The probability that we do not dealt a card with number 2 to 9 is 5/13
What is Probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given,
A pack of card = 52 cards
The Cards having Hearts = 13
The Cards having Spade = 13
The Cards having Diamond = 13
The Cards having Clubs = 13
According to question
The cards numbered from 2 to 9 are 8 cards, specifically 2, 3, 4, 5, 6, 7, 8, and 9.
But there are four suits: diamonds, hearts, spades, and clubs.
Therefore you multiply 8 by 4 to get 32
The probability of getting dealt one of those cards would be:
32/52, or
8/13
But we have to find the probability of not getting such cards
Thus,
1 - 8/13 = 5/13
Hence, the probability that you are not dealt a card with number from 2 to 9 will be 5/13
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For an outdoor concert by the city orchestra, concert organizers estimate that 11,000 people will attend if it is not raining. If it is raining, concert organizers estimatethat 7000 people will attend. On the day of the concert, meteorologists predict a 60% chance of rain. Determine the expected number of people who will attend thisconcert
Step 1
Given;
For an outdoor concert by the city orchestra, concert organizers estimate that 11,000 people will attend if it's not raining.
If it is raining, concert organizers estimate 7000 people will attend.
On the day of the concert, meteorologists predict a 60% chance of rain.
Step 2
Given that the probability of having rain is 60%
[tex]Pr(rain)=\frac{60}{100}=0.6[/tex]So the probability of not having rain is;
[tex]\begin{gathered} Pr(rain)+Pr(no\text{ rain\rparen=1} \\ Pr(no\text{ rain\rparen=1-Pr\lparen rain\rparen} \\ Pr(no\text{ rain\rparen=1-0.6=0.4} \end{gathered}[/tex]Step 3
Now, the expected number of people who will attend the concert will be:
=(probability of not having rain x number of expected guests when it does not rain) + (probability of having rain x number of expected guests when rains)
[tex]\begin{gathered} Pr(expected\text{ number of peope\rparen=\lparen0.4}\times11000)+(0.6\times7000) \\ Pr(expected\text{ number of peope\rparen=4400+4200=8600} \end{gathered}[/tex]Answer; So, the expected number of people who will attend the concert is 8600
21 Mr. Bracken has 2 children that like to sit in trees. Jedi weighs 20kg and Phin weighs 25kg. The tallesttree in their yard is 20m high. The shortest branch is 10m high. If Jedi climbs to the highest branch andPhin climbs to the lowest brach, how much potential energy does each child have and which child has themost potential energy?A Jedi has 200 J, Phin has 500 J, therefore Jedi has the most potential energyB Jedi has 400 J, Phin has 250 J, therefore Phin has the most potential energy.c Jedi has 400 J, Phin has 250 J, therefore Jedi has the most potential energy.D Jedi has 200 J, Phin has 500 J, therefore Phin has the most potential energy.
Potential energy = mass x gravity x height
Where:
mass (kilograms)
gravity = 9.8 m/s2 =10 m/s2 (rounded)
Heigth = meters
Phin's potential energy = 25 kg x 10 m/s2 x 10m = 2500 J
Jedi's potential energy= 20kg x 10 m/s2 x 20 m= 4000 J
Comparing, 4000 (jedi)>2500 Phin
Jedi has the most potential energy.
Correct option : C
Allen's goal is to have between 1,500 and 1,600 bottles in his collection. Write and solve a compound inequality to determine the number of weeks it will take Allen to reach his goal.
The compound inequality is 1500 < 300 + 25x < 1600, the solution is 48 < x < 52 and the number of weeks to reach his goal 48 to 52 weeks
How to determine the compound inequality?The given parameters from the question are
Existing collection = 300
Rate = 25 bottles each week
Represent the number of weeks by x and the total number of bottles with y
So, we have the following equation
y = Existing collection + Rate * x
This gives
y = 300 + 25x
Also, we have
The goal is to have between 1,500 and 1,600 bottles in his collection.
This means that
1500 < Total < 1600
So, we have
1500 < 300 + 25x < 1600
Evaluate the like terms
1200 < 25x < 1300
Divide by 25
48 < x < 52
Hence, the number of weeks is 48 to 52 weeks
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Possible question
Allen wants to add to his existing collection of 300 bottles. Starting today, he will collect 25 bottles each week.
Allen's goal is to have between 1,500 and 1,600 bottles in his collection. Write and solve a compound inequality to determine the number of weeks it will take Allen to reach his goal.
If you are given a rectangle, what are the degrees of its rotational symmetry? (I need all of them between but not including 0 and 360 degrees)
A rectangle is an Order 2 of symmetry because it matchs its fugure only 2 times while rotating through 360 degrees.
The degrees of symmetry can be calculated as:
[tex]\frac{360\degree}{\text{Order}}=\frac{360\degree}{2}=180\degree[/tex]We see that at 180 degrees of rotation the shape is identical to the original shape.
This does not repeat for any other angle between 0 and 360 degrees.
Answer: 180 degrees.
What do the following two equations represent?y-3=2(x - 3)y+5 = 2(x + 1) a. the same lineb. distinct parallel linesc. perpendicular linesd. intersecting, b it not perpendicular
Option A: The same line
Explanations:The slope-intercept form of the equation of a line can be written as:
y = mx + c
Where m is the slope
and c is the intercept
Let us express the two equations given in the slope-intercept form
For the first equation:
y - 3 = 2(x - 3)
y - 3 = 2x - 6
y = 2x - 6 + 3
y = 2x - 3
The slope, m = 2
The intercept, c = -3
For the second equation:
y + 5 = 2(x + 1)
y + 5 = 2x + 2
y = 2x + 2 - 5
y = 2x - 3
We can see that both equations simplify to y = 2x - 3, this means the both equations represent the same line
You need 30 ounces of chocolate chips to bake some cooldes. You already have 8 ounces of chocolate chips at home. Write an inequality that could beused to find how many ounces of chocolate chips you need to buy.whats the inequality:
Given:
Amount of chocolate chips needed = 30 ounces
Amount of chocolate you have already = 8 ounces
Let's find the inequality that can be used to find the ounces of chocolate chips you need to buy.
To write the inequality, we have:
8 + x ≥ 30
Where x represents the ounces of chocolate chips you need to buy.
Therefore, the inequality that could be used to fid how many ounces of chocolate chips needed is:
8 + x ≥ 30
ANSWER:
8 + x ≥ 30
Draw the following vectors using the scale 1 cm = 50 km/h. Plant the tail at the origin. A. 200 km/h on a bearing of 020° B. 75 km/h S 10° W C. 350 km/h NE
Solution
a)
200 km/h on a bearing of 020°
Scale 1 cm = 50 km/h.
[tex]Length\text{ = }\frac{200}{50}\text{ = 4cm}[/tex]b)
B. 75 km/h S 10° W
[tex]Lenght\text{ = }\frac{75}{50}\text{ = 1.5cm}[/tex]C. 350 km/h NE
[tex]Length\text{ = }\frac{350}{50}\text{ = 7cm}[/tex]Simplify the expression.
the expression negative one seventh j plus two fifths minus the expression three halves j plus seven fifteenths
negative 19 over 14 times j plus 13 over 15
negative 19 over 14 times j minus 13 over 15
negative 23 over 14 times j plus negative 1 over 15
23 over 14 times j plus 1 over 15
The expression is simplified to negative 23 over 14 times j plus negative 1 over 15. Option C
What is an algebraic expression?An algebraic expression can be defined as an expression mostly consisting of variables, coefficients, terms, constants and factors.
Such expressions are also known to be composed or made up of some mathematical or arithmetic operations, which includes;
AdditionSubtractionDivisionBracketMultiplicationParentheses. etcFrom the information given, we have that;
negative one seventh j = - 1/7jtwo fifths = 2/5three halves j = 3/2 jseven fifteenths = 7/15Substitute the values
- 1/7j + 2/5 - 3/2j - 7/15
collect like terms
- 1/7j - 3/2j + 2/5 - 7/15
-2j - 21j /14 + 6 7 /15
-23j/14 + -1/15
Hence, the correct option is negative 23 over 14 times j plus negative 1 over 15
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For a period of d days an account balance can be modeled by f(d) = d^ 3 -2d^2 -8d +3 when was the balance $38
Given a modelled account balance for the period of d days as shown below:
[tex]\begin{gathered} f(d)=d^3-2d^2-8d+3 \\ \text{where,} \\ f(d)\text{ is the account balance} \\ d\text{ is the number of days} \end{gathered}[/tex]Given that the account balance is $38, we would calculate the number of days by substituting for f(d) = 38 in the modelled equation as shown below:
[tex]\begin{gathered} 38=d^3-2d^2-8d+3 \\ d^3-2d^2-8d+3-38=0 \\ d^3-2d^2-8d-35=0 \end{gathered}[/tex]Since all coefficients of the variable d from degree 3 to 1 are integers, we would apply apply the Rational Zeros Theorem.
