The slope of the tangent line to the curve at (8, 2) is given by the derivative [tex]\frac{dy}{dx}[/tex] at that point. By the chain rule,
[tex]\dfrac{dy}{dx} = \dfrac{dy}{dt} \times \dfrac{dt}{dx} = \dfrac{\frac{dy}{dt}}{\frac{dx}{dt}}[/tex]
Differentiate the given parametric equations with respect to [tex]t[/tex] :
[tex]x = 4t \implies \dfrac{dx}{dt} = 4[/tex]
[tex]y = \dfrac4t \implies \dfrac{dy}{dt} = -\dfrac4{t^2}[/tex]
Then
[tex]\dfrac{dy}{dx} = \dfrac{-\frac4{t^2}}4 = -\dfrac1{t^2}[/tex]
We have [tex]x=8[/tex] and [tex]y=2[/tex] when [tex]t=2[/tex], so the slope at the given point is [tex]\frac{dy}{dx} = -\frac14[/tex].
The normal line to the same point is perpendicular to the tangent line, so its slope is +4. Then using the point-slope formula for a line, the normal line has equation
[tex]y - 2 = 4 (x - 8) \implies \boxed{y = 4x - 30}[/tex]
Alternatively, we can eliminate the parameter and express [tex]y[/tex] explicitly in terms of [tex]x[/tex] :
[tex]x = 4t \implies t = \dfrac x4 \implies y = \dfrac4t = \dfrac4{\frac x4} = \dfrac{16}x[/tex]
Then the slope of the tangent line is
[tex]\dfrac{dy}{dx} = -\dfrac{16}{x^2}[/tex]
At [tex]x = 8[/tex], the slope is again [tex]-\frac{16}{64}=-\frac14[/tex], so the normal has slope +4, and so on.
Select the correct answer. A system of linear equations is given by the graph. A diagonal curve declines from (negative 6, 4) through (negative 5, negative 3 point 2). A diagonal curve rises from (negative 7, negative 3) through (7, 0 point 2). Both curves intersect at (3 point 5, 2 point 2). What is the system shown? A. B. C. D.
The system of equations shown in this graph of a system of linear equations are:
y = -2/3xy = 3/4x - 5.How to determine the system of equations?In order to determine the required system of equations from this graph of a system of linear equations, we would find the slope of each line as follows:
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
For line 1, we have:
Points (x, y) = (0, 0) and (3, -2)
Slope = (-2 - 0)/(3 - 0)
Slope = -2/3.
Therefore, y = mx + c ⇒ y = -2/3x + 0.
For line 2, we have:
Points (x, y) = (0, -5) and (4, -2)
Slope = (-2 - (-5))/(4 - 0)
Slope = (-2 + 5)/(4 - 0)
Slope = 3/4.
Therefore, y = mx + c ⇒ y = 3/4x - 5.
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Answer:
O.B y = − 2/3x
y = 3/4x − 5
Step-by-step explanation:
triangle BIG is similar to triangle MOP. Find v
Answer:
v = 34 in
Step-by-step explanation:
triangle BIG is similar to triangle MOP
This means that the length of their corresponding sides
are proportional.
Then
[tex]\frac{v}{51} =\frac{60}{90}[/tex]
Then
90v = 51 × 60
then
90v = 3060
Then
v = 3060/90
Then
v = 34
You need 450 mL of a 65% alcohol solution. On hand, you have a 10% alcohol mixture. How much of the 10% alcohol mixture and pure alcohol will you need to obtain the desired solution?
You will need_____ mL of the 10% solution and___ mL of pure alcohol.
You will need 292.5 mL of the 10% solution and 2925 mL of pure alcohol.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
You require 450 mL of a 65% alcohol solution.
On hand, you have a 10% alcohol mixture.
Then the amount of the 10% alcohol mixture and pure alcohol that you need to obtain the desired solution will be
Let x be the amount of the 10% of alcohol is needed.
Then the equation will be
⇒ 450 · 0.65
⇒ 292.5 mL pure alcohol
Then the alcohol mixture will be
0.1x = 292.5
x = 2925 mL of alcohol mixture
You will need 292.5 mL of the 10% solution and 2925 mL of pure alcohol.
