Answer:
First find the x and y intercepts. Recall that intercepts intersect the x and y axis of a graph, therefore either the x or y value of a coordinate point must be 0 in order for it to be an intercept.
After you find the intercept, plot the them on the cartesian coordinate system and draw a straight line (it’s a linear equation) going through the two intercepts.
Side note: Not sure how credentials work on Quora yet. I meant to say I am a student
The equation of the lines can be plotted on the graph after calculating the coordinates on each line.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have two linear equation:
x = 4y
x + y = 7.0
To plot the linear equation first we will find the few coordinates to plot on the coordinate plane.
For the equation of line:
x = 4y
x 0 1 2 3 -1 -2 -3
y 0 4 8 12 -4 -8 -12
For the equation of line:
x + y = 7.0
x 0 1 2 3 -1 -2 -3
y 7 6 5 4 8 9 10
Thus, the equation of the lines can be plotted on the graph after calculating the coordinates on each line.
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There are 90 sixth graders at Wilson Middle School. Only 60% of the sixth graders will attend the morning assembly. How many sixth graders will be at the morning assembly?
A.44
B.54
C.64
D.74
Answer:
B, 54
Step-by-step explanation:
(x³ + ³) / (x - y)
Do not include parentheses in your answer.
The simplified expression of [tex]\frac{x^3 + (-y)^3}{(x - y}[/tex] is [tex]x^2+xy+y^2[/tex]
Complete questionSimplify the expression: (x³ + (-y)³) / (x - y)
Do not include parentheses in your answer.
How to simplify the expression?The expression is given as:
[tex]\frac{x^3 + (-y)^3}{(x - y}[/tex]
Open the inner bracket
[tex]\frac{x^3 -y^3}{(x - y}[/tex]
Apply the difference of two cubes to the numerator
[tex]\frac{(x-y)(x^2+xy+y^2)}{(x - y}[/tex]
Cancel out the common factors
[tex]x^2+xy+y^2[/tex]
Hence, the simplified expression of [tex]\frac{x^3 + (-y)^3}{(x - y}[/tex] is [tex]x^2+xy+y^2[/tex]
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^
Which is the graph of the linear inequality 2x - 3y < 12?
The graph of the linear inequality 2x – 3y < 12 is given below. Then the correct option is A.
The missing options are given below.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequality is given below.
2x – 3y < 12
Then the correct graph will be given below.
Then the correct option is A.
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Find the least number which when divided by 12, 18 and 20 leaves no reminder.
Answer:
180
Step-by-step explanation:
Find the LCM of 12, 18, and 20
[tex]12 = 2 \times 2 \times 3[/tex]
[tex]18 = 2 \times 3 \times 3[/tex]
[tex]20 = 2 \times 2 \times 5[/tex]
LCM = 2 × 2 × 3 × 3 × 5 = 180
Find the equation of the line with slope 43 and y-intercept (0,−3).
[tex]\triangleright[/tex]Hii! [tex]\triangleleft[/tex]
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}}}\circ\leftharpoonup[/tex] Equation: [tex]\bullet[/tex] y=43x-3 ✅
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}}}\circ\leftharpoonup[/tex]
Do you need to know the equation of the line with a slope of -43 and a y-intercept of (0,-3)? No problem! Luckily, there's a formula to find it! (:
The Slope Intercept FormulaThe slope intercept formula, [tex]\boldsymbol{y=mx+c}[/tex], comes in handy when we need to find the equation of a line!
In this formula,
"m" denotes the slope"c" denotes the y intercept-- ↩
This particular question provides us both "m" and "c."
m=43c=-3 (It's the second co-ordinate, the y co-ordinate, in the point "(0,-3)"Stickin the values
[tex]\boldsymbol{y=43x+(-3)}[/tex]
Simplify!
[tex]\boldsymbol{y=43x-3}[/tex]
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. \: Dream big. }[/tex]
--
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--
Determine the area of a sector with√20 radius meters, and central angle 30°.
I will mark brainliest!
Answer Options:
20πm²
5π/3m²
30πm²
π/3²
Answer: [tex]\frac{5\pi}{3}[/tex]
Step-by-step explanation:
[tex]A=(\sqrt{20})^{2}(\pi)\left(\frac{30}{360} \right)=\boxed{\frac{5\pi}{3}}[/tex]
please help! I need this quickly
write an equation in standard form of the line passing through the points (12,6) and (-3,11)
Answer:
x + 3y = 30
Step-by-step explanation:
We are given that a line contains the points (12,6) and (-3,11).
We want to write the equation of this line in standard form.
Standard form is written as ax+by=c, where a, b, and c are free integer coefficients, however a and b cannot be 0, and a cannot be negative.
Regardless, before we write an equation in slope-intercept form, we must first write the equation in a different form, such as slope-intercept form.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y-intercept.
So first, let's find the slope of the line.
The slope (m) can be found using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points.
Even though we already have 2 points, let's label their values to avoid any confusion and mistakes when calculating.
[tex]x_1=12\\y_1=6\\x_2=-3\\y_2=11[/tex]
Now substitute these values into the formula.
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{11-6}{-3-12}[/tex]
Subtract
m=[tex]\frac{5}{-15}[/tex]
Simplify
m=[tex]-\frac{1}{3}[/tex]
The slope is -1/3
Here is the equation of the line so far in slope-intercept form:
[tex]y=-\frac{1}{3} x + b[/tex]
We need to solve for b.
As the equation passes through (12,6) and (-3,11), we can use either one to help solve for b.
Taking (12, 6) for example:
[tex]6=-\frac{1}{3}(12) + b[/tex]
Multiply
[tex]6=-\frac{12}{3} + b[/tex]
Divide
6 = -4 + b
Add 4 to both sides.
10 = b
Substitute 10 as b in the equation.
[tex]y = -\frac{1}{3} x + 10[/tex]
Here is the equation in slope-intercept form, but remember, we want it in standard form.
In standard form, the values of both x and y are on the same side, so let's add -1/3x to both sides.
[tex]\frac{1}{3} x + y = 10[/tex]
Remember that a (the coefficient in front of x) has to be an integer, 1/3 is not an integer.
So, let's multiply both sides by 3 to clear the fraction.
[tex]3(\frac{1}{3} x + y) = 3(10)[/tex]
Multiply.
x + 3y = 30
Topic: finding the equation of the line (standard form)
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Write the factored form of the polynomial function with real coefficients, a lead coefficient of 1, and zeros
of -3, -3, 4, and 2.
y(x) =
The factored form of the polynomial function is y(x) = (x + 3)²(x - 4)(x - 2)
How to determine the factored form?The given parameters are:
Leading coefficient, a = 1Zeros = -3, -3, 4, and 2.Rewrite the zeros as:
x = -3, x = -3, x = 4 and x = 2
Set the zeros to 0
x + 3 = 0, x + 3 = 0, x - 4 = 0 and x - 2 = 0
Multiply the zeros
(x + 3) * (x + 3) * (x - 4) *(x - 2) = 0
Express as a function
y(x) = a(x + 3) * (x + 3) * (x - 4) *(x - 2)
Substitute 1 for a
y(x) = (x + 3)²(x - 4)(x - 2)
Hence, the factored form of the polynomial function is y(x) = (x + 3)²(x - 4)(x - 2)
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ƒ(x) = x² - x - 1
What is the average rate of change of f over
the interval -1 ≤ x ≤ 1?
Answer: -1
Step-by-step explanation:
[tex]f(-1)=(-1)^2 - (-1)-1=1\\\\f(1)=1^{2}-1-1=-1\\\\\therefore \frac{f(-1)-f(1)}{-1-1}=\frac{1-(-1)}{-1-1}=\frac{2}{-2}=\boxed{-1}[/tex]
An expression is shown below:
4ck2 + 10k2 − 16ck − 40k
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
Part A:
The greatest common factor is 2k
2k(2ck + 5k - 8c - 20)
Part B:
factor by grouping
2k (k(2c + 5) - 4(2c + 5))2k(k - 4)(2c + 5)2k(k - 4)(2c + 5) is the final factored form
Consider the given density curve.
A density curve is at y = one-third and goes from 3 to 6.
What is the value of the median?
3
4
4.5
6
Picture posted below
Answer: 4.5
Step-by-step explanation:
[tex]\frac{6+3}{2}=\boxed{4.5}[/tex]
We want to find the median for the given density curve.
The value of the median is 4.5. ({3+6)/2}
Let's see how to solve this.
First, for a regular set {x₁, ..., xₙ} we define the median as the middle value.
The difference between a set and a density curve is that the density curve is continuous, so getting the exact middle value can be harder.
Here, we have a constant density curve that goes from 3 to 6.
Because it is constant, the median will just be equal to the mean, thus the median is the average between the two extreme values.
Remember that the average between two numbers a and b is given by:(a + b)/2
So we get: m = (6 + 3)/2 = 4.5
So we can conclude that the value of the median is 4.5, so the correct option is the second one, counting from the top.
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for f(x)-4x+1 and g(x)-x^2-5, find (g/f) (x)
Answer:
A.
Step-by-step explanation:
let me know if you want an explanation :))
Answer:
A
Step-by-step explanation:
PLEASEEEEEE HELPPPPPPP!!! 50 POINTSSSSSS
12 = 6^2 + 7^2 - 2 (6) (7) (cosA)
solve for the cosA
Step-by-step explanation:
please mark me as brainlest
2. Use the relationship you established in part 1 to find the m your work. (1 point)
When faced with an unknown variable in a maths problem, it is advised to find the subject formula and then use it to solve the equation to find the answer.
What is an Unknown Variable?This refers to the type of variable in a given equation that has to be solved for because its properties or value is not known.
Hence, we can see that when faced with an unknown variable in a given math problem, it is better to find the subject formula, then input the value of this into an equation, to find the value of the variable.
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At the taco truck an order of 1 taco and 3 quesadillas cost $ 26.50. An order if 3 tacos and 1 quesadilla cost $19.50. for 5 tacos and 1 quesadilla. What is the cost of one taco and the cost of one quesadilla?
Answer:
The cost of 1 taco = $4
The cost of 1 quesadilla = $7.50
Step-by-step explanation:
Let the cost of tacos be x and the cost of quesadillas be y.
Given condition:x + 3y = 26.50 ------------------(1)
3x + y = 19.50 -------------------(2)
Multiply Eq. (2) by 3
3(3x + y) = 19.50 * 3
9x + 3y = 58.5 -----------------(3)
Subtract Eq. (3) from (1)
x + 3y - 9x - 3y = 26.50 - 58.50
x - 9x = -32
-8x = -32
8x = 32
Divide 8 to both sides
x = $4
Put x = 4 in (1)
4 + 3y = 26.50
Subtract 4 to both sides
3y = 26.50 - 4
3y = 22.50
Divide 3 to both sides
y = $7.50
So,
The cost of 1 taco = $4
The cost of 1 quesadilla = $7.50
[tex]\rule[225]{225}{2}[/tex]
4x^2+2xy-10y^2+9=0 what is the value of a,b,c and the discriminant?
basically you treat y like a number and not a variable
Answer:
a is 4
b is 2y
c is -10y²+9
discriminant is 4(41y²-36)
Step-by-step explanation:
4x²+2xy-10y²+9=0
rewrite in standard form of a quadratic equation like ax² + bx + c = 0
4x²+2yx-10y²+9=0
basically you treat y like a number and not a variable
a is the number with the x²
right away we know a is 4 because of 4x²
b is the one with x so in this formula b is 2y
c is the number without the x which in this case is -10y²+9
discriminant is
b² - 4ac
(2y)²- (4)(4)(-10y²+9)
4y²-(16)(-10y²+9)
4y²-(16)(-10y²+9)
4y²+160y²-144
164y²-144 =
4(41y²-36)
Which absolute value function, when graphed, will be wider than the graph of the parent function, f(x) = |x|?
f(x) = |x| + 3
f(x) = |x − 6|
f(x) = |x|
f(x) = 9|x|
The absolute value function that will be wider than the graph of the parent function, f(x) = |x| is (d) f(x) = 9|x|
How to determine the function?The parent function is given as:
f(x) =|x|
A wider function would have the following equation
f(x) = k|x|
Where:
k > 0
From the list of options, we have:
f(x) = 9|x|
Hence, the absolute value function that will be wider than the graph of the parent function, f(x) = |x| is (d) f(x) = 9|x|
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Answer:
getting to the point , D.
Step-by-step explanation:
trust
Please help my question is in the attachment!
Answer:
a = -9
b = -3
c = 11
d = 19
Step-by-step explanation:
a. x = -2
y= x² + 3x + 1
y= -2²+ 3(-2)+1
y= -4-6+1
y = -9
b. x= -1
y= x² + 3x+ 1
y= -1² + 3(-1) +1
y= -1 -3 + 1
y = -3
c. x =2
y = x² + 3x +1
y= 2²+ 3(2) +1
y= 4 +6 +1
y = 11
d. x= 3
y = x² +3x +1
y = 3² +3(3) +1
y= 9 +9 +1
y = 19
what is the answer please??
Answer:
See below
Step-by-step explanation:
Area of a circle = pi * r^2
for this circle : Area = 3.142 * 10 * 10 = 314.2 cm^2
The formula for area of a circle is [tex]\pi r^{2}[/tex]
So using pi as 3.142, we can do 3.142 • 100 which is 314.2 when moving place values.
Even though you did not ask, the circumference formula is 2[tex]\pi[/tex]r.
If we were given the same information, where the radius is 10, and we were solving circumference, then we would do 3.14 • 20 = 62.8.
Brainliest if helpful.
a supermarket display consists of boxes of cereal. the bottom row has 23 boxes. each row has three fewer boxes than the row below it. the display has six rows.
Answer:
93 boxes
Step-by-step explanation:
sixth row has 23 boxes
fifth row has 20 boxes
fourth row has 17 boxes
third row has 14 boxes
second row has 11 boxes
first row has 8 boxes
the total is thus 23+20+17+14+11+8=93
Question:-
[tex] \dfrac{1}{2} + \dfrac{1}{4} [/tex]
Help!!
:"(
[tex]{\huge \underline{{ \fbox \color{red}{A}}{\fbox \color{green}{n}}{\fbox \color{purple}{s}}{\fbox \color{brown}{w}}{\fbox \color{yellow}{e}}{\fbox \color{gray}{r } }}}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf \red{ \dfrac{1}{2} + \dfrac{1}{4} = \dfrac{3}{4} }[/tex]
Step by step explanation :-
The only thing you have to do is add the numerator to the denominator, in this case you have to add the first ones from the front, which can be these 2+1/4, which would result in 3/4, and this is called the Commutative Property.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bf \gray{ \dfrac{1}{2} + \dfrac{1}{4} = \dfrac{1}{4} + \dfrac{1}{2} }}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bf \green{\dfrac{2 + 1}{4} = \dfrac{1 + 2}{4} }}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed {\bf \blue{\dfrac{3}{4} = \dfrac{3}{4}} }[/tex]
Answer :- The answer is 3/4
¿What is commutative property?
It is to change different ways in order of the addends the result would be the same.
Example :-
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed {\bf \blue{\dfrac{a}{b} + \dfrac{c}{d}} = {\dfrac{c}{d} + \dfrac{a}{b}} }[/tex]
I hope I've helped : )
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: Final \:\: value = \cfrac{3}{4}[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{1}{2} + \cfrac{1}{4} [/tex]
[ take LCM ]
[tex]\qquad \tt \rightarrow \: \cfrac{2}{4} + \cfrac{1}{4} [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{2 + 1}{4} [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{3}{4} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
please answer this! (from khan academy 6th grade math)
Answer:
(-5, -7) and the x-axis
Step-by-step explanation:
when looking for a point that is 7 points away, we are looking for a difference of 7 in either the x-value or the y-value.
[remember: a point is written as (x, y) ]
We know that the x-value is -7, meaning that it is 7 units under the x-axis (meaning that it is 7 units away)
We know that our point, (2 , -7) has the same y-value as (-5, -7), so we are looking for a change in x. The difference (which is the change) between:
-5 and 2 is 7
(2 - (-5) = 2 + 5 = 7)
so, both the x-axis and the point (-5, -7) are 7 units away from (2, -7)
(the other point (-7, 7) is not near (2 , -7) at all--they have a larger difference on both the y-values, the x-values, and the length of if you made a diagonal line)
(I've attached an image to help you visualize what we're doing)
hope this helps!!
Given:
PLEASE HELP ASAP!
Part I: Use the given information to determine . Show all of your work.
Part II: Use complete sentences to explain the steps necessary in solving for . Justify your explanation by including all theorems, postulates, or definitions used.
The value of angle ∠DEC = 60 degree.
The complete question is
In the given the figure above, m∠BAC = 64° and m∠CBA = 56°.
Part I: Find the m∠DEC.
Part II: Explain the steps you took to arrive at your answer. Make sure to justify your answer by identifying any theorems, postulates, or definitions used.
What is a Triangle ?A triangle is a polygon with three sides and three vertices and three angles.
As it is given that
AB || CD
Let BC be the transversal , then
∠CBA = ∠DCB (alternate opposite angles)
∠DCB = 56 degree
As the sum of opposite interior angle sis equal to exterior angle therefore ∠ ECB = 120 degree
∠DCE = 120-56 = 64 degree
BC || DE
∠EDC = ∠DCB = 56 degree (alternate opposite angles)
Sum of all the interior angles of a triangle is equal to 180 degree
56 +64+∠DEC = 180
∠DEC = 60 degree.
