Select the ordered pairs that are solutions to the inequality 2x-3y greater than or equal to 12
Answers
The solution pairs are (8, 1), (-2, -6), and (-3, 1), as they satisfy the inequality 2x - 3y ≥ 12.
To determine which ordered pairs satisfy the inequality 2x - 3y ≥ 12, we can substitute each pair's coordinates into the inequality and check for validity.
For the first pair (1, -3):
2(1) - 3(-3) = 2 + 9 = 11 < 12 (Not valid)
For the second pair (8, 1):
2(8) - 3(1) = 16 - 3 = 13 ≥ 12 (Valid)
For the third pair (3, 2):
2(3) - 3(2) = 6 - 6 = 0 < 12 (Not valid)
For the fourth pair (-2, -6):
2(-2) - 3(-6) = -4 + 18 = 14 ≥ 12 (Valid)
For the fifth pair (2, 3):
2(2) - 3(3) = 4 - 9 = -5 < 12 (Valid)
For the sixth pair (1, 8):
2(1) - 3(8) = 2 - 24 = -22 < 12 (Not valid)
For the seventh pair (-3, 1):
2(-3) - 3(1) = -6 - 3 = -9 < 12 (Valid)
So, the ordered pairs that satisfy the inequality are (8, 1), (-2, -6), and (-3, 1).
To find which ordered pairs are solutions to the inequality 2x-3y ≥ 12, test each pair by plugging the values into the inequality and seeing if the result is greater than or equal to 12.
Explanation:To select the ordered pairs that are solutions to the inequality 2x-3y ≥ 12, we can test each ordered pair to see if it satisfies the inequality. For an ordered pair (x, y) to be a solution, the expression 2x - 3y when calculated must be greater than or equal to 12.
An example of how to test an ordered pair is as follows:
Let's take the ordered pair (6, 0). Plugging these values into the inequality gives us 2(6) - 3(0) which simplifies to 12. Since 12 is equal to 12, the ordered pair (6, 0) is a solution to the inequality.
To methodically find all solutions, one would typically graph the line 2x - 3y = 12 and then shade the region above it for 2x - 3y > 12, since all the points in that region would satisfy the inequality. However, without graphing, we can still test individual pairs to check if they satisfy the inequality condition.
Related Questions
What is the exact volume of the cylinder?, (a) 54in. (b) 108in. (c) 162in. (d) 324in.
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I followed the formula but why donMt have the answer right here
The unit of measure of an area equal to 1 km by 1m
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jane wants to fill her circular pool to a depth of 2m.determine the volume of water she needs,to the nearest cubic meter.
Answers
To find the volume of water needed to fill the pool to a depth of 2m, use the formula for the volume of a cylinder.
Explanation:To determine the volume of water needed to fill the circular pool to a depth of 2m, you can use the formula for the volume of a cylinder:
V = πr²h
Given that the pool is circular, h = 2m, and to the nearest cubic meter, you would need:
Volume of water = π( r )²( 2 )
Compare the volumes of the rectangular prisms shown below. Which of the containers will hold more, X or Y? In your final answer, include all of your calculations.
Answers
The volumes of the rectangular prism 'X' (126 cu.cm.) is greater than the volumes of the rectangular prism 'Y' (110 cu.cm.).
What is the volume of the rectangular prism?[tex]V=l\times w\times h[/tex]
where, 'l' be the length of the rectangular prism,
'w' is the width of the rectangular prism,
'h' is the height of the rectangular prism
For given question,
We have been given two rectangular prisms 'X' and 'Y'.
The dimensions of the rectangular prism 'X',
[tex]l=7~cm,w=3~cm,h=6~cm[/tex]
Using the formula for the volume of the rectangular prism,
[tex]\Rightarrow V=l\times w\times h\\\\\Rightarrow V=7\times 3\times 6\\\\\Rightarrow V=126~cu.cm.[/tex] ...................(i)
The dimensions of the rectangular prism 'Y',
[tex]l=5~cm,w=2~cm,h=11~cm[/tex]
Using the formula for the volume of the rectangular prism,
[tex]\Rightarrow V=l\times w\times h\\\\\Rightarrow V=5\times 2\times 11\\\\\Rightarrow V=110~cu.cm.[/tex] ...............(ii)
From (i) and (ii),
the volume of the rectangular prism 'X' is greater than the volume of the rectangular prism 'Y'.
