What is the equation of the graphed line in standard form? Responses y = 2x + 6 y, = 2, x, + 6 −2x+y=6 negative 2 x plus y equals 6 12x+y=6 negative 1 half x plus y equals 6 12x−y=−6 1 half x plus y equals negative 6 A line graphed on a Coordinate plane with x axis ranging from negative 10 to 10 and y axis ranging from negative 10 to 10. The line passes through the points begin ordered pair 0 comma 6 end ordered pair comma begin ordered pair 2 comma 7 end ordered pair.
The equation of the graphed line is y = 1/2 x + 6
How to determine the equation of the lineThe general formula for the equation of a graphed line is expressed with the formula;
y = mx + c
Where the parameters are;
y is a point on the y-axis of the graphm is the slope of the line of the graphx is a point on the x-axis of the graphc is the intercept of the line on the y -axis of the lineFrom the diagram shown, the values are;
(0, 6) and (2. 7)
The intercept is 6
The slope is expressed as; y₂ - y₁/x₂ - x₁
Substitute the values
Slope, m = 7 - 6/2 - 0
Slope, m = 1/2
Then, the equation is
y = 1/2 x + 6
Hence, the equation is y = 1/2x + 6
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A sandwich store charges a $10 delivery fee, and $4.50 for each sandwich.
How much does it cost for x sandwhiches?
Answer:
So for x sandwiches, the cost would be 10 + 4.5x dollars.
Step-by-step explanation:
The cost for x sandwiches can be calculated by adding the delivery fee to the cost of the sandwiches:
Cost = Delivery fee + Cost of sandwiches
Cost = 10 + 4.5x
how many 2/3 are in 4
The number of 2/3 parts in the number 4 will be 6.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The number of 2/3 parts in the number 4. Then the expression is given as,
⇒ 4 ÷ (2/3)
⇒ 4 x (3/2)
⇒ 2 x 3
⇒ 6
The number of 2/3 parts in the number 4 will be 6.
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Solve the equation.
Give your simplified answer as an improper fraction.
4(x + 5) = 6(2x - 1)
X=
Answer the following questions:
a.
1. Two numbers are in the ratio of 8: 9. Their sum is 136. What are the numbers?
2. Three numbers are in the ratio of 3: 2: 7. Their sum is 108. What are the numbers?
3. Four numbers are in the ratio 5: 6: 7: 8. The greatest of these is 24. Find the sum of
these numbers.
4. A piece of land was divided among three heirs. The eldest heir received three times as much as the youngest child, who received two times as much as the middle child. If the middle child received 12 hectares (ha) of land, what was the total area of land did they inherit?
5. The numbers are in the ratio 4: 5 and their sum is 108.
6. The numbers are in the ratio 6: 7: 8 and their sum is 63.
7. The numbers are in the ratio 2: 3: 5. The least of these is 48.
8. The numbers are in the ratio 3: 5: 7. The greatest of these is 75.
9. A class has 50 students. The ratio of males to females is 2: 3. How many males and
female students are there?
10. Cherie, Mona, and Kate shared 360 stamps in the ratio of 3: 4: 5, respectively. How many stamps did each of them have?
11. Forty marbles are in a bag. The ratio of red to yellow to blue to green marbles is
1: 2: 2: 3, respectively. How many of the marbles are colored yellow or green?
12. A tall shelf has 80 books. The ratio of fiction to nonfiction to a general reference to
children’s books is 6: 5: 2: 3, respectively. How many more children’s books are
there than general reference books?
1 Let's call the two numbers x and y. According to the ratio, x:y = 8:9, so y = (9/8)x. And since their sum is 136, x + y = 136, so we can substitute y = (9/8)x into this equation:
x + (9/8)x = 136
(17/8)x = 136
x = 64
So the two numbers are 64 and 72.
2 Let's call the three numbers x, y, and z. According to the ratio, x:y:z = 3:2:7, so y = (2/3)x and z = (7/3)x. And since their sum is 108, x + y + z = 108, so we can substitute y = (2/3)x and z = (7/3)x into this equation:
x + (2/3)x + (7/3)x = 108
(12/3)x = 108
x = 36
So the three numbers are 36, 24, and 84.