The trailing coefficient (coefficient of the constant term) is −35.
Find its factors (with plus and minus): ±1,±5,±7,±35. These are the possible values for dthat would give the zeros of the equation
Lets input x= 5
[tex]\begin{gathered} 5^3-2(5)^2-8(5)-35=0 \\ 125-2(25)-40-35=0 \\ 125-50-75=0 \\ 125-125=0 \\ 0=0 \end{gathered}[/tex]Since, x= 5 is a zero, then x-5 is a factor.
[tex]\begin{gathered} d^3-2d^2-8d-35=(d-5)(d^2+3d+7)=0 \\ (d-5)(d^2+3d+7)=0 \\ d-5=0,d^2+3d+7=0 \\ d=0, \end{gathered}[/tex][tex]\begin{gathered} \text{simplifying } \\ d^2+3d+7\text{ would give} \\ d=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ a=1,b=3,c=7 \end{gathered}[/tex][tex]\begin{gathered} d=\frac{-3\pm\sqrt[]{3^2-4\times1\times7}}{2\times1} \\ d=\frac{-3\pm\sqrt[]{9-28}}{2} \\ d=\frac{-3\pm\sqrt[]{-17}}{2} \end{gathered}[/tex]It can be observed that the roots of the equation would give one real root and two complex roots
Therefore,
[tex]d=5,d=\frac{-3\pm\sqrt[]{-17}}{2}[/tex]Since number of days cannot a complex number, hence, the number of days that would give a balance of $38 is 5 days
The top of the hill rises 243 feet above checkpoint 2, which is -162. What is the altitude of the top of the hill?
The altitude of the top of the hill or the difference in elevation point is 406 feet.
Difference in Elevation PointThe vertical distance between two points is called the difference in elevation. The process of measuring differences in elevation is called levelling , and is a basic operation in topographical surveys.
To determine the difference in elevation between two points, determine the elevation at each point and then calculate the difference.
Point A = 243 feetPoint B = -162 feetThe difference in elevation between the two points is
Point A - Point B = 243 - (-162) = 243 + 162 = 406
The difference in the elevation point is 406 feet.
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Solve these: state whether there is no solution, one solution specify it , or infinitely many Solutions.
Step 1:
Write the two systems of equations
y = 3x = 2
3x = y - 3
Step 2:
Substitute y from the first equation into the second equation
[tex]\begin{gathered} 3x\text{ = y - 3} \\ 3x\text{ = 3x + 2 - 3} \\ 3x\text{ - 3x = 2 - 3} \\ 0\text{ = 2 - 3} \\ 2\text{ = 3} \end{gathered}[/tex]Final answer
NO SOLUTION
Hello I need help completing this practice math problem, I will include a picture. Thank you so much!
To answer this question we will set and solve a system of equations.
Let k be the number of orders that Kala served on Monday, a be the number of orders that Abdul served, and j be the number of orders that Joe served.
Since they served a total of 71 orders, Kala served 5 fewer orders than Abdul, and Joe served 2 times as many orders as Abdul, then we can set the following system of equations:
[tex]\begin{gathered} k+a+j=71, \\ k=a-5, \\ j=2a\text{.} \end{gathered}[/tex]Substituting the second and third equation in the first one we get:
[tex]a-5+a+2a=71.[/tex]Adding like terms we get:
[tex]4a-5=71.[/tex]Adding 5 to the above equation we get:
[tex]\begin{gathered} 4a-5+5=71+5, \\ 4a=76. \end{gathered}[/tex]Dividing the above equation by 4 we get:
[tex]\begin{gathered} \frac{4a}{4}=\frac{76}{4}, \\ a=19. \end{gathered}[/tex]Finally, substituting a=19 in the second and third equation we get:
[tex]\begin{gathered} k=19-5=14, \\ j=2\cdot19=38. \end{gathered}[/tex]Answer:
Number of orders Kala served: 14.
Number of orders Abdul served: 38.
Number of orders Joe served: 19.
help me pleaseeeeeeeee
Answer:
x = -2
Step-by-step explanation:
f(x) = y
f(x) represents the y-axis
f(x) = -3 or y = -3 or y = (0, -3)
When y = -3, x = -2
x = -2
I hope this helps!
5. How would you solve the system of equations y = 5x + 1 and -2x + 3y =-10 ? What is the solution? *
SOLUTION:
Step 1:
In this question, we are given the following:
Solve the system of equations y = 5x + 1 and -2x + 3y =-10 ?
What is the solution?
Step 2:
The solution to the systems of equations:
[tex]\begin{gathered} y\text{ = 5x + 1 -- equation 1} \\ -2x\text{ + 3y = -10 -- equation 2} \end{gathered}[/tex]check:
Given y = -4 , x = -1
Let us put the values into the equation:
y = 5x + 1 and -2x + 3y = -10
[tex]\begin{gathered} y\text{ = 5x + 1} \\ -4=5(-1)\text{ + 1} \\ -4=-5+1 \\ -4\text{ = - 4 (COR}\R ECT) \end{gathered}[/tex][tex]\begin{gathered} -2x+3y\text{ = -10} \\ -2(-1)+3(-4)_{}_{} \\ 2-12=-10\text{ (COR}\R ECT) \end{gathered}[/tex]CONCLUSION:
The solution to the system of equations are:
[tex]\begin{gathered} \text{x = -1} \\ y=-4 \end{gathered}[/tex]
Write this trinomial in factored form. 5a² - 30 - 14
replace x with a for this exercise
we use this formula to factor
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a=5, b=-3 and c=-14
[tex]x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(5)(-14)}}{2(5)}[/tex][tex]\begin{gathered} x=\frac{3\pm\sqrt[]{9+280}}{10} \\ \\ x=\frac{3\pm\sqrt[]{289}}{10} \\ \\ x=\frac{3\pm17}{10} \end{gathered}[/tex]we have two roots
[tex]\begin{gathered} x=\frac{3+17}{10} \\ x=2 \end{gathered}[/tex]and
[tex]\begin{gathered} x=\frac{3-17}{10} \\ \\ x=-\frac{7}{5} \end{gathered}[/tex]so the simplified equation is
[tex](x-2)(x+\frac{7}{5})[/tex]now replace x for a
[tex](a-2)(a+\frac{7}{5})[/tex]The Following to wait table shows the number of student of the school who have a cell phone and or part-time job:
Explanation
in the column we have
-have cell phones
-do not have cell phones
-total
and
in the other side.
-have a part time job
-do not have part time job,
so to know the number of students whoh fit both conditions ( have a cell phone and have a part time job) we need to find the cell where both intersect each other
hence, the answer is
[tex]2)40[/tex]I hope this helps you
Find the equation in standard form of lines P that are A) parallel to and B) perpendicular to line L P(1,2); L: 3x-2y=1P(8,7);L: y= -4
To find if two lines are parallel, the slope must be the same.
so m=m
for P(1,2); L: 3x-2y=1
First, solve the equation for y:
3x-2y=1
Subtract both sides by 3x
3x-2y=1
3x-3x-2y =1-3x
-2y=1-3x
Now, divide both sides by -2y
-2y/-2 = 1-3x
y =1/-2 +3x/2
The parallel line using the point P(1,2)
y-y1 =m(x-x1)
Replace the values and solve for y.
y-2=3x/2 -1
y=3x/2+2
So the parallel lines is y=3x/2+2
To find a perpendicular line, when you multiply the slopes the result must be equal to -1.
So:
m1*m2 = -1
Replace m1=3/2
m1*m2 = -1
3x/2* m2 = -1
m2 = -1/(3x/2)
m2 = -2/3
To find the line use:
y-y1 =m(x-x1)
y-2=-2/3(x-1)
y-2=-2x/3 +2/3
y= -2x/3 +8/3
So y= -2x/3 +8/3 is the perpendicular line.
Graph a line that contains the point 2 (-5, -6) and has a slope of 3 Y 6 4 2 2 -6 -4 2 4 6 -4- -6-
the graph of a line passing through point
[tex](x_1,y_1)[/tex]with gradient m
is given by
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \Rightarrow y+6=3(x+5) \\ \Rightarrow y+6=3x+15 \\ \Rightarrow y=3x+9 \end{gathered}[/tex]Consider the following quadratic function Part 3 of 6: Find the x-intercepts. Express it in ordered pairs.Part 4 of 6: Find the y-intercept. Express it in ordered pair.Part 5 of 6: Determine 2 points of the parabola other than the vertex and x, y intercepts.Part 6 of 6: Graph the function
Answer:
The line of symmetry is x = -3
Explanation:
Given a quadratic function, we know that the graph is a parabola. The general form of a parabola is:
[tex]y=ax^2+bx+c[/tex]The line of symmetry coincides with the x-axis of the vertex. To find the x-coordinate of the vertex, we can use the formula:
[tex]x_v=-\frac{b}{2a}[/tex]In this problem, we have:
[tex]y=-x^2-6x-13[/tex]Then:
a = -1
b = -6
We write now:
[tex]x_v=-\frac{-6}{2(-1)}=-\frac{-6}{-2}=-\frac{6}{2}=-3[/tex]Part 3:For this part, we need to find the x-intercepts. This is, when y = 0:
[tex]-x^2-6x-13=0[/tex]To solve this, we can use the quadratic formula:
[tex]x_{1,2}=\frac{-(-6)\pm\sqrt{(-6)^2-4\cdot(-1)\cdot(-13)}}{2(-1)}[/tex]And solve:
[tex]x_{1,2}=\frac{6\pm\sqrt{36-52}}{-2}[/tex][tex]x_{1,2}=\frac{-6\pm\sqrt{-16}}{2}[/tex]Since there is no solution to the square root of a negative number, the function does not have any x-intercept. The correct option is ZERO x-intercepts.
Part 4:
To find the y intercept, we need to find the value of y when x = 0:
[tex]y=-0^2-6\cdot0-13=-13[/tex]The y-intercept is at (0, -13)
Part 5:
Now we need to find two points in the parabola. Let-s evaluate the function when x = 1 and x = -1:
[tex]x=1\Rightarrow y=-1^2-6\cdot1-13=-1-6-13=-20[/tex][tex]x=-1\Rightarrow y=-(-1)^2-6\cdot(-1)-13=-1+6-13=-8[/tex]The two points are:
(1, -20)
(-1, -8)
Part 6:
Now, we can use 3 points to find the graph of the parabola.
We can locate (1, -20) and (-1, -8)
The third could be the vertex. We need to find the y-coordinate of the vertex. We know that the x-coordinate of the vertex is x = -3
Then, y-coordinate of the vertex is:
[tex]y=-(-3)^2-6(-3)-13=-9+18-13=-4[/tex]The third point we can use is (-3, -4)
Now we can locate them in the cartesian plane:
And that's enough to get the full graph:
Jamie had 10 dogs. She killed 4 of them then bought another 3. She also ate 7 of them. How many dogs dose she have now?
Answer:
2 dogs
Step-by-step explanation:
10-4+3-7
6-4
2
Answer: 2 dogs
Step-by-step explanation:
QUESTION WHO KILLS AND EATS DOGS?????
f(1)=-12 and f(n)=2f(n-1) then find the value of f(6).
Notice that from the definition of f(n):
[tex]f(6)=2f(5)=2(2f(4))=2(2(2f(3)))=2(2(2(2f(2))))=2(2(2(2(2f(1)))))\text{.}[/tex]Therefore:
[tex]f(6)=2^5f(1)=2^5(-12)=32(-12)=-384.[/tex]Answer:
[tex]f(6)=-384.[/tex]Lindsay gets paid $15 per hour at her job. If we let s be her salary and h be the number of hours she has worked, write an equation that represents the direct variation.