Therefore, the volume of the rectangular prism 'X' (126 cu.cm.) is greater than the volume of the rectangular prism 'Y' (110 cu.cm.)
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Helppppppppppppppppppp
Answers
Remember that the question said estimate.
So
47% rounds to 50%
.5 and 1/2 are equal to 50%
89 rounds to 90.
You could say that:
1/2*90
0.5*90
90/2
These will all work and will give you the same answer.
I hope this helps!
~kaikers
To get a good estimate you would round 47% up to 50% and 89 up to 90. Since 50% is half, making one of your answers divide 90 by 2.
You can also round 47% to 50% and make it into a decimal, so .5. This means you can also multiply .5 by 90.
Lastly, you can round 47% to 50% and make it a fraction, which would be 1/2. Therefore, you can multiple 1/2 by 90 and get the same answer.
Overall, the correct answers should be A, B, and D.
Hope this helps!
Solve the recurrence relation for the variables indicated below: bn = 8bn-1 - 15bn-2 b1 = 2 b2 = 16 If the explicit formula for the sequence is written in the form bn = u(s1)n + v(s2)n then find s1 and s2 .
Answers
The recurrence relation is given by bn = 8bn-1 - 15bn-2 with b1 = 2 and b2 = 16.
How to depict the solution?Since it is linear homogeneous recurrence relation ,so first find its characteristic equation.
r² - 8r + 15 = 0
( r - 3 )( r - 5 ) = 0
r = 3 , 5
So, the general solution of the given recurrence relation is
bn = u(3)n + v(5)n ------------ ( 1 )
Now use the initial conditions b1 = 2 and b2 = 16.
From ( 1 ) , b1 = u(3)1 + v(5)1
2 = 3u + 5v ---------- ( 2 )
and b2 = u(3)2 + v(5)2
16 = 9u+ 25v------- ( 3 )
Solving ( 2 ) and ( 3 ) , we get u= - 1 and v = 1
Therefore, the required solution is bn = - (3)n + (5)n
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What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 5.5? A rectangle is shown. The length of the rectangle is labeled as 8 cm, and the width is labeled as 6 cm. Perimeter = 50 cm, area = 155.25 cm2 Perimeter = 50 cm, area = 1,452 cm2 Perimeter = 154 cm, area = 155.25 cm2 Perimeter = 154 cm, area = 1,452 cm2
Answers
P = 2W + 2L
Where,
W: width
L: long
We have then:
P = 2 (5.5 * 6) +2 (5.5 * 8)
P = 154 cm
The area of the rectangle is by definition:
A = (W) * (L)
Where,
W: width
L: long
We have then:
A = (5.5 * 6) * (5.5 * 8)
A = 1452 cm ^ 2
Answer:
Perimeter = 154 cm, area = 1,452 cm2
Answer:
the answer is 154 cm, area = 1,452 cm2 I took the test
Step-by-step explanation:
Ted is installing lighting in a new block of 12 apartments. He will need 60 metres of cable for each apartment. Each new spool holds 100 metres of cable. What is the smallest number of new spools that Ted will need for this job ??
Answers
The smallest number of new spools that Ted will need for this job is 8 spools of cable.
Given that, Ted is installing lighting in a new block of 12 apartments. He will need 60 metres of cable for each apartment. Each new spool holds 100 metres of cable.
We need to find the smallest number of new spools that Ted will need for this job.
What are the spools?A cylindrical device on which film, magnetic tape, thread, or other flexible materials can be wound; a reel.
Now, 60 meters per apartment x 12 apartments =720 total meters for all 12 apartments.
720 meters / 100 meters per spool =7.2 spools
so, Ted will need at least 8 spools of cable.
Therefore, the smallest number of new spools that Ted will need for this job is 8 spools of cable.
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An air freshener starts with 33 grams and evaporates. In each of the following situations define a function that gives the remaining mass of the air freshener (in grams) in terms of the number of days, t t, since the air freshener was first used.
Answers
A) The mass of the air freshener A decreases by 3.2 grams each day. Define a function, f, to represent this situation.
In this function, the mass of the air freshener A (m) is the dependent variable and the days (t) and the initial amount of the air freshener A (mi) are the independent variables. If the mass decreases by a fixed amount each day, you only have to multiply this amount by the number of days:
[tex]m=mi-(3,2*t)[/tex]
B) The mass of the air freshener B decreases by 3.2% each day. Define a function, g, to represent this situation.
This function is trickier since there isn't a fixed amount of decreasing. Instead, the rate of decreasing depends on the initial amount of the freshener (mi). You have to include this initial amount in the equation to correctly model it. This is how you do it:
[tex]m=mi-(mi* \frac{3,2}{100}*t) [/tex]
Have a nice day!
Ethan is 3 years older than twice his brother Adrian’s age write an expersion to represent Ethan’s age ; if Adrian is 6 how old is Ethan;
Answers
Expression: 6(2)+3
Ethan is 3 years older than twice his brother's age.
6(2)+3
12+3
15
Ethan is 15.
Happy studying!
~SimpleGirl~
2x + 3. Now substitute Adrian's age, 6, into x and solve.
2(6) + 3
12 + 3
15.
If Adrian is 6, then Ethan is 15.
help me please i dont know how to do all of this ill really appreciate it please
Answers
The expression: [tex]-14c-7(-19c-6)[/tex].
First step: Apply the Distributive Property; it is [tex]a(b + c) = ab + ac[/tex].
[tex]-14c-7(-19c-6)[/tex]
[tex]-14c+133c+42[/tex]
[A negative times a negative equals a positive.]
Next step: Combine like terms.
[tex]-14c+133c+42[/tex]
[tex]119c+42[/tex]
The simplified expression is [tex]119c+42[/tex].
Kayleen left home at noon and drove to boston.she got there at 4:00.if boston is about 280 miles away,what was kayleens average speed
Answers
---
Hope this helps!
Louis,Michelle, and Tonya were asked to find an equation for a function that passed through the points (1,6) and (8,12) Louis gave the function y 6(2)-112 Michelle gave the function y V2)22 Tonya gave the function y-6 3(x-1) Which students are correct?
Answers
I am sorry, but you have several typos in your equations, so I can't determine who is correct. Try to match the problems to the equation that I can, so you can determine the correct person.
Tonya seems to be the closest, but her slope is wrong.
You invest $5,000 in a savings account paying 4% interest compounded quarterly. How much is in the account after 5 years if there are no withdrawals and no additions to the account?
Answers
2 years is $5408
3 years is $5624.32
4 years is $5849.29
5 years is $6083.26
5000(1+0.04)^5
= 6083.264512
NOTE THE 5 IS WRITTEN AS A SQUARE
I am a closed shape made of 6 line segments. I have two angles less than right angle & no right angles. What shape am I?
Answers
A rectangle is drawn on a coordinate plane. Three vertices of the rectangle are points L(−7,14) , M(9,14) , and N(9,−12) . Point P is the fourth vertex of the rectangle. How long is the side of the rectangle connecting points L and P?
Answers
Answer:
the answer is 26 units
Step-by-step explanation:
Jeremy and Caitlin collect baseball cards. the ratio of Jeremy’s cards and Caitlin’s cards was 9 to 3. After Jeremy gave 12 carss to Caitlin, they had an equal number of cards. How many cards did Caitlin and Jeremy have at first? Explain.
Answers
PLEASE HELP
Law of sines:
Which represents the value of c?
Answers
Using the law of sins that is given, you can write the following proportion.
3/sin(40) = c/sin(45)
All you have to do to solve for C is to multiply by sin(45). In the proportion, the letter are the side lengths and the trig ratios are of the angle opposite the side.