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Solve for x using
cross multiplication.
2x=4 =
2x – 4
3
x + 1
2
x = [?]
Enter
Hello,
look at the picture
I think I made a small mistake and I need help to spot my mistake and the correct steps to solve my question, I hope someone can help me asap. I will be very much appreciated!!
(Question b)
The values of x in 2cos(2x) = 11cos(x) + 1 are x = 1.82 and x = 4.46
How to solve for x?The equation is given as:
2cos(2x) = 11cos(x) + 1
Expand cos(2x)
2(cos²(x) - sin²(x)) = 11cos(x) + 1
sin²(x) = 1 - cos²(x)
So, we have:
2(cos²(x) - 1 + cos²(x)) = 11cos(x) + 1
Evaluate the like terms
2(2cos²(x) - 1) = 11cos(x) + 1
Expand
4cos²(x) - 2 = 11cos(x) + 1
Rewrite as:
4cos²(x) - 11cos(x) - 2 - 1 = 0
4cos²(x) - 11cos(x) - 3 = 0
Let cos(x) = y.
So, we have
4y² - 11y - 3 = 0
Expand
4y² + y - 12y - 3 = 0
Factorize
y(4y + 1) - 3(4y + 1) = 0
Factor out 4y + 1
(y - 3)(4y + 1) = 0
Solve for y
y = 3 or 4y = -1
This gives
y = 3 or y = -1/4
Recall that y = cos(x)
So, we have:
cos(x) = 3 or cos(x) = -1/4
The cosine of x is always between -1 and 1 (inclusive).
So, we have:
cos(x) = -1/4
Take the arc cos
[tex]x =\cos^{-1}(-1/4)[/tex]
Evaluate the arccos (in radians)
x = 1.82 and x = 4.46
Hence, the values of x in 2cos(2x) = 11cos(x) + 1 are x = 1.82 and x = 4.46
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In a concert band, a the probability that a member is in the brass section is
0.50. The probability that a member plays trombone, given that he or she is in
the brass section, is 0.24.
What is the probability that a randomly selected band member is in the brass
section and plays trombone?
O A. 0.74
• B. 0.48
• C. 0.26
• D. 0.12
Using conditional probability, the probability that a randomly selected band member is in the brass section and plays trombone is:
D. 0.12
What is Conditional Probability?Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.For this problem, the events are:
Event A: Student in the brass section.Event B: Student plays trombone.Hence the parameters are:
P(A) = 0.5, P(B|A) = 0.24.
The probability of both events is found as follows:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(B|A)P(A) = 0.24 \times 0.5 = 0.12[/tex]
Hence option D is correct.
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Answer:
0.12
Step-by-step explanation:
just took it :)
Use any method to solve the equation. If necessary, round to the nearest hundredth. 9x2 = 17
A. 3 ,–3
B. 4.12, –4.12
C. 0.73, –0.73
D. 1.37, –1.37
Answer:
D. 1.37, -1.37
Step-by-step explanation:
9x² = 17
x² = (17 / 9)
x = ± √(17 / 9)
x = ± (√17) / 3
x = 1.37, - 1.37
If the coordinates of the endpoints of a diameter of the circle are known, the equation of a circle can be
found First, find the midpoint of the diameter, which is the center of the circle. Then find the radius, which is
the distance from the center to endpoint of the diameter. Finally use the center-radius form to find the equation.
Find the center-radius form for the circle having the endpoints
(9,2) and (-7,4) of a dmiameter.
Type an equation.).
The equation of the circle would be (x - 1)² + (y - 3)² = 65.
What is the equation of a circle?The equation of a circle with center (h,k) and radius, r in center radius form is given;
(x - h)² + (y - k)² = r²
The coordinates of the center of the circle can be calculated by the formula
((x₁ + x₂)/2, (y₁ + y₂)/2).
The point (x₁,y₁) = (9, 2) and (x₂,y₂) = (-7, 4).
So, ((9 -7)/2, (4 + 2)/2) = (1, 3).
Now, r² = (x₂ - x₁)² + (y₂ - y₁)².
Let (x₁, y₁) = (1, 3) and (x₂, y₂) = (-7, 4).
