Graph the function by the table. Is the function linear or nonlinear?
A. Nonlinear
B. Linear
Answers
Answer:
Option A - Non-linear
Step-by-step explanation:
Given : Graph the function by the table.
x y
1 12.3
2 19.6
3 26.6
4 34.2
5 41.5
To find : Is the function linear or nonlinear?
Solution :
The function is linear when there slopes are equal.
So, we find the slope of the points.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Taking point, [tex](x_1,y_1)=(1,12.3)[/tex] and [tex](x_2,y_2)=(2,19.6)[/tex]
[tex]m=\frac{19.6-12.3}{2-1}[/tex]
[tex]m=\frac{7.3}{1}[/tex]
[tex]m=7.3[/tex]
Taking point, [tex](x_1,y_1)=(2,19.6)[/tex] and [tex](x_2,y_2)=(3,26.6)[/tex]
[tex]m=\frac{26.6-19.6}{3-2}[/tex]
[tex]m=\frac{7}{1}[/tex]
[tex]m=7[/tex]
We have seen that slope between points are not equal.
Therefore, The given points are non-linear.
So, Option A is correct.
Related Questions
Polygons QRST and Q’R’S’T’ are shown on the coordinate grid: A coordinate plane with two polygons is shown. Polygon QRST has vertices Q at 3 comma negative 5, R at 2 comma negative 1, S at 5 comma 0, and T at 5 comma negative 4. Polygon Q prime R prime S prime T prime has vertices at Q prime negative 5 comma negative 4, R prime at negative 1 comma negative 3, S prime at 0 comma negative 6, and T prime at negative 4 comma negative 6. What set of transformations is performed on QRST to form Q’R’S’T’? A 180-degree clockwise rotation about the origin followed by a translation 1 unit to the right A 180-degree clockwise rotation about the origin followed by a translation 1 unit to the left A translation 1 unit to the left followed by a 270-degree counterclockwise rotation about the origin A translation 1 unit to the right followed by a 270-degree counterclockwise rotation about the origin
Answers
The transformation performed on QRST to form Q'R'S'T' is a 180-degree clockwise rotation about the origin followed by a translation 1 unit to the left.
Explanation:The transformation of the polygon QRST to Q’R’S’T’ involves a series of steps. To determine these steps, we look at the movement of each vertex from the original polygon to the new. The coordinates of Q change from (3, -5) in QRST to (-5, -4) in Q'R'S'T'. This signifies a 180-degree clockwise rotation about the origin followed by a translation. Given the options, the answer is ‘A 180-degree clockwise rotation about the origin followed by a translation 1 unit to the left.’
Let's walk through how this works: The rotation leaves us with points Q at (-3, 5), R at (-2, 1), S at (-5, 0) and T at (-5, 4). The translation of 1 unit to left then changes these coordinates to Q' at (-4, 5), R' at (-3, 1), S' at (-6, 0), and T' at (-6, 4), hence matching the given coordinates of Q'R'S'T'.
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Rotate 90 clockwise around the origin (-6,-2) (-3,1) (-1,1) (2,-4) please help me!
Answers
(-6,-2) to (-2,6)
(-3,1) to (1,3)
(-1,1) to (1,1)
(2,-4) to (-4,-2)
Solve the equation.
-5x + 2 = 67
A) x = 13
Eliminate
B) x = -13
C) x =
69
5
D) x = -
69
5
Answers
What is 6b/24b to the second in simplest form?
Answers
Find the Least Common Multiple of these two monomials:
9a^2bc^3 and 30ab^2c^3
9a^2b^2c^3
3ab^3
90ab^3
90a^2b^2c^3
Answers
Its 90 a^2b^2c^3
the LCM for 9 and 30 is 90
LCM for a = a^2 and ab^2 = a^2
LCM for b = bc^3 and abb^2 =b^2
LCM for c = bc^3 and c^3 = C63
so answer is 90a^2b^2c^3
Write an expression to find the difference in the maximum area and minimum area of a nys high school soccer field. Then evaluate the expression.
Max length 100yards
Max length 120 yards
Minimum width 55 yards
Maximum width 80 yards
Answers
Thus maximum area = 120 x 80 = 9,600 square yards.
