the number of girls is 75% of the number of boys.There are 28 students altogether. how many are girls and how many are boys?use a tape diagram
Answers
Let x be the number of boys
Let the number of girls be 75% of x = 75x/100
Boys + girls = 28
75x/100 + x = 28
0.75x + x = 28
1.75x = 28
Divide both-side of the equation by 1.75
x = 16
There a
Related Questions
Which equation best represents the volume,V, of this cylinder in terms of π
Answers
Answer:
[tex]V=18.75\pi[/tex]Step-by-step explanation:
The volume of a cylinder is represented by the following expression:
[tex]V=h\cdot\pi\cdot r^2[/tex]Then, in this case for a radius of 2.5 and height of 3:
[tex]\begin{gathered} V=3\cdot\pi\cdot2.5^2 \\ V=6.25\cdot3\cdot\pi \\ V=18.75\pi \end{gathered}[/tex]During 5/8 of the 72 physical education classes, Ethan played games involving running. During how many of this years physical education classes did Ethan have to run?
Answers
Ethan has to run in 45 classes
Here, we want to get the number of games that involved running
Mathematically, what we have to do here is to calculate the number in the fraction
We have this as;
[tex]\frac{5}{8}\text{ of 72 = }\frac{5}{8}\times\text{ 72 = 45}[/tex]John compares the graph of two functions.• The first function was y=3x +4.• The second function fits the values in the table below.22What is the distance between the y-intercepts of the two functions?O A. 5 unitsO B. 6 unitsO C. 4 unitsOD. 3 units
Answers
the y-intercept of a parabola is the y coordinate of the point where does the graph intersect the y-axis.
so from the figure, we can see that the parabola is intersecting the y-axis at (0, -6)
and it is intersecting the x-axis at (3,0)
thus. y-intercept is (0, -6) and x-intercept is (3,0)
that is option D
a shipping tube is shaped like a triangular prism the bases are equilateral triangles with edges of 5 in and a height of 4.3 in the tube is 14in long find the total surface area of the shipping tube
Answers
The figure is a triangular prism and the formular for total surface area of a triangular prism is represented below
[tex]\begin{gathered} \text{surface area = }bh+2ls+lb \\ \text{surface area=}(5\times4.3)+2(14\times5)+(14\times5) \\ \text{surface area=}21.5+140+70 \\ \text{surface area=}231.5in^2 \end{gathered}[/tex]The solid shape is made from a hemisphere and a cone.
The radius of the hemisphere is equal to the radius of the base of the cone.
The cone has a height of 10 cm.
The volume of the cone is 270π cm3.
Work out the total volume of the solid shape in cm³
.
Give your answer in terms ofπ .
Answers
The volume of the solid shape is 756 cm³ .
What is the volume of the solid shape?The volume of the solid shape is the sum of the volume of the hemisphere and the cone.
Volume of the solid shape = volume of the hemisphere + volume of the cone
Volume of the cone = 1/3πr²h
270π = 1/3πr² x 10
r² = (270π x 3) / 10π
r² = 81
r = √81
r = 9
Volume of a hemisphere = (2/3) × r³ × π
Volume of a hemisphere = 2/3 x 9³ × π
Volume of a hemisphere = 486π cm³
Volume of the solid shape = 486π cm³ + 270π cm³ = 756 cm³
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you start on the unit circle at 0 negative one and move 300 degrees counterclockwise which angle in degrees will you end up on the unit circle Answer Choices:30330210120
Answers
By definition, it is important to remember that a circle has 360 degrees.
According to the information given in the exercise, you start at this point on the unit circle:
[tex](0,-1)[/tex]Observe the following picture:
By definition, from the point (0,-1) to the point (1,0) there are 90 degrees.
Therefore, if you move 300 degrees counterclockwise from the point (0,-1), you can subtract 90 degrees from the 300 degrees in order to calculate which angle in degrees will you end up on the unit circle:
[tex]300\degree-90\degree=210\degree[/tex]Therefore, you will end up with 210 degrees.
The answer is: Third option.
Paula started reading a book and read 1/12 of the book on the first day. The next day, she read 1/3 of the book. How much does she still need to read the book?
Answers
ANSWER
7/12
EXPLANATION
We have that Paula first read 1/12 of her book. Then she read, 1/3 of the book.
First, we have to find how much of the book she has read.
We do that by adding the amounts she has read.
That is:
[tex]\begin{gathered} \frac{1}{12}+\frac{1}{3} \\ \frac{1+(4\cdot1)}{12}=\frac{1+4}{12} \\ =\frac{5}{12} \end{gathered}[/tex]Now, to find how much she still has to read, we have to subtract the fraction she has read from 1.
That is:
[tex]\begin{gathered} 1-\frac{5}{12} \\ \Rightarrow\text{ }\frac{12}{12}-\frac{5}{12} \\ =\frac{7}{12} \end{gathered}[/tex]Therefore, she still has to read 7/12 of the book.
Another photo is 20 inches long. How much wood is4needed for the frame? SHOW your WORK.
Answers
Given :
width of frame = 10.5 inches
length of frame = 20.75 inches
The amount of wood that she'll need for each photograph can be determined using the perimeter of the rectangular frame:
Perimeter(P) of rectangular frame:
[tex]\begin{gathered} P\text{ = 2l + 2w} \\ =\text{ 2 }\times\text{ 20.75 + 2}\times\text{ 10.5} \\ =\text{ 62.5 inches} \end{gathered}[/tex]Amount of wood needed in perimeter = 62.5 inches
i need help with this problem its a two step equation -17= -9- 8m
Answers
Mrs. Nolan hired a painter to paint the exterior of her house. It took the painter 3 days to paint her house. The painter agreed to a rate of $23 per hour with a 12-hour unpaid lunch break each day. The table shows when the painter clocked in and out each day.Before taxes, how much money did the painter make
Answers
Given that the painter took three days to paint the exterior of the house in the following timings.
Thursday 7.30 am to 5.15 pm = 9 hours 45 minutes
Friday 7.00 am to 4.40 pm = 9 hours 40 minutes
Saturday 8.30 am to 4.30 pm = 8 hours
Also, it is given that the rate 23 $ per hour, and there is a rest of 1/2 hour lunch break each day.
So total lunch break = 3 x 1/2 hours = 3/2 hours = 1.5 hours = 1 hour 30 minutes
Total working time = 9 hours 45 minutes + 9 hours 40 minutes + 8 hours
= 27 hours 25 minutes
For 1 hour the rate is $ 23
1 hour = $ 23
60 minutes = $ 23
1 minute = $ 23/60
Now we have to subtract the lunchtime from the total time.
Then,
Time for which he was paid = 27 hours 25 minutes - 1 hour 30 minutes
= 25 hours 55 minutes
So,
25 hours = $ 25 x 23 = $ 575
55 minutes = $ 55 x 23/60 = $ 21.08
Hence, the total money he was paid is = $ 575 + $ 21.08 = $ 596.08
Therefore the required answer is $ 596.08
What is mZS? Q 108° P R S m2S = O
Answers
First, we find arc RSP
[tex]\begin{gathered} 108=\frac{1}{2}\cdot RSP \\ \text{RSP}=2\cdot108=216 \end{gathered}[/tex]Arc RSP measures 216°.
Then,
[tex]\begin{gathered} 216+RQP=360 \\ \text{RQP}=360-216=144 \end{gathered}[/tex]Now, we find angle S
[tex]m\angle S=\frac{1}{2}\cdot144=72[/tex]Hence, angle S measures 72°.find the mean, median and mode of the following distribution:3, 5, 3, 4, 6, 8, 7, 9, 15
Answers
Given:
[tex]3,5,3,4,6,8,7,9,15[/tex][tex]\begin{gathered} \text{Mean}=\frac{3+5+3+4+6+8+7+9+15}{9} \\ \text{Mean}=\frac{60}{9} \\ \text{Mean}=6.6667 \end{gathered}[/tex]Ascending order : 3,3,4,5,6,7,8,9,15
Median : 5th term is the median
[tex]\text{Median}=6[/tex][tex]\text{Mode}=3[/tex]Karlo has $7,300 saved for a down payment towards the $26,700 car he wants to buy. He needs to have adown payment of at least 40% in order to get the lowest interest rate. How much more money would he need tosave?
Answers
The Solution:
Given:
The cost of car Karlo wants to buy is $26,700.
Karlo has saved = $7,300
We are required to find how much Karlo need to save more for the car.
Step 1:
Down payment of 40% of the total cost of the car is:
[tex]Down\text{ payment amount}=\frac{40}{100}\times26700=40\times267=\text{\$}10680[/tex]Step 2:
Subtract $10680 from $26700.
[tex]Amount\text{ to save more }=26700-10680=\text{\$}16,020[/tex]Therefore, the correct answer is $16,020.
a line segment has the endpoint T(2,4) and the midpoint of (3,6.5). find the coordinates of the other point B.
Answers
a line segment has the endpoint T(2,4) and the midpoint of (3,6.5). find the coordinates of the other point B.
we know that
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]In this problem we have
M=(3,6.5)
(x1,y1)=T(2,4)
(x2,y2)=B
substitute the given values in the formula above
[tex](3,6.5)=(\frac{2+x2}{2},\frac{4+y2}{2})[/tex]Find the value of x2 coordinate
3=(2+x2)/2
x2+2=6
x2=6-2=4
Find the value of y2 coordinate
6.5=(4+y2)/2
y2+4=13
y2=13-4=9
therefore
the coordinates of point B(4,9)
Jake drives Go-Karts at an average speed of 2.75 laps per minute. If the relationship between the number of laps completed and numberof minutes varies directly, how long would it take him to complete 41.25 laps?O A. 0.07 minutesOB. 15 minutesO C. 38.5 minutesO D. 113 minutes
Answers
Since the number of minutes and number of laps completed varies directly, therefore if 2.75 laps correspond to 1 min then:
[tex]\frac{2.75\text{laps}}{1\min}=\frac{41.25\text{laps}}{x\min }\text{.}[/tex]Solving for x we get:
[tex]x\min =\frac{41.25}{2.75}1\min =15\min \text{.}[/tex]Answer: Option B.
For a certain company, the cost function for producing x items is C(x)=40x+150 and the revenue function for selling x items is R(x)=−0.5(x−110)^2+6,050. The maximum capacity of the company is 150 items.Assuming that the company sells all that it produces, what is the profit function?P(x)=What is the domain of P(x)?The company can choose to produce either 70 or 80 items. What is their profit for each case, and which level of production should they choose?
Answers
To solve this question, follow the steps below.
Step 01: Find the profit function P(x).
Given
C(x) = cost of producing x units
R(x) = revenue when producing x units
Then, P(x) is = R(x) - C(x).
Substituting the equations in the formula:
[tex]P(x)=0.5*(x-110)^2+6050-(40x+150)[/tex]Solve the equation, by solving first the quadratic part.
[tex]\begin{gathered} P(x)=-0.5*(x^2-2*110*x+110^2)+6050-40x-150 \\ P(x)=-0.5x^2+110x-6050+6050-40x-150 \\ P(x)=-0.5x^2+110x-40x-150 \end{gathered}[/tex]Then, sum the like-terms.
[tex]P(x)=-0.5x^2+70x-150[/tex]Step 02: Find the domain.
Since the maximum capacity of the company is 150 items. So, x-maximum is 150.
The minimum number of products is 0.
Then, 0 ≤ x ≤ 150.
Domain: 0 ≤ x ≤ 150 or [0, 150].
Step 03: Compare the profit for x = 70 and x = 80.
[tex]\begin{gathered} P(x)=-0.5x^{2}+70x-150 \\ P(70)=-0.5*70^2+70*70-150 \\ P(70)=-2450+4900-150 \\ P(70)=2300 \end{gathered}[/tex][tex]\begin{gathered} P(x)=-0.5x^{2}+70x-150 \\ P(80)=-0.5*80^2+70*80-150 \\ P(80)=2250 \end{gathered}[/tex]Comparing both profits, the profit for x = 70 is greater. So, they should choose x = 70.
In summary:
(a) Profit equation:
[tex]P(x)=-0.5x^{2}+70x-150[/tex](b )Domain:
0 ≤ x ≤ 150 or [0, 150].
(c) Comparing x = 70 and x = 80.
Comparing both, the company should choose x = 70, because the profit is greater.
Write an equation of a line that passes through the given point and has the given slopethe correct blanks for the value of mand b.2.(-1, 4), slope - 1
Answers
The equation of a line in the slope intercept form is expressed as
y = mx + c
Where
m represents slope
c represents y intercept
We would find c by substituting x = - 1, y = 4 and m = - 1 into the slope intercept equation. It becomes
4 = - 1 * - 1 + c
4 = 2 + c
c = 4 - 2 = 2
The equation would be
y = - x + 2
The temperature fell by 3°F every hour during a 6-hour period. What
was the overall change in temperature during the 6-hour period?
PLS HELP THIS IS DUE TMR
Answers
Answer:
it decreased 18°F over 6 hours
Step-by-step explanation:
if it fell 3°F every hour for 6 hours just times it by 6
3x6=18
it decreased 18°F over 6 hours
Cuál es el MCD de 42 y 30 ?. Opción única. (3 puntos) 5 6 7 15
Answers
Greatest Common Factor:
The greatest common factor, or GCF, is the greatest factor that divides two numbers.
Given Numbers : 42 & 30
Factors of 42 : 7x3x2x1, 7x6x1,
Factors of 30=5x3x2x1, 5x6,1
Here the common factors of 42 & 30 are : 6,3, 2, 1
The greatest number in 6, 3, 2, 1 is 6
So, the greatest common factor is 6
The greatest common factor of 42 & 30 is 6
Answer: B) 6
find the x-intercept and the y-intercept of the graph of the equation 6X + 4y equals 72
Answers
the given equation is
6x + 4y = 72
divide the equation by 2
3x + 2y = 36
3x + 2y - 36 = 0
compare with ax+by +c = 0
a = 3
b = 2
c = -36
x-intercept will be, -c/a = -(-36)/3 = 12
y intercept will be c/b = -36/2 = -18
the table shows how many gummies a candy-maker can make in a certain number of hours
15 =1,500
25= 2,500
50= 5,000
what is the constant of proportionality? show your equation, work, and correct lables.
Answers
The constant of proportionality will be 100.
What is Proportional?
Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
The table shows how many gummies a candy-maker can make in a certain number of hours;
15 =1,500
25= 2,500
50= 5,000
Now,
We know that;
Th expression is,
⇒ y = kx
Where, K is constant of proportionality.
Here, By the first condition;
k = 1500/15
k = 100
By the second condition;
k = 2500/25
k = 100
By the third condition,
k = 5000/50
k = 100
Thus, The constant of proportionality will be 100.
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Which of the following is an example of independent events? A. Drawing a king from a standard deck of cards and then drawing an 8 without replacing the kingB. Four people are drawn successively without replacement from a group of 30 to represent the groupC. Spinning a 3 on a spinner and getting a head from a coin tossD. Selecting a head from a bag of 9 different colored breads and then selecting a second bead without putting the first back
Answers
Two events are independent if the fact that one takes palce does not affect the probability of the other. This means that spinning a spinner and tossing a coin are indepent events since the probabilities do not affect each other.
Plot three points for the line and graph the line. X-3y=6
Answers
x-3y = 6
Pick 3 points
Let x = 0
0 -3y = 6
Divide by -3
-3y/-3 = 6/-3
y = -2
(0,-2)
Let y =0
x - 3(0)=6
x = 6
(6,0)
Let x=3
3 - 3y = 6
Subtract 3 from each side
3-3y-3 = 6-3
-3y = 3
Divide by -3
-3y/-3 = 3/-3
y = -1
(3,-1)
For the first week of July, Sam Martinez worked 55 hours. Sam earns$8.60 an hour. His employer pays overtime for all hours worked in excess of 40 hours per week and pays
1.5 times the hourly rate for overtime hours. Calculate the following for the first week of July (round your responses to the nearest cent if necessary):
1) Regular Pay Amount;
2)Overtime Pay
3)Gross Pay
Answers
The regular pay amount for the first week of July is $344
The overtime pay amount for the first week of July is $193.50
The gross pay amount for the first week of July is $537.50
How to find the earnings of sam?Total hours Sam worked = 55 hoursTotal regular hours = 40 hoursOvertime hours = Total hours Sam worked - Total regular hours
= 55 - 40
= 15 hours
Amount Sam earn per hour for regular hours = $8.60
Total regular pay amount = Total regular hours × Amount Sam earn per hour for regular hours
= 40 × $8.60
= $344
Amount Sam earn per hour for overtime hours = $8.60 × 1.5
= $12.90 per overtime hour
Total overtime pay amount = Overtime hours × Amount Sam earn per hour for overtime
= 15 × $12.90
= $193.50
Total gross pay = Total regular pay amount + Total overtime pay amount
= $344 + $193.50
= $537.50
In conclusion, the regular, overtime and gross pay of Sam for the first week of July is $344, $193.50 and $537.50 respectively.
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Options for the first box: 6,500, 10,500, 11,500, 14,000Options for the second box are: 11,500, 18,500, 14,000, 10,500
Answers
Answer:
Explanation:
Given the equation:
y = -2500x + 19,000
For cars between 2 and 3 years,
The minimum is 2 and the maximum is 3 years
For the minimum, we have x = 2
So,
y = -2500(2) + 19000
= 14000
For maximum, we have x = 3
so,
y = -2500(3) + 19000
=
Bentley and Arianys are reading the same book. At the beginning of the month, Bentley was on page 39 and Arianys was on page 19. Bentley will read 16 pages per day and Arianys will read 18 pages per day. Let BB represent the page of the book that Bentley is on at the end of tt days into the month, and let AA represent the page of the book that Arianys is on at the end of tt days into the month. Write an equation for each situation, in terms of t,t, and determine whether Bentley or Arianys is farther along in the book after 15 days.
Answers
a) An equation representing the number of pages of the book that Bentley is on at the end of t days is A = 39 + 16t.
b) An equation representing the number of pages of the book that Arianys is on at the end of t days is B = 19 + 18t.
c) Arianys is farther along in the book after 15 days than Bentley because Arianys is on page 289 of the book while Bentley lags on page 279.
What is an equation?An equation is a statement showing the equality of two or more mathematical expressions.
Equations are depicted using the equation symbol (=).
The pages of the book already covered by Bentley at the beginning of the month = 39
The pages of the book already covered by Arianys at the beginning of the month = 19
Bentley's reading speed per day = 16 pages
Arianys' reading speed per day = 18 pages
The page already read by Bentley = A
The page already read by Arianys = B
Equations:For the pages already read by Bentley, A = 39 + 16t
For the pages already read by Arinys, B = 19 + 18t
After 15 days, who has read more?
Bentley, A = 39 + 16t = 39 + 16(15) = 279 pages
Arianys, B = 19 + 18t = 19 + 18(15) = 289 pages
Thus, using equations, we can conclude that Arianys can conclude the book faster than Bentley if it takes up to 15 days in the month to complete the book.
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8. Ms. Crockett is trying to teach her nephew to play baseball. Below is a rough sketch of Brandon pitching a baseball. You can model his throw with the quadratic h(t) = -16t^2 +29t + 6 where t is the seconds since the ball left Brandon's hand and h(t) is the height of the ball in feet.
Answers
a) b) We have to start by labeling the graph.
This graph relates the height in the vertical axis with the distance in the horizontal axis. The equation that relates y and x is different from h(t), as we are not representing time in the horizontal axis.
Then, both the height and the distance will have units of feet:
The highest point will be at the point where the height stop increasing and start decreasing.
c) We can use the equation fo h(t) to find the value of t when h(t) = 0, that is , when the ball touches the ground.
As h(t) is a quadratic equation, finding t for h(t) = 0 is finding the roots of the quadratic equation:
[tex]\begin{gathered} h(t)=-16t^2+29t+6 \\ t=\frac{-29\pm\sqrt[]{29^2-4\cdot(-16)\cdot6}}{2\cdot(-16)} \\ t=\frac{-29\pm\sqrt[]{841+384}}{-32} \\ t=\frac{-29\pm\sqrt[]{1225}}{-32} \\ t=\frac{29\pm35}{32} \\ t_1=\frac{29-35}{32}=-\frac{6}{32}=-0.1875 \\ t_2=\frac{29+35}{32}=\frac{64}{32}=2 \end{gathered}[/tex]As the first root is a negative number, it does not make sense in this case. The solution then is the other root, that has a value of t=2. As t is in seconds, we know that the ball reaches the ground 2 seconds after the launch.
Answer:
a) The labels and units are Height (in feet) for the vertical axis and Distance (in feet) for the horizontal axis.
b) The highest point corresponds to the point where the height stops increasing and starts decreasing.
c) The ball touches the ground 2 seconds after the launch.
Solve the equation 2-(y+9)<-3
Answers
Step 1:
Write the equation
[tex]\begin{gathered} 2\text{ - (y + 9) < -3} \\ 2\text{ - y - 9 < - 3} \\ -y\text{ < - 3 - 2 + 9} \\ \text{ - y < 4} \\ y\text{ > -4} \end{gathered}[/tex]Final answer
y > -4
In set-builder notations the solution set is
{y | y > -4}
In interval notation, the solution set is
[tex]\lbrack-3,\text{ }\infty)[/tex]what is the area of the triangle formed from (0,-1) (0,4) and (4,-1)
Answers
The area of the triangle is 10 square units formed from (0,-1), (0,4), and (4,-1).
What is the Area of a Triangle?A triangle is a closed shape composed of three angles, three sides, and three vertices.
The triangle is formed from (0,-1), (0,4), and (4,-1) which are given in the question.
As per the attached graph,
The length of the base of the triangle = 4 units
The length of the height of the triangle = 5 units
The area of the triangle = 1/2 × 4 × 5
The area of the triangle = 10 square units
Therefore, the area of the triangle is 10 square units formed from (0,-1), (0,4), and (4,-1).
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Hi I need the answer to the question quickly if possible please
Answers
The log function can be graphed using the vertical asymptote at x = 1 and the points (2,0), (5,1) & (3,0.5).
Given graph is [tex]g(x) = log_{4}(x-1)[/tex]
We have to find the asymptotes.
Set the argument of the logarithm equal to zero.
x - 1 = 0
Now add 1 to both the sides of the equation.
x - 1 + 1 = 0 + 1
= x = 1
The vertical asymptote occurs at x = 1
So, vertical asymptote: x = 1
Now, find the point at x = 2
Replace the variable x with 2 in the expression.
[tex]f(2) = log_{4}((2) - 1)[/tex]
Simplify the result
Subtract 1 from 2
[tex]f(2) = log_{4}(1)[/tex]
Logarithm base 4 of 1 is 0
f(2) = 0
The final answer is 0.
y = 0
Now find the point at x = 5
Replace the variable x with 5 in the expression.
[tex]f(2) = log_{4}((5) - 1)[/tex]
[tex]f(2) = log_{4}(4)[/tex]
Logarithm base 4 of 4 is 1
so, f(5) = 1
y = 1
Now find the point at x = 3
Replace the variable x with 3 in the expression.
[tex]f(2) = log_{4}((3) - 1)[/tex]
[tex]f(2) = log_{4}(2)[/tex]
Logarithm base 4 of 2 is [tex]\frac{1}{2}[/tex].
Rewrite as an equation.
[tex]log_{4}((2) = x[/tex]
Rewrite [tex]log_{4}((2) = x[/tex] in exponential form using definition of a logarithm. If x and b are positive real numbers and b does not equal 1, then [tex]log_{b}((x) = y[/tex] is equivalent to [tex]b^{y} = x.[/tex]
[tex]4^{x} = 2[/tex]
Create expressions in the equation that all have equal bases.
[tex](2^{2})^{x} = 2^{1}[/tex]
Rewrite [tex](2^{2})^{x} as 2^{2x}[/tex]
[tex]2^{2x} = 2^{1}[/tex]
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
2x = 1
solve for x
[tex]x = \frac{1}{2}[/tex]
The variable x is equal to [tex]\frac{1}{2}[/tex]
[tex]f(3) = \frac{1}{2}[/tex]
The final answer is [tex]\frac{1}{2}[/tex]
So, y = 0.5
The log function can be graphed using the vertical asymptote at x = 1 and the points (2,0), (5,1) & (3,0.5).
x y
2 0
3 0.5
5 1
Hence the answer is the log function can be graphed using the vertical asymptote at x = 1 and the points (2,0), (5,1) & (3,0.5).
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