Answers
Answer:[tex]\Large\boxed{First~choice.~y\leq \frac{1}{2}x+2 }[/tex]
Step-by-step explanation:
Determine the equation form of the inequalityGiven function form
Point-Slope form : y = mx + b
m = slopeb = y-interceptGiven the information from the graph
Since the graph crosses (0, 2), b = 2
Find the slope
Choose any two points from the graph
(x₁, y₁) = (0, 2)
(x₂, y₂) = (2, 3)
Slope = (y₂ - y₁) / (x₂ - x₁)
Slope = (3 - 2) / (2 - 0)
Slope = 1 / 2
m = 1 / 2
Therefore, the equation form of the inequality is y = (1/2)x + 2
Determine whether it is ≤ or ≥Since it is a solid line, the values on the line are also included. Thus, it must be either greater than or equal to, or less than or equal to.
The shaded region is below the solid line, therefore, it is ≤
Therefore, the inequality is [tex]\Large\boxed{y\leq \frac{1}{2}x+2 }[/tex]
To double-check the sign, we can substitute (0, 0) into the inequality to see whether it is true.
y ≤ (1/2) x + 2
0 ≤ (1/2) 0 + 2
0 ≤ 2 TRUE
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Related Questions
9. Safa is a resident of UAE where mobile numbers consist of 7 digits. She tells her friend that her mother's mobile number is the smallest number and father's is the greatest number that can be formed by using the digits 5,7,9,8. Help her friend to find her parents numbers. Each digit must be used at least once.
Answers
Answer:
Smallest number: 5555789
Largest number: 9999875
Step-by-step explanation:
Since each digit must be used at least once, the smallest number that can be formed with the digits 5, 7, 8 and 9 is 5555789 (ascending order of digits with smallest digit used four times
The largest number is 9999875 (descending order of digits with largest digit used four times)
Brandi's car holds 20 gallons of gasoline. Gas is $2.50 per gallon.
Domain:
Range:
Answers
Step-by-step explanation:
20 gallons of gasoline
gas is $ 2.50 per gallons
2.50 × 20
{(2×2)(0×.5)(0)}
domain=200
range=2.5
In a mathematics class, half of the students scored 79 on an achievement test. With the exception of a few students who scored 49, the remaining students scored 78. Which of the following statements is true about the distribution of scores?
Answers
Option C. The mean is less than the median in the distribution of the scores.
How to solve for the medianThe median is given as 79 + 78 / 2
= 78.5
The mode is 79 this is the number that has the highest frequency in the data.
The median is 78.5 this is the middle number in the set of scores of these students.
Hence the mean is less than the mode and the median given that it was it was brought down by the few scores of 49.
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The cosine law is writen as question, and 2 more Questions down below. Please solve.
Answers
When to use the law of cosine is explained below.
Using the labelled triangle, we have: sin D/d = sin E/e = sin F/f.
Using the sine law, the measure of angle M is: 74.9°.
What is the Cosine Law?The cosine law is given as, c = a² + b² - 2ab(cos C). It is used to solve a triangle with missing angle or side.
What are the Two Instances When the Cosine Law is Applied?When we are given two sides and an angle between the two sides, and we need to find the third side.
When we are given the all three sides of a triangle and we need to find the angles of the triangle.
What is the Law of Sines?Using the labelled triangle DEF in the diagram below, the law of sines is:
sin D/d = sin E/e = sin F/f.
How to Find Angle M using the Law of Sines?m∠N = 56°
n = 8.5 cm
m = 9.9 cm
Plug in the values into sin N/n = sin M/m:
sin 56/8.5 = sin M/9.9
sin M = (sin 56 × 9.9)/8.5
sin M = 0.9656
M = sin^(-1)(0.9656)
M = 74.9°
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What is (-7624928) * 997 + 7624928 * (-3)
Answers
Answer:
-7624928000 is the right answer.
Step-by-step explanation:
(-7624928) × 997 + 7624928 × (-3)
= -7602053216 + (-22874784)
= -7624928000 Ans..
Hope its helpful :-)
If so, please mark me as brainlist :-)
Answer:
Step-by-step explanation:
=(-7624928) * 997 + 7624928 * (-3)
=-7602053216+(-22874784)
=-7624928000
Find the ordered pair (s, t) that satisfies the system.