The minimum area of the school soccer field is given by the minimum length times the minimum width.
Thus maximum area = 100 x 55 = 5,500 square yards.
Therefore, the difference between the maximum area and the minimum area is 9,600 - 5,500 = 4,100 square yards.
The difference between the maximum and minimum area of the soccer field is found by calculating the maximum and minimum area using the given dimensions, and then subtracting the minimum area from the maximum area. Result is 4100 square yards.
Explanation:First, the area of a rectangle (like a soccer field) can be found with the formula Area = Length x Width. To find the difference between the maximum area and the minimum area of the field, we'll need to do two calculations.
For the maximum area, we'll use the maximum length of 120 yards and the maximum width of 80 yards: Max Area = 120 yards x 80 yards = 9600 square yards.
For the minimum area, we'll use the minimum length of 100 yards and the minimum width of 55 yards: Min Area = 100 yards x 55 yards = 5500 square yards.
Now you subtract the minimum area from the maximum area: 9600 square yards - 5500 square yards = 4100 square yards. This is the difference in area between the smallest and largest possible soccer fields.
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in an isosceles triangle there are two sided, called legs, that are the same length. the 3rd side is the base. if an isosceles triangle has a perimeter 345 cm and the base length 85 cm. what is the length of each leg
Answers
Answer:130
Step-by-step explanation:
James has 24 shirts, 18 pairs of pants , and 16 pairs of shoes in his closet, but one oc the shirts is his favorite. How many combinations of shirt, pants and shoes are possible assuming james wears his favorite shirt
Answers
multiply number of pants and number of shoes
18 * 16 = 288 combinations
He could possibly wear 288 different possible combinations of pants, shoes, and his favorite shirt.
Hope this helped!
Amaya's test scores in Algebra 1 are 78 and 91. She has one more test left and wants to earn a B for the course, which is from 80-89 inclusive. Write a compound inequality to represent the situation
Answers
80 ≤ (78 + 91 + x) / 3 ≤ 89
Multiply everything by 3:
240 ≤ 78 + 91 + x ≤ 267
240 ≤ 169 + x ≤ 267
Subtract 169 from everything:
240 - 169 ≤ x ≤ 267 - 169
71 ≤ x ≤ 98
Answer:
She needs to score between 71 and 98 to get a B for the course.
The compound inequality expression expressing the required score to obtain a B grade is 80 ≤ (169 + t) ≤ 89
Test scores :
78 and 91Range of B - grade:
80 - 89Let the her score in the last test = t
Final average score will be :
(78 + 91 + t) / 3 = (169+t) / 3To obtain a B grade :
80 ≤ Final average score Final average score ≤ 89The compound inequality expression can be expressed thus :
80 ≤ Final average score ≤ 89Therefore, the compound inequality expression is 80 ≤ (169 + t) ≤ 89
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What expression can only give you an amount that is possible
Answers
Hope this helps!
Which of the following inequalities is equivalent to 8 ≤ x.
Answers
Answer:
The answer is D
Step-by-step explanation:
In a cafeteria, there are the same number of 3-legged stools as there are of 4-legged chairs. If stools have 120 fewer legs than chairs, how many people can sit in this cafeteria?
Answers
3x+120=4x
x=120
120 stools in cafeteria
120 chairs in cafeteria
120+120=240
There 240 people can sit in this cafeteria
The cafeteria can seat 120 people.
Let's denote the number of 3-legged stools as S and the number of 4-legged chairs as C. According to the problem, there are the same number of stools and chairs, so we have:
S = C
Next, we are told that the stools have 120 fewer legs than the chairs. Since each stool has 3 legs and each chair has 4 legs, we can set up the following equation:
3S + 120 = 4C
Since S = C, we can substitute C for S in the equation:
3C + 120 = 4C
Now, let's solve for C:
120 = 4C - 3C
120 = C
Now that we know there are 120 chairs, and since the number of stools is the same as the number of chairs, there are also 120 stools. Each chair can seat one person, and each stool can also seat one person, so the total number of people that can be seated is the sum of the number of chairs and stools:
Total seating = C + S
Total seating = 120 + 120
Total seating = 240
However, since there are only 120 chairs and 120 stools, and we cannot have half a piece of furniture, the maximum number of people that can be seated is the number of chairs or stools, which is:
Total seating = 120
Therefore, the cafeteria can seat 120 people.
