The slope of the line is:
[tex]m=-\frac{3}{5}[/tex]To find the slope of a line with two points, P and Q, the formula is:
[tex]\begin{gathered} P=(x_p,y_p);Q=(x_q,y_q) \\ m=\frac{y_p-y_q}{x_p-x_q} \end{gathered}[/tex]Then if P = (-4, 1) and Q = (1, -2)
We can replace inthe formula:
[tex]m=\frac{1-(-2)}{-4-1}=-\frac{3}{5}[/tex]Given that 4 is a zero of the polynomial function f(x), find the remaining zeros.f(x) = x³ - 6x² + 25x - 68List the remaining zeros (other than 4).4(Simplify your answer. Type an exact answer, using radicals and i as needed. Use a cc
ANSWER
[tex]\begin{gathered} x=1+4i \\ x=1-4i \end{gathered}[/tex]EXPLANATION
Given:
[tex]\begin{gathered} f(x)=x^3-6x^2+25x-68 \\ \end{gathered}[/tex]Also,
One of the zeros: x = 4
Desired Outcome:
List the remaining zeros using radicals and i.
Simplify the polynomial using x - 4 = 0
Determine the remaining polynomials by simplifying x^2 - 2x + 17 = 0 using the quadratic formula
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]where:
a = 1,
b = -2
c = 17
Substitute the values
[tex]\begin{gathered} x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(17)}}{2(1)} \\ x=\frac{2\pm\sqrt{4-68}}{2} \\ x=\frac{2\pm\sqrt{-64}}{2} \\ x=\frac{2\pm\sqrt{64\times-1}}{2} \\ x=\frac{2\pm(\sqrt{64}\times\sqrt{-1})}{2} \\ x=\frac{2\pm8\sqrt{-1}}{2} \\ x=1\pm4\sqrt{-1} \\ \text{ Recall: }\sqrt{-1}\text{ = }i \\ x=1\pm4i \\ x=1+4i\text{ }or \\ x=1-4i \end{gathered}[/tex]
Find y if the line through (5, 1) and (6, y) has a slope of 3.
Answer:
Y = 32
Step-by-step explanation:
Y = mx + c, with a slope of 3
Y = 3x + c
Substitute values:
1 = 3 (5) + c
1 = 15 + c
c = -14
Rewrite formula:
Y = 3x - 14
Y = 3 (6) + 14
Y = 18 + 14
Y = 32
Hope this helps :)
Answer:
y = 4
Step-by-step explanation:
y = mx + b is the slope intercept form of a line.
We need an m (slope and a b(y-intercept)
They give us the slope, so we have to find the b
slope = 3
y = 1
x = 5
We need and x and y on the line and the point (5,1) gives us that.
y = mx + b
1 = 3(5) + b
1 = 15 + b Subtract 15 from both sides of the equation
-14 = b
Now we have the m (slope of 3) and the b (the y-intercept of -14)
y = mx + b
y = 3x -14 Now plug is the x (6) from the point given and solve for its y
y = 3(6) -14
y = 18 - 14
y = 4
An animal shelter spends $1.50 per day to care for each cat and $6.50 per day to carefor each dog. Gavin noticed that the shelter spent $97.00 caring for cats and dogs onMonday. Gavin found a record showing that there were a total of 18 cats and dogs onMonday. How many cats were at the shelter on Monday?
4 cats and 14 dogs.
Explanation:
Data :
Amount of cats : c = ?
Cost per cats : $1.50
Amount of dogs : d = ?
Cost per dogs : $6.50
Total spent for dogs and cats : $97.00
Total number of dogs and cats : 18
Formulas:
1.50c + 6.50d = 97.00
c + d = 18
Solution:
c + d = 18 => c = 18 - d
1.50(18 -d) + 6.50d = 97.00
27 - 1.50d + 6.50d = 97.00
27 - 1.50d + 6.50d - 27 = 97 -
is 6x0=O and example of distributive property?
we have that
Distributive property is the product of a factor and a sum (or difference) equals the sum (or difference) of the product
In this exanple
6x*0=0
Is not the product of a factor and a sum or difference
The width of a 2-by-4 piece of wood is actually 34 inches. Find the total width of 28 2-by-4s laid side-by-side. Simplify youranswer.o 126 inchesO 98 inches0784 inches844 inches
The of one 2-by-4 piece of wood is 3.5 inches
To find the width of 28 pcs of wood, just multiply the number of wood to the actual width which is 3.5 inches
So we have :
[tex]28\times3.5=98[/tex]The answer is 98 inches
Each of the letters a through H has one of the 8 values listed. no 2 letters have the same value. The Simple arithmetic problems are clues for determining the value of each letter. Simply guess and check to find the values for letters a through H. You must use numbers listed below.