Answers
Answer:
s is antecedent t is consepuent
If 2 = x3, then x equals
A 05
B 01
C | 1
D 5
Answers
Answer:
D.
Step-by-step explanation:
Of all closed rectangular boxes of volume 64 ft3, what is the smallest surface area?
Answers
The smallest surface area of cubic rectangular boxes = 96 ft²
What is surface area?An object with three dimensions is solid and has both height and depth. A sphere and a cube, for instance, have three dimensions, whereas a circle and a square do not.
A three-dimensional shape's total surface area equals the sum of its side's surface areas. The measured area of all surfaces of three-dimensional solids, such as cubes, spheres, prisms, and pyramids, is expressed in square units.
Since it is a closed rectangular box so, there will be two equal sides.
According to the given Information:Volume = 64 ft³
Volume of rectangular cube = hx²
Surface area of rectangular cube = 2x²+4hx
Equating the above equation we get, hx² = 64
h=64/x²
Put the value of h in surface area formula,
S = 2x² + 4(64/x²)*x
S = 2x² + 256/x
For the surface area to be minimum,
ds/dx = 0
4x - (256/x²) = 0
4x³ = 256
x³ = 64
x = 4 ft
Therefore, the smallest surface area
= 2(4)² + (256/4)
S = 32 + 64
= 96 ft²
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What is the range of the function in the graph?
Answers
The range of the function in the graph given can be expressed as: D. 20 ≤ s ≤ 100.
What is the Range and Domain of a Function?All the possible set of x-values that are plotted on the horizontal axis (x-axis) are the domain of a function. In order words, they are the inputs of the function.
On the other hand, all the corresponding set of x-values that are plotted on the vertical axis (y-axis) are the range of a function. In order words, they are the outputs of the function.
In the graph given below that shows a function, s is plotted on the vertical axis (y-axis), and its values starts from 20, up to 100. The range can be said to be all values of s that are from 20 to 100.
Therefore, the range of the function in the graph given can be expressed as: D. 20 ≤ s ≤ 100.
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the length of the sides of a triangle are in the ratio 3:4:5. find the lengths of the sides of the triangle if its perimeter is 96cm
Answers
Answer:
let the angles be 3x,4x&5x
Now,
perimeter (p)=sum of all sides
or, 96=3x+4x+5x
or, 96=12x
or,96/12=x
or,8=x
or,x=8
Then,
3x=3*8
=24
4x=4*8
=32
5x=5*8
=45
Can you help me in my math work
Answers
The LCM of 18 and 24 using the prime-factorization method is 72.
The LCM of 27, 81, and 54, using the division method is 162.
In the first question, we are asked to find the LCM of the given numbers using the prime factorization method.
(i) 18, 24.
Prime factorization gives:
18 = 2*3², and 24 = 2³*3.
The LCM is the product of the highest power of each prime factor.
Thus, LCM = 2³*3² = 8*9 = 72.
Thus, the LCM of 18 and 24 using the prime-factorization method is 72.
Doing similarly for other sub-parts, The LCM of:
(ii) 16, 40 is 80.
(iii) 30, 36 is 180.
(iv) 28, 44 is 308.
(v) 20, 32 is 160.
(vi) 20, 135 is 540.
(vii) 45, 75 is 225.
(viii) 36, 84 is 252.
(ix) 12, 18, 24 is 72.
(x) 25, 35, 45 is 1575.
(xi) 9, 15, 21 is 315.
(xii) 25, 50, 75 is 150.
In the second question, we are asked to find the LCM of the given numbers, using the division method.
(i) 27, 81, 54.
The division method gives:
[tex]\underline{2|27,81,54}\\\underline{3|27,81,27}\\\underline{3|9,27,9}\\\underline {3|3,9,3}\\\underline{3|1,3,1}\\{1|1,1,1}[/tex]
The LCM is the product of all the numbers used for division.
LCM = 2*3*3*3*3*1 = 162.
Thus, the LCM of 27, 81, and 54, using the division method is 162.
Doing similarly for other sub-parts, The LCM of:
(ii) 18, 45, 63 is 630.
(iii) 35, 55, 100 is 7700.
(iv) 210, 140, 315 is 1260.
(v) 112, 120, 150 is 8400.
(vi) 144, 180, 300 is 3600.
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2. Select true or false for each statement about the data above.
A. The most common length of ribbon is 11/
B. The sum of the longest and shortest lengths is 20¹
C. The difference between the longest and shortest
lengths is 2.
X
+
11
-
215
Part Two
A group of children picked oranges and made orange juice. The line plot below shows
the amount of juice each child made. Use the line plot below to answer questions 3-7.
X
x x
X
+
N
X
+
+ +
2²/12 2²/ 2/²/
Quarts of Orange Juice Made
3. What is the greatest amount of juice?
True False
416
True False
True False
XX
+
N
516
4. What is the least amount of juice?
5. What is the sum of the least and greatest amount of juice? Show your work.
X
+
M
6. What is the difference between the greatest and least amount of juice? Show your
work.
7. If the children were to share the juice equally, how much would each child get?
Show your work.
Answers
A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.
What is a line plot?A line plot can be defined as a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.
Based on the data provided in the complete question, we can logically deduce the following points:
Length of ribbon (11 1/4) = 3.Length of ribbon (10 3/4) = 1.Length of ribbon (10 1/2) = 1.Length of ribbon (10 7/8) = 1.Length of ribbon (10 5/8) = 1.Length of ribbon (9 7/8) = 1.In conclusion, graph C shown in the image attached below is a line plot which correctly shows the data from the table above.
The most common length of ribbon is 11 1/4: True.
The sum of the longest and shortest lengths is 20 1/8: False.
Sum = 11 1/4 + 9 7/8
Sum = 21 9/8 ≠ 20 1/8.
The difference between the longest and shortest lengths is 2 1/8: False.
Difference = 11 1/4 - 9 7/8
Difference = 1 3/8 ≠ 2 1/8 .
Part Two.The greatest amount of juice is equal to 3.
The least amount of juice is equal to 1 4/6.
The sum of the least and greatest amount of juice is:
Sum = 1 4/6 + 3
Sum = 4 4/6 = 4 2/3.
The difference between the greatest and least amount of juice is:
Difference = 3 - 1 4/6
Difference = 8/6 = 4/3.
How much would each child get?If the children were to share the juice equally, the amount of juice each would get should be calculated by determining the mean:
Mean = [F(x)]/n
Mean = (1 4/6 + 2 + 2 + 2 + 2 2/6 + 2 5/6 + 2 5/6 + 3)/8
Mean = 18.7/8
Mean = 2.3375 = 2 27/80.
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Complete Question:
Katie recorded the length, in inches, of the ribbon pieces she was going to use for a project. Use this information for questions 1 and 2.
11 1/4, 11 1/4, 10 3/4, 10 1/2, 10 7/8, 10 5/8, 9 7/8, 11 1/4,
1. Which line plot correctly shows the data?
Kent has two similar cylindrical pipes, pipe a and pipe b. the radius of pipe a is 6 cm, and the radius of pipe b is 2 cm. what is the ratio of the volume of pipe a to the volume of pipe b?
Answers
The ratio of the volume of pipe a to the volume of pipe b is 27:1 .
What is cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder.
Given that,
Radius of pipe a is 6 cm, and the radius of pipe b is 2 cm.
We know that the volume of cylinder is :- [tex]\pi r^{2}h[/tex]
where r is radius and h is height of the cylinder.
If two figures are similar then ratio of volume is equal to the cube of any dimension.
The ratio of the volume of Pipe a to the volume of Pipe b :-
[tex]\frac{V(a)}{V(b)}=\frac{6^{3} }{2^{3} }[/tex]
= [tex]\frac{27}{1}[/tex]
Hence, The ratio of the volume of pipe a to the volume of pipe b is 27:1 .
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The average (mean) mass of an apple is 14g. The total mass of the
apple basket is 182g. So, how many apples are there in the basket?
Answers
182/x = 14
We can rearrange this by multiplying both sides by x to get 182 = 14x
Then dividing both sides by 14 to get x equal to 182/14 which is 13
So there are 13 apples
If the 4 population assumptions in the hard-weinberg principle are met, what will happen to the allele frequencies?
Answers
The Hardy-Weinberg principle states that the frequency of alleles in a large randomly reproducing population will remain constant from generation to generation if certain assumptions are met.
