No, there cannot be a horizontal tangent at the point where the curve intersects the x-axis.
What is a curve on the graph?A smooth-drawn figure or line with a bend or turn is referred to as a curve.
A circle is an illustration of a curved shape.
The path, also known as the topological arc, is the name of the curve (or just arc).
If a curve is the continuous injective image of an interval or a circle, it is considered simple.
If a curve is determined by a continuous function, in other words.
So, it possible for the curve to have a horizontal tangent:
On the curve, horizontal tangents appear where:
x = -1 and y ≠ -1
y = 0 where the curve crosses the x-axis.
-1² + 2(-1) + 0⁴ + 4.0 ≠ 5
No, the point where the curve crosses the x-axis cannot have a horizontal tangent.
Therefore, no, there cannot be a horizontal tangent at the point where the curve intersects the x-axis.
Know more about the curve on the graph here:
https://brainly.com/question/27887527
#SPJ4
Complete question:
Consider the closed curve in the xy-plane given by : x²+2x+y⁴=4y = 5
Is it possible for this curve to have a horizontal tangent at points where it intersects the x-axis? explain your reasoning.
the correlation between two variables related to the same sample is a scaled quantitative measure. what is used to scale this measurement?
The correct option is the standard deviations of the variables.
What is correlation?
Any statistical relationship between two random variables or bivariate data, whether causal or not, is referred to in statistics as correlation or dependence.
Correlation is a term used to describe the linear relationship between two entities. When using a correlation tool, the variables must be present in quantities of two or more to test their relationship (degree of association).
In order to scale the measurement between two variables connected to a similar sample, the standard deviation measures dispersion.
The variables' standard deviations are the best choice as a result.
Option involving the standard errors of the variables is incorrect because standard error, which stands for standard deviation, determines the relationship between dependent and independent variables.
Option involving the coefficients of variation of two variables is incorrect because the coefficient expressing standard deviation and mean ratio determines how much variation there is.
Option The means of the variables are incorrect because they are not a scale for determining the correlation between two variables.
Hence, the correct option is the standard deviations of the variables.
To know more about correlation, click on the link
https://brainly.com/question/2088651
#SPJ4
Complete question:
The correlation between two variables related to the same sample is a scaled quantitative measure. What is used to scale this measurement?
- the standard deviations of the variables
- the standard errors of the variables
- the coefficients of variation of the two variables
- the means of the variables
measurements of variables must be sensitive to be able to measure differences between participants. however, if a measurement was not sensitive, and resulted in everyone scoring high, then this is called:
If a measurement was not sensitive, and resulted in everyone scoring high, then this is called a ceiling effect
Given,
Ceiling effect;-
When a large percentage of study participants get the highest scores on the observable variable, it is said that a ceiling effect has occurred. Discrimination between subjects at the top end of the scale is therefore impossible. For instance, a test could result in, say, 50% of the students receiving a perfect score.
Here,
To be able to measure participant differences, variables must be measured with sufficient sensitivity. However, if a test was insensitive and everyone received good scores, this is known as ceiling effect
Learn more about ceiling effect here;
https://brainly.com/question/28945421
#SPJ4
let g be a group of order 840, and suppose k is a subgroup of g of order 42. if h is a subgroup of g that contains k as a subgroup, what could the order of h be? explain
The order of H can be 84 , 210 or 420
One of the key theorems in abstract algebra is the Lagrange theorem. According to the Lagrange Theorem , In group theory, for any finite group say G, the order of subgroup H of group G is the divisor of the order of G. The order of the group represents the number of elements
According to the question,
Group G has order 840
Also , By Lagrange's theorem
|K| divides |H| , so order of h should be multiple of 42
|H| = 42k ------(1) (for some k)
And , H is subgroup of G
|G| should divides |H|
=> 42k should divides 840
=> k = 840/42 = 20
Since , H is proper subgroup of G
K < 20
So, either k =2 , 5 or 10
Hence , order of H can be 84 , 210 or 421
To know more about Lagrange's Theorem here
https://brainly.com/question/13391362
#SPJ4
if a string of length thirteen over {a, b, c, d} is chosen at random, what is the probability that it contains at least one pair of adjacent characters that are the same? (round your answer to the nearest tenth of a percent.)
