The table below shows selected points from a function.
The rate of change for the interval shown in the table is__ , so the function is a ____ function.
Answers
Answer:
The rate of change for the interval shown in the table is 1 , so the function is a linear function.
Step-by-step explanation:
See the table attached.
The table shows selected points from a function.
Now, the given interval is x = 1 to x = 4.
For, x = 1, f(x) = 2 and for x = 4. the function f(x) = 5.
Therefore, the rate of change for the interval shown in the table i.e slope of the line is [tex]\frac{5 - 2}{4 - 1} = 1[/tex] and it is constant throughout the interval so the function is a linear function. (Answer)
The rate of change for the interval shown in the table is constant , so the function is a linear function.
Note the following important points:
1. Linear Function:
If the difference between y values remains constant for any pair of consecutive points ([tex]y_2-y_1 = y_3-y_2 = y_4-y_3,[/tex]and so on), the function exhibits a constant rate of change, indicating a linear function. In this case, the rate of change would be the difference between two y values divided by the difference between their corresponding x values (e.g., [tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]).
2. Non-Linear Function:
If the difference between y values varies between consecutive points, the function would be non-linear. The specific type of non-linear function (e.g., quadratic, exponential) would require further analysis with more data points or additional information about the function's behavior.
In this case, as shown in the attached table, it is clear that
For [tex]x_1=1, y_1=f(x)=2[/tex].
For [tex]x_2=2, y_2=f(x)=3[/tex].
For[tex]x_3=, y_3=f(x)=4[/tex].
For [tex]x_4=, y_4=f(x)=5[/tex], and so on.
Thus the rate of change for the interval shown in the table or its slope is constant as evident from the following calculation.
[tex]\frac{(y_2-y_1)}{(x_2-x_1)}=\frac{3-2}{2-1}=1\\ \frac{(y_3-y_2)}{(x_3-x_2)}=\frac{4-3}{3-2}=1\\\frac{(y_4-y_3)}{(x_4-x_3)}=\frac{5-4}{4-3} =1[/tex].
So it is clear that, the rate of change for the interval shown in the table is constant , so the function is a linear function.
Related Questions
Job A pays $28.59 per hour. Job
B pays $25.71 per hour, but has
health benefits. Lauren will need
to buy health insurance for $6650
per year if it's not a job benefit. If
Lauren expects to work 2,000
hours during the year, and
ignoring taxes, which job should
Lauren take to have more
spending cash?
Answers
Answer:
Job B
Step-by-step explanation:
Job A:
Job A pays $28.59 per hour.
Lauren expects to work 2,000 hours during the year, so Lauren can expect to be paid
[tex]\$28.59\times 2,000=\$57,180[/tex]
Job B:
Job B pays $25.71 per hour.
Lauren expects to work 2,000 hours during the year, so Lauren can expect to be paid
[tex]\$25.71\times 2,000=\$51,420[/tex]
Health insurance costs $6,650. Add health insurance to job B payment:
[tex]\$51,420+\$6,650=\$58,070[/tex]
Since [tex]\$58,070>\$57,180,[/tex] Lauren should take job B
0.6 of it is 30
Find the number
Answers
Answer:
The number is 50.
Step-by-step explanation:
0.6x=30
x=30/0.6
x=50
Evaluate -|-8 - 2|
-6
-10
10
Answers
Answer:
-10
Step-by-step explanation:
Answer:
-6
Step-by-step explanation:
The diagram shows several planes, lines, and points.
Which statement is true about line h?
O Line h intersects line fat two points, A and B.
Line h is the intersection of planes Rand T.
Line h intersects plane pat point C.
© Line h has points on planes R P, and T.
Answers
Answer:
The true statement is Line h has points on planes R, P, and T
Step-by-step explanation:
The rest of the question is the attached figure
According to the graph, we will check which option is true.
a. Line h intersects line f at two points, A and B (Wrong)
Because: h intersects line f at B only.
b. Line h is the intersection of planes R and T (Wrong)
Because: g is the intersection of planes R and T
c. Line h intersects plane P at point C (Wrong)
Because: h intersects plane P at point B
d. Line h has points on planes R, P, and T (True)
Because h has the point B on the plane P, h has the point A on the plane T
and the points of h on the plane R
Answer:
Line h has points on planes R, P, and T
Step-by-step explanation:
did the test
in the three stacks of books there are 15 books, 9 books and 9 books if the books were rearranged so that the stack had the same number of books how many books would be even?