We have the following:
Let's start from the number C, which has two numbers that when adding it gives a number and subtracting two other numbers gives the same number C
C = 9, therefore:
[tex]\begin{gathered} F-D=9 \\ F=14 \\ D=5 \\ G+B=9 \\ G=3 \\ B=6 \\ 5+E=6\Rightarrow E=1 \\ 6+H=14\Rightarrow H=8 \\ A-9=8\Rightarrow A=17 \end{gathered}[/tex]Good morning, thanks for helping meHi, can you please help me with my math? Please help me please that's all I'm asking and thank you so much.
6.
(a)
The slope for the side AB is:
[tex]\begin{gathered} A=(-5,-4)=(x1,y1) \\ B=(5,-2)=(x2,y2) \\ m_{AB}=\frac{y2-y1}{x2-x1}=\frac{-2-(-4)}{5-(-5)}=\frac{2}{10}=\frac{1}{5}=0.2 \end{gathered}[/tex]The slope for the side BC is:
[tex]\begin{gathered} B=(5,-2)=(x1,y1) \\ C=(7,6)=(x2,y2) \\ m_{BC}=\frac{6-(-2)}{7-5}=\frac{8}{2}=4 \end{gathered}[/tex]The slope for the side DC is:
[tex]\begin{gathered} D=(-3,4)=(x1,y1) \\ C=(7,6)=(x2,y2) \\ m_{DC}=\frac{y2-y1}{x2-x1}=\frac{6-4}{7-(-3)}=\frac{2}{10}=\frac{1}{5}=0.2 \end{gathered}[/tex]And the slope for AD is:
[tex]\begin{gathered} A=(-5,-4)=(x1,y1) \\ D=(-3,4)=(x2,y2) \\ m_{AD}=\frac{4-(-4)}{-3-(-5)}=\frac{8}{2}=4 \end{gathered}[/tex](b) According to the previous results:
[tex]\begin{gathered} m_{AB}=m_{DC} \\ so \\ m_{AB}\parallel m_{DC} \end{gathered}[/tex][tex]\begin{gathered} m_{BC}=m_{AD} \\ so\colon \\ m_{BC}\parallel m_{AD} \end{gathered}[/tex](c) Since it has two pairs of parallel sides, also, The opposite sides are of equal length, we can conclude that this figure is a parallelogram
A population of bacteria grows according to function p(t) = p. 1.42^t, where t is measured in hours. If the initial population size was1,000 cells, approximately how long will it take the population to exceed 10,000 cells? Round your answer to the nearest tenth.
Given the function p(t) and the initial condition, we have the following:
[tex]\begin{gathered} p(t)=p_0\cdot1.42^t \\ p(0)=1000 \\ \Rightarrow p(0)=p_0\cdot1.42^0=1000 \\ \Rightarrow p_0\cdot1=1000 \\ p_0=1000 \end{gathered}[/tex]Therefore, the function p(t) is defined like this:
[tex]p(t)=1000\cdot1.42^t[/tex]Now, since we want to know the time it will take the population to exceed 10,000 cells, we have to solve for t using this information like this:
[tex]\begin{gathered} p(t)=1000\cdot1.42^t=10000 \\ \Rightarrow1.42^t=\frac{10000}{1000}=10 \\ \Rightarrow1.42^t=10 \end{gathered}[/tex]Applying natural logarithm in both sides of the equation we get:
[tex]\begin{gathered} 1.42^t=10 \\ \Rightarrow\ln (1.42^t)=\ln (10) \\ \Rightarrow t\cdot\ln (1.42)=\ln (10) \\ \Rightarrow t=\frac{ln(10)}{\ln (1.42)}=6.56 \end{gathered}[/tex]Therefore, it will take the population 6.56 hours to exceed 10,000 cells
Write the equation of the circle given the following graph.
Given:
Equation of a circle on a graph with center(3, -2).
To find:
Equation of a circle.
Explanation:
General eqution of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]Solution:
From the graph, we can see that center is (3, -2) and radius equal 3.
So, equation of a circle is
[tex](x-3)^2+(y+2)^2=3^2[/tex]Hence, this is the equation of a circle.
determine the volume of each rectangular or triangular prism round to the nearest tenth if necessary
Determine the volume of each rectangular or triangular prism round to the nearest tenth if necessary
____________________
volume = base (B)* height (H)
_____________________
Base area
Triangle
B = b*h/2
Rectangle
B= L1*L2
__________________
volume = base (B)* height (H)
H= 15
Triangle case
B = 4.8 *9.6 /2
B = 46.08 / 2
B= 23.04
V= 23. 04* 15
V= 345.6 in ^3
Use the given information to answer the questions and interpret key features. Use any method of graphing or solving.
A quadratic function describes the relationship between the number of products x and the overall profits for a company.
The roots of the quadratic function are given as x = 0 and x = 28. We also know the graph's vertex is located at (14, -40).
The quadratic equation can be written in terms of its roots x1 and x2 as:
[tex]f(x)=a(x-x_1)(x-x_2)[/tex]Substituting the given values:
[tex]\begin{gathered} f(x)=a(x-0)(x-28) \\ \\ f(x)=ax(x-28) \end{gathered}[/tex]We can find the value of a by plugging in the coordinates of the vertex:
[tex]f(14)=a\cdot14(14-28)=-40[/tex]Solving for a:
[tex]a=\frac{-40}{-196}=\frac{10}{49}[/tex]Substituting into the equation:
[tex]f(x)=\frac{10}{49}x(x-28)[/tex]The graph of the function is given below:
The company actually loses money on their first few products, but once they hit 28 items, they break even again.
The worst-case scenario is that they produce 14 items, as they will have a profit of -40 dollars. The first root tells us the profit will be 0 when 0 products are sold.
Simplify by combining like terms,8t3 + 8y + 7t3 + 6y + 9t2
The simplification of the expression will be; 15t³ + 9t² + 14y
What are equivalent expressions?Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions. To derive equivalent expressions of some expressions, we can either make them look more complex or simple.
Given that the expression as 8t³ + 8y + 7t³ + 6y + 9t²
Now combining like terms;
8t³ + 7t³ + 9t² + 8y + 6y
Simplify;
15t³ + 9t² + 14y
It cannot be solved further because of unlike terms in the expression.
Therefore, the simplification of the expression will be; 15t³ + 9t² + 14y
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entionaction f(x) = 4.12x +12. If f(x) = -2(5)*, what is f(2)?A100B.20fC227-2050C. -20D. -50boioht of 144I
Problem
We have the following expression given:
f(x)= -2(5)^x
And we want to find f(2)
Solution
so we can do the following:
f(2)= -2 (5)^2 = -2*25 = -50
In a certain country, the probability that a baby that is born is a boy is 0.52 and the probably that a baby that is born is a girl is 0.48. A family has two children. If X is the number of girls born to a family, find the probability that the family has 0, 1, or 2 girls.(a) Draw a tree diagram showing the possibilities for each outcome.(b) Create the binomial distribution table for p(X)
Given:
The probability that a baby that is born is a boy is 0.52.
The probability that a baby that is born is a girl is 0.48.
To find:
The probability that the family has 0, 1, or 2 girls.
Explanation:
Using the binomial distribution,
[tex]P(X=x)=^nC_xp^x(1-p)^{n-x}[/tex]Here,
[tex]\begin{gathered} n=2 \\ P(Birth\text{ of girls\rparen=}p=0.48 \\ P(B\imaginaryI rth\text{ of boys\rparen=}1-p=0.52 \end{gathered}[/tex]The probability that the family gets 0 girl child is,
[tex]\begin{gathered} P(X=0)=^2C_0(0.48)^0(0.52)^2 \\ =0.2704 \end{gathered}[/tex]The probability that the family gets 1 girl child is,
[tex]\begin{gathered} P(X=1)=^2C_1(0.48)^1(0.52)^1 \\ =0.2496 \end{gathered}[/tex]The probability that the family gets 2 girl children is,
[tex]\begin{gathered} P(X=2)=^2C_2(0.48)^2(0.52)^0 \\ =0.2304 \end{gathered}[/tex]So, the probability that the family has 0, 1, or 2 girls is,
[tex]\begin{gathered} P(E)=0.2704+0.2496+0.2304 \\ =0.7504 \end{gathered}[/tex]a) The tree diagram is,
b) The binomial distribution table for p(X) is,
solve the proportion 4/3 is equal to 9 / X
We need to solve for X.
The proportion is:
[tex]\frac{4}{3}=\frac{9}{X}[/tex]To solve for X, we cross multiply and then use algebra to solve. The process is shown below:
[tex]\begin{gathered} \frac{4}{3}=\frac{9}{X} \\ 4\times X=3\times9 \\ 4X=27 \\ X=\frac{27}{4} \end{gathered}[/tex]Given the following five-number summary, find the IQR.
2.9, 5.7, 10.0, 13.2, 21.1.
The IQR of the given series 2.9, 5.7, 10.0, 13.2, 21.1 is 15.4
In the given question, a five number summary is given as follows
2.9, 5.7, 10.0, 13.2, 21.1
We need to find the IQR
So, first we'll find the median of the given series
The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does.
So, the given series is already in ascending order. And the middle value is 10.0. So the median is 10.0
Now to find the IQR the given formula will be used,
IQR = Q3 - Q1
Where Q3 is the last term in lower series and Q1 is the last term in upper series
Lower series - 2.9, 5.7
Upper series - 3.2, 21.1
Q3 = 5.7 , Q1 = 21.1
IQR = Q3 - Q1 = 21.1 - 5.7 = 15.4 ( IQR is always positive)
Hence, the IQR of the given series 2.9, 5.7, 10.0, 13.2, 21.1 is 15.4
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20 quarts=_ 20_×(1 quart) =_20_×(1\4 gallon) =_20/4_gallons =_5_gallons
From the question, we are to convert 20 quartz to gallons.
Given
1 quartz = 1/4 gallons
20 quartz = x
Cross multiply and find x;
1 * x = 20 * 1/4
x = 20/4
x = 5
Hence 20 quartz is equivalent to 5 gallons
Find the sin t as a fraction in simplest terms
We are asked to determine the sinT. To do that let's remember that the function sine is defined as:
[tex]\sin x=\frac{opposite}{hypotenuse}[/tex]In this case, we have:
[tex]\sin T=\frac{VU}{VT}[/tex]To determine the value of VU we can use the Pythagorean theorem which in this case would be:
[tex]VT^2=VU^2+TU^2[/tex]Now we solve for VU first by subtracting TU squared from both sides:
[tex]VT^2-TU^2=VU^2[/tex]Now we take the square root to both sides:
[tex]\sqrt[]{VT^2-TU^2^{}}=VU[/tex]Now we plug in the values:
[tex]\sqrt[]{(6)^2+(\sqrt[]{36^{}})^2}=VU[/tex]Solving the squares:
[tex]\sqrt[]{36+36}=VU[/tex]Adding the values:
[tex]\sqrt[]{2(36)}=VU[/tex]Now we separate the square root:
[tex]\sqrt[]{2}\sqrt[]{36}=VU[/tex]Solving the square root:
[tex]6\sqrt[]{2}=VU[/tex]Now we plug in the values in the expression for sinT:
[tex]\sin T=\frac{6\sqrt[]{2}}{6}[/tex]Now we simplify by canceling out the 6:
[tex]\sin T=\sqrt[]{2}[/tex]And thus we obtained the expression for sinT.
Graph the following inequality.Note: To graph the inequality:Select the type of line below (solid or dashed).Plot two points on the line.Click on the side that should be shaded.
Given:
[tex]-4x-y>2[/tex]Consider the line,
[tex]-4x-y=2[/tex]Find the points on the line,
[tex]\begin{gathered} x=0 \\ -4(0)-y=2\Rightarrow y=-2 \\ x=1 \\ -4(1)-y=2\Rightarrow y=-6 \\ x=-1 \\ -4(-1)-y=2\Rightarrow y=2 \end{gathered}[/tex]The graph of the line is,
Now, find the region for inequality.
Consider any point from the right and the left side of the line and check which side satisfies the inequality.
[tex]\begin{gathered} R=(2,0) \\ -4x-y>2 \\ -4(2)-0=-8\text{ >2 is not true.} \end{gathered}[/tex]And,
[tex]\begin{gathered} L=(-2,0) \\ -4x-y>2 \\ -4(-2)-0=8>2\text{ is true} \end{gathered}[/tex]Therefore, the graph of the inequality is,
Note that inequality does not contain boundary points.
Hello! I need some help with this homework question, please? The question is posted in the image below. Q15
ANSWER:
A.
[tex]x=-1,-3,11[/tex][tex]f(x)=(x+3)(x-11)(x+1)[/tex]STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f(x)=x^3-7x^2-41x-33[/tex]To find the zeros of the function we must set the function equal to 0 in the following way:
[tex]x^3-7x^2-41x-33=0[/tex]We reorganize the equation in order to be able to factor and calculate the zeros of the function, like this:
[tex]\begin{gathered} x^3-7x^2-41x-33=0 \\ -7x^2=-8x^2+x^2 \\ -41x=-33x-8x \\ \text{ Therefore:} \\ x^3-8x^2+x^2-33x-8x-33=0 \\ x^3-8x^2-33x=-x^2+8x+33 \\ x(x^2-8x-33)=-(x^2-8x-33) \\ x^2-8x-33 \\ -8x=3x-11x \\ x^2+3x-11x-33 \\ x(x+3)-11(x+3) \\ (x+3)(x-11) \\ \text{ we replacing} \\ x(x+3)(x-11)=-1 \\ x(x+3)(x-11)+(x+3)(x-11)=0 \\ (x+3)(x-11)(x+1)=0 \\ x+3=0\rightarrow x=-3 \\ x-11=0\rightarrow x=11 \\ x+1=0\rightarrow x=-1 \end{gathered}[/tex]Therefore, the zeros are:
[tex]x=-1,-3,11[/tex]And in its factored form the expression would be:
[tex]f(x)=(x+3)(x-11)(x+1)[/tex]What tip will Brady get if a customer adds a 15% tip to his $18.52 meal cost?
Brandy will get a tip of $2.778
Here, we want to get the amount of tip Brandy will get
In the question, the tip is 15% of $18.52
That will mathematically be;
[tex]\begin{gathered} \frac{15}{100}\text{ }\times\text{ \$18.52} \\ \\ =\text{ }\frac{277.8}{100}\text{ = \$2.778} \end{gathered}[/tex]Base on table above is the scenario a proportional relationship
No
Explanations:A relationship is called a proportional relationship if it has two variables that are realated by the same ration. In this case there will be a proportionality constant.
In this table:
Let Height be represented as H
Let Time be represented as T
For the relationship to be a proportional relationship, it must obey the relation:
[tex]\begin{gathered} H\propto\text{ T} \\ H\text{ = kT} \\ \text{Where k is the proportionality constant} \end{gathered}[/tex]When T = 3, H = 15
Using H = kT
15 = 3k
k = 15 / 3
k = 5
When T = 6, H = 30
H = kT
30 = 6k
k = 30 / 6
k = 5
When T = 12, H = 45
H = kT
45 = 12k
k = 45 / 12
k = 3.75
Since the constant of proportionality is the the same for the three cases in the table, the scenario is not a proportional relationship
Find the area of the shaded part of the figure if a=6, b=7, c=4. (I need help on this)
To obtain the area(A) of the shaded part of the figure, we will sum up the area of the triangle and the area of the rectangle.
Let us solve the area of the triangle(A1) first,
The formula for the area of the triangle is,
[tex]A_1=\frac{1}{2}\times base\times\text{height}[/tex]where,
[tex]\begin{gathered} base=b=7 \\ height=a=6 \end{gathered}[/tex]Therefore,
[tex]A_1=\frac{1}{2}\times7\times6=21unit^2[/tex]Hence, the area of the triangle is 21 unit².
Let us now solve for the area of the rectangle(A2)
The formula for the area of the rectangle is
[tex]A_2=\text{length}\times width[/tex]Where,
[tex]\begin{gathered} \text{length}=b=7 \\ \text{width}=c=4 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} A_2=7\times4=28 \\ \therefore A_2=28\text{unit}^2 \end{gathered}[/tex]Hence, the area of the rectangle is 28unit².
Finally, the total area of the shaded area is
[tex]\begin{gathered} A=A_1+A_2=21+28=49 \\ \therefore A=49unit^2 \end{gathered}[/tex]Hence, the area of the shaded part is 49unit² (OPTION A).
Gretchen is planting a rectangular garden. she wants to use 9 square feet for tulips.if garden has length of 8 feet by 3 feet, how much room will she have left for rest of her flowers
Given: the garden has a shape of a rectangle
The garden has a length of 8 feet by 3 feet
So, the area of the garden =
[tex]8\cdot3=24ft^2[/tex]she wants to use 9 square feet for tulips.
So, the remaining for rest of her flowers = 24 - 9 = 15 square feet
Andre is looking at apartments with 1 of his friends. They want the monthly rent to be no more than $1000. If the roommates split the rent evenly among the two of them, what is the maximum rent each will pay?
We have the next inequality
[tex]2x\le1000[/tex]where x is the rent of each person
[tex]\begin{gathered} x\le\frac{1000}{2} \\ x\le500 \end{gathered}[/tex]The maximum rent each will pay is $500
64 is 2/3percent of what number
We have to find the number x for which 64 is the 2/3.
In 2005 there were 744 radio stations, by 2015 that number had increased by 13.8%. How many radio stations in 2015?
Answer: We have to find the radio stations in 2015, which is 13.8% more than the radio stations in 2005 which were 744:
[tex]\begin{gathered} x=\text{ Radio stations in 2015} \\ \\ x=(1.138)\times(744) \\ \\ x=846.672 \\ \\ x\approx847 \end{gathered}[/tex]use the information provided to write the equation of each circle. center: (12,-13)point on circle: (18, -13)
Answer:
[tex](x-12)^2+(y+13)^2=36[/tex]Explanation:
Given:
• Center: (12,-13)
,• Point on circle: (18, -13)
First, we find the length of the radius.
[tex]\begin{gathered} r=\sqrt[]{(18-12)^2+(-13-(-13)_{})^2} \\ =\sqrt[]{(6)^2} \\ r=6\text{ units} \end{gathered}[/tex]The general equation of a circle is given as:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Substituting the centre, (h,k)=(12,-13) and r=6, we have:
[tex]\begin{gathered} (x-12)^2+(y-(-13))^2=6^2 \\ (x-12)^2+(y+13)^2=36 \end{gathered}[/tex]The equation of the circle is:
[tex](x-12)^2+(y+13)^2=36[/tex]Instructions: Complete the following table, computing each students' mean, median, mode, and range: Math Test Scores ( picture attached ) What is the mean score for Test 2? What is the mode of Test 7? ________What is the median score of Test 4? ________What is the range of Test 6? ________
The completed worksheet is the following:
This worksheet involves three measures of central tendency: Mean, Median, Mode and Range
Mean: To get the mean of a dataset, add up all the data and divide by the number of datum (or inputs)
Median: To get the median of a dataset, sort the data in ascending order, and choose the central datum.
For example, if you have a dataset with 7 inputs, sort it in ascending order and select the 4th datum, as there would be 3 values above and 3 below (Hence it being the central datum).
Mode: The mode is the most repeated value of a dataset.
Range: The range is the difference between the biggest and smallest values of a dataset.
15. When x =9, which number is closest to the value of y on the line of best fit in the graph below? 121917
We have a scatter plot.
We have to find the closest value to y on the line of best fit when x = 9.
We can estimate a line of best fit by hand in the graph as:
Although we have a data point where x = 9 and y =9, the line of best fit is kind of in between the two groups of points.
When we draw the line like this, the estimated value from the line of best fit when x = 9 is y = 12, as we can see in the graph.
Answer: 12