret your remainder
Answers
Answer:
Each student is gonna sell 13 candy bars, and there is gonna be 1 bar unsold, because they sold equal amount of candy bars.Step-by-step explanation:
If there are 4 students, they need to sell 53 candy bars, and they will sell the same amount each one, we just have to divide:
[tex]\frac{53}{4} =13.25[/tex], or [tex]13\frac{1}{4}[/tex]
Because the division is not exact, we have a remainder of 1.
This can be interpreted as 1 candy is not sold, because they are gonna sell equally, so in that case each one would sell 13 candy bars, and one will be unsold.