Answers
Answer:
There would be 11 books in each stack, to have the same number.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Books in stack 1 = 15
Books in stack 2 = 9
Books in stack 3 = 9
2. If the books were rearranged so that the stack had the same number of books how many books would be even?
Total books = Books in stack 1 + Books in stack 2 + Books in stack 3
Total books = 15 + 9 + 9
Total books = 33
Total books/Number of stacks = Number of books per stack to be the same
33/3 = Number of books per stack to be the same
Number of books per stack to be the same = 11
What is solution of 8x-2y =1 and -4x+y = 3
Answers
Answer: it has no solution
Step-by-step explanation:
8x - 2y = 1 ..................... equation 1
-4x + y = 3 ...................... equation 2
solving the system of linear equation by substitution method . From equation 2 , make y the subject of the formula.
y = 3 + 4x .......................... equation 3
substitute equation 3 into equation 1 .
8x - 2(3 + 4x ) = 1
8x - 6 - 8x = 1
8x- 8x - 6 = 1
-6 = 1
this means that the equation has no solution
5[8 (7 — 4) divided by 6]
What is the value of the expression?
Please please please answer!
Answers
Answer:
20
Explanation:
PEMDAS
Jackie is thinking of one number and Adrian is thinking of another. Camila thought if I take these two numbers, they have a product of 567 and a difference of six. Jackie’s number is higher than Adrian’s. What are Jackie’s and Adrian’s numbers?
Answers
Answer:
Jackie: 27Adrian: 21Step-by-step explanation:
Integers with a product of 567 are ...
567 = 1·567 = 3·189 = 7·81 = 9·63 = 21·27
The last of these pairs of factors have a difference of 6, so they are the answers.
Jackie's number is 27; Adrian's number is 21.
_____
You could let "a" represent Adrian's number and write the equation ...
a(a +6) = 567
a^2 +6a +9 = 576 . . . . . complete the square
(a +3)^2 = 24^2 . . . . . . . write as squares
a = -3 +24 = 21 . . . . . . . . take the positive square root; subtract 3
Adrian's number is 21; Jackie's number is 27.
What’s is the least common multiple of 5,4,3
Answers
Answer:
Step-by-step explanation:
The LCM of 5,4,3 is 5×4×3=60
How would you solve 4n-2n=4?
Answers
Answer:
n = 2
Explanation:
Simplify both sides of the equation
4n − 2n = 4
4n + −2n = 4
(4n + −2n) = 4 (Combine Like Terms)
2n = 4
2n = 4
Divide both sides by 2
2n / 2 = 4 / 2
n = 2
4n-2n=4
4n-2n= 2n
2n=4
÷2
n=2
old mcdonald has 100 chickens and goats in the barnyard. Altogether, there are 284 feet. How many chickens and how many goats are in the barnyard?
Answers
Answer:
58 chickens, 42 goats
Step-by-step explanation:
there are a total of 100 chickens and goats
c + g = 100....c = 100 - g
there are 284 feet....chickens have 2 feet and goats have 4 feet
2c + 4g = 284
2(100 - g) + 4g = 284
200 - 2g + 4g = 284
-2g + 4g = 284 - 200
2g = 84
g = 84/2
g = 42 <===== goats
c + g = 100
c + 42 = 100
c = 100 - 42
c = 58 <==== chickens
Final answer:
To solve the problem, set up equations based on the number of feet each animal has, then use substitution to find there are 58 chickens and 42 goats in the barnyard.
Explanation:
How to Solve Problems Involving Numbers of Chickens and Goats
Old McDonald has 100 chickens and goats in the barnyard, and altogether, there are 284 feet. To find out how many chickens and how many goats are there, we can set up a system of equations based on the information given. A chicken has 2 feet and a goat has 4 feet. Let's assign the variable C to represent the number of chickens and G to represent the number of goats.
