Both f(x) and g(x) include domain values of [12,), and both functions increase over the interval (12, ∞).
What is the Function?A relationship between a set of inputs (the domain) and a set of potential outputs (the range) is known as a function. This relationship has the feature that each input is associated to exactly one output.
The notation f(x) is often used to express a function in mathematics, where f is the name of the function and x is the input value, also known as the argument of the function. When f(x) is calculated, it indicates the function's output value for the given input value x.
First, both functions have a domain that includes all values of x greater than or equal to 12, which is expressed as [12,) in interval notation.
Second, both functions increase over the interval (12, ∞), meaning that as x increases beyond 12, the values of the functions also increase without bound. This is because the exponential function 12^x and the square root function √(x - 12) both become increasingly steep as x increases, leading to a sharp increase in their values.
Therefore, Both f(x) and g(x) include domain values of [12,), and both functions increase over the interval (12, ∞).
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A pendulum is a weight attached to a fixed rod, as shown in the figures. Suppose that during an experiment, a pendulum moves back and forth in a periodic manner. At the beginning of the experiment , when the time is t = 0 seconds , the pendulum is at a point halfway between its maximum and minimum distances from the wall, 2.5 m away from the wall (Figure 1) and moving toward the wall. The pendulum first reaches its minimum distance from the wall , 1 m from the wall , when t = 1 second (Figure 2). When t = 4 seconds, the pendulum is back to a point halfway between its maximum and minimum distances from the wall. The pendulum continues to move back and forth so that the distance between the pendulum and the wall over time can be modeled by a sinusoida ! function .
An automobile company is running a new television commercial in five cities with approximately the same population. The following table shows the number of times the commercial is run on TV in each city and the number of car sales (in hundreds). Find the Pearson correlation coefficient r for the data given in the table. Round any intermediate calculations to no less than six decimal places, and round your final answer to three decimal places.
Therefore , the solution of the given problem of data plot comes out to be value (r) is roughly 0.975.
Data plot: What is it?The most typical way to display data in a graph is to demonstrate how two additional factors relate to one another. Digital and hand-drawn sketches are both acceptable. From the beginning position, move two or more pieces to the correct and three pieces up. The reference system must display the numerals for positions 2, 3, and 4. In your points, be very clear. The pinkish haze with the letter P stands in for the number 2.3.
Here,
We must compute several numbers in order to determine the Pearson correlation coefficient r for the information provided in the table.
Before anything else, we figure out the average and standard deviation of the amount of TV airings (x) and car sales (y):
mean(x) = (40 + 30 + 20 + 50 + 10) / 5 = 30
mean(y) = (30 + 20 + 10 + 40 + 20) / 5 = 24
These mean numbers allow us to determine the standard deviation:
=> SX = √ (( (40-30)² + (30-30)² + (20-30)² + (50-30)² + (10-30)²) / 4)
≈> 15.81
=> SY = √(( (30-24)²+ (20-24)² + (10-24)² + (40-24)² + (20-24)²) / 4)
≈> 8.16
Next, we determine x and y's covariance:
=> cov(x,y) =
=> [(40-30)(30-24) + (30-30)(20-24) + (20-30)(10-24) + (50-30)(40-24) + (10-30)(20-24)] / 4
≈> 125
Last but not least, we can figure out the Pearson association coefficient:
0.975 r = cov(x,y) / (s x * s y)
As a result, the table's data's Pearson correlation value (r) is roughly 0.975. This shows a significant positive correlation between the volume of car purchases and the frequency of the TV ad.
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Question 11 (1 point)
Mary Ellen is making a table cloth for a client's dining room. She selected some pale-
yellow linen from a craft store and has it laid out on her work table to cut into the
correct shape. What tool is Mary Ellen MOST LIKELY going to use to cut the linen?
Scissors
Shears
A measuring tape
A Color Scheme Guide
Answer:
Mary Ellen is MOST LIKELY going to use shears to cut the linen.
The box plot shows some information about the distribution of the amounts of money spent by some male students on their holidays.
i got part b correct but i cant figure out part a, please help
The interquartile range for the amounts of money spent by some male students on their holidays is £ 160.