The total number of possible strings that can be chosen is 4^13, since there are 13 characters and 4 possible choices for each character, b, c, d). Now, we need to determine the number of strings that contain at least one pair of adjacent characters that are the same in this probability.
To do this, we'll consider each letter in the string and calculate the number of possible strings that contain at least one pair of adjacent characters that are the same for that letter. For the first letter in the string, there are 4 strings that contain at least one pair of adjacent characters that are the same (aa, bb, cc, dd).For the second letter in the string, there are 4 strings that contain at least one pair of adjacent characters that are the same (ab, be, cd, dc).For the third letter in the string, there are 4 strings that contain at least one pair of adjacent characters that are the same (ac, bd, ca, db.).For the fourth letter in the string, there are 4 strings that contain at least one pair of adjacent characters that are the same (ad, bc, da, cb).
We can continue this process for each letter
We get probability as 83.3%
Learn more about probability here
https://brainly.com/question/12226830
#SPJ4
if you could please help me that would be great.
550 tickets were sold for a game for a total of $687.50. if adult tickets sold for $1.50 and children's tickets sold for $1.00, how many of each kind of ticket were sold?
9514 1404 393 each kind of ticket were sold if 550 tickets were sold for a game for a total of $687.50. if adult tickets sold for $1.50 and children's tickets sold for $1.00,
adult: 325
children's: 225
It usually works well to let a variable represent the higher-value item in the mix. Here, we can let 'a' represent the number of adult tickets sold. Then the total revenue is ...
1.50a +1.00(550 -a) = 687.50
0.50a = 162.50 . . . . . . . . . . . . . subtract 550 and collect terms
a = 325
c = 550 -325 = 225
325 adult and 225 children's tickets were sold
learn more about of ticket here
https://brainly.com/question/25006383
#SPJ4
suppose there are n independent trials of an experiment with k>3 mutually exclusive outcomes, where p i represents the probability of observing the ith outcome. what would be the formula of an expected count in this situation?
The probability for observing the expected count will be given by [tex]E_i = nP_i[/tex]
Consider an experiment with n independent trials and k > 3 mutually incompatible outcomes.
Where [tex]P_i[/tex] stands for the likelihood of seeing the i-th result.
Hence for the nth expected result on i will be given by multiplying the i-th probability with the expected variable n.
Hence [tex]E_i = n\times P_i[/tex]
∴ [tex]E_i = nP_i[/tex] provides the predicted numbers for each potential outcome.
where pi is the likelihood of seeing the i-th result.
The predicted count of the i-th result is called [tex]E_i[/tex].
When two events cannot occur concurrently at the same moment, they are said to be mutually exclusive in accordance with probability theory. Or, to put it another way, discontinuous events are said to be mutually exclusive.
There is no possibility of two occurrences occurring simultaneously if they are viewed as separate events. If two events do not take place at the same time, they are said to be mutually exclusive. If a coin is tossed, the outcome will always be either head or tail; we cannot get both.
To learn more about probability visit:
https://brainly.com/question/28336197
#SPJ4
A tollbooth collected $900 on a day
in which a total of 1,100 cars and
trucks passed through. Cars pay a
$0.75 toll, and trucks pay a $1.25
toll. How many cars paid the toll
that day?
Using system of linear equations, the number of cars and trucks that parked are 950 and 150 respectively.
System of linear equationThe system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.
To solve this problem, we have to write out two equations and solve the unknown variable.
x = carsy = trucksx + y = 1100 ...eq(i)
0.75x + 1.25y = 900 ...eq(ii)
From equ(i)
x = 1100 - y ..eq(iii)
Put eq(iii) into eq(ii)
0.75(1100 - y) + 1.25y = 900
y = 150
Put y = 150 in equation (i)
x + 150 = 1100
x = 1100 - 150
x = 950
x = 950, y = 150
Learn more on system of linear equations here;
https://brainly.com/question/13729904
#SPJ1
A line with a slope of –14 passes through the point (3,3). What is its equation in point-slope form? Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
The required equation of the line is given as y = -14x + 45.
What is the equation for a straight line?A straight line can be written in the form of equation as, y = mx + c.
Two straight lines intersect each other only at one point.
When two straight lines are parallel to each other the angle between them is zero.