Leia is operating a digital spinner game in which a player spins an arrow and is given a prize based on where the spinner lands. Leia can program the probability of each of the outcomes. The stuffed teddy bear is the best prize, so she programs the spinner so that the probability of not getting a bear twice in a row is greater than 3 times the probability of getting the teddy bear in one spin.
Write an inequality that compares the probability of getting the teddy bear to the probability of not getting the teddy bear, using p to represent the probability of getting the teddy bear in one try.
Answers
In the problem, we are given that the probability of getting a bear is equal to p. Where probability is the share of successful outcome in this case is the bear) over total outcomes (total amount of prizes).
The likelihood of not receiving a bear two times in a row is containing of 2 tries:
try 1: 1st spin gets a bear, 2nd spin does not receive a bear
total probability of try 1 = p * (1 – p)
try 2: 1st spin does not get a bear, 2nd spin gets a bear
total probability of try 1 = (1 – p) * p
The total probability of the 2 tries is just the sum of the 2:
Overall probability of not getting a bear twice in a row= p * (1 – p) + (1 – p) * p
Simplifying this will give us:
Overall probability of not getting a bear twice in a row = 2p * (1 – p)
Therefore, the likelihood of not receiving a bear twice in a row > 3 times the probability of getting the teddy bear. Rewriting the statement, will give us the inequality of 2p * (1 – p) > 3 p
To compare the probability of getting the teddy bear to the probability of not getting the teddy bear, use the inequality p^2 + 3p - 1 < 0.
Explanation:To write an inequality that compares the probability of getting the teddy bear to the probability of not getting the teddy bear, we can use the inequality sign. Let's represent the probability of getting the teddy bear in one try as 'p'. Since we want the probability of not getting a bear twice in a row to be greater than 3 times the probability of getting the teddy bear in one spin, we can write the inequality as:
1 - p * p > 3p
Simplifying the inequality, we get:
1 - p^2 > 3p
Then, rearranging the terms, we get:
p^2 + 3p - 1 < 0
This is the inequality that compares the probability of getting the teddy bear to the probability of not getting the teddy bear.
To solve X/0.4 = 10, you would: Add 0.4 Subtract 0.4 Multiply 0.4 Divide by 0.4
Answers
Help plz 6r – 12 = 6
Answers
6r = 6+12
6r = 18
18/ 6 = 3
r = 3
6r - 12 = 6
Add 12 to both sides.
6r = 18
Divide.
r = 3
Lets check our answer.
6(3) - 12 = 6
18 - 12 = 6
6 = 6 It makes sense so r = 3 is the answer.
I hope this helps love! :)
The gas tank in Ms. Brown's car holds a total of 15 gallons. At any given time, how many gallons, g, will Ms. Brown have to pump into her car to fill her tank given the fraction of the tank,f, already filled?
A. g = 15f
B. g = f15/f
C. g = 15−15f
D. g = 15-15/f
Answers
Answer:
c cause i took the sat practice
The number of gallons (g) that Ms. Brown have to pump into her car to fill her tank will be g = 15 – 15f. Then the correct option is C.
What is a fraction number?A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.
The gas tank in Ms. Brown's car holds a total of 15 gallons.
At any given time.
The number of gallons (g) that Ms. Brown have to pump into her car to fill her tank given the fraction of the tank, f, already filled will be
The gas in a tank will be
⇒ 15f
Then number of gallons (g) will be
⇒ 15 – 15f
Then the correct option is C.
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Sanjay rides his bike to work 15 kilometers in two days. He works five days per week. How many weeks will Sanjay need to ride his bike to work in order to ride 150 kilometers?
Answers
Sanjay needs to ride his bike for 3 weeks to cover a distance of
150 kilometers.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Sanjay rides his bike to work 15 kilometers in two days.
∴ In one day he rides (15/2) = 7.5 kilometers.