We are given two pieces of information which we will translate into two equations:
Equation 1: C + G = 100 (since there are 100 chickens and goats in total)
Equation 2: 2C + 4G = 284 (since chickens have 2 feet and goats have 4 feet)
To solve for C and G, we can multiply Equation 1 by 2 to align it with the coefficients of Equation 2:
2C + 2G = 200
Now, subtract this new equation from Equation 2 to solve for G:
(2C + 4G) - (2C + 2G) = 284 - 200
2G = 84
G = 42
With G known, we can substitute it back into Equation 1 to find C:
C + 42 = 100
C = 58
Therefore, there are 58 chickens and 42 goats in the barnyard.
if the origin is the midpoint of the line segment joined by the points (2,3) (x,y) find x and y
Answers
Answer:
(- 2, - 3 )
Step-by-step explanation:
Given the endpoints of a segment (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
[0.5(x₁ + x₂), 0.5(y₁ + y₂ ) ]
Here (x₁, y₁ ) = (2, 3) and (x₂, y₂ ) = (x, y) and the midpoint = (0, 0), thus
0.5(2 + x) = 0 , that is
2 + x = 0 ( subtract 2 from both sides )
x = - 2
0.5(3 + y) = 0, that is
3 + y = 0 ( subtract 3 from both sides )
y = - 3
Thus (x, y) = (- 2, - 3 )
Raj has a $25 budget to spend on decorations for a party he has already spent $18.60 he now wants to get some helium balloons that’s cost $0.80 each write and solve an inequality to show the number of balloons the raj could buy
Answers
Answer:
The number of balloons Raj could buy is 8.
Step-by-step explanation:
Given:
Raj has a $25 budget to spend on decorations for a party.
He has already spent $18.60.
He wants to get some helium balloons that’s cost $0.80 each.
Now, to write and solve an inequality to show the number of balloons Raj could buy.
Let the number of balloons be [tex]x.[/tex]
Cost of each balloons = $0.80.
So, the total cost of balloons = [tex]0.80x.[/tex]
He already spent = $18.60.
Total budget Raj has = $25.
Now, to solve an inequality to show the number of balloons:
[tex]0.80x+18.60\leq 25[/tex]
Subtracting both sides by 18.60 we get:
[tex]0.80x\leq 6.40[/tex]
Dividing both sides by 0.80 we get:
[tex]x\leq 8.[/tex]
Therefore, the number of balloons Raj could buy is 8.
Madison Middle School spends $750 per year on club activities. They spend at least twice the amount on after school activities. Write an inequality that represents how much they spend on after school activities
Answers
Answer:
x≥1500
Step-by-step explanation:
Finn bought 12 movie tickets. Student tickets cost $4, and adult tickets
cost $8. Finn spent a total of $60. Write a system of equations
to find the number of student and adult tickets Finn bought.
Answers
Answer:
x=9(student cost)
y=3(adult cost)
12=4x+8y
60=4x+8y
Answer:
x=9(student cost)
y=3(adult cost)
12=4x+8y
60=4x+8y
Step-by-step explanation:
Consider the Piece-Wise graph described by the following equation:
Determine the coordinates of the point on the graph where x=3.
(3, 1)
(3, 3)
(3, 5)
(3, 13)
Answers
Answer:
(3, 5 )
Step-by-step explanation:
when x = 3, that is x ≥ 3, thus
y = 2x - 1 = 2(3) - 1 = 6 - 1 = 5 ⇒ (3, 5 ) is the point on the graph
2/5 times 25 help I got game day tomorrow
Answers
Answer:
10
Step-by-step explanation:
You are doing:
(2/5) * 25
You can do it two ways, first divide, then multiply, OR multiply, then divide.
In this case, I will multiply, then divide:
First, multiply:
(2 * 25)/5 = (50)/5
Next, divide:
50/5 = 10
10 is your answer.
~
if you get 17 out of 20 questions correct on your next test what percent of the test did you answer correctly?