Given that,
The slope of the line is -14.
And, the point it passes through is (3, 3).
The equation of the line for given data can be written as follows,
(y - 3)/(x - 3) = -14
=> y - 3 = -14(x - 3)
=> y = -14x + 42 + 3
=> y = -14x + 45
Hence, the equation of the line for the given point and slope can be written as y = -14x + 45.
To know more about straight line equation click on,
brainly.com/question/21627259
#SPJ1
Find the length of the third. If necessary, round to the nearest tenth 18 12
Answer:
Since it appears that you are talking about a triangle, if the third side that you are looking for is the hypotenuse, then you can use the Pythagorean theorem, a^2 + b^2 = c^2. In this case, the length of the side, if it would be the hypotenuse, would be approximately 21.63.
Step-by-step explanation:
Hope this helped! :D
I need help with this please
Answer:
He spent 4&1/10 hours
Step-by-step explanation:
2&1/2+1&3/5
=5/2+8/5
=25/10+16/10
=41/10
4&1/10
Lexi is rehydrating after an intense workout. She drinks 1/4 of a gallon every 50 minutes, or 5/6 of an hour. How many gallons of water does she drink in one hour?
Lexi drinks 3/10 gallon of water in one hour.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Lexi drinks water in 50 minutes = 1/4 gallon
To find water that Lexi drinks in one hour,
Use ratio property,
50 minutes = 1/4 gallon
1 minute = 1/(4 x 50)
60 minutes = 60/(4 x 50)
60 minutes = 3/10 gallon
Lexi drinks 3/10 gallon of water in 1 hour.
To know more about Ratio on:
https://brainly.com/question/23724140
#SPJ1
The sum of the digits of a three-digit number is 13. The tens digit, t, is 1 more than the hundreds digit, h. The units digit, u, is 3 more than the sum of the tens and hundreds digits. Which system of equations can be used to find each digit?.
Using the system of equations we get the values of 3 digit number as:
238
Given:
The sum of the digits of a three-digit number is 13.
The tens digit, t, is 1 more than the hundreds digit, h. The units digit, u, is 3 more than the sum of the tens and hundreds digits.
we are asked to determine each digit of the given number:
we frame the equation as:
tens digit (t) = 1+h
hundreds digit (h) = h
units digit (u) = 3+(t+h)
hence,
h + (1+h) + (3+(t+h)) = 13
open the brackets.
h+1+h+3+(t+h)=13
substitute t value from the above mentioned state.
h+1+h+3+((1+h)+h)=13
h+1+h+3+1+h+h=13
arrange the like terms and add.
4h + 5 = 13
4h = 13-5
4h=8
h = 8/4
h = 2
hence we get the hundreds digit as 2.
now substitute it to get t and u value.
t = 1+h
t = 1+2
t = 3
tens digit = 3
u = 3+(t+h)
u = 3+(3+2)
u = 3+5
u = 8
units digit = 8
Hence we get the number as 238 whose sum is 13 when added.
Learn more about Linear equations here:
brainly.com/question/4074386
#SPJ4
A line with a slope of –12 passes through the points (–3,–6) and (r,–10). What is the value of r?
The value of r is r = -8/3, for a line that has slope -12, passes through points (-3, -6) and (r, -10)
What is slope ?Slope is a notation that shows that a surface of which one end or side is at a higher level than another surface.
Slope formula = (y₂-y₁)/(x₂-x₁)
Given that,
A line that has slope -12, passes through points (-3, -6) and (r, -10).
To find the slope of the line that passes through points (-3, -6) and (r, -10),
Use slope formula,
m = (y₂-y₁) / (x₂-x₁)
m = (-10 + 6) / r - (-3)
m = -4 / (r+3)
Since a line that has slope -12 passes through the points (-3, -6) and (r, -10),
Therefore, both will have the same slope,
-4 / (r+3) = -12
r + 3 = 1/3
r = 1/3 - 3
r = -8/3
The required value of r is -8/3.
To know more about Slope on :
https://brainly.com/question/16180119
#SPJ1
I need help with this linear equation.
The linear equation of the relationship is L = -8t + 40.
The amount Austin paid back each week is: $8.
How to Write a Linear Equation?A linear equation is straight line graph, which can be expressed as y = mx + b, in slope-intercept form. In the slope-intercept form, we have:
The value of m as the slope of the linear equation.The value of b as the initial value or y-intercept.Slope = change in y / change in x.
Using two pairs of values from the table given, (1, 32) and (2, 24):
Slope (m) = (32 - 24) / (1 - 2)
m = 8/-1
m = -8.
Find the y-intercept (b) by substituting m = -8 and (x, y) = (1, 32) into y = mx + b:
32 = -8(1) + b
32 = -8 + b
32 + 8 = b
40 = b
b = 40
Substitute b = 40 and m = -8 into L = mt + b:
L = -8t + 40
Using the linear equation, the amount Austin paid back each week is: $8.
Learn more about linear equation on:
https://brainly.com/question/4074386
#SPJ1
If 10400 dollars is invested at an interest rate of 8 percent per year, find the value of the investment at the
end of 5 years for the following compounding methods, to the nearest cent.
(a) Annual: $
(b) Semiannual: $
(c) Monthly: $
(d) Daily: $
The interest estimated by compounding methods are-
(a) Annual: n = 1; CI = $860
(b) Semiannual: n = 2; CI = $862.
(c) Monthly: n = 12; CI = $865
(d) Daily: n = 365; CI = $855
Explain the term compound interest?When you add the interest you have already earned back into the principal balance, you are earning compound interest, which increases your profits.The formula for computing the compound interest is -
CI = A - P
A = P(1 + r/100nt)∧rt
In which,
CI = compound interestP = principal ($10,400)n = number of times compoundedr = rate of interest (8%)t = time (5 year)(a) Annual: n = 1
A = 10,400(1 + 8/500)∧5
A = 10,400 x 1.08
A = 11,260
CI = 11,260 - 10,400
CI = $860
(b) Semiannual: n = 2
A = 10,400(1 + 8/1000)∧10
A = 10,400 x 1.089
A = 11,262
CI = $862.
(c) Monthly: n = 12
A = 10,400(1 + 8/6000)∧60
A = 10,400 x 1.083
A = 11,265
CI = $865
(d) Daily: n = 365
A = 10,400(1 + 8/182500)∧1825
A = 10,400 x 1.0832
A = 11,255
CI = $855
To know more about the compound interest, here
https://brainly.com/question/3989769
#SPJ4
When 27 is subtracted from the square of a number, the result is 6 times the number. Find the negative solution, please! I need help-
Hence, the negative solution is [tex]x=-3[/tex].
What is the equation?
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Here given that,
When [tex]27[/tex] is subtracted from the square of a number, the result is [tex]6[/tex] times the number.
So we can write the equation is
[tex]x^2-27=6x\\x^2-6x-27=0\\x^2-9x+3x-27=0\\x(x-9)+3(x-9)=0\\(x+3)(x-9)=0\\x=-3,9[/tex]
Hence, the negative solution is [tex]x=-3[/tex].
To know more about the equation
https://brainly.com/question/12788590
#SPJ1
BRAINLIEST !!! The data below are the heights of mothers (x values) and their corresponding
daughters (y values)
X Y
63 59
67 65
64 65
60 61
65 65
67 67
59 61
60 63
58 60
72 71
63 62
a. Calculate the correlation coefficient of the data.
b. Based on the correlation coefficient, is there a correlation between the heights of
daughters and mothers? Explain your answer.
Answer:
a. The correlation coefficient of the data is 0.817.
b. Yes, there is a correlation between the heights of daughters and mothers. The correlation coefficient of 0.817 indicates a strong positive correlation, meaning that as the height of the mother increases, the height of the daughter also increases.
you have been asked to assemble a two person team from among your five person team. how many different teams are there
If you have been asked to assemble a two person team from among your five person team, then there are 10 different teams
Total number of members for the team = 5
Number of members that we need to assemble = 2
Here we have to use the combination
The combination is defined as the number of ways of selecting samples from the collection and the order of the collection does not matter
The number of combination of 2 members from a 5 member team = [tex]5C_2[/tex]
= 5! / 2!(5-2)!
= 5! / 2! × 3!
= (5 × 4 × 3!) /(2! × 3!)
= (5 × 4) / 2
= 20 / 2
= 10
Therefore, there are 10 different teams
Learn more about combination here
brainly.com/question/28720645
#SPJ4
all of the following increase the width of a confidence interval except a. decreased sample size b. increased sample size c. increased confidence level d. increased variation
The width of a confidence interval except increased sample size.
What is the Confidence Interval?
An area surrounding a measurement that indicates how accurate it is is called a confidence interval.
The following points clear the answer of given question:
The width of the confidence interval decreases as the sample size increases.The width increases as the standard deviation increases.The width increases as the confidence level increases. The width increases as the significance level decreases.Hence, The width of a confidence interval except increased sample size.
To know more about Confidence Interval visit,
https://brainly.com/question/15712887
#SPJ4
Write the equation of the circle centered at (5,-2) with diameter 14.
Answer:
Step-by-step explanation:
On a recent test, students had to determine whether the relation represented by the ordered pairs (4,5), (9,15), (14,22), (18,37) is a function. Bobby drew the arrow diagram on the right and said the relation was not a function. What error did Bobby most likely make? (The answer is NOT B I just chose that before and it was wrong!)
The error that Bobby most likely made in verifying if the relation is a function is given as follows:
C. Bobby drew the incorrect arrow diagram. The correct arrow diagram of the relation is a function. Bobby's arrow diagram is not a function.
When does a relation represents a function?A relation represents a function if each value of the input is mapped to only one value of the output.
The ordered pairs from this data-set are given as follows:
(4,5), (9,15), (14,22), and (18,37).
The input and the output for the pairs are given as follows:
The input of 4 is mapped to the output of 5.The input of 9 is mapped to the output of 15.The input of 14 is mapped to the output of 22.The input of 18 is mapped to the output of 37.Each value of the input is mapped to only one value of output, hence the relation represents a function.
However, Bobby made a mistake, in mapping the point (9, 15), as he mapped an input of 14 to an output of 9, and thus it would not represent a function. Hence the correct statement is given by option C.
More can be learned about relations and functions at https://brainly.com/question/12463448
#SPJ1
Endure all, a manufacturer of batteries claims that the lifetime of their batteries is normally distributed with a mean of 500 hours and a standard deviation of 40 hours. What is the probability that an endure all battery selected at random will last more than 550 hours?.
Based on the z-score, an Endure All battery selected at random has a 10.56% chance of lasting more than 550 hours.
What are z-scores?How closely a value relates to the mean of a set of values is expressed by a Z-score.
The Z-score is created using standard deviations from the mean.
A data point's total value is equal to the mean value when the Z-score of the data point is equal to 0.
So, in order to determine how far the raw score deviates from the mean, the Z score is used.
The following steps are used to determine the Z score:
z = (x - μ)/σ
We know that: x > 550 and μ = 500, σ = 40
z = 550 - 500 / 40
z = 1.25
The graph of the normal distribution indicates:
P(z > 1.25) = 1 - P(z < 1.25)
P(z > 1.25) = 1 - 0.8944
P(z > 1.25) = 0.1056
Therefore, based on the z-score, an Endure All battery selected at random has a 10.56% chance of lasting more than 550 hours.
Know more about the z-scores here:
brainly.com/question/25638875
#SPJ4
Speedometer readings for a vehicle (in motion) at 7-second intervals are given in the table. t (sec) v (ft/s) 0 7 14 21 28 Estimate the distance traveled by the vehicle during this 35-second period using the velocities at the beginning of the time intervals. distance traveled feet Give another estimate using the velocities at the end of the time periods. distance traveled feet License Points possible: 1 This is attempt 1 of 1.
Another estimate is given as L6, R6, and M3 using the velocities at the conclusion of the time periods.
The table provides speedometer readings of velocity for a moving vehicle at 7-second intervals. t (sec) v (ft/s) 0 7 14 21 28 Using the speeds at the start of the time intervals, calculate the distance the car went during this 35-second span. travel distance in feet
Just figure out the rectangles' surface areas. Always draw the picture; it will be really helpful.
L6 = 10(0+9+31+56+71+68) \sR6 = 10(9+31+56+71+68+50) \sM3 = 20(9+56+68)
Learn more about velocity here
https://brainly.com/question/18084516
#SPJ4
What kind of triangle is this?
Answer:
Obtuse
Step-by-step explanation:
Obtuse because one angle is more than 90 degrees.
Could you please give me brainiest for this? It would help me a lot! Thank you!
A hobby store prices model train track using a proportional relationship between the length of track (in inches) and the cost in dollars. If 6. 4 inches of track costs $16, what is the constant of proportionality?.
$2.50 is found to be the proportionality constant for the relationship between the length of track (in inches) and the cost in dollars.
Define the term constant of proportionality?The ratio connecting two given numbers in what is regarded as a proportional relationship is the constant of proportionality. Constant ratio, consistency index, unitary rate, constant variable variation, and even rate of change are other names for said constant of proportionality.Direct proportionality is represented by the equation y = kx.
Where:
dependent variable = yx = unrelated variableK is the proportionality constant.The price of the track is the dependent variable in this situation.
The tracks' length is an independent variable.
$16 = 6.4k
k = 16 / 6.4
k = $2.5
Thus, the constant of proportionality for the relationship between the length of track (in inches) and the cost in dollars is found as $2.5.
To know more about the constant of proportionality, here
https://brainly.com/question/28413384
#SPJ4
Determine whether the pair of lines appear to be parallel or perpendicular.
1. The lines are perpendicular because they are always the same distance apart and never intersect.
2. The lines are parallel because they are always the same distance apart and never intersect.
3. The lines are parallel because they intersect at a right angle.
4. The lines are perpendicular because they intersect at a right angle.
Answer:
4
Step-by-step explanation:
The lines are perpendicular because they intersect at a right angle.
=
Find the quadratic function y = a(x-h)2 whose graph passes through the given points.
(12,-10) and (8,0)
Answer:
y = -5/8(x -8)²
Step-by-step explanation:
You want the function of the form y = a(x -h)² that passes through the points (12, -10) and (8, 0).
Vertex formThe vertex form of the equation of a quadratic is ...
y = a(x -h)² +k . . . . . . quadratic with vertex (h, k)
Comparing this to the given equation, we see that k=0. This means the point (8, 0) is the vertex and h = 8.
Scale factorThe value of 'a' can be found using the other point.
(x, y) = (12, -10)
-10 = a(12 -8)²
-10 = 16a
-5/8 = a . . . . . . divide by 16 and reduce the fraction
The quadratic function is y = -5/8(x -8)².
__
Additional comment
The equation can also be found using technology to do a quadratic regression with the constraint that the vertex is on the x-axis.
ben wants to triple his spaghetti sauce recipe, which calls for 2 pound 8 ounces of ground turkey. how much ground turkey will he need?
He needs 2.5 pounds of ground turkey.
Given,
In the question:
Ben wants to triple his spaghetti sauce recipe, which calls for 2 pound 8 ounces of ground turkey.
To find the how much pounds ground turkey will he need?
Now, According to the question:
Let's know:
How do you convert ounces to pounds formula?
In other words, dividing a number of ounces by 16 will get you an answer in pounds. In our example, dividing the baby's weight in ounces by 16 gets us 160/16 = 10 lbs.
We know that there are 16 ounces in 1 pound,
It is meaning that 8 ounces is half a pound.
Adding this to the 2 pound gives 2 + 1/2 = 2.5 pounds of ground turkey.
Hence, 2.5 pounds of ground turkey.
Learn more about Ounces at:
https://brainly.com/question/19387548
#SPJ4
Please answer! Will give brainliest!
The required linear functions are A(t) = 50t + 100 and B(t) = 25t + 200 which are represented in the attached graph. Company A is cheaper if the time is less than 4 hours.
As per the given question, we can write the linear functions as:
A(t) = 50t + 100
B(t) = 25t + 200
We can determine time t when both companies charge the same rate by equating the two equations.
50t + 100 = 25t + 200
Subtract 25t from both sides and subtract 100 from both sides
25t = 100
Divide both sides by 25
t = 4
At 4 hours both companies charge the same rate. So Company A is cheaper if the time is less than 4 hours.
After 4 hours, company B is cheaper.
Since both functions are linear, we only need two points to plot each one onto a graph.
Thus, the required linear functions are A(t) = 50t + 100 and B(t) = 25t + 200 which are represented in the attached graph.
Learn more about the Linear functions here:
https://brainly.com/question/13738061
#SPJ1