What is the 7th row of Pascal's triangle?OA. 16 15 35 156 1OB.17 21 35 35 2171OC. 16 15 20 15 61D. 15 10 10 51
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Each number inside Pascal Triangle is the sum of the two numbers above. So, we have that the 7th row is the last row from the piocture below. Therefore, the answer is option B
Related Questions
In an experiment involving a treatment applied to 5 test subjects, researchers plan to use a simple random sample of 5 subjects selected from a pool of 7 available subjects. How many different random samples are possible?
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Solution:
The number of ways to select 5 from 7 (when order does not matter) is;
[tex]\begin{gathered} ^7C_5=\frac{7!}{(7-5)!5!} \\ \\ ^7C_5=\frac{7\times6\times5!}{2!\times5!} \\ \\ ^7C_5=21 \end{gathered}[/tex]ANSWER: 21 ways
6c + 14 = -5c + 4 + 9csolve for c
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This is a simple question we just need to reorganize our equation and solve it to find the value of "c" as follows:
We can see while we are reorganizing our equation we move some numbers and variables from a term to another and when we do that we need to change its sign as we did above. Now let's keep going on our calculation:
As we can see, our final answer is c = -5
Determine the amount of the ordinary annuity at the end of the given period. (Round your final answer to two decimal places.)$200 deposited quarterly at 6.9 for 6 years
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For solving this question it is necessary to apply the formula
[tex]FV=P\cdot(\frac{(1+r)^n-1}{r})[/tex]Where:
FV = future value of the account;
P= deposit = $200
r = quarterly percentage - use decimal=0.069
n = number of deposits = 4* 6=24
[tex]\begin{gathered} FV=P\cdot(\frac{(1+r)^n-1}{r}) \\ FV=200\cdot(\frac{(1+\frac{0.069}{4})^{24}-1}{\frac{0.069}{4}}) \\ FV=200\cdot(\frac{(1+0.01725)^{24}-1}{0.01725}) \\ FV=200\cdot(\frac{(1.01725)^{24}-1}{0.01725}) \\ FV=200\cdot\frac{0.5075}{0.01725}=5884.38 \\ FV=5884.38 \end{gathered}[/tex]FV=$5884.38
The equation for a proportional relationship is y=531. The graph of therelationship passes through the point (1,58) which represents the
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The given equation is
[tex]y=5.8x[/tex]Where 5.8 is the constant of proportionality.
Additionally, the point (1, 5.8) represents the constant of proportionality because it's telling the constant ratio of change between variables.
Therefore, the answer is a constant ratio of change.
Hi there,i am having some trouble solving the following two questions relating to extrema and intervals:
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We have the following function:
[tex]y=ln|x^2+x-20|[/tex]The graph of this function is given by:
We know that a function is increasing is the first derivative is greater than zero. The derivative of the given function is given by
[tex]\frac{dy}{dx}=\frac{2x+1}{x^2+x-20}[/tex]Then, the condition is given by
[tex]\frac{dy}{dx}=\frac{2x+1}{x^{2}+x-20}>0[/tex]which implies that
[tex]\begin{gathered} 2x+1>0 \\ then \\ x<-\frac{1}{2} \end{gathered}[/tex]By means of this result and the graph from above, f(x) is increasing for x in:
[tex](-5,-\frac{1}{2})\cup(4,\infty)[/tex]Now, the function is decreasing when
[tex]\frac{dy}{dx}<0[/tex]which give us
[tex]\begin{gathered} \frac{dy}{dx}=\frac{2x+1}{x^{2}+x-20}<0 \\ 2x+1<0 \\ then \\ x>-\frac{1}{2} \end{gathered}[/tex]Then, by means of this result and the graph from above, the function is decreasing on the interval:
[tex](-\infty,-5)\cup(-\frac{1}{2},4)[/tex]In order to find the local extremal values, we need to find the second derivative of the given function, that is,
[tex]\frac{d^2y}{dx^2}=\frac{d}{dx}(\frac{2x+1}{x^2+x-20})[/tex]which gives
[tex]\frac{d^2y}{dx^2}=\frac{(x^2+x-20)(2)-(2x+1)(2x+1)}{(x^2+x-20)^2}[/tex]or equivalently
[tex]\frac{d^2y}{dx^2}=\frac{2(x^2+x-20)-(4x^2+4x+1)}{(x^2+x-20)^2}[/tex]which can be written as
[tex]\frac{d^2y}{dx^2}=\frac{2x^2+2x-40-4x^2-4x-1}{(x^2+x-20)^2}[/tex]then, we get
[tex]\frac{d^2y}{dx^2}=\frac{-2x^2-2x-41}{(x^2+x-20)^2}[/tex]From the above computations, the critical value point is obtained from the condition
[tex]\frac{dy}{dx}=\frac{2x+1}{x^{2}+x-20}=0[/tex]which gives
[tex]\begin{gathered} 2x+1=0 \\ then \\ x=-\frac{1}{2} \end{gathered}[/tex]This means that the critical point (maximum or minimum) is located at
[tex]x=-\frac{1}{2}[/tex]In order to check if this value corresponds to a maximum or mininum, we need to substitute it into the second derivative result, that is,
[tex]\frac{d^{2}y}{dx^{2}}=\frac{-2(-\frac{1}{2})^2-2(-\frac{1}{2})-41}{((-\frac{1}{2})^2+(-\frac{1}{2})-20)^2}[/tex]The denimator will be positive because we have it is raised to the power 2, so we need to check the numerator:
[tex]-2(-\frac{1}{2})^2-2(-\frac{1}{2})-41=-\frac{2}{4}+1-41=-40.5[/tex]which is negative. This means that the second derivative evalueated at the critical point is negative:
[tex]\frac{d^2y}{dx^2}<0[/tex]which tell us that the critical value of x= -1/2 corresponds to a maximum.
Since there is only one critical point, we get:
f(x) has a local minimum at x= DNE
f(x) has a local maximum at x= -1/2
The variables x = 3/4,y= 2/9 z = 6 are related in such a way that zvaries jointly with x and y.Find z when x = --3 and y = 5.
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Given:
x=3/4, y=2/9 and z=6
z varies jointly with x and y.
From the above data, we can obtain a relation connecting x and z.
The relation connecting z and x can be written as,
[tex]z=8x[/tex]Putting x=3/4 in the above equation,
[tex]z=8\times\frac{3}{4}=6[/tex]So, the relation z=8x is satisfied.
Similarly, the relation between z and y can be written as
Simplify (combine like terms): -8x^4 + 7x^3 + 5x + 4x^4 - 6x^3 +2
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We will have the following:
[tex]-8x^4+7x^3+5x+4x^4-6x^3+2=(-8x^4+4x^4)+(7x^3-6x^3)+5x+2[/tex][tex]=-4x^4+x^3+5x+2[/tex]in CDE, J is the centroid. If JF=15 find EJ
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From the figure, J is the centroid. Hence, the lines DH, FE and CG are medians.
Therefore, we can apply the 2/3 rule, that is, the centroid is 2/3 of the way from the vertex to the opposite midpoint.
In other words, we can write
[tex]JE=\frac{2}{3}FE[/tex]since, we know that FE=FJ+JE, we have
[tex]JE=\frac{2}{3}(FJ+JE)[/tex]and, from this equation we can find JE since FJ=15:
[tex]JE=\frac{2}{3}(15+JE)[/tex]The, we obtain
[tex]\begin{gathered} JE=\frac{2}{3}(15)+\frac{2}{3}JE \\ JE-\frac{2}{3}JE=\frac{2}{3}(3\cdot5) \\ \end{gathered}[/tex]in which we moved (2/3)JE to the left hand side and we wrote 15 as 3*5. Now, it reads
[tex]\begin{gathered} \frac{3}{3}JE-\frac{2}{3}JE=2\cdot5 \\ \frac{1}{3}JE=10 \\ JE=3\cdot10 \\ JE=30 \end{gathered}[/tex]Therefore, JE=EJ=30.
There are five performers who represent the Kami access weekend at a comedy club how many different ways are there to schedule this appearances
Answers
SOLUTION
Given the question in the image, the following is the solution to the problem
Step 1: Scheduling n performers is found by n! ways...so five performers gives 5! The different number of ways for 5 performers therefore mean:
[tex]\begin{gathered} 5!=5\times4\times3\times2\times1 \\ =120\text{ ways} \end{gathered}[/tex]Hence, there are 120 different ways of scheduling these appearances.
Write the letter for the correct answer in the blank at the right of ea1. Which of the following sets of values completes the function tableInput (x)4x + 2Output (y)454(4) +24(5) +24(6) +26A. 16, 20, 24B. 18, 19, 20C. 18, 22, 26D. 0,1,22. Molly is buying packages of party favors for herbirthday nartyr Iaina tlR
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The missing column is the output for the function, so we just need to evaluate the expression in the second column.
For the second row, we have:
[tex]4(4)+2[/tex]We first evaluate the multiplication and then the addition:
[tex]4(4)+2=16+2=18[/tex]For the third row, we have the same steps:
[tex]4(5)+2=20+2=22[/tex]And for the last too:
[tex]4(6)+2=24+2=26[/tex]Thus, the outputs are 18, 22, 26, alternative C.
I need help with this practice I attempted this practice previously and my attempt is in the picture
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We will draw a sketch for the given triangle to find its area
The area of the triangle will be
[tex]A=\frac{1}{2}\times XY\times ZM[/tex]Since ZX = ZY = 7, then the triangle is isosceles
Then the height ZM will bisect the base XY
Then we can find ZM by using Pythagoras Theorem
[tex]\begin{gathered} ZM=\sqrt[]{7^2-3^2} \\ ZM=\sqrt[]{49-9} \\ ZM=\sqrt[]{40} \\ ZM=2\sqrt[]{10} \end{gathered}[/tex]Since XY = 6, then
The area of the triangle is
[tex]\begin{gathered} A=\frac{1}{2}\times6\times2\sqrt[]{10} \\ A=6\sqrt[]{10}\text{ square units} \end{gathered}[/tex](See image below) The point A(-15) is rotated 270° clockwise about the origin. The coordinates of A' are?
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Given:
A (-1,5) rotated 270 clockwise.
Find: A' coordinates
Sol:.
(x,y) Rotated by 270 become (y,-x).
A = (-1,5)
[tex]\begin{gathered} A=(-1,5) \\ A^{\prime}=(5,-(-1)) \\ A\text{'=(5,1)} \end{gathered}[/tex]I need help with this practice problem It has an additional pic of a graph that I will include.
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Given:
The function is given as,
[tex]f(x)=\sin (\frac{\pi x}{2})\text{ . . . . . . (1)}[/tex]The objective is to plot the graph of the function.
Explanation:
To find the maximum point, consider x = 1 in the equation (1),
[tex]\begin{gathered} f(1)=\sin (\frac{\pi(1)}{2}) \\ f(1)=\sin (\frac{\pi}{2}) \\ f(1)=1 \end{gathered}[/tex]Thus, the coordinate is (1,1).
To find the minimum point, consider x = -1 in equation (1).
[tex]\begin{gathered} f(-1)=\sin (\frac{\pi(-1)}{2}) \\ f(-1)=\sin (\frac{-\pi}{2}) \\ f(-1)=-\sin (\frac{\pi}{2}) \\ f(-1)=-1 \end{gathered}[/tex]Thus, the coordinate is (-1,-1).
To plot the graph:
The graph of the function will be,
Hence, the graph of the function is obtained.
How do I rearrange 2x + y = -3 Into a Y = mx + b
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Solution
Given
[tex]2x+y=-3[/tex]Move the term 2x to the right-hand side and change its sign
[tex]y=-2x-3[/tex]Therefore, the required answer is
[tex]y=-2x-3[/tex]Each participant must pay $14 to enter the race. Each runner will be given a T-shirt that cost race organizers $3.50. If the T-shirt was the only expense for the race organizers, which of the following expressions represents the proportion of the entry fee paid by each runner that would be donated to charity? is it $14.00÷($14.00-$3.50)
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From the statement of the problem, we know that each participant:
• pays $14 to enter the race,
,• receives a T-shirt that cost $3.50 to the organizers.
The earnings minus the cost of the T-shirts will be donated to charity, so for each participant, the donation will be $14 - $3.50. So the proportion of the entry fee paid by each runner that would be donated to charity is:
[tex]\frac{14.00-3.50}{14.00}[/tex]Answer
A. ($14.00 - $3.50) / $14.00
Graph the line that has a slope of 1/7 and includes the point (0,5)
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Given the slope 1/7 and point (0,5) we are asked to graph a line.
To do this, the first thing we need to do is to plot the given data.
Plot the given point (0,5)
Next, since we know that the slope of a line is rise/run, given the slope 1/7, it means that from the point (0,5) we will "rise" 1 unit or move 1 unit up, and then "run" 7 units, or move 7 units to the right.
And then, we just connect the two points to form a line
Point A is located at (-3,5). Find its new coordinates after it is reflected along the x-axis then dilated using a scale factor of 4 with center of dilation at the origin.
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We have (-3,5)
The rule for reflection around the x-axis is
[tex](x,y)\rightarrow(x,-y)[/tex]so the point after the reflection is around x-axis
[tex](-3,5)=(-3,-5)[/tex]for the dilatation we need to multiply the point find above by 4
[tex]A^{\prime}=(-3(4),-5(4))=(-12,-20)[/tex]Jim has a new job and earns a salary of $46,000. Valorie has a new job and earns a salary of $59,000. Jim will receive a salary increaseof $2,700 per year and Valorie will receive a salary increase of $1,500 per year. Based on this information, which TWO statements arecorrect?es )A)It will take 10 years for Jim to earn the same salary as Valorie.B)It will take 12 years for Jim to earn the same salary as Valorie.D)When solved for x, 46,000x + 2,700 = 58,000x + 1,500 gives the number ofyears it will take Jim to earn the same salary as Valorie.When solved for x, 46,000 + 2,700x = 58,000 + 1,500x gives the number ofyears it will take Jim to earn the same salary as Valorie.When solved for x, 46,000x + 2,700x = 58,000x + 1,500x gives the numberof years it will take Jim to earn the same salary as Valorie.E)
Answers
Let's use the variable x to represent the number of years.
So, if the initial salary of Jim is $46,000 and it increases by $2,700 each year, after x years, his salary is:
[tex]46000+2700x[/tex]Doing the same for Valorire, her salary is:
[tex]58000+1500x[/tex]In order to find after how many years their salary will be the same, we can equate both salaries and calculate the value of x:
[tex]\begin{gathered} 46000+2700x=58000+1500x \\ 2700x-1500x=58000-46000 \\ 1200x=12000 \\ x=\frac{12000}{1200} \\ x=10 \end{gathered}[/tex]So let's check each option:
A.
True, it takes 10 years to they have the same salary.
B.
False, after 12 years Jim's salary is higher than Valorie's salary.
C.
False, the variable x should multiply the increase per year in the salary, not the initial salary.
D.
True, that's the equation and procedure we used.
E.
False, the variable x should multiply just the increase per year in the salary, not the initial salary.
So the correct options are A and D.
Krista wants to paint her house. she buys 7 1/2. gallons of paint. she uses 3/5 of the paint on the front of her house and then buys 1. 1/2. more gallons of paints how many gallons of paint does she have left
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We know that 7 1/2 is equivalent to 15/2.
If she uses 3/5, then it would remain 9/2 gallons.
[tex]\frac{15}{2}\cdot\frac{3}{5}=\frac{9}{2}=4.5[/tex]Then, she buys 1 1/2, which is equivalent to 1.5 or 3/2.
So, she has 6 gallons of paint.[tex]4.5+1.5=6[/tex]Step 1 of 2: Reduce the rational expression to lowest terms x/x^2 - 4xStep 2 of 2: Find the restricted values of X, if any, for the given rational expression.
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We have the following expression:
[tex]\frac{x}{x^2-4x}[/tex]Step 1. Reduce the rational expression to the lowest tem
By factoring the variable x, we get
[tex]\frac{x}{x(x-4)}[/tex]We can cancel x out as long as x is different from zero. Then one restricted value is x=0. So, If x is different from zero, our expression can be reduced to
[tex]\frac{x}{x^2-4x}=\frac{1}{x-4}[/tex]but x must be different from 4.
Step 2. Find the restricted values of x.
Since x can not be zero or four, the restricted values are x=0 and x=4
Before sketching the graph, determine where the function has its minimum or maximum value so you can place your first point there.
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We will have the following:
*The zeros in the function are at the values:
[tex]\begin{gathered} -0.5|x-2|=-2\Rightarrow|x-2|=4 \\ x=-2 \\ x=6 \end{gathered}[/tex]So, the zeros are at x = -2 an x = 6.
*The x-intercepts are at the points:
[tex](-2,0)[/tex]And
[tex](6,0)[/tex]*The y-intercept is at the point:
[tex]y=-0.5|0-2|+2\Rightarrow y=1[/tex]So, the y-intercept is located at the point:
[tex](0,1)[/tex]Which equation represents a line which is parallel to the line Y = -4/5x -8?
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1) Since we have a line described by this equation y=-4/5x -8, and it is written in the slope-intercept form. It is convenient for us to rewrite those into the slope-intercept form.
a) 5y-4x=-10 Add 4x to both sides
5y = -10 +4x Divide both sides by 5
y= -10/5 +4/5x
y= 4/5x -2
b) 5x-4y = -20 Subtract 5x to both sides
-4y= -20 -5x Divide both sides by -4
y = 5 +5/4x
y= 5/4x +5
c) 5x +4y = -24
4y = -24 -5x
y = -6 -5/4x
d) 4x +5y= 35
5y= 35-4x
y= 7-4/5x
2) Since Parallel lines have the same slope, then the line parallel to Y = -4/5x -8 is y= 7-4/5x (4x +5y=35)
Sarah can edge a large lawn in 3 hours. Jesse can edge a similar lawn in 2.5 hours. How long would it take Sarah and Jesse if they worked together?
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It takes sarah 3 hours to edge the lawn
so her rate = 1 lawn/ 3 hours
Jesse takes 2.5 hours, so his rate = 1 lawn / 2.5 hours
Together they will take a combined rate of sarah + Jesse
= 1/3 lawn/hour + 1/2.5 lawn/hour
= 1/3 + 1/5/2
= 1/3 + (1 x 2/5)
= 1/3 + 2/5 = 11/15 lawn/hour = 1/r
r = 1/11/15 = 15/11
The time = 15/11 =1 4/11 hours
[tex]\text{The time = 1}\frac{4}{11}hours[/tex]
Answer:
The time = 15/11 =1 4/11 hours
Step-by-step explanation:
Bonnie deposits $250 into a new savings account. The account earns 3.5% simple interest per year No money is added or removed from the savings account for 6 years. What is the total amount of money in her savings account at the end of the 6 years?
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Let's begin by identifying key information given to us:
Principal (p) = $250
Interest rate (r) = 3.5% = 3.5/100 = 0.035
Time (t) = 6 years
The simple interest is given by:
[tex]\begin{gathered} A=p(1+rt) \\ A=250(1+0.035\cdot6) \\ A=259(1+0.21) \\ A=250(1.21) \\ A=\text{\$}302.50 \end{gathered}[/tex]write the division expression in words and as a fraction: h ÷ 16
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we have
[tex]h\div16[/tex]in words will be
h between 16
in fraction will be
[tex]\frac{h}{16}[/tex]list all congruent pairs of congruent angles and write the ratios of the corresponding side lengths
Answers
Scale factor = 8/6 = 4/3 = 1.33333
Pairs of congruent angles;
m
m
m
Ratio of the coresponding side lengths
AC: BC = LN : MN
4.5 : 6 = 6 : 8
a dart hits the dartboard shown find the probability that it lands in the shaded regions? I don't know how to do this help
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The probabiity of a dart landing on the shaded regions is 0.2125
Here, we want to find the probability that the dartboard hits the shaded regions
Mathematicaly, all we have to do is to calculate the portion of the board that is shaded
All we have to do is to subtract the area of the 4 circles from the area of the given square
Area of the square is the square of its side
We have this as;
[tex]\text{Area of square = 4}\times4=16m^2[/tex]The circles are similar
Thus, their areas are same
We only need to calculate the area of one of the circles and multiply by four
As we can see, 4 m represents the diameters of two circles combined
The diameter of one of the circles will thus be 2 m
The radius we will need in the calculations is half of this
We have the radius as 2/2 = 1 m
The area of the circles is thus;
[tex]4\times\pi\times r^2\text{ = 4}\times3.142\text{ }\times1^2=12.6m^2[/tex]The area of the shaded part is thus;
[tex]16-12.6=3.4m^2[/tex]So, the probability of the dart hitting the shaded portion will be;
[tex]\frac{3.4}{16}\text{ = 0.2125}[/tex]I need help with this problem I don’t understand it. The question is. Find the value of X___degreesY___degreesZ___degrees
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SOLUTION
The fugure in the picture is a trapezoid.
Adjacent angles between the bases of a trapezoid are suplementary (add up to 180 degrees)
The bases of this trapezoid are the parallel sides PT and AR, so
[tex]x\degree+y\degree=180\degree[/tex]Now, since the trapezoid is an isosceles trapzoid, then the base angles will be equal, hence
[tex]x=53\degree[/tex]Hence x = 53 degrees
Then
[tex]\begin{gathered} x+y=180\degree \\ 53+y=180\degree \\ y=180-53 \\ y=127\degree \end{gathered}[/tex]hence y = 127 degrees
Also since it is an isosceles triangle the sides TR and AP would be equal
Hence z = 8
A figure skating school offers introductory lessons at $25 per session. There is also a registration fee of $30. Write a linear equation in slope- intercept form that represents the situation.Part B: You want to take at least 6 lessons, what is the cost.
Answers
Given:
Registration fee = $30
Fee per session = $25
To write a linear equation in slope-intercept form, we have:
Using the general slope intercept form:
y = mx + b
where
y = Total fee
m = fee per session
x = number of lessons
b = registration fee
Therefore, we have:
y = 25x + 30
Part B.
To find the cost if you want to take at least 6 lessons:
y = 25(6) + 30
= 150 + 30
= 180
The cost of taking at least 6 lessons is $180
ANSWER:
a) y = 25x + 30
b) $180
I'm trying to graph the equation:y=1/4x + 3y=2x +10please help
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To graph the equation, the easiest way to get its coordinates is when x = 0 and y = 0.
Let's apply these conditions to get the coordinates of the equation.
a.) y = 1/4x + 3
when,
x = 0 y = 0
y = 1/4(0) + 3 (0) = 1/4x + 3
y = 3 0 - 3 = 1/4x + 3 - 3
-3 = 1/4x
-3(4) = x
-12 = x or x = -12
Thus, the coordinates for equation y = 1/4x + 3 are (0,3) and (-12,0).
Let's now plot the graph of the equation,
The same steps will also be applied to make a graph of equation y = 2x + 10.