3 Let's call the four numbers a, b, c, and d. According to the ratio, a:b:c:d = 5:6:7:8, so b = (6/5)a, c = (7/5)a, and d = (8/5)a. And since the greatest of these is 24, d = 24, so we can substitute c = (7/5)a and d = (8/5)a into this equation:
a + (6/5)a + (7/5)a + (8/5)a = 24
(27/5)a = 24
a = 24 * 5/27 = 8
So the four numbers are 8, 9.6, 10.4, and 24. And the sum of these numbers is 8 + 9.6 + 10.4 + 24 = 52
4 Let's call the three heirs' land area x, y, and z. Since the eldest heir received three times as much as the youngest child, who received two times as much as the middle child, we can write the equation:
x = 3y and y = 2z
So we can substitute y = 2z into x = 3y to get:
x = 3 * 2z = 6z
And since the middle child received 12 ha of land, we can substitute z = 12 into x = 6z to get:
x = 6 * 12 = 72
So the total area of land they inherited is x + y + z = 72 + 2 * 12 = 96 ha.
5 Let's call the two numbers x and y. According to the ratio, x:y = 4:5, so y = (5/4)x. And since their sum is 108, x + y = 108, so we can substitute y = (5/4)x into this equation:
x + (5/4)x = 108
(9/4)x = 108
x = 36
So the two numbers are 36 and 45.
6 Let's call the three numbers x, y, and z. Then, we have:
x:y:z = 6:7:8
x + y + z = 63
To find the values of x, y, and z, we can use the first ratio to write x, y, and z as multiples of the same number. Let's call that number t:
x = 6t
y = 7t
z = 8t
We can use the second equation to solve for t:
6t + 7t + 8t = 63
21t = 63
t = 3
So, the three numbers are:
x = 6t = 6 * 3 = 18
y = 7t = 7 * 3 = 21
z = 8t = 8 * 3 = 24
7 Let's call the three numbers a, b, and c. Then, we have:
a:b:c = 2:3:5
a = 48 (the least of these)
To find the values of b and c, we can use the first ratio to write b and c as multiples of a:
b = 3a = 3 * 48 = 144
c = 5a = 5 * 48 = 240
8 Let's call the three numbers p, q, and r. Then, we have:
p:q:r = 3:5:7
r = 75 (the greatest of these)
To find the values of p and q, we can use the first ratio to write p and q as multiples of r:
p = 3r/5 = 3 * 75/5 = 45
q = 5r/7 = 5 * 75/7 = 50
9 Let's call the number of male students m and the number of female students f. Then, we have:
m:f = 2:3
m + f = 50
To find the values of m and f, we can use the first ratio to write m and f as multiples of the same number. Let's call that number t:
m = 2t
f = 3t
We can use the second equation to solve for t:
2t + 3t = 50
5t = 50
t = 10
So, the number of male students is:
m = 2t = 2 * 10 = 20
And the number of female students is:
f = 3t = 3 * 10 = 30
10 Let's call the number of stamps that Cherie has x, the number of stamps that Mona has y, and the number of stamps that Kate has z. Then, we have:
x:y:z = 3:4:5
x + y + z = 360
To find the values of x, y, and z, we can use the first ratio to write x, y, and z as multiples of the same number. Let's call that number t:
x = 3t
y = 4t
z = 5t
We can use the second equation to solve for t:
3t + 4t + 5t = 360
12t = 360
t = 30
So, Cherie has:
x = 3t = 3 * 30 = 90 stamps
Mona has:
y = 4t = 4 * 30 = 120 stamps
Kate has:
z = 5t = 5 * 30 = 150 stamps
11 The marbles are divided in the ratio 1:2:2:3, so there are 2 x 2 = 4 times as many yellow and blue marbles as there are red marbles. Therefore, there are 2 + 2 = 4 red marbles. Hence, there are 4 x 2 = 8 yellow and blue marbles. Furthermore, there are 3 times as many green marbles as there are red marbles, meaning there are 3 x 4 = 12 green marbles. Therefore, the total number of yellow and green marbles is 8 + 12 = 20.
12 According to the ratio, there are 6:5:2:3 of fiction to nonfiction to general reference to children's books. So the number of each category can be calculated as follows:
Fiction: 6/16 x 80 = 30 books
Nonfiction: 5/16 x 80 = 25 books
General reference: 2/16 x 80 = 10 books
Children's books: 3/16 x 80 = 15 books
So, there are 15 - 10 = 5 more children's books than general reference books.
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a developmental psychologist studies the number of words that seven infants have learned at a particular age. the numbers are 10, 12, 8, 0, 3, 40, and 18. figure the (a) mean, (b) median, and (c) standard deviation for the number of words learned by these seven infants. (d) explain what you have done and what the results mean to a person who has never had a course in statistics
The mean of 13 words, median of 10 words, and standard deviation of 13.20 words give us an idea of the central tendency and variability of the number of words learned by the seven infants.
(a) Mean: The mean is the average of the values and can be calculated by adding all the values and dividing by the number of values. For the number of words learned by the seven infants, the mean can be calculated as follows:
mean = (10 + 12 + 8 + 0 + 3 + 40 + 18) / 7 = 91 / 7 = 13
So the mean number of words learned by the seven infants is 13 words.
(b) Median: The median is the middle value in a set of values. If the number of values is odd, the median is the middle value. If the number of values is even, the median is the average of the two middle values.
0, 3, 8, 10, 12, 18, 40
The median is 10 words.
(c) Standard Deviation: The standard deviation is a measure of the spread or variability of a set of values.
First, the deviations from the mean are calculated as follows:
10 - 13 = -3
12 - 13 = -1
8 - 13 = -5
0 - 13 = -13
3 - 13 = -10
40 - 13 = 27
18 - 13 = 5
Next, the squared deviations are calculated:
(-3)^2 = 9
(-1)^2 = 1
(-5)^2 = 25
(-13)^2 = 169
(-10)^2 = 100
27^2 = 729
5^2 = 25
The variance is then calculated as the average of the squared deviations, divided by the number of values (n - 1):
variance = (9 + 1 + 25 + 169 + 100 + 729 + 25) / (7 - 1) = 1058 / 6 = 176.33
Finally, the standard deviation is calculated as the square root of the variance:
standard deviation = sqrt(variance) = sqrt(176.33) = 13.20
(d) Explanation: The mean, median, and standard deviation are measures of the central tendency and variability of a set of values. The mean is the average of the values and gives an idea of the typical value.
In this case, The mean tells us that the typical number of words learned by the seven infants is 13 words, the median tells us that half of the infants learned more than 10 words and half of the infants learned less, and the standard deviation tells us that the values are spread out around the mean with a deviation of about 13 words.
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find p(the trip will take 25 minutes)
The values of the probabilities are 4/7, 2/7 and 5/7
How to determine the values of the probabilitiesp(the trip will take 25 minutes)
From the question, we have the following parameters that can be used in our computation:
25 minutes = 8
Total = 14
So, we have
P(25 minutes) = 8/14 = 4/7
p(the trip will take 20 minutes)
From the question, we have the following parameters that can be used in our computation:
20 minutes = 4
Total = 14
So, we have
P(20 minutes) = 4/14 = 2/7
p(the trip will take atleast 25 minutes)
From the question, we have the following parameters that can be used in our computation:
At least 25 minutes = 8 + 2 = 10
Total = 14
So, we have
P(At least 25 minutes) = 10/14 = 5/7
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timmy and susie both work at the Monster Burger. Timmy works for 40 hours and makes 720 dollars. He has been working there longer than susie who makes only 600 dollars in the same amount of time. Monster Burger employees are given a 50 cent raise a year.
Answer:
Timmy has been working at Monster Burger longer than Susie, which explains why he earns more money. Monster Burger employees are given a 50 cent raise each year, so Susie's salary will likely increase over time as she continues to work there.
Step-by-step explanation:
It is possible to determine how long Susie has been working at Monster Burger by using the information given. Since Timmy makes 720 dollars working 40 hours and Susie makes 600 dollars working the same hours, we can calculate their hourly wages:
Timmy's hourly wage: 720 / 40 = 18 dollars
Susie's hourly wage: 600 / 40 = 15 dollars
Since Monster Burger employees are given a 50 cent raise a year, this means that Susie's hourly wage has increased by 50 cents * x years, where x is the number of years Susie has been working there. Thus, we have:
15 + (0.50 * x) = 18
Solving for x, we get:
x = (18 - 15) / 0.50 = 6 years
Therefore, Susie has been working at Monster Burger for 6 years.
Gabriela bought a new pair of glasses at the store when they were having a
30
%
30%30, percent off sale.
If the regular price of the pair of glasses was
$
72
$72dollar sign, 72, how much did Gabriela pay with the discount?
The amount of money Gabriela paid for the pair of glasses after the discount is $50.4
How much did Gabriela pay with the discount?Regular price of the pair of glasses= $72
Percentage discount= 30%
Amount Gabriela actually paid= Regular price of the pair of glasses - (Percentage discount of Regular price of the pair of glasses)
= 72 - (30% × 72)
= 72 - (0.3 × 72)
= 72 - 21.6
= $50.4
Therefore, Gabriela paid $50.4 for the pair of glasses after deducting discount.
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Hey, does anyone know the answer to this problem? I’m struggling with it
Answer:
Step-by-step explanation:
the total perimeter is 33 so all of the sides are equal to it.
33=3x+13+12
then combine like terms
33=3x+25
subtract from each side
(33)-25=(3x+25)-25
8=3x
divide by 3
x=2 2/3
Kendall has only quarters and dimes in her pocket. The total value of these coins is $1.50. The equation below can be used to find q, the number quarters, and d, the number of dimes in her pocket. If Kendall has 4 quarters in her pocket, how many dimes are in her pocket? 25g + 10d = 150
Answer:
Kendall must have 5 dimes in her pocket.
Step-by-step explanation:
First, let's write down all the information that is given to us:
q = number of quarters ["q, the number quarters"]
d = number of dimes ["d, the number of dimes"]
q = 4 ["Kendall has 4 quarters in her pocket"]
25q + 10d = 150
Since the value of q is given to us, our equation now has one unknown variable, d, and we can solve for it.
25q + 10d = 150 [Plug in q]
25(4) + 10d = 150 [Simplify]
100 + 10d = 150 [Subtract 100 from both sides]
10d = 50 [Divide both sides by 10]
d = 5
So, since d=5, Kendall must have 5 dimes in her pocket.
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Please help! True or false
3x + 6 is equivalent to 9x
Step-by-step explanation:
false.
3x + 6x is equivalent to 9x
but not 3x + 6. 6 is a constant added term. not a multiplication factor. so, it cannot be combined with a multiplication factor.
but 3x + 6 = 9x
has one solution, one value of x for which this equation is true :
3x + 6 = 9x
6 = 6x
x = 1
so, for x = 1 (and only for x = 1) this is true. for any other value of x this is false.
therefore, the general equivalent statement is false.
a bakery sells apple pies for $12.85. if the pie has a diameter of 10 inches, what is the approximate cost per square inch? round to the nearest hundredth
The cost per square inch is $0.16 per square inches ( nearest hundredth)
What is area?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
The area of a circular pie = πr²
= 3.14 × (10/2)² since r = d/2
= 3.14 × 5²
= 78.5 square inches
apple pies are sold for a cost of $12.85
Therefore the cost per square inches
= 12.85/78.5
= $0.16(nearest hundredth) per square inches
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order these fractions from least to greatest 5 1/11, 5.576, 5.57, 101/20
Answer: 101/20, 5 1/11, 5.57, 5.576
Step-by-step explanation:
I hope this is correct :D
Trigonometric Identities
50 points btw!!
Use trigonometric identities to solve each equation within the given domain.
a) –sin2(x) = cos(2x) from [–π, π]
b) 3 tan(x) = 2 sin(2x) from [0, 2π)
c) sec(x) cos(3x) = 0 from [–π/2 ,π/2]
d) 1 – cos(x) = 2 – 2 sin^2(x) from (–π, π)
e) 4cos^4 (x) – 5cos^2(x) + 1 = 0 from [0, 2π)
if you answer all thank you so much this helps a lot!
Step-by-step explanation:
a)
-sin(2x) = cos(2x)
sin(2x) = cos(2x)
2sin(x)cos(x) = cos(2x)
2sin(x)cos(x) = 1 or -1
sin(x) = +/-√(1/2) or sin(x) = 0
x = (2n+1)π/4 or x = nπ
b)
3 tan(x) = 2 sin(2x)
tan(x) = 2/3 sin(2x)
sin(2x) = 3 tan(x)/2
cos^2(x) = (1 - sin^2(x)) = (1 - (3 tan(x)/2)^2)/4
x = nπ/2 + arctan(2√(2)/3) or x = nπ/2 + arctan(-2√(2)/3)
c)
sec(x) cos(3x) = 0
cos(x) = 0 or cos(3x) = 0
x = nπ/2 or x = (3n+1)π/6
d)
1 - cos(x) = 2 - 2sin^2(x)
cos(x) = 2sin^2(x) - 1
2sin^2(x) = cos(x) + 1
sin^2(x) = (cos(x) + 1)/2
sin(x) = +/- √((cos(x) + 1)/2)
e)
4cos^4(x) - 5cos^2(x) + 1 = 0
cos^2(x) = (1 ± √(5))/2
x = arccos(±√((1 + √(5))/2)) or x = arccos(±√((1 - √(5))/2))
Note: n is any integer in the given domain.