The assumptions are:
No mutations.No migration into or out of the populationNo selection, andNo genetic drift.What is the hardy-Weinberg principle?The Hardy-Weinberg principle, also known as the Hardy-Weinberg equilibrium, model, theorem, or law in population genetics, holds that in the absence of additional evolutionary factors, allele and genotype frequencies in a population would remain constant from generation to generation.A population is not evolving while it is in Hardy-Weinberg equilibrium. Discover how violations of Hardy-Weinberg assumptions result in evolution.
When a population reaches Hardy-Weinberg equilibrium for a gene, it stops evolving and allele frequencies remain constant over generations.Hardy-Weinberg's assumptions include no mutation, random mating, no gene flow, infinite population size, and no selection.If the assumptions for a gene are not met, the population may evolve for that gene (the allele frequencies of the gene may change).Therefore, the Hardy-Weinberg principle states that the frequency of alleles in a large randomly reproducing population will remain constant from generation to generation if certain assumptions are met.
The assumptions are:
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A circle is shown. Chords A C and B D intersect at point E.
Chords AC and BD intersect at E, with BD = 7 units, DE = 2 units, and AE = 4 units.
What is the length of segment CE?
units
Answers
Expert-verified answer
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amitnrw
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40.8K answers
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Given : Chords A C and B D intersect at point E. Length of Different segments is given in terms of x
To find : Length of chord BD
Solution:
Chords A C and B D intersect at point E.
=> AE * CE = BE * DE
AE = x
CE = x + 12
BE = x + 2
D = x + 5
=> x(x + 12) = (x + 2)(x + 5)
=> x² + 12x = x² + 7x + 10
=> 5x = 10
=> x = 2
BD = BE + DE
= x + 2 + x + 5
= 2x + 7
putting x = 2
=> BD = 2 (2) + 7
Applying the intersecting chord theorem, the length of segment CE in is: 2.5 units.
What is the Intersecting Chords Theorem?In geometry, the intersecting chords theorem is the theorem that defines the relation of the four line segments formed when two chords of a circle intersect each other at a point in the circle.
According to the intersecting chords theorem, the products of the lengths of the line segments that are formed on each chord are congruent or equal to each other.
In the diagram given, we have chords AC and BD intersecting at point E to form the following line segments:
BE = BD - DE = 7 - 2 = 5 units
DE = 2 units
AE = 4 units
CE = ?
Based on the intersecting chord theorem, we have:
(BE)(DE) = (AE)(CE)
Plug in the values
(5)(2) = (4)(CE)
10 = 4(CE)
Divide both sides by 4
10/4 = 4(CE)/4
2.5 = CE
CE = 2.5 units
Thus, applying the intersecting chord theorem, the length of segment CE in the circle given is: 2.5 units.
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The pair of triangles below have
two corresponding parts marked
as congruent. What additional
information is needed for a AAS
congruence correspondence?
Answers
Answer:
option c
Step-by-step explanation:
option c is a correct answer
The exterior surface of a farm silo needs to be painted. if one gallon of paint covers 224 square feet, what is the minimum number of gallons needed to paint the silo? keep in mind that the bottom of the silo is not painted. use π = 3.14
Answers
The gallons needed to paint the silo is 10.
How many gallons is needed to paint the silo?A cylinder is a three-dimensional object. It is a prism with a circular base. The total surface area of cylinder can be determined by adding the area of all its faces.
Total surface area of the cylinder excluding its base = 2πrh +πr²
Where:
r = radius h = heightTSA = (2 x 3.14 x 10 x 30) + (3.14 x 10²)
314 + 1884 = 2198 ft²
Number of gallons needed = 2198 / 224 = 9.81 = 10 gallons
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A high school principal reports that the average sat math score for last year’s graduating class is 520. a sample is taken of this year’s graduating class is taken and the average sat math score is reported to be 530. how would you compare the last two graduating classes?
Answers
Based on the average SAT Math score that the graduating classes got, the comparison is that this year's graduating class did better than last year's graduating class.
How can both classes be compared?The average score is used to show the general trend of scores that students were able to attain.
The average score of 530 that this year's graduating class attained is higher than the average of the previous graduating year which is 520.
This means that on average, this year's graduating class did better than that of last year because their general trend was higher.
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if an average orange weighs 75 g, how many oranges would weigh 4.5 kg?
