Select the ordered pairs that are solutions to the inequality 2x-3y greater than or equal to 12
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.
The formula h-15=3.2t gives the height h in inches of a plant t weeks after planting. Which is the rate at which the plant height is increasing?
Consider the following graph of a quadratic function. Which of the statements are true? Select all that apply.
A. The function is decreasing over the interval x<-1
B. The range of the function is all real numbers.
C. The function is increasing over the interval x<-1
D. The domain of the function is all real numbers
E. The function has a relative minimum at (-1,5)
Answer:
Option C,D and E are correct.
Step-by-step explanation:
Clearly from the graph we could say that it is a graph of a quadratic function.so we will work on each of the following options:
A)
Clearly from the graph we could see that the graph is increasing on both the sides of -1.
Hence, option A is wrong. ( The function is decreasing over the interval x<-1).
B)
As the function is a quadratic function hence the range contains all the real numbers greater than or equal to 5 below 5 it won't take any value.
Hence option B is wrong.(The range of the function is all real numbers).
C)
clearly we could see that the function is increasing in the interval x<-1.
Hence, option C is correct.
D)
The function is defined for all of the real numbers.
Hence option D is correct. (The domain of the function is all real numbers).
E)
Clearly from the graph we could see that the function has minimum value at -1 and the graph is increasing before and after that.
Hence, option E is correct.( The function has a relative minimum at (-1,5) ).
Answer:
C,D,E
Step-by-step explanation:
how do i do these inverse trig
To do inverse trig functions on a calculator, enter the value and press either the arcsin, arccos and arctan buttons OR [tex]sin^{-1}, cos^{-1}, tan^{-1}[/tex] buttons. The functions arcsin(x), arccos(x) and arctan(x) are the inverse functions of the 3 main trigonometric functions sin(x), cos(x), and tan(x) formed by a reflection across the line y=x. This results in the (x,y) points of sin(x), cos(x) and tan(x) switching their order (y,x) in each inverse. Form a ratio of the side lengths, press the corresponding inverse function and you will find x = 35.6 degrees and y = 54.4 degrees.
Further ExplanationSine/ Cosine/Tangent
In trigonometry, there are three main functions sine, cosine, and tangent based on the ratios of sides corresponding to angles within a right triangle. The ratio for sine is opposite / hypotenuse. The ratio for cosine is adjacent / hypotenuse. The ratio for tangent is opposite / adjacent.
Notice in this triangle, 109 and 134 are the adjacent and hypotenuse to the angle x. This is the cosine function and thus Cos(x) = 109 / 134. 109 and 134 are also the opposite and hypotenuse to the angle y. This is the sine function and thus sin y = 109 / 134. To solve for x and y, use the inverse function arcsin and arccos.
Arcsin
As the arcsin(x) is the inverse of the sin(x) function, its function is defined as having inputs and outputs which have been reversed. The input of arcsin is the triangle side ratios (opposite / hypotenuse) and they align to the angle outputs of this function. For example, if sin (30) = 1/2 then arcsin(1/2) = 30. By pressing the arcsin button on your calculator it reverses the inputs and outputs. The expression sin y = 109/ 134 becomes arcsin (109/134) = y and y = 54.4 degrees.
Arccos
As the arccos(x) is the inverse of the cos(x) function, its function is defined as having inputs and outputs which have been reversed. The input of arccos is the triangle side ratios (adjacent / hypotenuse) and they align to the angle outputs of this function. For example, if cos (60) = 1/2 then arccos(1/2) = 60. By pressing the arccos button on your calculator it reverses the inputs and outputs. The expression cox x = 109/ 134 becomes arccos (109/134) = x and x = 35.6 degrees.
Learn More Finding the Inverse of a Trig Function: https://brainly.com/question/4143682 Arcsin Inverse Function: https://brainly.com/question/1388658Reciprocal Trig Functions versus Inverse Trig Functions: https://brainly.com/question/3917841Category
Grade: High School - 10/11
Subject: Algebra 2
Chapter: Inverse Trig Functions
Help me on questions 1, 2, and 3
What is the surface area of the cube with the rectangular prism
155 in
270 in
300 in
310 in
The distance between two towns is 12 5/8 miles. Mr.Lang has driven 4 5/12 miles of distance. How much farther does he have left to go?
The library is 2 miles from the post office. How many yards is the library from the post office?
Need the answer ASAP
Please help and please explain the answer.
Are the triangles similar? If they are, identify the similarity ratio.
A. Yes, the similarity ratio is 1:4
B. Yes, the similarity ratio is 1:5
C. Yes, the similarity ratio is 1:3
D. No, the triangles are not similar
So, I feel like D is out of the equation. Because the only difference is the shape and size. I was staring to lean towards C. Can anyone give me their two cents on this?
Answer: C is the correct answer.
Step-by-step explanation:
Answer:
C. Yes, the similarity ratio is 1:3
Step-by-step explanation:
The two triangles are similar because the corresponding sides are proportional.
The length of the side of the smaller triangle that is 3 units corresponds to the length of the side of the bigger triangle that is 9 units.
These two sides are in the ratio [tex]3:9[/tex].
When we simplify this ratio, we get [tex]1:3[/tex].
The length of the side of the smaller triangle that is 6 units corresponds to the length of the side of the bigger triangle that is 18 units.
These two sides are in the ratio [tex]6:18[/tex].
When we simplify this ratio, we get [tex]1:3[/tex].
The length of the side of the smaller triangle that is 5 units corresponds to the length of the side of the bigger triangle that is 15 units.
These two sides are in the ratio [tex]5:15[/tex].
When we simplify this ratio, we get [tex]1:3[/tex].
Therefore the similarity ratio is [tex]1:3[/tex].
Can u do 17-20 solve the equation please and show work
Which steps should be followed to use a scale drawing and a new scale to find the new length of a soccer field? Add the numerator of the new scale to the old length to get the new length. Subtract the new length from the old length to find the difference in lengths. Write a proportion using the new scale as the first ratio. Set the first ratio equal to the ratio of the length of the original field compared to a variable that represents the new length of the field. Solve the proportion to find the new length of the field. Write a ratio comparing the scale drawing length to the actual length of the field, and simplify.
The function f(x) =g(x), where f(x) =2x-3 and g(x) =x^2-5
Answer:
x=2.732
Step-by-step explanation:
Given are two functions
f(x) = 2x-3 and g(x) = [tex]x^2-5[/tex]
WE have to find the approximae value when these two funcitons are equal
Since we are asked to find only positive value we can refer table and do
f(2) >g(2) but f(3)<g(3) Hence there is one solution between 2 and 3.
f(2.5)>g(2.5). So the root lies between 2.5 and 3 since change of sign takes place here
x f g
2.6 2.2 1.76
2.7 2.4 2.229
2.72 2.44 2.398
2.73 2.46 2,453
2.732 2,464 2.464
Hence answer is x =2,732
Which statement is NOT true?
F. A set of ordered pairs that describes a function cannot have any y-value repeated.
G. A table of values describes a function if all the x-values are different.
H. A mapping is a function if each x-value is paired with exactly one y-value.
J. A graph describes a function if no point on the graph lies directly above or below another of the graph.
PLEASE HELP!!!!! 11 POINTS TO CORRECT ANSWER
please solve this: 0.45-0.05+0.2-0.5
Steve has $360 in a savings account in the bank. He runs 3% interest each month how much interest would he earn in one month
Write an equation of the line that is perpendicular to the line y = 2x + 8, and which passes through the point (6,-2).
Answer: y= -1/2 + 1
Step-by-step explanation: To solve this problem, first determine the slope of your line. Since perpendicular lines have slopes that are opposite reciprocals of each other,we know that the slope is -1/2. Then plug your slip (-1/2) and point (6,-2) into the equation y=mx+b to solve for b. The resulting value for b is 1.
Mrs.Hilt has a pizza that is 35 inches in diameter. What is the radius of that pizza.
The radius of a pizza that is 35 inches in diameter is 17.5 inches, which is found by dividing the diameter by two.
The question about Mrs. Hilt's pizza with a diameter of 35 inches is asking for the radius of the pizza. To find the radius of a circle when given the diameter, you simply divide the diameter by two. Therefore, the radius of the pizza is 17.5 inches, since 35 inches divided by 2 equals 17.5 inches. This is a basic geometry concept often covered in middle and high school math classes.
Point A, located at (-2, 4), is translated down 6 units. What are the coordinates of A'?
(-8, 4)
(-8, -2)
(-2, -2)
(-2, 4)
if prq is a straight line, find the number of degrees in <w.
given: 2w, 30°
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A health club increased its membership from 80 to 240 people. What is the percent increase in membership?
The percent of increase is 200%
Answer and the work are provided in the image attached.
Use the distributive property to simplify the expression below
5x(x-4)
You have 15 coins in your pocket: 4 quarters, 3 pennies, 5 dimes, and 3 nickels. Why wouldn't theoretical probability be a good way to predict which coin you pull out of your pocket?
convert 4 7/8 to a decimal using long division
Audrey is buying a new car for 32998.00 she plans to put 4200.00 down if she make monthly payments of 525 for the next 5 years what APR did she pay
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Which of the following inequalities matches the graph?