a gray squirrel population was introduced in a certain region 27 years ago. biologists observe that the population doubles every nine years, and now the population is 680. (a) what was the initial squirrel population? squirrels (b) what is the expected squirrel population, p, t years after introduction? p(t)
The gray squirrel population t years after introduction is P(t) = [tex]340 x 2^(t/9).[/tex]
The formula for the gray squirrel population, p, t years after the introduction of the population is [tex]P(t) = P0 x 2^(t/9)[/tex], where P0 is the initial population. We can use this formula to answer both (a) and (b). For (a), we can substitute t = 0 and P(t) = 680, to solve for P0. This gives us that the initial population of gray squirrels was 340. For (b), we can substitute t = 27 (the number of years since introduction) and P(t) = 680, to solve for P(27). This gives us that the expected population of gray squirrels t years after introduction is 1360. Therefore, the formula for the gray squirrel population t years after introduction is [tex]P(t) = 340 x 2^(t/9)[/tex].
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2x-48=8x a. one solution b. no solution
Answer:
a. one solution (x = -8)
Step-by-step explanation:
You want to know how many solutions there are for the equation 2x -48 = 8x.
SolutionThis is a 2-step linear equation.
Step 1: subtract 2x from both sides.
-48 = 6x
Step 2: divide by the coefficient of x.
-48/6 = -8 = x
There is one solution: x = -8.
__
Additional comment
When x terms are on both sides of the equal sign, there will be one solution if their coefficients are different.
If the coefficients are the same, the number of solutions may be 0 or infinite, depending on the constant value(s).
in a sample of 19 small candles, the weight is found to be 3.72 ounces with a standard deviation of 0.963 ounces. what would be the 87% confidence interval for the size of the candles?
Answer:
(3.369, 4.071)
Step-by-step explanation:
if the price of milk increases from $3.99 to $5.99 per gallon, this will cause a .
The percent decrease of the average gas price from january to February is 7.85%
How to find percent decrease of the average gas price from january to February
Average gas price in January = $4.33 per gallon
Average gas price in February = $3.99 per gallon
Change in average gas price = Average gas price in January - Average gas price in February
= $4.33 - $3.99
= $0.34
Percent decrease in average price = Change in average gas price / Average gas price in January × 100
= $0.34 / $4.33 × 100
= 0.078521939953810 × 100
= 7.85%
In conclusion, the price of gas has decreased at a percentage of 7.85% from January to February.
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complete question
Gas prices averaged $4.33 per gallon in january and $3.99 per gallon in february. what was the percent decrease of the average gas price from january to february?
4. Decide whether the polygons are similar, not similar, or not enough information is given. If similar, write a similarity statement. If not, explain why.
The given polygons WXYZ and PQRS are similar.
What are Similar Figures?Similar figures are those figures which are having the same shape, but the sizes are different.
Since the shape of similar figures are same, the corresponding angles of the figures will be equal.
And the corresponding sides will be proportional.
From the polygons WXYZ and PQRS, given,
∠X = ∠Q
∠W = ∠P
∠Y = ∠R
∠Z = ∠S
So the figures are similar.
WX / PQ = XY / QR = YZ / RS = WZ / PS
Hence the given figures are similar.
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Miguel ran 80 meters in 20 seconds while Trina ran 40 meters in 15 seconds. If they continue to run at this pace, who will finish an 800-meter race first? Explain your reasoning.
Miguel finish an 800-meter race first.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
Miguel ran 80 meters in 20 seconds while Trina ran 40 meters in 15 seconds.