Answers
Answer: 60 oranges
Step-by-step explanation:
Given information
Weight = 75 g / orange
Total = 4.5 kg
Given formula
Total = Number of oranges × Average weight
Convert Kilogram unit to Gram
1 kg = 1000 g
4.5 kg = 4.5 × 1000 = 4500 g
Substitute values into the given formula
Total = Number of oranges × Average weight
Number of oranges = Total / Average weight
Number of oranges = 4500 / 75
Simplify by division
[tex]\Large\boxed{Number~of~oranges~=~60}[/tex]
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Please let me know if you have any questions
Answer:
60 oranges
Step-by-step explanation:
Let the unknown number of oranges be x.Given that,The average weight of an orange ⇒ 75g
Total weight of oranges ⇒ 4.5 kg
Therefore,Number of oranges Weight ( in grams)
1 75 g
x (4.5 × 1000) g
To find the number of oranges we can make an expression like this.1 ⇒ 75
x ⇒ 4500
Use cross multiplication and find the value of x.
75x = 4500 × 1
75x = 4500
Divide both sides by 75.
x = 60
Therefore, 60 oranges would weight 4.5kgSelect the reason that best supports statement 2 in the given proof.
Answers
Answer:
Transitive property
The reason that best supports statement 2 in the given proof is division property of equality. Therefore, the correct answer is option D.
Given that, 3(m∠A)=90° and m∠B=m∠A.
We need to prove m∠B=30°.
According to the division property of equality, the quotients of an equation remain equal when both sides are divided by a common real integer that is not equal to 0.
Here,
Statement: Reason:
1. 3(m∠A)=90° 1. Given
2. m∠A=30° 2. Division property of equality
3. m∠B=m∠A 3. Reflexive property
4. m∠B=30° 4. Transitive Property
Therefore, the correct answer is option D.
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Currently, tommy is five times as old as bianca. in eight years, tommy will only be three times as old as bianca. How old is tommy right now?
Answers
The age of Tommy is currently 40-years old
According to the statement
we have given that the tommy is five times as old as bianca and in eight years, tommy will only be three times as old as bianca.
And we have to find the present age of the tommy.
So, This is a question involving the ratio of ages.
Let the ages of Tommy and Bianca in the present be T and B respectively.
STEP 1: Let:
T = 5B
T + 8 = 3 (B+8)
Then
STEP 2: We can substitute T with 5B since the two variables are equal, to create:
5B + 8 = 3 (B + 8)
Then
STEP 3: Finally, we can expand and solve:
5B + 8 = 3B + 24
2B = 16
B = 8
T = 5B = 5 x 8 = 40
T = 40
Therefore, The age of Tommy is currently 40-years old
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Every person has blood type O, A, B, or AB. A random group of people are blood-typed, and the results are shown in the table. A 2-column table with 4 rows is shown. The first column is labeled Blood Type with entries O, A, B, AB. The second column is labeled Number of People with entries 22, 20, 6, 2. Use the table to determine the following probabilities. The probability that a randomly chosen person from this group has type B is . The probability that a randomly chosen person from this group has type AB is . The probability that a randomly chosen person from this group has type B or type AB blood is .
Answers
Has type B= 6/50= 3/25 = 12%
Has type AB= 2/50 = 1/25 = 4%
Has type B or type AB = 8/50 = 4/25 = 16%
Solve:
4(2 + a) = 24
A =
Answers
Answer:
a=4Step-by-step explanation:
Simplify both sides of the equation:
4 (2 + a) = 24
( 4 )( 2 ) + ( 4 )( a ) = 24 (Distribute)
8 + 4a = 24
4a + 8 = 24
subtract 8 from both sides:
4a + 8 − 8 = 24 − 8
4a = 16
Divide both sides by 4:
4 a/4 = 16/4
a = 4
Multiple bracket out first:
4 x 2 =8
4 x a = 4a
8 +4a = 24
-8
4a. = 16
÷4
a = 4
Hope this helps!
A
(5x − 3)°
B
E
(7x+15)°
D
(6y + 7)°
C
Answers
Answer:
The value of x = 14 ...
