Stefan said that the y-intercept for the graph of the function f(x)=3log(x−7)+1 is 1. He also said that as x approaches positive infinity, the graph of f(x) approaches positive infinity. Describe which of Stefan's statements, if any, are incorrect, and, if so, correct the statements.

Answers

Answer 1

Answer:

see below

Step-by-step explanation:

f(x)=3log(x−7)+1

There is no y intercept

log (x) does not intercept the y axis.  This shifts the function 7 units to the right so the graph will not intercept the y axis

Answer 2

Answers:

His first statement is incorrect

His second statement is correct.

======================================

Explanation:

The first statement is incorrect because plugging x = 0 into f(x) leads to

f(x) = 3*log(x-7)+1

f(0) = 3*log(0-7)+1

f(0) = 3*log(-7)+1

We stop here because we cannot take the log of a negative number (unless you want a complex number but that's for another time). This means that x = 0 is not in the domain. The domain is x > 7 to ensure that x-7 > 0. That way we avoid taking the log of a negative number, and taking the log of zero as well.

The vertical asymptote is at x = 7 and the log curve is entirely to the right of it, so there's no way it's reaching the y axis.

Simply put: there is no y intercept for this function.

---------------------

The second statement is correct.

The function y = log(x) has y go off to infinity when x does.

The same applies to y = 3log(x) and y = 3log(x-7) and y = 3log(x-7)+1

We can say it "rises to the right" as another way of describing part of the end behavior.

A graph can confirm this as shown below.

Stefan Said That The Y-intercept For The Graph Of The Function F(x)=3log(x7)+1 Is 1. He Also Said That

Related Questions

PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS

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It would be closest to C (7,-9)

Which polygon has fewer than five lines of symmetry?

Answers

Answer:

Regular Polygons

Step-by-step explanation:

In a factory 80 workers were female and 120 male what was the percentage of female workers?​

Answers

Answer: Percentage of female workers = 40%

Step-by-step explanation: No of Female workers = 80

                                             No of Male workers = 120

                                             Total No of workers = 120+80= 200

                                             percentage of female workers =80 of 200%= 40

What type of number -75 A)rational number B)irrational C) integer D) whole number E)natural number. Reply quickly

Answers

Answer:

Rational number

Step-by-step explanation:

Hope this helps

Answer:

Your answer is: A) Rational

A rational number is any integer, fraction, terminating decimal, or repeating decimal.

Step-by-step explanation:

Hope this helped : )

If the skyscraper is 952 feet high, approximately how long will it take for the baseball to hit the ground? (Estimate your answer to one decimal place.)​

Answers

The function of the baseball is a quadratic function

The baseball hits the ground after 7.7 seconds

How to determine when the baseball hits the ground?

The function is given as:

h(t) = -16t^2 + v0t + h0

Where:

v0 = 0 --- the initial velocity

h0 = 952 -- the height of the skyscraper

So, we have:

h(t) = -16t^2 + 952

When the baseball hits on the ground, h(t) = 0.

So, we have:

-16t^2 + 952 = 0

Collect like terms

-16t^2 =- 952

Divide both sides by -16

t^2 =59.5

Take the square root of both sides

t =7.7

Hence, the baseball hits the ground after 7.7 seconds

Read more about quadratic functions at:

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a triangle has an area of 68 ft and a height of 16 ft what is the length of the base​

Answers

Answer:

8.5

Step-by-step explanation:

First we need to know the formula is BxH/2 for triangles. First we would do 68x2=136. Then we would do 136/16 which would give you 8.5! Hope this helps!

A triangle having area of 68 ft and a height of 16 ft, the length of the base for a triangle is, 8.5 ft

What is the area?

An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².

Given that,

a triangle has an area of 68 ft

a height of 16 ft

the length of the base​ = ?

Area of triangle = 1/2×base×height

                    68 = 1/2×base×16

                base =  8.5 ft

Hence, the length of the base is 8.5 ft

To learn more about Area check:

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Select the correct answer from each drop-down menu.

Answers

Answer:

x = 95 , y = 147 , z = 128

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the two opposite interior angles.

x is an exterior angle of the triangle , then

x = 45 + 50 = 95

vertex of triangle ( with x in it ) = 180 - 95 - 52 = 180 - 147 = 33

the vertex and y are adjacent angles on a straight line and sum to 180 , then

y = 180 - 33 = 147

z is an exterior angle of the triangle , then

z = 95 + 33 = 128

After 1 year, $50,000 deposited in a savings account with simple interest had earned $4,000 in interest. What was the interest rate? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years. ​

Answers

Answer:

the interest rate should be 8% let me know if u want me to explain it

The Starlight Bowling Alley charges $6 to rent shoes and $8 per game. Cameron has
only $42 to spend. Which inequality represents this scenario if X represents the
number of games Cameron can play?

Answers

Hmmmmmmmmmmmmmm ummmmmmmmm hmmmmmmmmmmm..

Answer:

4.5 Games

Step-by-step explanation:

42 Minus 6 (shoes)= 36

36 divided by 8 (each game) would equals 4.5

What is the slope in this equation

Answers

2, rise over run is 2/1 which means the slope is 2

If f(x) = 7 4x and g (x) = startfraction 1 over 2 x endfraction, what is the value of (startfraction f over g endfraction) (5)? eleven-halves startfraction 27 over 10 endfraction 160 270

Answers

The value of the function [tex]\frac{f}{g} (5)[/tex] is 270.

Given functions are:

[tex]f(x) = 7+4x\\\\g(x) = \frac{1}{2x}[/tex]

What is the  [tex]\frac{f}{g} (x)[/tex] ?

[tex]\frac{f}{g} (x)[/tex] is the ratio of functions f(x) and g(x) i.e. [tex]\frac{f(x)}{g(x)}[/tex].

So, [tex]\frac{f}{g} (x) =\frac{7+4x}{\frac{1}{2x} }[/tex]

[tex]\frac{f}{g} (x) =2x(7+4x)[/tex]

[tex]\frac{f}{g} (5) =2*5(7+4*5)[/tex]

[tex]\frac{f}{g} (5) =270[/tex]

Therefore, the value of the function [tex]\frac{f}{g} (5)[/tex] is 270.

To get more about functions visit:

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Answer:

270

Step-by-step explanation:

edge2022

Answer number 2 and 3 please

Answers

Answer:

c

Step-by-step explanation:

Here are the answers

1. Not sufficient sides
2. c
3. b
4. a
5.1ft
6. 15m
7. 31.4in

Hope this helps!

5.023 x 10^10
Write this out as a normal number.​

Answers

Answer:5.023E10

Step-by-step explanation:

please help me which is a function and why

Answers

Answer:

576

Step-by-step explanation:

-67+ r7  

Question: Researchers in Pakistan wanted to better understand the effects of anthracycline (a chemotherapeutic drug) on the hearts of young children. More information on the details of their study can be found here: https://datadryad.org/stash/dataset/doi:10.5061/dryad.cg849
((The data set can be downloaded. After going to the website, the download is to the right)).

One variable the researchers calculated in these children was the E/A ratio. The E/A ratio is a measurement that reflects the health of the heart. The (E) velocity is greater than the late (A) velocity in a healthy heart. Particularly low or particularly high elevated E/A ratios indicate signs of heart issues.


The mean E/A ratio of the 110 patients in the study was 1.35. The standard deviation was 0.33.


1. One patient had an E/A ratio of 0.73. What is the z-score for this patient?


2. Assuming the population of E/A ratio scores is approximately normally distributed, what's the probability that a randomly selected person has a smaller E/A ratio than the patient in question 1?


3. Another patient had an E/A ratio of 1.96. What's the z-score for this patient? What's the probability that a randomly selected patient has a higher E/A ratio?


4. Which patient has a more extraordinary E/A ratio? Why? Be sure to refer to the z-scores to support your answer.

Answers

Using the normal distribution, it is found that:

1. His z-score was of Z = -1.88.

2. There is a 0.0301 = 3.01% probability that a randomly selected person has a smaller E/A ratio than the patient in question 1.

3. Z-score of z = 1.85, there is a 0.0322 = 3.22% probability that a randomly selected patient has a higher E/A ratio.

4. Due to the higher absolute value of the z-score, the first patient had a more extraordinary result.

Normal Probability Distribution

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem:

The mean is of [tex]\mu = 1.35[/tex].The standard deviation is of [tex]\sigma = 0.33[/tex].

Item 1:

Considering his ratio, we have that X = 0.73, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{0.73 - 1.35}{0.33}[/tex]

[tex]Z = -1.88[/tex]

His z-score was of Z = -1.88.

Item 2:

The probability is the p-value of Z = -1.88, hence, there is a 0.0301 = 3.01% probability that a randomly selected person has a smaller E/A ratio than the patient in question 1.

Item 3:

Score of X = 1.96, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1.96 - 1.35}{0.33}[/tex]

[tex]Z = 1.85[/tex]

The probability is 1 subtracted by the p-value of Z = 1.85, hence, 1 - 0.9678 = 0.0322 = 3.22% probability that a randomly selected patient has a higher E/A ratio.

Item 4:

Due to the higher absolute value of the z-score, the first patient had a more extraordinary result.

More can be learned about the normal distribution at https://brainly.com/question/24663213

Grace Charges $12 An Hour To Babysit And an Additional $20 for Homework help Write an Expression that can be used to find the total amount of money Grace makes for an hour
Plaese help

Answers

Answer:

12h+20=M

Where H=hours babysitting and M= money made or total amount

in this case since it's only an hour the equation would be 12(1)+20=M

12*1=12 and 12+20=32 so in the one hour with homework help would give you 32=M just for one hour.

Note that the 20 never changes considering it's only the charge for helping with homework and not over an hour.

But since this only asked for an hour and never specified if it was with the homework help here's this

12h=M

Step-by-step explanation:

Hope this helped.

Solve for x.
What is the solution for x in the equation?

please help.

A.

B.

C.

D.

Answers

X=4 The answer is A

Multiply the sides by 3 to get no fractions

Answer:

B

Step-by-step explanation:

5/3x + 4 = 2/3x

5/3x - 2/3x = - 4

x= - 4

How is the product of 2 and –5 shown using integer tiles? 2 positive tiles and 5 negative tiles. 2 negative tiles and 5 positive tiles. 5 negative tiles and 5 negative tiles. 5 positive tiles and 5 positive tiles.

Answers

Answer:

C

Step-by-step explanation:

5 negative tiles and 5 negative tiles.

The product of 2 and - 5 is shown in 'option 3' with 5 negative tiles and 5 negative tiles.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

The product of 2 and - 5.

After multiply, we get;

⇒ 2 × - 5 = - 10

Thus, The correct option is,

⇒ 5 negative tiles and 5 negative tiles.

Learn more about the multiplication visit:

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Question 2 please fas

Answers

Answer:

a = 3, b = 2

Step-by-step explanation:

It is given that both the polynomials are equal.

Therefore, h(x) = k(x)

[tex] {x}^{3} + (a + b) {x}^{2} - 4x + 2 \\ = {x}^{3} + 5 {x}^{2} - (2a - b)x + 2 \\ \\ equating \: like \: terms \: on \: both \: sides \\ (a + b) {x}^{2} = 5 {x}^{2} \\ \implies \: a + b = 5.....(1) \\ \\ - (2a - b)x = - 4x \\ 2a - b = 4....(2) \\ \\ adding \: equations \: (1) \: and \: (2) \\ \\ 3a = 9 \\ \implies \: a = \frac{9}{3} \\ \huge \red{ \boxed{\implies \: a = 3}} \\ \\ substituting \: a = 3 \: in \: equation \: (1) \\ 3 + b = 5 \\ \implies \: b = 5 - 3 \\ \huge \purple{ \boxed{ \implies b = 2}}[/tex]

The area of the cross-section of this cuboid is 7 cm2. The cuboid is 4 cm long.

Answers

7 cm squared * 4 cm = 28 cm cubed

A dinner plate is in the shape of an isosceles right triangle, the leg is 13 inches. What is the perimeter of the plate, round your answer to the nearest tenth?

Answers

Answer: 18.4 inches

Step-by-step explanation:

Help ME PLEASE EXPLAIN HURRY!!!!!
Find the value of x.

Answers

Answer: 38

Step-by-step explanation: this is a 90 degree angle and 90-52= 38

c) What is the value
of the digit 7 in the number 4.7237 as a fraction

Answers

Answer:

7/10, 7/10,000

Step-by-step explanation:

There are two digits 7.

The one to the left is in the tenths place, so its value is 7/10.

The one tot eh right is in the ten-thousandths place, so its value is 7/10,000.

Answer:

THE ONE IN THE TENTHS PLACE WOULD BE 7/10

THE ONE N THE MILLOINTHS PLACE WOULD BE 7/1,000,000

Step-by-step explanation:

Good Luck!

100 POINTS!!!

The y-intercept of a function can be found by:

A. Making x = 0

B. Making y + 0

C. Making x = 2

D. Making y = 2

EXPLAIN

Answers

Answer:

making x=0

Step-by-step explanation:

it gives you the points where the point intersects the y-axis

Answer:

A: Making x = 0

Step-by-step explanation:

The y-intercept of a function is where x is zero (i.e. [tex]f(0)[/tex])

1+1+1+1+1+(18+18463)+496464+94643448=​

Answers

95,158,398

THAT SHOULD BE DA ANSWER

Answer:

It guess it should be 95158398

ASAP ! GOD BLESS U!!!

Answers

Answer:

24 square metres

Step-by-step explanation:

Its basic math. You do 4 x 6 and you get the area.

Please help me solve this ! Which figure can be formed from the net?

Answers

Answer:

A

Step-by-step explanation:

It is th eonly one with a asquare base and it maches the net.

Have an amazing day!

PLEASE RATE!

Option A is correct!

How??

First of all, it's base is square just like the net. The net in option D also has a square base.Now, Confusion is there that which one is correct?To understand that, look at the dimensions. The dimensions of Figure in Option A matches the net completely.. Hence, it is the correct option!!~

Elsa 65 miles per hour for 162. 5 miles how many hours

Answers

Answer:

2:29:32

Step-by-step explanation:

time = distance/speed= 162mi/65

=162/65 =2.49231

=2 hours 29 minutes 32 seconds

=02:29:32 (hh:mm:ss)

Hope this helps!

The 4th and the last terms of an A.P. are 11 and 89 respectively. If there are 30 terms in the A.P., find the A.P. and its 23rd term.​

Answers

[tex]\underline{\underline{\large\bf{Given:-}}}[/tex]

[tex]\red{\leadsto}\:[/tex][tex]\textsf{} [/tex][tex]\sf Number \: of \:terms \: in \: A.P,n = 30[/tex]

[tex]\red{\leadsto}\:[/tex][tex]\textsf{} [/tex][tex]\sf Fourth \: term ,a_4 = 11 [/tex]

[tex]\red{\leadsto}\:[/tex][tex]\textsf{} [/tex][tex]\sf last\:term, a_{30} = 89 [/tex]

[tex]\underline{\underline{\large\bf{To Find:-}}}[/tex]

[tex]\orange{\leadsto}\:[/tex][tex]\textsf{ } [/tex][tex]\sf The \: A.P. [/tex]

[tex]\orange{\leadsto}\:[/tex][tex]\textsf{ } [/tex][tex]\sf 23rd\: term, a_{23} [/tex]

[tex]\\[/tex]

[tex]\underline{\underline{\large\bf{Solution:-}}}\\[/tex]

The nth term of A.P is determined by the formula-

[tex]\green{ \underline { \boxed{ \sf{a_n = a+(n-1)d}}}}[/tex]

where

[tex]\sf a = first \:term[/tex][tex]\sf a_n = nth \: term[/tex][tex]\sf n = number \:of \:terms [/tex][tex]\sf d = common \: difference [/tex]

Since ,

[tex]\sf a_4 = 11 [/tex]

[tex]\longrightarrow[/tex] [tex]\sf a+(4-1) d= 11 [/tex]

[tex]\longrightarrow[/tex] [tex]\sf a+3d= 11\_\_\_(1) [/tex]

[tex]\sf a_{30}= 89 [/tex]

[tex]\longrightarrow[/tex] [tex]\sf a+(30-1)d=89[/tex]

[tex]\longrightarrow[/tex][tex]\sf a+29d= 89\_\_\_(2)[/tex]

Subtracting equation (1) from equation(2)

[tex]\begin{gathered}\\\implies\quad \sf a+29d-(a+3d) = 89-11 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a+29d-a-3d = 78 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a-a+29d-3d = 78 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf 26d = 78 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf d = \frac{78}{26} \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf d = 3 \\\end{gathered} [/tex]

Putting the value of d in equation (1) -

[tex]\begin{gathered}\\\implies\quad \sf a+3(3) = 11 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a = 11-9 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a = 2 \\\end{gathered} [/tex]

First term of A.P, a = 2

Second term of A.P.,[tex]\sf a_2= 2+(2-1)\times 3[/tex]

[tex]\quad\quad\quad\sf =2+3[/tex]

[tex]\quad\quad\quad\sf =5 [/tex]

Third term of A.P.,[tex]\sf a_3= 2+(3-1)\times 3[/tex]

[tex]\quad\quad\quad\sf =2+6[/tex]

[tex]\quad\quad\quad\sf =8 [/tex]

[tex]\longrightarrow[/tex]Thus , The A.P is 2,5,8,. . . . . .

Now,

[tex]\begin{gathered}\\\implies\quad \sf a_n = a+(n-1)d \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a_{23 }= 2+(23-1)\times 3 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a_{23} = 2+22 \times 3 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a_{23} = 2+66 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a_{23} = 68 \\\end{gathered} [/tex]

[tex]\longrightarrow[/tex]Thus , 23rd term is 68.

The balanced equation below shows the products that are formed when pentane (c5h12) is combusted. c5h12 8o2 right arrow. 5co2 6h2o what is the mole ratio of oxygen to pentane? 1:6 6:8 8:1 5:8

Answers

The mole ratio of the oxygen to pentane will be 8:1

What is the mole ratio?

A mole ratio is ​a ratio between the amounts in moles of any two compounds involved in a chemical reaction

A chemical equation is said to be a balanced chemical equation if it has an equal number of all the constituent atoms on both sides of the reaction arrow.

The balanced chemical reaction for the combustion of pentane is as follows:

[tex]\rm C_5H_{12}+8O_2--- > 5CO_2+6H_2O[/tex]

From the above-balanced chemical equation, it is clear that 1 mol of [tex]C_5H_{12}[/tex] reacts with 8 moles  [tex]O_2[/tex] to form 5 moles of [tex]CO_2[/tex]

Thus the mole ratio of the oxygen to pentane will be 8:1

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Answer:

8:1

Step-by-step explanation:

edge

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