Answers
Answer:
85%
Step-by-step explanation:
Just use a calculator to divide 17 by 20. That gives you .85. To convert into a percent, multiply by 100, giving you an 85%.
A trick I use to convert decimals into percents is to jut move the decimal point 2 spaces to the right.
You answered 85% of the test questions correctly.
To find the percentage of questions answered correctly, we can use the formula:
Percentage = (Number of questions answered correctly / Total number of questions) × 100
In this case, you answered 17 out of 20 questions correctly. Plugging these values into the formula:
Percentage = (17 / 20) × 100
Percentage = 0.85 × 100
Percentage = 85
Therefore, you answered 85% of the test questions correctly.
To know more about " Percentage. ." here
https://brainly.com/question/24877689
#SPJ6
5 minus what equals 4.329
Answers
Final answer:
5 minus 0.671 equals 4.329.
Explanation:
The student is asking for the number that, when subtracted from 5, equals 4.329. To find this number, you subtract 4.329 from 5:
5 - x = 4.329
Solving for x, you subtract 4.329 from 5:
x = 5 - 4.329
x = 0.671
Therefore, 5 minus 0.671 equals 4.329. When dealing with subtraction, it's important to round the result correctly, just as with other operations such as addition, multiplication, and division.
F^-1(4) when f(x) = 3x - 4/ 5
Answers
Answer: [tex]f^{-1}(4)=\frac{8}{5}[/tex]
Step-by-step explanation:
1. You need to find the Inverse function [tex]f^{-1}(x)[/tex]:
- Given the function f(x):
[tex]f(x) = 3x - \frac{4}{ 5}[/tex]
- Rewrite it with [tex]f(x)=y[/tex]:
[tex]y= 3x - \frac{4}{ 5}[/tex]
- Now you must solve for "x":
[tex]y+\frac{4}{ 5} = 3x\\\\(y+\frac{4}{ 5})(3)=x\\\\x=\frac{y}{3}+\frac{4}{15}[/tex]
- Now you must exchange the variables:
[tex]y=\frac{x}{3}+\frac{4}{15}[/tex]
- Then:
[tex]f^{-1}(x)=\frac{x}{3}+\frac{4}{15}[/tex]
2. Substitute [tex]x=4[/tex] into the Inverse function and then evaluate:
[tex]f^{-1}(4)=\frac{(4)}{3}+\frac{4}{15}\\\\f^{-1}(4)=\frac{8}{5}[/tex]
what is the slope a ski run that rises 8 feet for every horizontal change of 72 feet
Answers
Answer:
the slope of the ski run is 9
Which salt is the most common found in ocean water?
A.) calcium carbonate
B.) magnesium
C.) potassium
D.) sodium chloride
Answers
Answer:
sodium chloride
Step-by-step explanation:
sea salt is basically sodium chloride
Answer:
Sodium chloride is the most abundant salt
Step-by-step explanation:
Sally found 58 seashells on the beach, she gave Jason some of her seashells. She has 28 left. How many seashells did she give to Jason?
Answers
Sally gave 30 shells to Jason
Solution:
Given that, Sally found 58 seashells on the beach, she gave Jason some of her seashells
She has 28 left
To find: Number of sea shells she gave to Jason
From given,
Total number of shells she found = 58
Remaining shells = 28
Therefore,
Number of sea shells she gave to Jason = Total number of shells she found - Remaining shells
Number of sea shells she gave to Jason = 58 - 28 = 30
Thus Sally gave 30 shells to Jason
4. A Christmas promotion included a $2.5 mail-
promotion included a $2.5 mail-in rebate for the purchase of a 10-liter bome
K and a store coupon for $1.39 off a 5-liter bottle of vegetable oil. Jesse Gatling
bought one 10-liter bottle of milk for $33.00 and a 5-liter bottle of vegetan
$26.89. Calculate his total cost if an envelope costs $0.10 and a stamp costs $
5. An Apple iPod sells for $781.29 and has a mail-in rebate for
$55.00. Determine the cost after the rebate if an envelope
costs $0.13 and a stamp costs $0.40.