[tex] c = \frac{3 \sin(45 \degree)}{\sin(40 \degree)} [/tex]
EXPLANATION
The sum of the interior angles of the given triangle is
[tex]180 \degree[/tex]
This implies that
[tex]A + 95 \degree + 45 \degree = 180 \degree[/tex]
We group like terms to get,
[tex]A = 180 - 140[/tex]
[tex]A = 40 \degree[/tex]
The law of sines is given by,
[tex] \frac{ \sin(A) }{a} = \frac{ \sin(B) }{b} = \frac{ \sin(C) }{c} [/tex]
Based on our known values, we use,
[tex] \frac{ \sin(A) }{a} = \frac{ \sin(C) }{c} [/tex]
We now substitute the values to get,
[tex] \frac{ \sin(40 \degree) }{3} = \frac{ \sin(45 \degree) }{c} [/tex]
We reciprocate both sides of the equation to get,
[tex] \frac{ 3}{\sin(40 \degree)} = \frac{ c }{\sin(45 \degree)} [/tex]
We now multiply both sides by
[tex] \sin(45 \degree) [/tex]
to get,
[tex] \frac{3 \sin(45 \degree)}{\sin(40 \degree)} =c[/tex]
or
[tex] c = \frac{3 \sin(45 \degree)}{\sin(40 \degree)} [/tex]
The correct answer is B.
what is the answer
solve 4.8+n=6.2
Answers
Now you have n = 1.4
The price of a shirt was $38. It was reduced by 20% and then again by 10%.
a. What is the final price of the shirt?
b. What would the price of the shirt be if it were reduced by 30% from the original?
c. Explain why the two prices in a. and b. differ.
Answers
b)38*(1-30%)=26.6
c)Because in question one when you take off the 10% it is 10% of the already off price but when you take off 30% it is taking off from the original price
Answer:
A- The final price of the shirt was $27.36.
B- If it were reduced by 30% from the original price, the price of the shirt would be $26.6.
C- There is a difference between both prices because in the first case, the discount is split, making a first discount on a larger basis, and the second on a smaller basis, already made the first discount.
In contrast, at the second price, the entire percentage is made on the major basis. Therefore, the discount is larger.
Step-by-step explanation:
A- The final price of the shirt is determined by the following calculation:
(38 x 0.8) x 0.9 = FINAL PRICE
38 is multiplied by 0.8 because the price was reduced by 20% (0.2 is the 20% of 1, that is, of a unit. Therefore, the remaining price would be that 0.8 or 80%)
Then, using the same logic, we have to multiply that result by 0.9 in order to get the final price.
Therefore:
(38 x 0.8) x 0.9 = 30.4 x 0.9 = 27.36
B- Here, we would have to multiply 38 x 0.7, which gives a result of 26.6
Bill is a car salesman he earns $200 for every car he sales plus a 3% commission if Bill sells three cars in one week for a total of $32,343 what are his total earnings for this week
Answers
(0.03)*$32,343 = $907.29 commission
total earnings = $907.29 + $600
= $1,507.29
What's the name of the line segment in the diagram below? A. B. C. D.
Answers
The straight line above it represents a line segment. One arrow represents a ray. Two represent an infinite line.
In the diagram, the line/segment ends, which is represented by the two points.
Which expression can be simplified by applying the additive inverse property
Answers
We have to identify the expression in which Additive inverse identity is applied.
Additive inverse property states that "The additive inverse of a number 'x' is a number that when it is added to 'x', yields zero".
Consider the first expression,
A. [tex] -329-164+513+206+(-164) [/tex]
There are no such numbers, which will yield zero on addition. Hence, additive inverse property is not applied here.
B. [tex] 1.6+0.2-1.8-0.5 [/tex]
There are no such numbers, which will yield zero on addition. Hence, additive inverse property is not applied here.
C. [tex] -\frac{7}{10}-\frac{3}{4}+1\frac{1}{2}+(-\frac{7}{10}) [/tex]
There are no such numbers, which will yield zero on addition. Hence, additive inverse property is not applied here.
D. [tex] 9\frac{3}{4}\+4\frac{5}{8}+(-9\frac{3}{4}+(2\frac{3}{5}) [/tex]
Here, [tex] 9\frac{3}{4} [/tex] when added to [tex] -9\frac{3}{4} [/tex] will yield zero. Therefore, [tex] -9\frac{3}{4} [/tex] is the additive inverse of [tex] 9\frac{3}{4} [/tex].
So, in option D, Additive inverse property is applied.