So, r² = (-7 -1)² + (4 - 3)²
= -8² + 1² = 64 + 1 = 65.
With center (h,k) = (1, 3) and r² = 65, we have
Thus, the equation would be (x - 1)² + (y - 3)² = 65.
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Pierre Hugo is handling the estate of a prominent businesswoman. The will states that the surviving spouse is to receive 1/3 of the estate and the remaining 2/3 of the estate will be divided equally among 3 surviving children. What fraction of the estate does each child receive?
Each child will receive 0.125 (or 12.5%) of the estate.
If the surviving spouse gets one half of the estate, the other half has to be divided among the four surviving children.
What is the fraction?
A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.
So it's 0,5 divided among the 4 surviving children.
That is 0.125 or 12.5% of the estate.
Each child will receive 0.125 of the estate. a
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Solve the following system of equations by graphing. 9x-2y= -8
The solution of the equation are
(0, 4)(1, 8.5)(-0.66, 1)(-0.44, 2)What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Given:
9x -2 y =-8
By graph we can see that the solution for the graph is
(0, 4)
(1, 8.5)
(-0.66, 1)
(-0.44, 2)
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What steps should be taken to complete the conversion?
To complete the conversion, the following will be gotten:
12880 m
How to convert distance?Using conversion technique,
8 mi / 1 × 1.61 k / 1 mi × 1000m / 1k
we have to cancel out similar units in the numerator and denominator.
Therefore,
8 mi / 1 × 1.61 k / 1 mi × 1000m / 1k
8 / 1 × 1.61 / 1 × 1000m / 1 = 12.88 / 1 × 1000m
Hence,
12.88 / 1 × 1000m = 12880 m
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Which statements are true of the given function?
Check all that apply.
01²2=2²
Of(0) = 2/1/20
O f(1) = -1
Of(2)=1
□f(4)=1/12/2
Step-by-step explanation:
23 by 13 is the answer cause 23 i s23
The statements that are true of the given function f(x) = 1/2x + 3/2 are:
f(0) = 3/2
f(2) = 7/2
f(4) = 7/2
We have,
Let's evaluate the given function f(x) = 1/2x + 3/2 for the given values of x and check which statements are true:
f(-1/2) = 1/2 * (-1/2) + 3/2 = -1/4 + 3/2 = (6 - 1)/4 = 5/4 = 1.25
Statement: f(-1/2) ≠ 2 (False)
f(0) = 1/2 * 0 + 3/2 = 0 + 3/2 = 3/2
Statement: f(0) = 3/2 (True)
f(1) = 1/2 * 1 + 3/2 = 1/2 + 3/2 = 4/2 = 2
Statement: f(1) ≠ -1 (False)
f(2) = 1/2 * 2 + 3/2 = 1 + 3/2 = 2 + 3/2 = 4/2 + 3/2 = 7/2
Statement: f(2) = 7/2 (True)
f(4) = 1/2 * 4 + 3/2 = 2 + 3/2 = 4/2 + 3/2 = 7/2
Statement: f(4) = 7/2 (True)
Therefore,
The statements that are true of the given function f(x) = 1/2x + 3/2 are:
f(0) = 3/2
f(2) = 7/2
f(4) = 7/2
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Dana's phone has zero battery. After charging her phone for 1 minute, it has
2% battery. After 2 minutes, her phone has 6% battery. Based on this, predict
the number of minutes it will take for Dana to charge her phone's battery so
that it has 50% power and 90% power.
From the first two inference, it takes her phone 1 minute to charge 2% i.e 1 minute of charge = 2% of battery.
Therefore; charging from scratch,
1 min = 2%
x mins = 50%.
using cross multiplication,
x mins = (50% × 1 min) ÷ 2%.
x = 25 mins.
For 90%, applying the same formula,
y min = (90% × 1 min) ÷ 2%
y = 45 mins.
So from zero percent, it will take Dana's phone 25 minutes to charge to 50% and 45 minutes to charge to 90%.
solve for a
-1/4a - 4 = 7/4a -3
Answer:
21 because -1/4a - 4 is 22
Chang caught a 3- pound fish. How much did it weigh in ounces? 4 Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answer:
Step-by-step explanation:
pounds to ounces: 16 ounces in a pound a trick to know is if you look at the pound symbol lb it looks like 16 in a way so 16*3= 48 48 is your answer
Kitty has invested £5500 for 3 years in a savings account. She is paid 6% per annum compound interest. How much did she have in her savings account at the end of the 3 years?
The value of her investment at the end of 3 years is £10955.08
How to determine the value?The given parameters are
Principal, P = £5000Rate, r = 6%Time, t = 3 yearsThe value is then calculated as:
Value = P * P(1 + r)^t
So, we have:
Value = 5000 + 5000 * (1 + 6%)^3
Evaluate the expression
Value = 10955.08
Hence, the value of her investment at the end of 3 years is £10955.08
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Kim's car gas tank holds 2 gallons of gas and gets M miles per gallon and she drove D miles. lf gas cost $1.25 per gallon how many gallons had to be replaced?
Answer:
see below
Step-by-step explanation:
D miles / M miles per gallon = gallons used
Please Help I’m confused give clear answers thank you
Answer:
1: [tex]y=-1x-3[/tex]
2: [tex]y=0.8x+4.2[/tex]
3: [tex]y=2x-3[/tex]
Step-by-step explanation:
Question 1: When lines are parallel, that means they're slope is the same and there y-intercept is different. So the first step is to calculate the slope of BC. If you look at BC you'll notice it goes down by 2 and goes forward by 2 so the slope is -2/2 or -1. This completes one part of the slope-intercept form which is y=mx+b where m is the slope and b is the y-intercept. The y-intercept will be calculated using the point A. since the equation passes through point A
-1 = (-2)(-1) + b
-1 = 2 + b
-3 = b
y=-1x-3
Question 2: Same concept here, if you look at AC, you'll see it "rises" by 4 and "runs" by 5, thus the slope is 4/5. Since it passes through B we'll use that to find the y-intercept
5 = (4/5)(1) + b
5 = 4/5 + b
b = 4.2
Question 3: It "rises" by 6 and "runs" by 3, thus the slope is 6/3 which is 2.
Plug in known values
3=(3)(2) + b
3 = 6 + b
-3 = b
A train goes from springfield, MA, to boston at 40 mph. On the way back, it returns with a speed 80 mph. If it takes an hour less time to return, what is it's average speed?
The average speed for the entire journey will be 53.333 miles per hour.
What is the average speed?The average speed is the ratio of the total distance traveled to the total time taken by the body. Its unit is m/sec.
The distance from the Springfield, MA, to Boston is, L
v₁ is the velocity during traveling from Boston to Springfield, MA
v₂ is the velocity during traveling from Springfield, MA to Boston
t₁ is the time needed to travel from Boston to Springfield, MA
t₂ is the time needed to travel from Springfield, MA to Boston
t is the total time period of the journey
v is the average speed
From the formula of distance;
Distance = speed × time
The speed of train for the going from Springfield, MA, to Boston is 40 mph. The time period is calculated as;
L = v₁ × t₁
t₁ = L/v₁
t₁ = L/40
The speed of train for the going from Boston to Springfield, MA, is 80 mph. The time period is calculated as;
L = v₂ × t₂
t₂ = L/v₂
t₂ = L/80
The total time is taken;
t = t₁ + t₂
t = (L/40)+( L/80)
t=3L/80
The ratio of total distance traveled to the total time spent by the body is known as average speed, calculated as;
Average speed = Total distance / Total time
v = 2L / (3L/80)
v= (2L × 80)/3L
v = 160 / 3
v = 53.333 miles per hour.
Hence the average speed for the entire journey will be 53.333 miles per hour.
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Mr. Robert charges $50 per hour for math tutoring and charges $40 per hour for language arts tutoring. How many hours of math tutoring must be mixed with 5 hours of ELA Tutoring to make $45 per hour?
5 hours of math tutoring must be mixed with 5 hours of arts tutoring to make $45 per hour.
Mr. Robert charges $50 per hour for math tutoring and charges $40 per hour for language arts tutoring.
Let, he mixed x hours of math tutoring to 5 hours of arts tutoring.