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A business student is interested in estimating the 95% confidence interval for the proportion of students who bring laptops to campus.
He wishes a precise estimate and is willing to draw a large sample that will keep the sample proportion within five percentage points
of the population proportion. What is the minimum sample size required by this student, given that no prior estimate of the population
proportion is available?
(You may find it useful to reference the z table. Round intermediate calculations to at least 4 decimal places
and "2" value to 3 decimal places. Round up your answer to the nearest whole number.)
Using the z-distribution, the minimum sample size required by this student is of 385.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
We want a margin of error of M = 0.05, with no prior estimate, hence [tex]\pi = 0.5[/tex], then we have to solve for n to find the minimum sample size.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.05\sqrt{n} = 1.96(0.5)[/tex]
[tex]\sqrt{n} = 1.96 \times 10[/tex]
[tex](\sqrt{n})^2 = (1.96 \times 10)^2[/tex]
n = 384.16
Rounding up, the minimum sample size is of 385.
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The graph shown below expresses a radical function that can be written in the form F(x) = a(x+ k)^1/n+ C. What does the graph tell you about the value of a in this function?
For the function F(x)=[tex]a(x+k)^{1/n}+C[/tex] the value of a is less than zero and the correct option is option d.
Given the value of function F(x)=[tex]a(x+k)^{1/n}+C[/tex].
We have to put the function equal to 0 for finding the nature of a and C is a fixed number in the function :
a[tex](x+k)^{1/n}[/tex]+C=0
a[tex](x+k)^{1/n}[/tex]=-C
a=-C/[tex](x+k)^{1/n}[/tex]
Since negative sign is coming before a and the value of rest of the expression cannot be negative so the value of a should b negative which means less than 0. The rest of the expression cannot be negative because it has a power of 1/n which only gives positive values like modulas.
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What is the value of n in the equation 2n² + 4n = 0? What is the value of n in the equation 2n² + 4n = 0 ?
N = 0
2(0)² + 4(0) = 0
0 + 0 = 0
The scale on a map shows that 200 miles is represented by 5 inches on a map. Which proportion can be used to find the distance on the map, x, that represents 50 miles? StartFraction 5 over 200 EndFraction = StartFraction x over 50 EndFraction StartFraction 200 over 5 EndFraction = StartFraction x over 50 EndFraction StartFraction 50 over 200 EndFraction = StartFraction 5 over x EndFraction StartFraction 5 over 50 EndFraction = StartFraction x over 200 EndFraction
The proportion can be used to find the distance on the map (x) that represents 50 miles will be x/50 = 5 / 200. Then the correct option is A.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
The scale on a map shows that 200 miles is represented by 5 inches on a map.
Then the proportion can be used to find the distance on the map (x) that represents 50 miles will be
x/50 = 5 / 200
Then the correct option is A.
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7. Sapna travelled 48 km to meet her parents. She travelled the first 18 km by car and the remaining distance by train. Find the fraction of the journey sapna travelled by car and train
The fraction of the journey Sapna traveled by car and train is 3/8 and 5/8 respectively.
We know that fraction is an expression in mathematics used to denote the division of two whole numbers.
Given that the total distance = 48 km.
The distance Sapna traveled by car = 18 km.
So, the fraction is = distance traveled by car/total distance = 18/48 = 3/8
The distance Sapna traveled by train = 48 - 18 km = 30 km.
So, the fraction is = distance traveled by train/total distance = 30/48 = 5/8
Therefore the fraction of the journey Sapna traveled by car and train is 3/8 and 5/8 respectively.
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The radius of a circle is 4 millimeters. What is the circle's area? Use 3.14 for pi.
(The answer MUST BE ONE OF THE ANSWERS BELOW)
Answer:
50.24 mm^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2 where r is the radius
A = 3.14 ( 4)^2
= 50.24 mm^2
Answer:
c. 50.24 square millimeters
Step-by-step explanation:
Radius of circle = 4 milimeters.
Area of a circle = πr²
Area = 3.14 × 4² (π = 3.14)
= 50.24 square millimeters
PLEASE HELP
The function
shown.
Select from the drop-down menus to correctly describe the end
f (x).
behavior of
f(x) = -2(0.25) + 1is
As x decreases without bound, the graph of
Choose...
Choose...
As x increases without bound, the graph of
f (x)
‹ƒ (x)
f(x)
1 2
5
4
3
2
1
-4-3-2-11.
3
1
2 3
4 5
4
6
5 6
7 8