The answer is
Answers
Final answer:
To find the final cost of an Apple iPod after a mail-in rebate and the cost of mailing the rebate (envelope and stamp), subtract the rebate amount from the original price and add the mailing costs. The total cost after these calculations is $726.82.
Explanation:
Let's tackle the Apple iPod rebate calculation problem. An Apple iPod sells for $781.29 and has a mail-in rebate for $55.00. To calculate the cost after the rebate, you must also consider the costs of an envelope and a stamp, which are $0.13 and $0.40, respectively. The formula for the final cost after applying the mail-in rebate, including the expenses for an envelope and a stamp, is as follows:
Calculate the rebate price by subtracting the rebate amount from the original price: $781.29 - $55.00 = $726.29.
Add the costs of the envelope and stamp to the price after rebate: $726.29 + $0.13 + $0.40 = $726.82.
The final cost of the iPod after the rebate and additional costs is $726.82.
Solve for x in the equation x squared minus 4 x minus 9 = 29. x = 2 plus-or-minus StartRoot 42 EndRoot x = 2 plus-or-minus StartRoot 33 EndRoot x = 2 plus-or-minus StartRoot 34 EndRoot x = 4 plus-or-minus StartRoot 42 EndRoot
Answers
Answer:
The correct answer is A. x = 2 +/- √42
Step-by-step explanation:
Let's solve for x the quadratic equation, this way:
x² - 4x - 9 = 29
x² - 4x - 38 = 0
Using the quadratic formula, we have:
x = [- (-4) +/- √ -4² - 4 * -38]/2
x = 4 +/- √ 16 + 152/2
x = 4 +/- √ 168/2
x = 4 +/- √ 4 * 42/2
x = 4 +/- 2 √42/2
x = 2 +/- √42
The correct answer is A. x = 2 +/- √42
Answer:
the answer is A on edg2020
Step-by-step explanation:
Find the value of x. Round to the nearest degree.
Select one:
a. 53
b. 37
c. 49
d. 39
Answers
Answer:
a. 53
Step-by-step explanation:
The side with length 15 is opposite the right angle, so it is the hypotenuse of the right triangle.
For angle x, the side measuring 12 is the opposite leg.
Our 3 items of interest are: angle, opposite leg, hypotenuse.
The trig ratio that relates the opposite leg to the hypotenuse is the sine ratio.
sin x = opp/hyp
sin x = 12/15
sin x = 0.8
Now we take the inverse sine of 0.8 to find the measure of the angle.
x = sin^(-1) 0.8 = 53 deg
What is the answer to the problem 1 + -4
Answers
Answer:
-3
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
cuz its like 4-1
-12 * 7/2
Please explain
Answers
Answer:-42
Step-by-step explanation:
-12*7/2
Is also represented like this
-12/1*7/2 proper fraction
Multiple -12*7 and divide by 2
-84/2= -42
Answer:
Using BIDMAS the answer equates to -42.
Step-by-step explanation:
Determine the slope of the line that passes through points (0, -4) and (-1,2).
6
-6
-1/6
1/6
Answers
Answer:
B) -6
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(2-(-4))/(-1-0)
m=(2+4)/(-1)
m=6/-1
m=-6
the answer is B, -6, because if you graph it the line goes down and it rises up 6
f(1)=−1.8 f(n)=f(n−1)⋅9 Find an explicit formula for f(n)
Answers
Answer:
f(1) = - 1.8
f(n) = f(1) x 9ⁿ⁻¹
Step-by-step explanation:
f(1) = - 1.8
f(n) = f(1) x 9ⁿ⁻¹
f(1) = - 1.8 x 9⁰ = -1.8
f(2) = - 1.8 x 9¹
f(3) = - 1.8 x 9²
check:
f(1)=−1.8
f(n)=f(n−1)⋅9
f(2) = f(1) x 9 = -1.8 x 9¹
f(3) = f(2) x 9 = (- 1.8 x 9) x 9 = -1.8 x 9²
Answer: f(n)= -1.8*9^n-1
Step-by-step explanation: