In the figure, PQ is parallel to RS. (see picture)
Which of the following angles has a measure equal to 100°?
A) a
B) b
C) c
D) d
Answer:
A
Step-by-step explanation:
Because B corresponds with 80 and a line segment is 180 degrees b + a =180 and a would be 100.
A store sells pajamas in two sizes.
• The child size is for people less than `60` inches tall.
• The adult size is for people `60` inches tall or more.
Juan’s height is `145` centimeters.
Would he fit the child or adult size
What is the answer
he would fit the child size
his height is 145cm and we want to convert it into inches so the formula is
length/2.54=
145cm/2.54=57.08in
so juan is 57.08 inches, so he fits the child size.
Let A and B be nxn matrices. Which of the following statements are always true? (i) If det(A) = det(B) then det(A − B) = 0. (ii) If A and B are symmetric, then the matrix AB is also symmetric. (iii) If A and B are skew-symmetric, then the matrix AT + B is also skew-symmetric.
The statement "If det(A) = det(B), then det(A - B) = 0" is not always true. The determinant of a matrix is not additive under subtraction.
Therefore, the determinant of the difference of two matrices does not necessarily equal zero even if the determinants of the individual matrices are equal. Counterexamples can be easily constructed.
The statement "If A and B are symmetric, then the matrix AB is also symmetric" is not always true. The product of two symmetric matrices is not necessarily symmetric. Counterexamples can be easily constructed.
The statement "If A and B are skew-symmetric, then the matrix AT + B is also skew-symmetric" is always true. A skew-symmetric matrix has the property that its transpose is equal to the negative of the original matrix. Therefore, taking the transpose of AT + B results in -(AT + B), which is the negative of the original matrix. Hence, the matrix AT + B is also skew-symmetric.
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the main sailboat has the dimensions shown in figure at the right . what is the height of the main sail? Then round to the nearest tenth as needed.)
Answer:
h = 14.49 feet.
Step-by-step explanation:
From the attached figure,
Base = 14 ft
Height = h
Angle = 46°
We need to find the height of the main sail. To find it we can use trigonometry.
The relation between height, base and angle is given by :
\(\tan\theta=\dfrac{\text{Height}}{\text{Base}}\\\\\tan(46)=\dfrac{h}{14}\\\\h=\tan(46)\times 14\\\\h=14.49\ ft\)
So, the height of the main sail is 14.49 feet.
The quotient of 24 and x equals 14 minus 2 times x.
Answer:
X = 4, 3
Step-by-step explanation:
I don't know if that's what you were looking for
What percent of 80 is 32?
F) 25%
G) 2.5%
H) 0.4%
J) 40%
K) None
Answer:
40%
Step-by-step explanation:
you divide the little number by the bigger number than move the decimal point two places to the right
J is the correct answer since 80×(40/100) = 32
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Find the 17th term of an arithmetic sequence whose first term is 12 and whose common difference is 6. Type answer as an integer (no decimals).
Answer:
Step-by-step explanation:
n17 = ?
n = 17
d = 6
a1 =12
a17 = a1 +(n - 1)d
a17 = 12 + (17 - 1)*6
a17 = 12 + 16*6
a17 = 12 + 96
a17 = 108
According to recent data, women make up what percentage of workers in science and technology (STEM) fields in Canada and the United States, respectively?
A. 34% and 40%
B. 23% and 26%
C. 17% and 26%
D. 25% and 27%
E. 34% and 26%
According to recent data, women make up 34% and 26% of workers in science and technology (STEM) fields in Canada and the United States, respectively. The correct option is A. 34% and 26%.
According to recent data, women make up 34% and 26% of workers in science and technology (STEM) fields in Canada and the United States, respectively. This indicates that women are still underrepresented in STEM fields, despite the fact that there has been an effort to attract more women to STEM fields.
In both Canada and the United States, women have made significant progress in breaking down gender barriers in STEM fields. However, there is still work to be done to close the gender gap and increase representation of women in STEM fields.
Women's representation in STEM fields has increased in both Canada and the United States in recent years, but the percentage of women in STEM fields is still significantly lower than the percentage of men. More efforts are needed to close the gender gap in STEM fields and encourage more women to pursue STEM careers.
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For the following frequency distribution of quiz scores, how many individuals took the quiz (N)?
X f
5 6
4 5
3 5
2 3
1 2
ANSWERS:
A. 5
B. 15
C. Cannot determine
D. 21
The number of individuals who took the quiz is D) 21.
To determine the total number of individuals who took the quiz (N), we need to sum up the frequencies (f) in the given frequency distribution. The frequency (f) represents the number of individuals who obtained each score.
Let's add up the frequencies:
6 + 5 + 5 + 3 + 2 = 21
The total frequency is 21, which means that 21 individuals took the quiz. Each score represents a certain number of individuals who obtained that score, and by adding up all the frequencies, we get the total number of individuals.
Therefore, the correct answer is D. 21.
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Let A,B be two events with P(A)=0.2 and P(B)=0.4. Then which of the following cannot be the possible value of P(A∪B)?
A) 0.3
B) 0.4
C) 0.5
D) 0.6
The answer is (D) 0.6. Using the given probabilities, we can calculate P(A∪B) by adding P(A) and P(B), and subtracting the probability of their intersection.
To find the value of P(A∪B), we need to consider the relationship between the two events A and B. The union of two events A and B represents the occurrence of either event A or event B or both.
The probability of the union of two events can be calculated using the formula:
P(A∪B) = P(A) + P(B) - P(A∩B)
Here, P(A∩B) represents the probability of the intersection of events A and B, which is the occurrence of both events A and B.
Since we are given that P(A) = 0.2 and P(B) = 0.4, we can substitute these values into the formula to find the possible values of P(A∪B).
Let's calculate the values for each option:
A) P(A∪B) = 0.2 + 0.4 - P(A∩B) = 0.6 - P(A∩B)
B) P(A∪B) = 0.4 + 0.4 - P(A∩B) = 0.8 - P(A∩B)
C) P(A∪B) = 0.5 + 0.4 - P(A∩B) = 0.9 - P(A∩B)
D) P(A∪B) = 0.6 + 0.4 - P(A∩B) = 1 - P(A∩B)
From the given options, we can see that the only value that cannot be the possible value of P(A∪B) is (D) 0.6. This is because the probability of an event cannot exceed 1 (100%). Since P(A∪B) represents the probability of either event A or event B or both, it cannot be equal to or greater than 1. Therefore, 0.6 is not a possible value for P(A∪B).
In conclusion, the answer is (D) 0.6.
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What is the solution set for the inequality,
4 (x − 3) − 7x ≥ 6
The most appropriate choice for linear inequation will be given by
Solution set = {\(x \epsilon \mathbb{R}, x \leq 6\)}
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by \(>\), \(<\), \(\geq\), \(\leq\) sign
A one degree inequation is known as linear inequation.
Here,
\(4(x - 3) - 7x \geq 6\\4x -12 - 7x \geq 6\\-3x -12\geq 6\\-3x \geq 6 + 12\\-3x \geq 18\\x \leq \frac{18}{3}\\x \leq 6\)
Solution set = {\(x \epsilon \mathbb{R}, x \leq 6\)}
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4(x^2-2x) +(x-1)(x^2+x+1)-x(x^2-4)
Answer:
4x^2−4x−1
if u need an explanation tell me
Answer:
4x² - 4x - 1
Step-by-step explanation:
Given
4(x² - 2x) + (x - 1)(x² + x + 1) - x(x² - 4) ← distribute all parenthesis
= 4x² - 8x +x ³ + x² + x - x² - x - 1 - x³ + 4x ← collect like terms
= 4x² - 4x - 1
1. A university computer science department offers three sections of a core class: A, B, and C. Suppose that in a typical full-length semester, section A holds about 250 students, B holds 250, and C has 100.
(a) How many ways are there to create three teams by selecting one group of four students from each class?"
(b) How many ways are there to create one four-person group that may contain students from any class?
(c) How many ways can sections A, B, and C be split into groups of four students, such that each student ends up in exactly one group and no group contains students from different classes?
(d) Once the groups are split, how many ways are there to select a lead strategist and different lead developer for each group?
(e) Due to a global pandemic, the group-formation policy has changed and there is no longer a restriction on group size. What is the size of the smallest group that is guaranteed to have a member from each section?
(f) How many students are required to be in a group to guarantee that three of them share the same birthday? Is a group of this size possible under the new policy?
(g) Students are ranked by grade at the end of the semester. Assuming that no two students end with the same grade, how many such rankings are possible?
A group from the class in the previous question has identified a bug in their code that will take a minimum of 16 tasks T = {t1...t16} to resolve. How many ways are there to assign the tasks if
(h) the tasks are distinguishable?
(i) the tasks are indistinguishable?
(j) the tasks are distinguishable and each group member completes the same number of tasks?
(k) the tasks are indistinguishable and each group member completes the same number of tasks?
(a) Answer: Here, we need to find how many ways are there to select one group of four students from each of the three classes A, B and C.i.e., Therefore, the number of ways to create three teams by selecting one group of four students from each class is (250C4) * (250C4) * (100C4).
(b) Answer: We need to select four students from 250 students of section A, 250 students of section B, and 100 students of section C such that there are no restrictions. Therefore, the number of ways to create one four-person group that may contain students from any class is (250 + 250 + 100)C4.
(c) Answer: Here, we need to find how many ways can sections A, B, and C be split into groups of four students, such that each student ends up in exactly one group and no group contains students from different classes. Next, we need to allocate these groups to the 3 classes such that no class gets the group it initially had. There are 3 ways to do this. Therefore, the total number of ways is (250C4) * (250C4) * (100C4) * 3.
(d) Answer: Each group has 4 students and we have 3 groups. Therefore, there are 3 lead strategists and 3 lead developers to be selected. Therefore, the total number of ways is P(3,3) * P(4,3) * P(4,3) * P(4,3).
(e) Answer: The size of the smallest group that is guaranteed to have a member from each section is 3.
(f) Answer: The number of students required to be in a group to guarantee that three of them share the same birthday is 22. Yes, a group of this size is possible under the new policy.
(g) Answer: The total number of possible rankings is P(600, 600).
(h) Answer: The number of ways to assign 16 distinguishable tasks to 4 members is 4^16.
(i) Answer: This is equivalent to finding the number of ways to partition 16 into 4 non-negative parts, which is (16+4-1)C(4-1).
(j) Answer: We need to find the number of solutions in non-negative integers to the equation x1+x2+x3+x4 = 16. The number of such solutions is (16+4-1)C(4-1). The number of ways to assign the distinguishable tasks to each group is 4! * 4! * 4! * 4!.
Therefore, the total number of ways is (16+4-1)C(4-1) * 4! * 4! * 4! * 4!.
(k)Answer: We need to find the number of solutions in non-negative integers to the equation x1+x2+x3+x4 = 4. The number of such solutions is (4+4-1)C(4-1).
Therefore, the total number of ways is (4+4-1)C(4-1).
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Need help please and ty
The correct statements regarding the dilation are given as follows:
c. The side lengths of trapezoid E'F'G'H' are 1/3 times the corresponding side lengths of trapezoid EFGH.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
In the context of this problem, due to the transformation, we have a transformation with the scale factor given as follows:
k = 1/3.
Hence:
The side lengths of trapezoid E'F'G'H' are 1/3 times the corresponding side lengths of trapezoid EFGH.The angle measures remain constant.Hence option c is correct.
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Kiara peeled 2 oranges every 4 hours. At that rate, how many would she peel in 12 hours?
please put an explanation, thank you!