So, to ride his bike for 150 kilometers he needs (150/7.5) = 20 days.
We know 1 week is 7 days.
∴ Sanjay needs (20/7) = 2.86 weeks, but weeks comes in integers and we'll choose 3 weeks as in 2 weeks he won't be able to cover a distance of 150 kilometers.
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Sal brought $7.50 to the fair and Karma brought $8.75 to the fair. Which expression shows the total amount they brought?
A) $8.75 - $7.50 = $16.25
B) $8.75 + $7.50 = $15.25
C) $8.75 - $7.50 = $1.25
D) $8.75 + $7.50 = $16.25
Answers
Answer:
The answer to the question is a
What is the quotient of 59,584 ÷ 14?
A. 4,156
B. 4,256
C. 5,156
D. 5,256
Answers
Answer:
B
Step-by-step explanation:
We can divide using the calculator by entering in 59, 584 first followed by 14 before the division sign.
We can also perform long division:
__4256_____
14 | 59, 584
-56____
35
-28____
78
-70____
84
-84____
0
IS THIS TRUE OR FALSE
A dilation is a function because every point on the pre-image corresponds to exactly one point on the image.
Answers
Select the graph of the solution. Click until the correct graph appears. 3x + 1 < 7 (line graph)
Answers
3x < 7 - 1
3x < 6 ...divide both sides by 3
x < 6/3
x < 2
there will be an open circle on 2....because the problem has no equal sign...the line will be shaded to the left...because it is less then.
The solution of the inequality [tex]3x + 1 < 7[/tex] is [tex]\boxed{x < 2}.[/tex]
Further explanation:
There are two types of the interval close interval and open interval.
If the values of [tex]\text{x}[/tex] doesn’t includes the number than it is represented by hollow dot on the number line and if the values of [tex]\text{x}[/tex] includes the number than it is represented by the solid dot on the number line.
Given:
The inequality is [tex]3x + 1 < 7.[/tex]
Explanation:
The given inequality is [tex]3x + 1 < 7.[/tex]
Subtract 1 from both side of the inequality.
[tex]\begin{aligned}3x + 1 - 1 &< 7 - 1\\3x &< 6\\\end{aligned}[/tex]
Now divide both sides by 3.
[tex]\begin{aligned}\frac{{3x}}{3} &< \frac{6}{3}\\x&< 2\\\end{aligned}[/tex]
The solution of the inequality [tex]3x + 1 < 7[/tex] is [tex]\boxed{x < 2}.[/tex]
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Compound inequalities
Keywords: solution, [tex]3x + 1 < 7[/tex], inequalities, graph, compound inequality, graph representation, number line, close interval, open interval, line graph.
Lydia is trying to prove that a quadrilateral in a coordinate plane is a square. First, she uses the slope formula to prove that there are two pairs of parallel sides. Next, she uses the distance formula to prove that all sides are equal. What additional step must Lydia perform before reaching a conclusion that the quadrilateral is a square?
A) Use the distance formula to prove that the diagonals of the quadrilateral are not equal.
Eliminate
B) Use the slope formula to prove that four right angles exist as a result of perpendicular sides.
C) Use the midpoint formula to prove that the diagonals of the quadrilateral do not bisect each other.
D) Use the Pythagorean Theorem to prove that the diagonals of the quadrilateral are twice the length of each side.
Answers
Its B
Answer:
slope
Step-by-step explanation:
Using the sample statistics, construct a 9999% confidence interval estimate of the mean body temperature of all healthy humans. do the confidence interval limits contain 98.6degrees°f? what does the sample suggest about the use of 98.6degrees°f as the mean body temperature?
Answers
Part A:
What is the best point estimate of the mean body temperature of all healthy humans?
The sample mean is the point estimate of the population mean.
Given that the sample mean is 98.7 degrees F, therefore, the best point estimate is 98.7 degrees F.
Part B:
Using the sample statistics, construct a 99% confidence interval estimate of the mean body temperature of all healthy humans.
Since the sample size is large, we can assume that the population is approximately normal.