How to find the interquartile range ?To find the interquartile range (IQR) on a box plot, the IQR is the difference between the upper and lower quartiles. The upper quartile (Q3) is the median of the upper half of the data, and the lower quartile (Q1) is the median of the lower half of the data.
The interquartile range for the amount spent by male students on their holidays is :
= Q3 - Q 1
= 800 - 640
= £ 160
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80 pts! please correct answer
What is the end behavior of this radical function?
f(x)=4\sqrt{x-6 }
A.
As x approaches positive infinity, f(x) approaches positive infinity.
B.
As x approaches negative infinity, f(x) approaches positive infinity.
C.
As x approaches positive infinity, f(x) approaches negative infinity.
D.
As x approaches negative infinity, f(x) approaches negative infinity.
Answer:
The end behavior of the given radical function f(x) = 4√(x-6) as x approaches positive infinity is option A: As x approaches positive infinity, f(x) approaches positive infinity.
Step-by-step explanation:
This is because as x approaches positive infinity, the value inside the square root (x-6) also approaches positive infinity. As the square root of a positive number is also positive, f(x) approaches positive infinity.
We can also see this by using the concept of limits. As x approaches positive infinity, the limit of f(x) can be evaluated as:
lim f(x) = lim 4√(x-6)
x→∞ x→∞
= 4√(lim(x-6))
x→∞
Since the limit of (x-6) as x approaches positive infinity is positive infinity, we have:
lim f(x) = 4√(∞) = ∞
x→∞
Therefore, as x approaches positive infinity, f(x) approaches positive infinity.
Answer:
Step-by-step explanation:
The end behavior of the given radical function f(x) = 4√(x-6) as x approaches positive infinity is option A: As x approaches positive infinity, f(x) approaches positive infinity.
This is because as x approaches positive infinity, the value inside the square root (x-6) also approaches positive infinity.
As the square root of a positive number is also positive, f(x) approaches positive infinity.
We can also see this by using the concept of limits.
As x approaches positive infinity, the limit of f(x) can be evaluated as:
lim f(x) = lim 4√(x-6)x→∞ x→∞= 4√(lim(x-6))x→∞.
Since the limit of (x-6) as x approaches positive infinity is positive infinity, we have:
lim f(x) = 4√(∞) = ∞x→∞.
Therefore, as x approaches positive infinity, f(x) approaches positive infinity.
To emphasize the slow increase in sales, it would be best for Samantha to use graph B or graph A for her presentation
Answer:
Graph A
Step-by-step explanation:
As can be seen, the trend in graph A is increasing with each month but not seemingly by as much as graph B;
This is because the scale of the y-axis in graph B has smaller increments;
This creates the impression of a slow increase in sales even though the data in both graphs is actually the same.
Answer: graph A.
appear to increase less.
Step-by-step explanation:
Jamie bought a shirt and a jacket for a total price of $164. The cost of the jacket was $17 more than twice the price of the shirt
The price οf the jacket was $115.
Let's start by defining sοme variables tο represent the unknοwn quantities:
Let x be the price οf the shirt
Let y be the price οf the jacket
Frοm the prοblem statement, we knοw that:
y = 2x + 17 (the cοst οf the jacket was $17 mοre than twice the price οf the shirt)
x + y = 164 (the tοtal cοst οf the shirt and jacket was $164)
We can use these twο equatiοns tο sοlve fοr the values οf x and y. One way tο dο this is tο substitute the expressiοn fοr y frοm the first equatiοn intο the secοnd equatiοn, and then sοlve fοr x:
x + (2x + 17) = 164
3x + 17 = 164
3x = 147
x = 49
Nοw that we knοw the price οf the shirt is $49, we can use the first equatiοn tο sοlve fοr the price οf the jacket:
y = 2x + 17
y = 2(49) + 17
y = 115
Therefοre, the price οf the jacket was $115.
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Ayudaaaaa no sé cuando vaya a venir a revisar estoooolo
Si 25$ representa el 15% de una cuenta cuanto hay en total en la cuenta?