Ben walked 2/5 mile. Tonya walked 1/4 mile. What fraction of a mile did they walk in total?
Answer:
13/20 of a mile
Step-by-step explanation:
2/5 x 4 = 8/20
1/4 x 5 = 5/20
8/20 + 5/20 = 13/20
On Monday, a packaging company put together 450x packages of 45 cashews. On Tuesday, the company put together 175 less packages with 15x more cashews in each bag. Which of the following equations could be used to determine how many cashews were packaged on Tuesday?
Answer:
275x packages of 720 cashews
Step-by-step explanation:
450-175=275
(a+1)b
a=15 and b=45
(15 + 1) x 45 = 720
The local farmers market has oranges on sale for 5 for 1.80
What is the cost of one orange ?
Answer:.36 cent
1Step-by-step explanation:1.80 divided by 5
Help me with this quick please
On solving the provided question, we can say that from provided graphs we say \(x^2 = 4y + 7\) =.> \(x^2 = 15 = > x = \sqrt{15}\)
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
here,
from provided graphs we say
\(x^2 = 4y + 7\)
y = 2
\(x^2 = 15 \\x = \sqrt{15}\)
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determine the shape and explain what type of distribution the data has. 110, 107, 105, 108, 108, 107, 108, 105, 106, 87, 85, 88, 89, 92, 95, 96, 94, 95, 91, 90, 100, 99, 98, 97, 95, 92, 105
Answer:
it is right skewed
Step-by-step explanation:
So since the mean is bigger than the median it would be right skewed so everything going to the left
b=32 c= 51 find all missing sides and angles of right triangle
To find the missing sides and angles of a right triangle with side b = 32 and side c = 51, we can use the Pythagorean theorem and trigonometric ratios.
Let's denote the missing side as a and the angles as A and B, with B being the right angle.
Using the Pythagorean theorem, we know that in a right triangle, the sum of the squares of the two legs (a and b) is equal to the square of the hypotenuse (c):
a^2 + b^2 = c^2
Plugging in the given values, we have:
a^2 + 32^2 = 51^2
a^2 + 1024 = 2601
a^2 = 1577
a ≈ 39.73
Therefore, the length of the missing side a is approximately 39.73.
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summer is planning to build a small snowcone shed that is walkable from three different schools. It is7/8 miles from north junior high .0.68 from South elementary, and 5/6 miles from Westside Elementary. Order the schools from closest to farthest away from summer snow cones.
The order of the schools from the closest to farthest away from summer snow cones is South Elementary < West Side Elementary < North Junior High .
In the question ,
it is given that
the Summer is planning to build a small snow cone shed .
the distance from north junior high = 7/8 miles = 0.875 miles
the distance from South elementary = 0.680 miles
the distance from West Side elementary = 5/6 miles = 0.833 miles
From , above result we see that
the farthest from summer snow cone is north junior high which is 0.875 miles .
the nearest from summer snow cone is South Elementary which is 0.680 miles .
So , the order from closest to farthest is
South Elementary < West Side Elementary < North Junior High
Therefore , The order of the schools from the closest to farthest away from summer snow cones is South Elementary < West Side Elementary < North Junior High .
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Describe the error in finding the distance between A(6, 2) and B(1,-4). X AB = V(6-2)2 +[1-(-4)] = 142 +52 = V 16 + 25 = 141
The distance between two points can be calculated using the formula;
\(d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\)For points;
\(A(x_1,y_1)\text{ and B}(x_2,y_2)\)Given the points;
\(\begin{gathered} A\left(6,2\right)and \\ B\left(1,-4\right) \end{gathered}\)The distance between the two points can be calculated using the above formula;
\(\begin{gathered} AB=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\ AB=\sqrt{(-4-2)^2+(1-6)^2} \\ AB=\sqrt{(-6)^2+(-5)^2} \\ AB=\sqrt{36+25} \\ AB=\sqrt{61} \end{gathered}\)The distance between the two points is;
\(AB=\sqrt{61}=7.81\)The heights of a sample of 15 students are recorded in the stemplot below.
A stemplot titled heights of students has values 59, 61, 62, 63, 63, 64, 65, 65, 66, 67, 67, 67, 67, 69, 73.
What is the mean height, in inches, of this sample?
65
65.2
66
67
Answer:
To find the mean height of the sample, we need to sum up all the values and divide them by the total number of values.
Sum of values = 59+61+62+63+63+64+65+65+66+67+67+67+67+69+73 = 964
Total number of values = 15
Mean height = sum of values / total number of values = 964/15 = 64.2666... ≈ 65.2
Therefore, the mean height, in inches, of this sample is approximately 65.2.
The answer is B.
you design a new app for cell phones. your revenue for x downloads is given by f(x)=3x. your profit is $20 less than 90% of the revenue for x downloads create a function p to model the profit. find the profit for 90 downloads
Answer:
The Break Even point is the point at which the cost=revenue 14,980+20x=30x 14,980=10x 1,498=x a. 1,498 units must be sold to break even. At $20 per unit, the dollar amount will be $29,960 b. The profit function is P(x)=R(x)-C(x) So P(x)=30x-(14,980+20x) If you want to solve for this equation just enter the value of x we found for the break even point to get the answer.
Hoped I helped
The profit for 90 downloads will be;
⇒ P = $223
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Your revenue for x downloads is given by,
⇒ f(x) = 3x
And, Your profit is $20 less than 90% of the revenue for x downloads create a function p to model the profit.
Now,
Since, Your revenue for x downloads is given by,
⇒ f(x) = 3x
And, Your profit is $20 less than 90% of the revenue for x downloads create a function p to model the profit.
Hence, We can formulate;
⇒ P = 90% of f (x) - 20
⇒ P = 90/100 × 3x - 20
⇒ P = 270x/100 - 20
⇒ P = 2.7x - 20
So, The profit for 90 downloads will be;
⇒ P = 2.7 × 90 - 20
⇒ P = $223
Thus, The profit for 90 downloads = $223
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Male and female teachers were asked whether they preferred to use a whiteboard or a projector while teaching. The responses are summarized in
the table.
Male
Female
Total
Projector Whiteboard Total
22 10 32
28 15 43
50 25 75
What is the approximate probability that a teacher prefers projectors and is female?
A 0. 121
B. 0. 373
OC. 0. 560
D. 0. 651
E 0. 867
Probability that a teacher prefer projector & is female candidate is =
Total Female prefer whiteboard/Total people = 28/75 = 0.373
Given that the information below:
Male people prefer projector - 22
Female people prefer projector - 28
Total people prefer projector - 50
Male people prefer Whiteboard - 10
Female people prefer whiteboard - 15
Total people prefer whiteboard - 25
Total number of Male people - 32
Tota lnumber of Female people - 43
Total number of people - 75
Here the solution given below :
Probability that a teacher prefer projector & is female candidate is =
Total Female prefer whiteboard/Total people = 28/75 = 0.373
The correct option of this question is B) 0.373. Explation is given above.
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If you were constructing a 99% confidence interval of the population mean based on a sample of n=30 where the standard deviation of the sample S=0.05, the critical value of t will be 2.7564 2.4922 2.7969
The critical value of t for constructing a 99% confidence interval with a sample size of 30 and a sample standard deviation of 0.05 is 2.7564.
A confidence interval is a range of values within which the population parameter is estimated to lie with a certain level of confidence. In this case, we are constructing a 99% confidence interval for the population mean. The critical value of t is used to determine the width of the confidence interval.