Then, Income from x hours of math tutoring = $50x
Income from 5 hours of arts tutoring = 5×$40 = $200
Total mixed income in (x+5) hours = $(50x+200)
According to the question, in mixed process he make $45 per hour. So, for (x+5)hours he earns $(x+5)45
So, The equation becomes,
50x+200 = (x+5)45
⇒ 50x+200 = 45x+225
⇒ 50x-45x = 225-200
⇒ 5x = 25
⇒ x = 25/5
⇒ x = 5
So, 5 hours of math tutoring must be mixed.
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If abcd is dilated by a factor of 3, the coordinate of a would be?
Answer: (-9, -3)
Step-by-step explanation:
A = (-3, -1)
A' = (-3, -1)*3 = (-9, -3)
10 Points please help with my calculus HW
A point moves along the curve y = squareroot of X , in such a way that the y-component of the position of the point is increasing at a rate of 5 units per second. At what rate is the x-component changing for each of the following values?
(a) x = 1/5
dx/dt = ___?___
(b) x = 1
dx/dt=___?___
(c) x=4
dx/dt = ___?___
Thank you
The values based on the calculus computed will be 10✓5, 10✓1, and 20.
How to calculate the value?dy/dt = 5 units.
Differentiate with respect to t.
dx/dt = 1/2✓x dx/dt
dyldt = 5.
dx/dt = 2✓x × 5 = 10✓x
a. When x = 1/5
dx/dt = 10 × ✓1/5 = 10✓5
b. x = 1
Differentiate it
dx/dt = 10✓1
c. x = 4
dx/dt = 10✓4 = 20
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Simplify by using radical. Rationalize denominators. 2a^-1/2
Answer:
[tex] \dfrac{2\sqrt{a}}{a} [/tex]
Step-by-step explanation:
[tex] 2a^{-\frac{1}{2}} = [/tex]
[tex]= 2 \times \dfrac{1}{\sqrt{a}}[/tex]
[tex]= 2 \times \dfrac{1}{\sqrt{a}} \times \dfrac{\sqrt{a}}{\sqrt{a}}[/tex]
[tex] = \dfrac{2\sqrt{a}}{a} [/tex]
Use the Histogram below to answer. Please help
The Empirical Rule is also referred to as the 68-95-99.7 rule and it can be defined as a statistical rule which states that:
The middle 68% of a normal distribution would be within 1 standard deviation of its mean.The middle 95% of a normal distribution would be within 2 standard deviations of its mean.The middle 99.7% of a normal distribution would be within three standard deviations of its mean.By applying the empirical rule to the data contained in the histogram, we can logically deduce the following points:
There is approximately 95% of the data between -2 and 102.There is approximately 68% of the data between 1 standard deviation of its mean.Read more on Empirical Rule here: https://brainly.com/question/10093236
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Question 9 of 10
Which of the following lists of ordered pairs is a function?
OA. (2, 5), (3, 6), (6,9)
OB. (2, 5), (3, 6), (2, 1)
C. (-1, 2), (2, 3), (3, 1), (2, 5)
O D. (1, 2), (4, 0), (3, 5), (4,3)
Answer: A. (2, 5), (3, 6), (6,9)
Step-by-step explanation:
Each value of x maps onto only one value of y.
Sam drops a ball from a height of 144 feet. How long will it take for the ball
to hit the ground? Ignore the air resistance.
Answer:
3 seconds for the ball to hit the ground.
Step-by-step explanation:
To calculate how long it will take for an object to drop(with no force of velocity), use [tex]-16t^{2}[/tex] and 144 will be our initial height, so we use the equation:
[tex]f(x) = -16t^{2} + 144[/tex]
Now, lets simplify this equation. We have a GCF (greatest common factor) of -16, which goes into 144, 9 times. Your simplified equation will look like this.
[tex]f(x) = -16(t^{2} - 9)[/tex]
When we have two squares in a group of parentheses, we must simplify that. Therefore, we use the sum and difference pattern. The sum and difference pattern requires a -3 and 3, because two positives and/or two negatives would not result in a -9, so we must use one positive, and one negative. Therefore, we keep the GCF of -16, simplify [tex]t^{2} -9[/tex], to get a final equation of:
[tex]f(x) = -16(t-3)(t+3)[/tex]
Now, we solve for t to see how long it will take for the ball to reach the ground with no added velocity.