A linear function or a direct variation function is represented by:
[tex]y=kx[/tex]where k is the constant rate of chante, in this case $15 per hour.
s=y= salary of Lindsay
h=x= hours she has worked
Then, the equation that represents the situation would be:
[tex]s=15h[/tex]how do i expand -4(-x-8)
Answer:
4x+32
Step-by-step explanation:
mutiply the -4 to both numbers inside parentheses. negative * negative= positive. -4*-x=4x, -4*-8=32
A store manager or tshirts so that 15 out of every 35 are a medium. How many medium Tshirts would you expect to find when there are 126 T-shirt's on a rack?
Given:
Out of every 30 t-shirts, 15 are medium.
Let's find the number of medium t-shirts you expect to find when there are 126 t-shirts on a rack.
We have:
35 t-shirts = 15 medium
126 t-shirts = x medium
Now, let's solve for x.
Apply the proportioanlity equation:
[tex]\frac{35}{15}=\frac{126}{x}[/tex]Cross multiply:
[tex]\begin{gathered} 35x=126\times15 \\ \\ 35x=1890 \end{gathered}[/tex]DIvide both sides by 35:
[tex]\begin{gathered} \frac{35c}{35}=\frac{1890}{35} \\ \\ x=54 \end{gathered}[/tex]Therefore, there will be 54 medium t-shirts when there are 126 t-shirts.
ANSWER:
54
P(B) = 2/3P(An B) = 1/6What will P(A) have to be for A and B to be independent?1/211/121/45/6
P(B) = 2/3
P(An B) = 1/6
What will P(A) have to be for A and B to be independent?
Remember that
Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true
substitute given values
1/6=P(A)*(2/3)
solve for P(A)
P(A)=1/4whats x+7, y equals and how do i find it?
The figure HGD was translated 7 units right; and then it was translated 9 units up. This can be shown as:
(x, y) → (x + 7, y + 9)
Answer = 9
I’ve done all the other parts, I simply need you to graph the proabola!
Given
[tex]y=x^2-4x+3[/tex]Find
Graph the parabola of the given function
Explanation
[tex]y=x^2-4x+3[/tex]solve the equation
[tex]\begin{gathered} x^2-4x+3=0 \\ x^2-3x-x+3=0 \\ x(x-3)-(x-3)=0 \\ (x-1)(x-3)=0 \\ x=1,3 \end{gathered}[/tex]vertex can be found by using the formula,
[tex]-\frac{b}{2a}=-\frac{-4}{2}=2[/tex]x = 2 , substitute this in equation to get y value,
y = -1
if x = 0 then y =3 and if y= 0 then x = 1, 3
Final Answer
A study of consumer smoking habits includes 177 people in the 18-22 age bracket ( 48 of whom smoke), 146 people in the 23-30 age bracket ( 31 of whom smoke), and 81 people in the 31-40 age bracket ( 28 of whom smoke). If one person is randomly selected from this sample, find the probability of getting someone who is age 18-22 or does not smoke.A. 0.319B. 0.854C. 0.173D. 0.729
From the question,
Age 18 - 22 has 177 people, 48 of whom smoke.
Age 23-30 has 146 people, 31 of whom smoke.
Age 31-40 has 81 people, 28 of whom smoke.
People who do not smoke = (177- 48)+(146-31)+(81-28) = 129 + 115 +53 = 297 people.
People within age 18-22 who do not smoke = 129
Total number of events = 404
[tex]\begin{gathered} p(18-22\text{ or does not smoke) = }\frac{(177+297-129)}{404} \\ p(18-22\text{ or does not smoke)}=\frac{345}{404}=0.853960396 \\ p(18-22\text{ or does not smoke)}\approx0.854 \end{gathered}[/tex]Hence, option B is the answer.
Write the following ratio using two other notations: 1/3
Given:
[tex]\frac{1}{3}[/tex]To write the given fraction into two other notations, we use "to" for word notation while ":" for number notation.
Therefore, the answers are:
1 to 3
1:3
choose the correct letter ( this is not being graded it is review )
we have the points
(-2,6) and (-3,-7)
step 1
Find out the slope
m=(-7-6)/(-3+2)
m=-13/-1
m=13
step 2
Find out the equation in slope-intercept form
y=mx+b
we have
m=13
point (-2,6)
substitute and solve for b
6=13(-2)+b
6=-26+b
b=32
therefore
y=13x+32
step 3
Convert to standard form
AX+By=C
y=13x+32
13x-y=-32 -------> is equivalent to -13x+y=32
therefore
the answer is option D