Which graph represents the solution set of the system of inequalities?
−3x+y>1
y≥x−1
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 :)
Whitney earns $180.50 for 25 hours of work how much does Whitney earn per hour
How much is the rate.i need help
What's the answer to this problem
Plz help me
I only need the answer to number 10
plz help me
-5/4 =-1.25
-14/25 = -0.56
-13/8 = -1.625
Runner D finished 2nd it is the smallest number
Runner B was 5th
Gas is $2.09 per gallon; how much will it cost to get 10 gallons of gas?
Question 2 options:
$20.90
$12.09
$7.91
$4.10
How can you tell the difference between a terminating decimal and a repeating decimal?
Simplify.
-2(3)² - 8 ÷ 2 + 6
A) -18
B) -16
C) -7
D) 7
I need help finding the least common multiple for each pair
Which of the following is a net of a rectangular prism?
A. Z
B. X
C. W
D. Y
do you have to do some math to answer both of these or do you just answer yes ✅ or no
Q is not the midpoint of PR and G is the midpoint of FH.
Determine if Q is the midpoint of PR:
First, we set up the equation:
PQ + QR = PR
5(x + 2) + 8x - 3 = 72
5x + 10 + 8x - 3 = 72
13x+ 7 = 72
Solving for x :
13x = 65
x = 5
Check if PQ and QR are equal when x = 5:
PQ = 5(x + 2) = 5(5 + 2) = 5 × 7 = 35
QR = 8x - 3 = 8 × 5 - 3 = 40 - 3 = 37
Since PQ ≠ QR , Q is not the midpoint of PR.
Determine if G is the midpoint of FH:
First, we set up the equation:
FG + GH = FH
4x + 24 = 7x + 6
4x + 24 = 7x + 6
24 - 6 = 7x - 4x
18 = 3x
x = 6
Check if FG and GH are equal when x = 6 :
FG = 4x = 4 × 6 = 24
GH = 24
Since FG = GH, G is the midpoint of FH.
PLZZZZZ HELP ME! :) XDDD
The graph of the equation y= 1
/2
x - 3 is shown. Determine the value of y for the point (4, y).
A)
-2
B)
-1
C)
0
D)
1
Please help!!! I don’t get any of this can someone please explain what to do and how I can get my answer????
Can someone help me with 7 1/2 ÷ 1 9/10 please and thank you
8+4a+6.2−9a simplify
Solve for x: one over eight(8x + 15) = 24
To solve for x in the equation 1/8(8x + 15) = 24, distribute 1/8 to both terms inside the parentheses, simplify, subtract (15/8) from both sides, convert the whole number to a fraction, combine like terms, and calculate the numerator.
Explanation:To solve for x in the equation 1/8(8x + 15) = 24, we need to isolate x on one side of the equation. Here are the steps:
Distribute the 1/8 to both terms inside the parentheses: (1/8)(8x) + (1/8)(15) = 24Simplify: x + (15/8) = 24Subtract (15/8) from both sides: x = 24 - (15/8)Convert the whole number 24 to a fraction with common denominator 8: x = (192/8) - (15/8)Combine like terms: x = (192 - 15)/8Calculate the numerator: x = 177/8Therefore, the solution to the equation is x = 177/8 or x = 22.125 (rounded to three decimal places).
To solve for x, multiply both sides of the equation by 8 to eliminate the fraction, then simplify the equation and solve for x by dividing both sides by 8.
Explanation:To solve for x, we can start by multiplying both sides of the equation by 8 to eliminate the fraction:
1/8(8x + 15) = 24
(8x + 15) = 24 * 8
8x + 15 = 192
Next, we can subtract 15 from both sides of the equation:
8x = 192 - 15
8x = 177
Finally, we divide both sides of the equation by 8 to solve for x:
x = 177/8
x = 22.25
Clea attends music lessons every 2 weeks, dance class every 3 weeks, and has a dental appointment every 6 weeks. If she attends all three this week, when will she attend all three again
Adolfo earned $650 last week.he paid $97.50 in gederal income tax.He paid one third that amount for state income tax and other taxes combined.What was Adolfo's pay after taxes?EXPLAIN how u found your answer.
What’s 7 meters equal as cm
I need to simplify this... (4a^3+7a^2b+6b^3) + (a^3+2a^2b+4b^3)
The Gonzalez family is taking a cruise that costs e,082.24 for a family of four. How much does it cost per person?
Identify the coordinates of P(–5, 7) after a rotation of 180° about the origin. a. P’ = (5, 7) c. P’ = (5, –7) b. P’ = (–5, –7) d. P’ = (7, –5)
find the slope of the line that contains the following points A : [ 17 , -12 ] and [ 17 , 8 ] and B [ 6 , -2 ] and [ -3 , 1 ]
Suppose two mice live in a barn. The number of mice quadruples every three months. The function f(x)=2•4^x models this situation. How many mice will be in the barn after two years?
Mr. Itol's assistant takes twice as long to complete a computer task as Mr. Itol. If it takes both experts 6 hours to complete the task, how long will it take each of them to do the job alone? PLEASE HELP
Answer: Hence, Mr. Itol takes 9 hours, and his assistant takes 18 hours alone.
Step-by-step explanation:
Let the number of hours Mr. Itol takes be 'x'.
Let the number of hours Mr. Itol's assistant takes be '2x'.
Total number of hours both experts take = 6 hours
According to question, we get that
[tex]\dfrac{1}{x}+\dfrac{1}{2x}=\dfrac{1}{6}\\\\\dfrac{2+1}{2x}=\dfrac{1}{6}\\\\\dfrac{3}{2x}=\dfrac{1}{6}\\\\18=2x\\\\x=\dfrac{18}{2}\\\\x=9[/tex]
Number of hours taken by him = x = 9 hours
Number of hours taken by his assistant = 2x = [tex]2\times 9=18\ hours[/tex]
Hence, Mr. Itol takes 9 hours, and his assistant takes 18 hours alone.
I WILL MARK BRAINLY
Which decimal number is equal to 2/3 ?
0.6
0.66
_
0.6
0.67
What is 3/5 written as a decimal?
0.12
0.3
0.6
1.67
Which decimal number is equal to 7/9 ?
0.7
_
0.7
0.78
_
0.78
Karl bought 312 gallons of milk that cost $2.70 per gallon.
What was the total cost of the milk?
Enter your answer in the box.
A decimal rounded to the nearest hundredth is 6.32 the decimal is greater than 6.32 what could this decimal be?
what are the steps to drawing a triangle when
the angle of D = 110°
the angle of E = 30°
and EF = 5cm
one day at lunch , a restaurant served 178 burgers, 63 grilled cheese sandwiches, and 37 salads.
Estimate about how many meals the restaurant served for lunch that day.
A. 80
B. 180
C. 280
D. 160
Number of meals served by restaurant for the lunch is estimated as option C. 280.
To estimate how many meals the restaurant served for lunch that day, you can add up the number of each item served:
Number of burgers = 178
Number of grilled cheese sandwiches = 63
Number of salads = 37
Now, to get a rough estimate of the total number of meals served, add these quantities together:
Total meals served = 178 (burgers) + 63 (grilled cheese sandwiches) + 37 (salads) = 278
Therefore, the choices provided are close to this estimate is option is C. 280.
learn more about estimate here
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x+2y=23
5x+10y=55
solve please