The 99% confidence interval of a data set with sample mean [tex]\bar{x}=98.7[/tex] and sample standard deviation, s = 0.64 and degree of freedom = 105 - 1 = 104 is given by:
[tex]C.I.=\bar{x}\pm1.665\left( \frac{s}{\sqrt{n}} \right) \\ \\ =98.7\pm1.665\left( \frac{0.64}{\sqrt{105}} \right) \\ \\ =98.7\pm1.665(0.0625) \\ \\ =98.7\pm0.104=\bold{(98.596, \ 98.804)}[/tex]
It can be seen from above that the confidence interval is between 98.596 and 98.804 which contains 98.6 degrees F.
This suggests that the mean body temperature could very possibly be 98.6 degrees F.
Suppose you have already been waiting for one hour for a taxi. what is the probability that one arrives within the next 10 minutes?
Answers
The probability of one arrives within the next 10 minutes when he already been waiting for one jour for a taxi is,
P (X > 70 | X > 60) = P (X > 10) = 1 – P (X ≤ 10) = 1 – {1 – e ^ -((1 / 10) 10)} = e ^ -1
= 0.3679
The probability of one arrives within the next 10 minutes when he already been waiting for one hour for a taxi is 0.3679
A magazine has 96 pages. there are advertisements on 75% of those pages. how many pages do not have advertisements?
Answers
There are 24 pages in the magazine that do not have advertisements.
To find the number of pages without advertisements in a 96-page magazine, we first calculate the number of pages with advertisements.
Calculate 75% of 96 (since 75% of the pages have advertisements).
[tex]\( 75\% \times 96 = 0.75 \times 96 = 72 \)[/tex] pages with advertisements.
Subtract the pages with advertisements from the total number of pages to find the pages without advertisements.
[tex]\( 96 - 72 = 24 \)[/tex] pages without advertisements.
So, there are 24 pages in the magazine that do not have advertisements.
A total of 15000 is to be divided between jon and wendy with jon to receive 2500 less than wendy how much will she receive
Answers
j = w - 2500
w - 2500 + w = 15,000
2w - 2500 = 15,000
2w = 15,000 + 2,500
2w = 17500
w = 17500/2
w = 8750 <=== what wendy receives
j = w - 2500
j = 8750 - 2500
j = 6250...what Jon receives
Wendy will get $8750.
We have a total of 15000 that is to be divided between Jon and Wendy with Jon to receive 2500 less than Wendy how much will she receive.
We have to determine how much money will Wendy receive.
A total of 20 chocolates are to be divided between you and your brother such that you will get 6 more chocolates than your brother. How many chocolates will your brother get?Assume your brother gets x number of chocolates.
Then, you will get - x + 5.
Therefore -
x + x + 6 = 20
2x = 14
x = 7
According to the question -
Assume that Wendy receives $x.
Then Jon will receive $(x - 2500).
Then -
x + x - 2500 = 15000
2x = 17500
x = 8750
Hence, Wendy will get $8750.
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−3.1+(−0.35)
Write your answer as a decimal.
Answers
The answer in decimal to the expression −3.1+(−0.35) is - 3.45.
What is decimal?A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts.
Given:
The expression: - 3.1 + (-0.35)
Use the sign convention given below to solve the above expression,
[tex]+ + - =[/tex] sign of the larger number,
[tex]-+- = -[/tex]
[tex]+\times - = -[/tex]
Here when the bracket opens use the second sign convention,
- 3.1 - 0.35 = - 3.45
Therefore, the answer in decimal to the expression −3.1+(−0.35) is - 3.45.
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Identify the segment bisector of JK
Answers
Answer:
A segment whose length is 9 units.
Step-by-step explanation:
A segment whose length is 9 units.
All we have is a bisection that divides equally segment JK in two parts. And M is the Midpoint what reassures us that JM=MK, so plugging in:
3x+15=8x+25
3x-8x=25-15
-5x=10
5x=-10
x=-2
JM=3(-2)+15 =9
MK=8(-2)+25=9
Answer:
Step-by-step explanation:
Does a negative exponent result in a negative answer
Answers
(3a3 − 5b3) + a3 + b3 = (a3 + b3).
Answers
Answer:
-2
6
Step-by-step explanation: