Answer:
2x+11
Step-by-step explanation:
2(x+3)+5
Distribute
2x+ 6 +5
Combine like terms
2x+11
Answer:
2x + 11
Step-by-step explanation:
First distribute 2 to the x + 3
2x + 6 + 5
Combine the constants
6+5=11
2x + 11
The simplified expression is 2x + 11
find the perimeter of of the shaded figure. ? units
Answer:
38 Units
Step-by-step explanation:
7 each down each side
10 each across top and bottom
2 more for each indent on bottom
7+7+10+10+2+2
14+20+4
38
The function h(t) = -4.92f^2 + 17.69f + 575 is used to model the height of an object being tossed from a tall building, where h(t) is the height in meters and t is the time in seconds. What are the domain and range?
Answer:
rounded to 3 decimal places ...
domain: [0, 12.757]range: [0, 590.901]Step-by-step explanation:
The function can be put into vertex form:
h(t) = -4.92(t -(1769/984))^2 +575 +4.92(1769/984)^2
h(t) ≈ -4.92(t -1.79776)^2 +590.90122
The value of h(t) is zero for ...
t = √(590.90122/4.92) +1.79776 ≈ 12.75686
For practical purposes, the domain of the function is those values of t between the time the object is tossed and the time it hits the ground. That is, the domain is ...
0 ≤ t ≤ 12.75686
The range is the set of useful vertical heights, so extends from 0 to the maximum height, given by the vertex.
The range is 0 ≤ h(t) ≤ 590.90122.
_____
Alternate interpretation of the question
The function h(t) is defined for all values of t, so that could be considered the domain.
The function h(t) only gives values less than its vertex value, so the range could be considered to extend from negative infinity to that maximum.
Which of the following best describes the slope of the line below?
PLSSS HELP
The slope is zero. Slope formula is Y=mx+b and since B is 1.5 and it is a straight line, Y=mx+1.5. What plus 1.5 is 1.5? 0. Hope this helps.
1. An LG Dishwasher, which costs $800, has a 20% chance of needing to be replaced in the first 2 years of purchase. A two-year extended warrantee costs $112.10 on a dishwasher. What is the expected value of the extended warranty assuming it is replaced in the first 2 years?
2. Approximately 10% of all people are left-handed. Consider a grouping of fifteen (15) people.
a. State the random variable.
b. Write the probability distribution.
c. Draw a histogram.
d. Describe the shape of the histogram.
e. Find the mean.
f. Find the variance.
g. Find the standard deviation.
Step-by-step explanation:
The expected value of the extended warrant is calculated as follow.
Value of Waranty
= 800 x 20% − 112.10
= 800 x 20/100 − 112.10
= 47.9
The expected value of the extended warranty assuming it is replaced in the first 2 years is given as follow.
Expected value=800-112.10=>687.90
Therefore, required expected value of extended warranty is 687.90
2.
Given information:
Number of Trials (n) = 15
Probability of Success (p) = 0.10
a) Let X represents the number of left-handed people.
b) The probability distribution follows binomial distribution.
X ∼ Binomial distribution
The probability distribution is given as follow.
P(X = x) = ^nCx(p)^x(1 − p)^n − x
c)The histogram is given as follow. (See attachment)
d) The shape of histogram is skewed right.
e) The mean is calculated as follow.
Mean
=n x p
= 15 x 0.10
= 1.5
f) The variance is calculated as follow.
Variance
= n x p x q
= 15 x 0.10 x 0.90
= 1.35
g) The standard deviation is calculated as follow.
Standard deviation
=√n x p x q
=√15 x 0.10 x 0.90
= 1.162
9. ABCD is a square and ABK is an equilateral triangle outside the square,
Find measurment of angle DKC
Answer:
< DKC = [tex]60^{0}[/tex]
Step-by-step explanation:
A square is a quadrilateral that has equal length of side. While an equilateral triangle is one with equal length of sides and equal values of angles.
Given square ABCD and that equilateral triangle ABK is outside the square, both figures share side AB. This shows that the length of the sides of the triangle is the same as the length of the side of the square.
i.e /AD/ = /CD/ = /BC/ = /AB/ = /AK/ = /KB/
Thus, < DKC = [tex]60^{0}[/tex] (property of angles in an equilateral triangle)
What are the factors of 2x + 3x 54? Select two options
2x - 9
2x6
2x + 6
X-6
x+6
Answer:
(2x -9)(x +6)Step-by-step explanation:
Perhaps you're factoring ...
2x² +3x -54
= 2x² +12x -9x -54 . . . . rewrite 3x appropriately
= 2x(x +6) -9(x +6) . . . . factor pairs of terms
= (2x -9)(x +6) . . . . . . . . finish the factoring
The factors are (2x -9) and (x +6).
Bernard bought 8gal of paint. Convert the volume to liters. Round to the nearest tenth
Answer:
In one gallon of paint there are about 3.8 liters so 8 gallons is about 30.3 liters.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
a
Step-by-step explanation:
because as absolute value gets smaller the line gets steeper
r
Please answer this correctly
Answer:
416
Step-by-step explanation:
plz mark brainliest!
Answer:
385
Step-by-step explanation:
use l x w
14x19
16x3
7x10
385
Solve for a.
ab + c = d
Answer:
a=(d-c)/d
Step-by-step explanation:
ab+c=d
ab=d-c
a= (d-c)/b
You are situated 300 feet from the base of Tower Glitz Plaza watching an external elevator descend down the side of the building. At a certain instant the elevator is 500 feet away from you, and its distance from you is decreasing at a rate of 16 ft/sec. How fast is the elevator descending at that instant?
Answer:
18.66 ft/s
Step-by-step explanation:
The distance between you and the elevator is given by:
[tex]h=\sqrt{x^2+y^2}[/tex]
The rate of change for the distance between you and the elevator is given by:
[tex]\frac{dh}{dt}=\frac{dh}{dy}*\frac{dy}{dt}[/tex]
[tex]-16=\frac{dh}{dy}*\frac{dy}{dt}[/tex]
[tex]\frac{dh}{dy}=\frac{d}{dy} (\sqrt{x^2+y^2})\\[/tex]
Applying the chain rule:
[tex]u=x^2+y^2\\\frac{dh}{dy}=\frac{d\sqrt u}{du} *\frac{du}{dy}\\\frac{dh}{dy}=\frac{1}{2\sqrt u} *2y\\\frac{dh}{dy}=\frac{y}{\sqrt {(x^2+y^2)}}[/tex]
Therefore, at x=300 and y = 500, dy/dt is:
[tex]-16=\frac{y}{\sqrt {(x^2+y^2)}}*\frac{dy}{dt}\\-16=\frac{500}{\sqrt {(300^2+500^2)}}*\frac{dy}{dt}\\\frac{dy}{dt}=-18.66\ ft/s[/tex]
The elevator is descending at 18.66 ft/s.
Borland, Inc., has a profit margin of 5.6 percent on sales of $13.6 million. If the firm has debt of $6.4 million and total assets of $9.8 million, what is the firm’s ROA?
Answer:
ROA = 7.77 percent
Step-by-step explanation:
Borland, Inc., has a profit margin of 5.6 percent on sales of $13.6 million
Thus, profit = 5.6% of $13.6 million
profit = 5.6 / 100 * $13.6 million = $0.7616 million
Profit is same as net income
Formula for ROA (return on asset) = net income/ total asset
total asset as given = $9.8 million
Thus, ROA = $0.7616/ $9.8 = 0.0777
ROA in percentage = 0.0777*100 = 7.77
Thus, ROA is 7.77 percent .
A city has 5 new houses for every 7 old houses. If there are 45 new houses in the city, how many old houses are there?
Answer:
63
Step-by-step explanation:
Make a ratio:
5 : 7 = 45 : x
x = 63
J.D. Power and Associates conducts vehicle quality surveys to provide automobile manufacturers with consumer satisfaction information about their products (Vehicle Quality Survey, January 2010 ). Using a sample of vehicle owners from recent vehicle purchase records, the survey asks the owners a variety of questions about their new vehicles, such as those shown below. For each question, state whether the data collected are categorical or quantitative and indicate the measurement scale being used.
a. What price did you pay for the vehicle?
b. How did you pay for the vehicle? (Cash, Lease, or Finance)
c. How likely would you be to recommend this vehicle to a friend? (Definitely Not, Probably Not, Probably Will, and Definitely Will)
d. What is the current mileage?
e. What is your overall rating of your new vehicle? A 110 -point scale, ranging from I for
unacceptable to 10 for truly exceptional, was used.
Answer:
Categorical data includes
b. How did you pay for the vehicle? (Cash, Lease, or Finance)
c. How likely would you be to recommend this vehicle to a friend? (Definitely Not, Probably Not, Probably Will, and Definitely Will)
e. What is your overall rating of your new vehicle? A 1 to 10 point scale, ranging from I for unacceptable to 10 for truly exceptional, was used.
Quantitative data includes
a. What price did you pay for the vehicle?
d. What is the current mileage?
Step-by-step explanation:
Categorical data refers to the kind of data in which the variables are grouped based on a particular quality, ticking a particular box or satisfying some specific requirements.
It uses one or more qualitative property/properties to assign variables into a limited, usually fixed groups or categories. Note that the qualitative property might be a grouped data of numerical values. As long as there are easily separable and recognizable groups, it is categorical data.
This is also called qualitative data.
Quantitative data is a data that is strictly about numerical values. A dataset that consists of numerical values of the members of the dataset. Deals almost exclusively with numbers, usually ungrouped.
So, examining the given datasets one at a time
a. What price did you pay for the vehicle?
The answer to this question is a numerical value and for various customers, it builds up a dataset of strictly numerical values. Hence, this resulting data is a quantitative data.
b. How did you pay for the vehicle? (Cash, Lease, or Finance)
The answers to this question can only take 3 forms; Cash, Lease or Finance, indicating that all the variables in the dataset can only take on limited, fixed number of groups/categories. Hence, this dataset is a categorical data.
c. How likely would you be to recommend this vehicle to a friend? (Definitely Not, Probably Not, Probably Will, and Definitely Will)
The answers to this question too can take on 4 limited, fixed categories or groups, Hence, it's easy to see that this dataset is also categorical data.
d. What is the current mileage?
The answer to this question is a numerical value. Various answers from numerous persons would lead to a data of numbers. Hence, this is a quantitative data.
e. What is your overall rating of your new vehicle? A 1 to 10 point scale, ranging from I for unacceptable to 10 for truly exceptional, was used.
Limited, fixed categories or groups (10 groups) are also available for this data, hence, it is easily a categorical data.
Hope this Helps!!!
The local swim team is considering offering a new semi-private class aimed at entry-level swimmers, but needs at minimum number of swimmers to sign up in order to be cost effective. Last year's data showed that during 8 swim sessions the average number of entry-level swimmers attending was 15. Suppose the instructor wants to conduct a hypothesis test. The alternative hypothesis for this hypothesis test is: "the population mean is less than 15". The sample size is 8, LaTeX: \sigmaσ is known, and alpha =.05, the critical value of z is _______. Group of answer choices
Answer:
The signficance level is 0.05 and then based in the alternative hypothesis we can find a critical value who accumulates 0.05 of the area in the normal standard curve in the left and we got:
[tex] z_{\alpha/2}= -1.64[/tex]
Step-by-step explanation:
[tex]n=8[/tex] the same size given
[te]\sigma[/tex] the population deviation is known
For this case we want to test if the population mean is less than 15 and that represent the alternative hypothesis and the complement would be the null hypothesis. So then the system of hypothesis are:
Null hypothesis: [tex]\mu \geq 15[/tex]
Alternative hypothesis: [tex]\mu <15[/tex]
The signficance level is 0.05 and then based in the alternative hypothesis we can find a critical value who accumulates 0.05 of the area in the normal standard curve in the left and we got:
[tex] z_{\alpha/2}= -1.64[/tex]
my last question and im done, please help!
Answer:
2 acute and one right.
Step-by-step explanation:
plz mark brainliest!
Answer:
2 acute 1 right, you asked for ASAP so theres no explanation
You cant mix right and obtuse, and you cant have more than 1 obtuse in a triangle. There has to be at least 2 acute angles.
Suppose that weekly income of migrant workers doing agricultural labor in Florida has a distribution with a mean of $520 and a standard deviation of $90. A researcher randomly selected a sample of 100 migrant workers. What is the probability that sample mean is less than $510
Answer:
[tex] z=\frac{510-520}{\frac{90}{\sqrt{100}}}= -1.11[/tex]
And we can find the probability using the normal standard distribution table and with the complement rule we got:
[tex]P(z<-1.11)= 0.1335[/tex]
Step-by-step explanation:
For this problem we have the following parameters:
[tex] \mu = 520, \sigma = 90[/tex]
We select a sample size of n =100 and we want to find this probability:
[tex] P(\bar X <510) [/tex]
The distribution for the sample mean using the central limit theorem would be given by:
[tex]\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})[/tex]
And we can solve this problem with the z score formula given by:
[tex] z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score formula we got:
[tex] z=\frac{510-520}{\frac{90}{\sqrt{100}}}= -1.11[/tex]
And we can find the probability using the normal standard distribution table and with the complement rule we got:
[tex]P(z<-1.11)= 0.1335[/tex]
Which of the following best forms the figure shown
Answer:
2 rays that meet at an endpoint
Step-by-step explanation: A ray starts with a dot, or point and continues on forever with an arrow. There are two rays in that drawing that start at the same endpoint.
Answer:
2 rays that meet at an endpoint.
Step-by-step explanation:
A ray is straight but has one endpoint and the other end go on infinitely.
A line is straight and goes on infinitely.
A line segment is straight and has two endpoints.
The picture shows two rays meeting at an endpoint.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
D. It would be less steep
Step-by-step explanation:
The first graph moves at a rate of 5/1 which is a greater fraction than 3/4
The second graph is shallow due to the close points in x and y that are able to be conducted The first Graph rapidly increases at a way higher rate making it VERY steepWhile both are linear the second strays away in terms of plot lines!Please help!
When representing a frequency distribution with a bar chart, which of these bars will be the shortest?
A. A bar representing a frequency of 24
B. A bar representing a frequency of 48
C. A bar representing a frequency of 36
D. A bar representing a frequency of 12
Answer:
D
Step-by-step explanation:
12 is lowest.
A bar chart is one of the most commonly used representations or visually translate groups of data.
We have given that,
When representing a frequency distribution with a bar chart.
What is the frequency distribution?
frequency distribution, a graph or data set organized to show the frequency of occurrence of each possible outcome of a repeatable event observed many times.
It is drawn in such a way that the x-axis of the graph would represent the items and the y-axis will be for the frequency.
Out of the choices given, the shortest among the bars will be that would frequency is only 36.
Hence, the answer to this item is the letter C.
To learn more about the frequency distribution visit:
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how many significant numbers in 34.6209
Answer:
6
Step-by-step explanation:
Consider the following.x = t − 2 sin(t), y = 1 − 2 cos(t), 0 ≤ t ≤ 8πSet up an integral that represents the length of the curve.8π0 dtUse your calculator to find the length correct to four decimal places.
The length of the parametric curve (call it C ) is given by
[tex]\displaystyle\int_C\mathrm ds=\int_0^{8\pi}\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]
We have
[tex]x=t-2\sin t\implies\dfrac{\mathrm dx}{\mathrm dt}=1-2\cos t[/tex]
[tex]y=1-2\cos t\implies\dfrac{\mathrm dy}{\mathrm dt}=2\sin t[/tex]
Now,
[tex]\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2=5-4\cos t[/tex]
so that the arc length integral reduces to
[tex]\displaystyle\int_0^{8\pi}\sqrt{5-4\cos t}\,\mathrm dt[/tex]
which has an approximate value of 53.4596.
An observer at the top of a 532 foot cliff measures the angle of depression from the top of the cliff to a point on the ground to be 4 degrees. What is the distance from the base of the cliff to the point on the ground? Round to the nearest foot.
Answer:
Distance from the base of the cliff to the point on the ground = 7608 feet
Step-by-step explanation:
Given: Height of the cliff is 532 feet, angle of depression from the top of the cliff to a point on the ground is equal to 4 degrees.
To find: distance from the base of the cliff to the point on the ground
Solution:
In ΔABC,
[tex]\angle ACB=4^{\circ}[/tex] (Alternate interior angles)
For any angle [tex]\theta[/tex], [tex]\tan \theta =[/tex] side opposite to angle/side adjacent to angle
[tex]\tan C=\frac{AB}{BC}[/tex]
Put [tex]AB=532\,,\,\angle C=4^{\circ}[/tex]
[tex]\tan 4^{\circ}=\frac{532}{BC}\\\\BC=\frac{532}{\tan 4^{\circ}}\\\\=7607.95\\\\\approx 7608\,\,feet[/tex]
Distance from the base of the cliff to the point on the ground = 7608 feet
3/11 ÷ 3/11
and
9/10 ÷ 3/5
PLZ HELP ME
Answer:
3/11 divided by 3/11 is 1
9/10 divided by 3/5 is 1 1/2 (1.5)
Step-by-step explanation:
Answer:
1
1.5
Step-by-step explanation:
3/11 ÷ 3/11 = 1
9/10 ÷ 3/5 = 3/2 ≈ 1.5
A ball travels on a parabolic path in which the height (in feet) is given by the expression $-25t^2+75t+24$, where $t$ is the time after launch. At what time is the height of the ball at its maximum?
Answer:
The height of the ball is at it's maximum 1.5 units of time after launch.
Step-by-step explanation:
Suppose we have a quadratic function in the following format:
[tex]h(t) = at^{2} + bt + c[/tex]
If t is negative, the maximu value of h(t) will happen at the point
[tex]t_{MAX} = -\frac{b}{2a}[/tex]
In this question:
[tex]h(t) = -25t^{2} + 75t + 24[/tex]
So
[tex]a = -25, b = 75, c = 24[/tex]
Then
[tex]t_{MAX} = -\frac{b}{2a} = -\frac{75}{2*(-25)} = 1.5[/tex]
The height of the ball is at it's maximum 1.5 units of time after launch.
The width of the rectangle is 2 more than the length. The area of the rectangle is 63 square inches. How long is the width?
Answer:
9 inches
Step-by-step explanation:
Area of rectangle= length ×width
Let the length of the rectangle be x inches.
Width of rectangle= (x +2) inches
since the width is 2 more than the length.
63= x(x+2)
63= x(x) +2x
Bringing constant to one side,
x² +2x -63= 0
(x +9)(x-7) = 0 (factorise)
x+9= 0 or x-7= 0
x= -9 or x= 7
(reject)
width of rectangle
= 7+2
= 9 inches
*We reject x= -9 since the length of the rectangle cannot be a negative number.
Determine whether the study depicts an observational study or an experiment.
A study is conducted to determine if there is a relationship between stomach cancer and alcohol consumption.alcohol consumption. Everyone treated at a hospital for stomach cancer was asked Everyone treated at a hospital for stomach cancer was asked about their alcohol consumption.
a. The study is an experiment because the researchers control one variable to determine the effect on the response variable.
b. The study is an observational study because the researchers control one variable to determine the effect on the response variable.
c. The study is an observational study because the study examines individuals in a sample, but does not try to influence the response variable.
d. The study is an experiment because the study examines individuals in a sample, but does not try to influence the variable of interest.
Answer:
Option c
Step-by-step explanation:
The study is an observational study. An observational study is made when the researchers collect data based on what they see, hear or observe without any form of manipulation or treatment plan from the researchers. Thus, in this case, the study is an observational study because the study examines individuals in a sample, but does not try to influence the response variable/influence their responses.
Venera sent a chain letter to her friends, asking them to forward the letter to more friends.
The relationship between the elapsed time t, in months, since Venera sent the letter, and the number of
people, P(t), who receive the email is modeled by the following function:
3t+7
P(t) = 2
Complete the following sentence about the monthly rate of change in the number of people who receive
the email.
Round your answer to two decimal places.
Every month, the number of people who receive the email is multiplied by a factor of
Answer:
It is multiplied by a factor of 8
Step-by-step explanation:
Every month, the number of people who receive the email is multiplied by a factor of 8.
What is an exponent?Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as
y = a(b)ˣ
Venera sent a chain letter to her friends, asking them to forward the letter to more friends.
The relationship between the elapsed time t, in months, since Venera sent the letter, and the number of people, P(t), who receive the email is modeled by the following function:
[tex]\rm P(t) = 2^{3t+7}[/tex]
Every month, the number of people who receive the email is multiplied by a factor will be
For t = 2, we have
P(2) = 2³⁽²⁾⁺⁷
P(2) = 2¹³
For t = 3, we have
P(3) = 2³⁽³⁾⁺⁷
P(3) = 2¹⁶
Then the factor will be
⇒ P(3) / P(2)
⇒ 2¹⁶ / 2¹³
⇒ 2³
⇒ 8
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Data on return-to-pay ratios was collected from CEOs of companies within both the low-tech industry and the consumer products industry.
Low-Tech Consumer Products
Sample size 14 12
Sample mean 157 218
Sample Variance 1563 1602
Assume population variances are unequal.
(a) The point estimate of the difference between the means of the two populations is
(b) The standard error for the difference between the two means is
(c) The correct distribution to use is :
t-distribution with 26 degrees of freedom
t-distribution with 23 degrees of freedom
normal distribution
t-distribution with 24 degrees of freedom
Answer:
Step-by-step explanation:
The confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
Where
x1 = sample mean of low-tech industry
x2 = sample mean of consumer products industry
s1 = sample standard deviation low-tech industry
s2 = sample standard deviation for consumer products industry
n1 = number of samples of low-tech industry
n2 = number of samples of consumer products industry
a) x1 - x2 is the point estimate of the difference between the means of the two populations
Therefore,
Point estimate = 157 - 218 = - 61
b) the formula for standard error is expressed as
√(s1²/n1 + s2²/n2)
Variance = standard deviation²(s²)
s1² = 1563
s2² = 1602
Standard error = √(1563²/14 + 1602²/12) = 623.2
c) Degree of freedom =
(n1 - 1) + (n2 - 1) = (14 - 1) + (12 - 1) = 24
t-distribution with 24 degrees of freedom
According to the data given, we have that:
a) 61
b) 15.65
c) t-distribution with 24 degrees of freedom
Item a:
The point estimate is the difference between the two sample means, hence:
218 - 157 = 61.
Item b:
For each sample, the standard errors are:
[tex]s_l = \sqrt{\frac{1563}{14}} = 10.57[/tex]
[tex]s_h = \sqrt{\frac{1602}{12}} = 11.54[/tex]
For the difference of the two means, it is:
[tex]s = \sqrt{s_l^2 + s_h^2} = \sqrt{10.57^2 + 11.54^2} = 15.65[/tex]
Item c:
Samples of 14 and 12, hence 14 + 12 - 2 = 24 df.
A similar problem is given at https://brainly.com/question/12490448
(a) Use a linear approximation to estimate f(0.9) and f(1.1). f(0.9) ≈ f(1.1) ≈ (b) Are your estimates in part (a) too large or too small? Explain. The slopes of the tangent lines are negative, but the tangents are becoming steeper. So the tangent lines lie below the curve f. Thus, the estimates are too large. The slopes of the tangent lines are negative, but the tangents are becoming steeper. So the tangent lines lie below the curve f. Thus, the estimates are too small. The slopes of the tangent lines are positive, but the tangents are becoming less steep. So the tangent lines lie above the curve f. Thus, the estimates are too large. The slopes of the tangent lines are positive, but the tangents are becoming less steep. So the tangent lines lie above the curve f. Thus, the estimates are too small.
Answer:
(Missing part of the question is attached)
[tex]L(x)=2x+3[/tex]
Estimates are too large.
Step-by-step explanation:
Suppose the only information we know about the function is:
[tex]f(1)=5[/tex]
where the graph of its derivative is shown in the attachment
(a)If the function [tex]f\\[/tex] is differentiable at point [tex]x=1[/tex] , the tangent line to the graph of [tex]f[/tex] at 1 is given by the equation:
[tex]y=f(1) +f'(1)(x-1)[/tex]
So we call the linear function:
[tex]L(x)=f(1) +f'(1)(x-1)[/tex]
We know the [tex]f(1)=5[/tex] as it is given in the question, and [tex]f'(1)=2[/tex] from the graph attached. Substitute in the equation of [tex]L(x)[/tex].
[tex]L(x)=5+2(x-1)\\L(x)=5+2x-2\\L(x)=2x+3\\[/tex]
(b)At x=1, [tex]f'(x)[/tex] is positive but it is decreasing. However. if we draw the tangent lines, we see that the tangent lines are becoming less steeper, so the tangent lines lie above the curve [tex]f[/tex]. Thus, The estimates are too large.