The formula for calculating the confidence interval for the population mean is:
Confidence interval = sample mean ± (critical value) * (standard deviation of the sample / square root of the sample size)
Given that the sample size is 30 (n = 30) and the standard deviation of the sample is 0.05 (S = 0.05), we need to find the critical value of t for a 99% confidence level. The critical value of t depends on the desired confidence level and the degrees of freedom, which is equal to n - 1 in this case (30 - 1 = 29). Looking up the critical value in a t-table or using statistical software, we find that the critical value of t for a 99% confidence level with 29 degrees of freedom is approximately 2.7564.
Therefore, the 99% confidence interval for the population mean would be calculated as follows: sample mean ± (2.7564) * (0.05 / √30). The final result would be a range of values within which we can be 99% confident that the true population mean lies.
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Point S and point T are shown on the number line below. The distance between the two points is r units. Point Q is shown on a second number line. Plot the points on the number line that are r units away from point Q.
The distance between two points in a two-dimensional plane can be calculated using the quadratic formula. It involves finding the square root of the sum of the squares of the differences between the x and y coordinates.
To plot the points on the number line that are r units away from point Q, we need to find the two points that are r units away from Q.
First, we need to determine whether point S is to the left or right of point T on the number line. If S is to the left of T, then r is equal to the distance from Q to the left of Q on the second number line. If S is to the right of T, then r is equal to the distance from Q to the right of Q on the second number line.
Once we have determined the direction of r, we can plot the two points that are r units away from Q on the second number line. To do this, we simply mark off a distance of r units to the left or right of Q, depending on the direction of r, and plot the two points at these locations.
For example, if S is to the left of T and r is equal to the distance from Q to the left of Q on the second number line, we would mark off a distance of r units to the left of Q and plot the two points at these locations. Similarly, if S is to the right of T and r is equal to the distance from Q to the right of Q on the second number line, we would mark off a distance of r units to the right of Q and plot the two points at these locations.
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When we identify a nonsignificant finding, how does p relate to alpha?
a. p is greater than alpha. b. p is less than or equal to alpha. c. p is the same as alpha. d. p is not related to alpha.
answer is b Answer:
Step-by-step explanation:
When we identify a nonsignificant finding, p relates to alpha in the following way:
b. p is less than or equal to alpha.
Explanation:
In hypothesis testing, a p-value is the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true. On the other hand, alpha is the level of significance or the probability of rejecting the null hypothesis when it is true.
The common convention is to set the level of significance at 0.05 or 0.01, which means that if the p-value is less than alpha, we reject the null hypothesis. On the other hand, if the p-value is greater than alpha, we fail to reject the null hypothesis.
Therefore, when we identify a nonsignificant finding, it means that the p-value is greater than the alpha, and we fail to reject the null hypothesis. Hence, option (b) is the correct answer.
Line q passes through the points (3,5) and (-2,4)
10) The second pair of coordinate on the line parallel to q and passes through the point (1, 0) is (-5, 0).
11) The second pair of coordinate on the line perpendicular to q and passes through the point (3, 5) is (2, 0).
What is a slope?When the ratio is expressed as a quotient ("rise over run"), the same number is provided for every two distinct locations on the same line. There is a negative "rise" on a descending line.
Given,
Line q passes through (3, 5), (-2, 4)
(y-y₁)=m(x-x₁)
(y-5)=((4-5)/(-2-3))(x-3)
(y-5)=(-1/-5)(x-3)
-5y+25=-x+3
x-5y+22=0
10) Given point is (0,1)
Slopes are equal for parallel lines.
So, (y-1)/(x-0)=(-1/-5)
-5y+5= -x
x-5y+5=0Let y=0 then,
x= -5
Therefore, the second pair of coordinate on the line parallel to q and passes through the point (1, 0) is (-5, 0).
11) The equation of a line perpendicular to q is,
(y-y₁)=(-1/m)(x-x₁)
(y-5)=5(x-3)
y-5=5x-15
5x-y-10=0
Let y=0 then,
5x-10=0
x=2
Therefore, the second pair of coordinate on the line perpendicular to q and passes through the point (3, 5) is (2, 0).
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