[tex]t=-3,3[/tex]
Time can never be negative, when we are talking about a present-time situation. Therefore, we can not have -3 as an answer, and we have 3 as a final answer. It will take 3 seconds for the ball to reach the ground.
The sum of series of 4+ 15 + 26 + ….. + 213
Decompose the terms in the sum as
[tex]4 + 15 + 26 + \cdots + 213 = 4 + (4 + 11) + (4 + 2\times11) + \cdots + (4 + 19\times11)[/tex]
so there are 20 terms in the sum. Then our sum simplifies to
[tex]4 + 15 + 26 + \cdots + 213 = 4\times20 + (0+1+2+\cdots+19)\times11[/tex]
Now, if
[tex]S = 1 + 2 + 3 + \cdots + 17 + 18 + 19[/tex]
we can reverse the order of terms to get the same sum,
[tex]S = 19 + 18 + 17 + \cdots + 3 + 2 + 1[/tex]
so that doubling up the sum gives
[tex]2S = (1 + 19) + (2 + 18) + \cdots + (18 + 2) + (19 + 1) = 19\times20 \implies S=19\times10=190[/tex]
So, our sum evaluates to
[tex]4 + 15 + 26 + \cdots + 213 = 4\times20 + 190\times11 = \boxed{2170}[/tex]
i need help with this only answer
Answer:
27.03 or 27 3/100
Step-by-step explanation:
Plug in numbers
The solution to the fraction expression at x = 1¹/₁₀ is: 10.97
How to solve Fraction Problems?The fraction expression is given as:
3(5 - ¹/₆x) + ¹/₈(32 + 6x) + 7.3x - 5 * 0.05x
Breaking this down gives us:
15 - ¹/₂x + 4 + ³/₄x + 7.3x - 0.25x
= 19 - 7.3x
Now, we want to plug in 1¹/₁₀ for x.
1¹/₁₀ can be expressed as ¹¹/₁₀ and as such:
19 - 7.3(¹¹/₁₀) = 10.97
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1. Write a linear equation with the given information
Through (4,-5), parallel to y = -x + 1(4 Points)
2. Write a linear equation with the given information
Through (2,-1), perpendicular to y = -2/3x + 5(4 Points)
(please step by step thank you)
1. The equation of the parallel line is y = -x - 1.
2. The equation of the perpendicular line is y = 3/2x - 4.
What are the Equations of Parallel and Perpendicular Lines?Lines that are parallel have the same slope while slope values for perpendicular lines are negative reciprocals.
1. The slope (m) of y = -x + 1 is -1. Substitute m = -1 and (x, y) = (4, -5) into y = mx + b:
-5 = -1(4) + b
-5 = -4 + b
-5 + 4 = b
b = -1
Substitute b = -1 and m = -1 into y = mx + b
y = -x - 1
2. The slope (m) of y = -2/3x + 5 is -2/3.
Negative reciprocal of -2/3 is 3/2.
Substitute m = 3/2 and (x, y) = (2, -1) into y = mx + b:
-1 = 3/2(2) + b
-1 = 3 + b
-1 - 3 = b
b = -4
Substitute b = -4 and m = 3/2 into y = mx + b
y = 3/2x - 4
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Which of the following graphs is described by the function given below?
y = x²-4x-12
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Graph B is the graph that describes the function.
What is a quadratic graph?A quadratic graph is a graph of quadratic functions which have the power of the variable as 2. They are usually u-curved or inverted v-curved.
Analysis:
if we solve the quadratic function, y = [tex]x^{2}[/tex] -4x -12
when the curve touches the x-axis y = 0
[tex]x^{2}[/tex] -4x -12 = 0
[tex]x^{2}[/tex] -6x +2x -12 = 0
x(x-6) +2(x-6)
(x+2)(x-6) = 0
x = -2 or 6
From the graph, The second graph(graph B) shows the points on the x-axis x = -2 and x = 6.
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