The value of ∠AED = ( 7x + 15) = 7(14) + 15 = 113
The value of ∠AEB = 5x-3 = 5(14) -3 = 67
Step-by-step explanation:
=> ∠BEC = ∠AED { vertically opposite angles }
∠AED = (7x + 15)°
=> ∠AEB + ∠BEC = 180° { linear pair }
=> ( 5x-3) + ( 7x+15) = 180°
=> 5x -3 + 7x + 15 = 180°
=> 12x + 12 = 180°
=> 12( x +1 ) = 180°
=> x+1 = 180/12
=> x +1 = 15
=> x = 15-1
=> x = 14
What is the equilibrium expression for the reaction below?
N₂(g) +
3H₂(g)2NH₂(g)
OA.
B.
OC.
OD.
3 [N₂] [H₂]
2 [NH]
[NH₂7²2
[N₂][H₂]
[NH₂]
[N₂] [H₂]
[N₂] + 3 [H₂]
2[NH₂]
Answers
The equilibrium expression is written as [NH3]^2/[N2] [H2]^3.
What is equilibrium constant?A reaction involves the conversion of reactants to products. Now we know that the number that shows us the extent to which we can convert the reactants to products is given by the equilibrium constant. If the equilibrium constant is large and positive, then the reaction tends towards the conversion of reactants to products. on the other hand, when the reaction has a small equilibrium constant, then the reaction tends towards the reactants.
Thus, the magnitude of the equilibrium constant tells us how easily reactants are converted into products and this is necessary when we are trying to predict the direction in which a reaction will go or make calculations.
Given a reaction; N₂(g) + 3H₂(g) ----> 2NH3(g) we can now write the expression for the equilibrium of the reaction as;
K = [NH3]^2/[N2] [H2]^3
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Kaitlin, Joe, and Miguel have a total 96 of in their wallets. Kaitlin has 6 less than Joe. Miguel has 4 times what Joe has. How much does each have?
Answers
Answer:
15, 11, 60
Step-by-step explanation:
Let Joe's amount be x
x + x - 6 + 4x = 96
6x - 6 = 96
6x = 90
x = 15
Joe has 15
Kaitlin has 11
Miguel has 60
during the drive from the church to the graveyard , you cover 16,4 km in 1,5 hours . calculate your average speed
Answers
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Avg. speed = 11 km/h[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Average speed (v) :
[tex]\qquad❖ \: \sf \:v = \cfrac{total \: \: distance \: \: covered}{total \: \: time \: \: taken} [/tex]
[tex]\qquad❖ \: \sf \:v = \dfrac{16.4}{1.5} [/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\qquad❖ \: \sf \:v = 11 \: \: kmph[/tex]
Which number is equivalent to (1/3)^-4
A 81
B −1/81
C −1/12
D 12
Answers
The fraction (1/3)⁻⁴ is equal to 81.
Given that:
Fraction: (1/3)⁻⁴
Rewrite the expression by applying the rule that states a negative exponent is equal to the reciprocal of the positive exponent:
(1/3)⁻⁴= 1 / (1/3)⁴
Now, let's simplify (1/3)⁴:
(1/3)⁴ = (1/3) × (1/3) × (1/3) × (1/3)
(1/3)⁴ = 1/81
So, the expression becomes:
1 /(1/3)⁴ = 1 / (1/81)
Now, dividing by a fraction is equivalent to multiplying by its reciprocal:
1 / (1/81) = 1 × 81 = 81
Therefore, the fraction (1/3)⁻⁴ is equal to 81.
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please help me with 3.2
Answers
The measure of the angle ∠PQR is 90 degrees
How to prove that ∠PQR is 90 degrees?The equation of the line PQ is given as:
3x - y - 2 = 0
The coordinates of the QR are given as:
(0, -2) and (6, -4)
Make y the subject in 3x - y - 2 = 0
y = 3x - 2
The slope of the above line is
m1 = 3
Next, we calculate the slope (m2) of points Q and R.
So, we have:
m2 = (y2- y1)/(x2 - x1)
This gives
m2 = (-4 + 2)/(6 - 0)
Evaluate
m2 = -1/3
The slopes of perpendicular lines are opposite reciprocals.
m1 = 3 and m2 = -1/3 are opposite reciprocals.
This means the lines PQ and QR are perpendicular lines.
The angle at the point of perpendicularity is 90 degrees
Hence, the measure of the angle ∠PQR is 90 degrees
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