Si 25 dólares representan el 15% de una cuenta, podemos usar una regla de tres simple para determinar cuánto hay en total en la cuenta:
15% -----> $25
100% ----> ($25 x 100)/15
100% ----> $166.67
Por lo tanto, hay $166.67 en total en la cuenta.
Find an equation for the graph.
The equation for the trigonometric graph is y = 2sin4x
What is a trigonometric graph?A trigonometric graph is the graph of a trigonometric function.
Since we desire to find the equation of the graph, we then want to use the equation for the general sine graph.
y = AsinBx where
A = amplitude and B = 2π/T where T = period.Now, A = (maximum - minimum)/2
From the graph,
maximum = 2 and minimum = -2So, we now substitute the variables into the equation, thus
A = (maximum - minimum)/2
= [2 - (-2)]/2
= (2 + 2)/2
= 4/2
= 2
Also B = 2π/T
Now from the graph, T = π/2
So, we substitute for B in the equation for B, thus
B = 2π/T
= 2π/(π/2)
= 2π × 2/π
= 4
We then substitute A and B into y, thus
y = AsinBx
= 2sin4x
So, y = 2sin4x
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Add one number to each column of the table so that it shows a function. Do not repeat an ordered pair that is in the table.
Click on the numbers you want to select and drag them into the table.
x y
6 6
3 8
9 12
7 8
x y
Find x,y value
Given numbers- 3,6,7,8,9,12
The values of x and y such that the table represents a function are given as follows:
x = 8, y = 7.
When does a relation represents a function?A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.
The input-output pairs for the function in this problem are given as follows:
An input of 6 is mapped to an output of 6.An input of 3 is mapped to an output of 8.An input of 9 is mapped to an output of 12.An input of 7 is mapped to an output of 8.Hence the x-value can only by 8 or 12, and we choose y = 8, while the y-value is free, hence we choose y = 7.
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Question 1
Find the unpaid balance, new interest, and purchasing power on the credit card after the minimum monthly payment is made. The interest charge for unpaid balances is 18% per year.
Credit Card Balance = $5000
Credit Limit = $5000
Minimum Payment = $125.00
After making the minimum payment of $125, the unpaid balance on the credit card is $4875, the new interest charge is $75, and the purchasing power is $50.
How to find the purchasing power?If the minimum monthly payment of $125 is made, we can calculate the new balance, unpaid balance, and interest charge as follows:
The interest rate per month is (18% per year) / 12 = 1.5% per month.
First, we calculate the interest charge for the month on the unpaid balance:
Interest charge = (1.5% per month) x ($5000 unpaid balance)
Interest charge = $75
Next, we subtract the minimum payment from the unpaid balance to get the new unpaid balance:
Unpaid balance = $5000 - $125
Unpaid balance= $4875
Then, we add the interest charge to the new unpaid balance to get the new balance:
New balance = $4875 + $75
New balance = $4950
Finally, we can calculate the purchasing power as the credit limit minus the new balance:
Purchasing power = $5000 - $4950
Purchasing power = $50
Therefore the unpaid balance on the credit card is $4875, the new interest charge is $75, and the purchasing power is $50.
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2. The graph of f(x) = -x² +8x+ 20 is sketched below. The graph intersects the x-axis at (-2;0) and (10;0), and the y — axis at (0; 20). The point (4;36) is the turning point of f. -2 20 0 Y (4:36) 1 10 the a is called th T
What is the standard error σM for this sample? (rounded to the nearest tenth: e.g. 2.2)
To calculate the standard error σM for a sample, we can use the formula [tex]σM = s / \sqrt{n}[/tex], where s: sample standard deviation and n: sample size.
The formula for calculating the standard error, M, which indicates the standard deviation of the sampling distribution of the mean, is as follows:
[tex]σM = σ / \sqrt{n}[/tex]
where σ: population standard deviation and n: sample size.
If we don't know the population standard deviation, we estimate it using the sample standard deviation s. We use formula:
[tex]σM = s / \sqrt{n}[/tex]
We can apply the method above with the sample size n and the sample standard deviation s if we are given a sample and asked to determine the standard error M for this sample.
By adding up each value in the sample and dividing by the sample size, we can determine the sample mean x, from which we may compute the sample standard deviation. The sample variance is then determined by adding up the squared deviations between each value and the sample mean, then dividing the result by the sample size less one. Lastly, we calculate the sample standard deviation by taking the square root of the sample variance.
Once we have calculated the sample standard deviation s and the sample size n, we can plug these values into the formula for σM:
[tex]σM = s / \sqrt{n}[/tex]
and calculate standard error.
In conclusion, the formula M = s / [tex]\sqrt{n}[/tex]n, where s: sample standard deviation and n: sample size, can be used to compute the standard error M for a sample.
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Using the growth accounting equation, if the growth rate of output is 5 percent, the growth rate of labor is 4 percent, the growth rate of technology is 3
percent, and a = 0.8, then the growth rate of capital can be estimated to be:
Multiple Choice
O
1.2 percent.
1.5 percent.
2.0 percent.
1.0 percent.
The answer is (B) 1.5 percent.
You can find the growth accounting equation by using:
Growth rate of output equals Technology growth rate plus a* Capital growth rate plus (1-a*Labor growth rate)
Inputting the values provided yields:
5% equals 3% plus (0.8 * Capital Growth Rate) plus (0.2 * 4%).
When we simplify the equation, we obtain:
Capital growth rate equals (5% - 3% - 0.2%) / 0.8, or 1.5%
As a result, the capital growth rate is predicted to be 1.5%.
(B) 1.5 percent is the right answer.
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On a farm there are 600 animals distributed in two areas. Of the 600 animals, 4/6 are in zone A and the rest in zone B.
What part of the animals is in zone b?
How many animals are there in each part?
Answer:
[tex]A=\frac{4}{6} *600 = 400\\B=\frac{2}{6} *600 = 200[/tex]
Find the value of x.
Answer:
8
Step-by-step explanation:
line WL is a straight line intersecting line GZ at J so angles LJW is 180o
therefore
LJG + GJH + HJW = 180
9x + 90 + 18 = 180
9x = 180 - 90 - 18
9x = 72
x = 72/9 = 8
Consider the graph of 5x² + 8x + 4y² - 4y = 70.
If the graph of 5x² + 8x + 4y - 4y = 70 is stretched horizontally by a factor of 3, the equation of the stretched graph will be
If the graph of 5x² + 8x + 4y² - 4y = 70 is stretched vertically by a factor of 7, the
equation of the stretched graph will be
To stretch the graph horizontally by a factor of 3, we need to multiply the x-coefficient by 1/3. Similarly, to stretch the graph vertically by a factor of 7, we need to multiply the y-coefficient by 1/7. Therefore:
Horizontally stretched graph: 5(1/3x)² + 8(1/3x) + 4y² - 4y = 70
Simplifying:
(5/9)x² + (8/3)x + 4y² - 4y = 70
Vertically stretched graph: 5x² + 8x + 4(1/7y)² - 4(1/7)y = 70
Simplifying:
5x² + 8x + (4/49)y² - (4/7)y = 70
A theme park's rides are rated as mild, moderate and
max. They have restrictions requiring that passengers
have heights of at least 42 inches, 48 inches, and 54
inches, respectively. Suppose the population of children
attending the park has a mean height of 53 inches with
a standard deviation of 4 inches.
If a child is chosen randomly, what is the probability
that: (Round all answers to nearest thousandths)
a) the child can go on all rides?
b) the child can participate in only mild and moderate
rides?
c) the child can only go on mild rides?
d) the child is excluded from all rides?
Answer:
the probability that a child is excluded from all rides is 0.5000 (rounded to three decimal places).
Step-by-step explanation:
We can use the standard normal distribution to solve this problem. We first need to standardize the height requirements using the population mean and standard deviation.
a) To find the probability that a child can go on all rides, we need to find the probability of getting a height of at least 54 inches.
z-score = (54 - 53) / 4 = 0.25
Using a standard normal table or calculator, we find that the probability of getting a z-score of 0.25 or greater is 0.4013.
Therefore, the probability that a child can go on all rides is 0.4013 (rounded to three decimal places).
b) To find the probability that a child can participate in only mild and moderate rides, we need to find the probability of getting a height between 42 inches and 48 inches.
First, we find the z-scores for each height requirement:
z-score for 42 inches = (42 - 53) / 4 = -2.75
z-score for 48 inches = (48 - 53) / 4 = -1.25
Using a standard normal table or calculator, we find that the probability of getting a z-score between -2.75 and -1.25 is 0.2375.
Therefore, the probability that a child can participate in only mild and moderate rides is 0.2375 (rounded to three decimal places).
c) To find the probability that a child can only go on mild rides, we need to find the probability of getting a height of less than 42 inches.
z-score = (42 - 53) / 4 = -2.75
Using a standard normal table or calculator, we find that the probability of getting a z-score of -2.75 or less is 0.0030.
Therefore, the probability that a child can only go on mild rides is 0.0030 (rounded to three decimal places).
d) To find the probability that a child is excluded from all rides, we need to find the probability of getting a height less than 42 inches or greater than 54 inches.
First, we find the z-scores for each height requirement:
z-score for 42 inches = (42 - 53) / 4 = -2.75
z-score for 54 inches = (54 - 53) / 4 = 0.25
Using a standard normal table or calculator, we find that the probability of getting a z-score of less than -2.75 or greater than 0.25 is 0.0987 + 0.4013 = 0.5000.
Therefore, the probability that a child is excluded from all rides is 0.5000 (rounded to three decimal places).
The radius of a cylindrical construction pipe is 2.5 ft. If the pipe is 20 ft long, what is its volume…..
I need help with this please
The volume and sum of the composite shape is 13L² and 13V³ respectively
What is a square?A square is a closed two-dimensional shape (2D shape) with four sides that are equal and parallel to each other. Also, In Euclidean Euclidean geometry, a square is a regular quadrilateral which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles
The composite is made up of 13 squares in total
The area of 1 square is given as A = S²
The volume of the composite is 13L³ units
Hence there are 13 squares. the sum of the areas and volume of the square is 13 S²
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Pls help !! Find the equation of a line parallel to that passes y= 4/3x+4 through the point (3,-7).
An equation of a line parallel to that passes y = 4/3x + 4 through the point (3, -7) include the following: A. y + 7 = 4/3(x - 3).
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.Since y = 4x/3 + 4, the slope is equal to 4/3.
At data point (3, -7) and a slope of 4/3, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-7) = 4/3(x - 3)
y + 7 = 4/3(x - 3)
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10. In the diagram shown, AC is congruent to DC and ZA and ZD are both right angles. SS | RS 1. GIVEA ACANC ELL X-3 en 1. AC DC LA CALD are rt L's 2 LBCB Reflex Hue propert 344DBC LAB ALE HL Fungh D Prov
Answer:
4Step-by-step explanation:
Find the slope between the following points:(-5,5),and (3,-12) *
m = (-12 - 5) / (3 - (-5))
m = (-17) / (3 + 5)
m = (-17) / 8
Therefore, the slope between the points (-5, 5) and (3, -12) is -17/8.
Please mark this answer as brainliest if possible.
Joel bought a container of yogurt that held 8 cups of yogurt. He used a 0.25-cup serving of the
yogurt each day. When 7.25 cups of the yogurt remained, how many 0.25-cup servings had Joel
used from the container?
0.75
2
3
29
Answer:
3
Step-by-step explanation:
Amount used:
8 - 7.25 = 0.75
He used 0.75 cup
Each day he had 0.25 cup.
0.75/0.25 = 3
Answer: 3
In the United States, 41% of 18 to 29-year-olds said in a survey held in March 2020 that they turrently subscribed to Hulu. What is the probability in a random sample of 55 18 to 29-year-olds that 20 will say they currently have a subscription to Hulu?
The probability in a random sample of 55 18 to 29-year-olds that 20 will say they currently have a subscription to Hulu is: 0.087.
How to find the probability?This is a binomial distribution problem, where n = 55 and the probability of success (i.e. a person subscribing to Hulu) is p = 0.41.
The probability mass function of a binomial distribution is:
P(X = x) = (nCx) * p^x * (1-p)^(n-x)
where nCx is the binomial coefficient (i.e. the number of ways to choose x items from n items).
So, in this case, we want to find P(X = 20):
P(X = 20) = (55C20) * 0.41^20 * (1-0.41)^(55-20)
P(X = 20) ≈ 0.087
Therefore, the probability that in a random sample of 55 18 to 29-year-olds, 20 will say they currently have a subscription to Hulu is approximately 0.087or 8.7%.
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Please help me on this: 90 BRAINLY POINTS. Yuri bakes lemon bars in a pan shaped like a right rectangular prism. The volume of the pan is 150 cubic inches. The width of the pan is 7 1/2 inches, and its height is 2 inches.
What is the length of the pan?
Enter your answer in the box
Answer:
length of the pan is 10 inches
Step-by-step explanation:
Volume = length x width x height
V = lwh
l = (V) / (wh) = (150 in³) / (7.5 in)(2 in) = 10 in
A single serving of a cereal breakfast bar contains 18 grams of carbohydrates. This is 6%
of the daily recommended allowance for a 2000-calorie diet. How many grams of
carbohydrates are recommended each day for a person on a 2000-calorie diet?
10. A concert was recently held at the civic auditorium. All 5000 tickets were sold.
a. 25% of the tickets were reserved seats that sold for $45 each. What was the total
amount in sales for the $45 tickets?
b. 15% of the tickets were reserved seats that sold for $35 each. What was the total
amount in sales for the $35 tickets?
c. The remainder of the tickets were general admission. How many general admission
tickets were sold?
d. If each general admission ticket sold for $20, what was the total amount in sales for
the general admission tickets?
e. What was the total amount for all ticket sales?
Answer:
Step-by-step explanation:
a. 25% of 5000 tickets = 0.25 x 5000 = 1250 tickets
Total sales of $45 tickets = 1250 x $45 = $56,250
b. 15% of 5000 tickets = 0.15 x 5000 = 750 tickets
Total sales of $35 tickets = 750 x $35 = $26,250
c. General admission tickets = Total tickets - Reserved tickets
= 5000 - 1250 - 750
= 3000 tickets
d. Total sales for general admission tickets = Number of general admission tickets x Price per ticket
= 3000 x $20
= $60,000
e. Total sales = Sales of $45 tickets + Sales of $35 tickets + Sales of general admission tickets
= $56,250 + $26,250 + $60,000
= $142,500
Two similar triangles have a scale factor of 2/3. The area of the larger triangle is 27 what is the area of the smaller triangle
The area of the smaller triangle is 12 square units
How to determine the area of the smaller triangleIf the scale factor between two similar triangles is 2/3
It means that every length of the smaller triangle is 2/3 the length of the corresponding side of the larger triangle.
So, the ratio of their areas is the square of the scale factor
This is represented as
(area of smaller triangle) / (area of larger triangle) = (2/3)^2 = 4/9
We are given that the area of the larger triangle is 27
So, we have
Area of smaller triangle/27 = 4/9
Multiplying both sides by 27, we get:
Area of smaller triangle = (4/9) * 27
Evaluate
Area of smaller triangle = 12
Hence, the area of the smaller triangle is 12.
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(8x+17), (12x-39) find m
The measure of the angle M is 129 degrees
How to determine the valueIt is important to note that the properties of a parallelogram are;
Opposite sides are equalOpposite angles are congruentSame-Side interior angles (consecutive angles) are supplementary, that is, 180 degreesEach diagonal of a parallelogram divides it into two congruent trianglesThe diagonals of a parallelogram bisect each otherThen, we have that;
m< M = m < K
substitute the values
12x - 39 = 8x + 17
collect the like terms, we have;
12x - 8x = 17 + 39
Add the collected like terms, we get;
4x = 56
divide both sides by the coefficient of 4, we get;
4x/4 = 56/4
Divide the values
14
Then, m < M = 12(14) -39 = 129 degrees
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The complete question:
In the parallelogram, Find mZN: K (8x + 17)9 (12x - 39)8 01;0 - Lx'An M Ax+8x +17 + iax -3 = 360 3ax-33 = H0 +3 42 20 22X 7 x=17.30
Write an equivalent expression for 24x + 16