Hence, The speed of Miguel is,
⇒ Speed = Distance / Time
⇒ Speed = 80 / 20
⇒ Speed = 4 m/s
And, The speed of Trina is,
⇒ Speed = Distance / Time
⇒ Speed = 40/15
⇒ Speed = 2.67 m/s
Cleary, The speed of Miguel is faster than Trina.
Hence, Miguel finish an 800-meter race first.
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A giant rectangular sheet of cardboard, 20 m x 10 m, is made into a lidless box by cutting squares out of the corners. The volume this box can hold is 96 m3. What are the possible dimensions of the squares that were cut out of the corners to create this box?
Look for relationships which two functions have the same rate of change
• A Y= 0.5x-1
•B y= 4x-7
•C n=0.6r+1
•D t= 0.5n+1
The solution is, Their rate of change is respectively 0.5.
• A. y = 0.5x - 1
• D. t= 0.5n + 1
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
here, we have,
The slope-intercept form of the equation of a straight line is:
y=mx+c
where, m= rate of change.
From the given equations, the two that have the same rate of change are:
• A. y = 0.5x - 1
• D. t= 0.5n + 1
Their rate of change is respectively 0.5.
The correct choices are A and D.
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A ships sails 8km north and then 10km east. How far is it from its starting point to the nearest km?
Solve the system using substitution.
4x + 3y = 23
x - 5y = 0
Answer:
y=1 x=5
Step-by-step explanation:
from the second equation
x=5y
then,when we substitute the equation
4(5y)+3y=23
20y+3y=23
23y=23
y=1
if and only if,x=5y and y=1
then x=5
P = 14.7+
The total pressure, P, in pounds per square inch, f feet below the ocean's surface is given by
the equation above. What is the pressure at the ocean's surface in pounds per square inch?
A) 0
B) 14.7
C) 22.5
D) 331
The solution is Option B.
The pressure at the ocean's surface is given by the equation A = 14.7 pounds per square inches
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
P = 14.7 + ( f/22.5 ) be equation (1)
where P is the total pressure in pounds per inch²
And , f is the height in feet below the ocean's surface
Now , pressure at the ocean's surface is when f = 0
Substitute the value of f = 0 in equation (1) , we get
P = 14.7 + ( 0/22.5 )
On simplifying the equation , we get
P = 14.7 pounds/inch²
Hence , the equation is P = 14.7 pounds/inch²
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Find the other endpoint
Endpoint: (-10, 5), midpoint: (3, -7)
Answer:
the answer is in the picture.. if you have any questions feel free to ask
Logan needs to order some new supplies for the restaurant where he works. The
restaurant needs at least 505 spoons. There are currently 238 spoons. If each set on
sale contains 15 spoons, which inequality can be used to determine x, the minimum
number of sets of spoons Logan should buy?
Which pair is equivalent A:2/6 and 2/4 B: 3/6 and 1/2 C:5/12 and 1/3 D:4/8and 4/6
Answer:B
Step-by-step explanation:
If you simplify 3/6 you will get 1/2
Please help with 2 and 3
Based on the provided lines and angles;
The true statements are: A, B, D, and E∠5 = 75°; ∠11 = 75°; ∠16 = 65°Let's discuss each problem we have:
Problem 2: Parallel lines m and n are cut by transversal l
Statement A: ∠1 = ∠5 is correct because both are corresponding angles and congruent.
Statement B: ∠2 = ∠4 is correct because both are vertical angles and congruent
Statement C: ∠2 = ∠7 is incorrect because ∠7 is the corresponding angle of ∠3 which is the supplementary angle of ∠2
Statement D: ∠3 and ∠6 form a linear pair is correct because both are consecutive interior angles and supplementary
Statement E: ∠4 and ∠5 are supplementary is correct because both are consecutive interior angles.
Problem 3: Parallel lines a and b are cut by transversal c and d
∠1 = 115°
∠8 = 105°
∠5 is adjacent and the supplementary angle of ∠8, then:
∠5 + ∠8 = 180°
∠5 + 105° = 180°
∠5 = 75°
∠11 is the alternate exterior angle of ∠5 and both are congruent, then:
∠11 = ∠5 = 75°
∠16 is the corresponding angle of ∠4 and congruent. ∠4 is the adjacent and supplementary of ∠1, then:
∠16 = ∠4
∠4 + ∠1 = 180°
∠16 + ∠1 = 180°
∠16 + 115° = 180°
∠16 = 65°
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