Thomas correctly spell 18 out of 20 words on his last spelling quiz. What decimal represent the portion of the rights that Thomas spelled correctly
Answers
I used a rather ghetto way to answer this question.
first, I multiplied 20 by 5 to get it to 100 then I multiplied 18 by the same number (5) and got 90. That makes 90 out of 100 which is 0.90
Final answer:
Thomas spelled 18 out of 20 words correctly, which, when divided, gives us 0.9. This decimal represents the portion of the words he spelled correctly on his quiz.
Explanation:
To find the decimal that represents the portion of words Thomas spelled correctly on his quiz, we follow a simple process of division and conversion to a decimal.
Thomas spelled 18 out of 20 words correctly. So, we divide 18 by 20 which equals 0.9. This is the decimal that represents the portion of words Thomas spelled correctly.
when 80% of a number is added to the number, the result is 252. what is the number
Answers
The Expression: 0.8x + x = 252 Can Explain The Answer If x = 140.
Or: 1.8 Times x = 252 If x = 140.
3+7x<26 help me with this equaton
Answers
-3 -3
7x < 23
divide by 7 to isolate x (variable)
x< 7/23 final answer
On a winter’s day, 9 degrees Fahrenheit is the highest temperature recorded. Write an inequality that represents the temperature t in degrees Fahrenheit at any time on this day.
Answers
Answer: The inequality that represents the temperature t in degrees Fahrenheit at any time on this day is [tex]t\leq 9[/tex] degree Fahrenheit.
Explanation:
It is given that on a winter’s day, 9 degrees Fahrenheit is the highest temperature recorded. It means the temperature on this day must be less than or equal to 9 degree Fahrenheit.
Let t represents the temperature in degrees Fahrenheit at any time on this day. Then,
[tex]t\leq 9[/tex]
Therefore, the inequality that represents the temperature t in degrees Fahrenheit at any time on this day is [tex]t\leq 9[/tex] degree Fahrenheit.
Answer:
[tex]t\leq 9^{0}F[/tex]
Step-by-step explanation:
We have been given that highest temperature recorded on a winter’s day is 9 degrees Fahrenheit and we are asked to write an inequality that represents the temperature t in degrees Fahrenheit at any time on this day.
Since we know that highest temperature can't exceed 9 degrees Fahrenheit on the given day and it will be less than or equal to 9.
Therefore, our inequality will be,[tex]t\leq 9^{0}F[/tex]
evaluate x - 2y if x = -3 and y = -6
Answers
= -3 - 2(-6)
= - 3 + 12
= 9
What is the slope of the line in the graph?
Answers
The slope of the line in the given graph with the coordinates (x₁ , y₁ ) = (4, 5) and (x₂ , y₂) = (2, 3) is equal to 1.
The slope of a line is calculated by rise over run.
Here is the formula for calculating the slope of a line:
Slope = (y₂ - y₁) / (x₂ - x₁)
Here, the points (x₁ , y₁ ) = (4, 5) and (x₂ , y₂) = (2, 3) are on the line. Plugging these points into the formula, we get:
Slope
= (3 - 5) / (2 - 4)
= (-2) / (-2)
= 1
Therefore, the slope of the line is 1.
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to function properly, rainwater outflow pipe must drop exactly 1 inch for every 25 inches of horizontal distance. A 40 foot long rain water pipe runs under the edge of a roof. What is the vertical distance, in inches, the pipe bust drop between its ends? Round your number to the nearest tenth.
Answers
480 inches / 25 inches = 19.2 Inches dropped.
Answer: Hence, There is vertical distance of 19 inches the pipe must drop between its ends.
Step-by-step explanation:
Since we have given that
Rainwater outflow pipe must drop exactly 1 inch for every 25 inches of horizontal distance.
For 1 inch = 25 inches of vertical distance the pipe must drop.
If there is a 40 foot long rain water pipe runs under the edge of a roof.
Then, we need to find the vertical distance in inches the pope must drop.
First, we change 40 feet into inches.
Since 1 foot = 12 inches
40 feet = 40×12 inches = 480 inches
So, Vertical distance the pipe must drop is given by
[tex]\dfrac{480}{25}\\\\=19.2\ inches[/tex]
Hence, There is vertical distance of 19.2 inches ≈ 19 inches the pipe must drop between its ends.