If man travels "3-miles", turns left ,travel "6-miles", then turn left again travels "8-miles", then he is "7.8-miles" away from the starting point, No option is correct.
The man travel 3 miles straight, so we let the "starting-point" be (0,0),
So, the point after travelling 3 miles straight will be (0,3),
Next, he turns left and travels 6 miles(now facing downwards),
So, the coordinate becomes (6,3);
Next, he Turns left again(now facing right) and travels "8 miles" to the right .
So, the final-coordinate becomes (6, -5).
Now, we calculate the distance between the final point (6, -5) and the starting point (0,0) using the distance formula, which is the square root of the sum of squares of differences in "x" and "y" coordinates:
So, Distance = √((6-0)² + (-5-0)²),
⇒ Distance = √(36 + 25),
⇒ Distance = √61 ≈ 7.8 miles.
Therefore, The distance is approximately 7.81 miles, which is not present in any of the option, So, no option is correct.
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a threat to internal validity occurs only if a potential design confound varies _________with the independent variable. group of answer choices spontaneously especially systematically haphazardly
A threat to internal validity occurs only if a potential design confound varies systematically with the independent variable.
In experimental research, an independent variable is a variable that the researcher manipulates or systematically varies in order to study its effect on the dependent variable. It is called "independent" because it is not influenced by any other variables in the experiment, and its effects on the dependent variable can be observed and measured independently of any other factors.
Only when a possible design confound fluctuates systematically with the independent variable does internal validity come under threat. In other words, it might be challenging to distinguish between the effects seen on the dependent variable and the independent variable if there is a component that fluctuates consistently or predictably with changes in the independent variable. Internal validity is less likely to be threatened by random or unplanned variation.
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A threat to internal validity occurs only if a potential design confound varies systematically with the independent variable. This means that if the confound varies randomly or haphazardly, it is less likely to affect the results of the study.
This means that the confound is consistently related to the independent variable, making it difficult to determine if the observed effects are due to the independent variable or the confound. If the confound varies spontaneously or haphazardly, it is less likely to pose a threat to internal validity, as it would not be consistently associated with the independent variable.
However, if the confound is related to the independent variable in a consistent and predictable way, it can introduce bias and undermine the internal validity of the study. It is important for researchers to carefully control for potential confounds and ensure that any observed effects are truly due to the independent variable and not some other factor.
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a=
B=
C=
what is A,B and C
A. (-1, A)
B. (2, infinite)
C: (-infinite, - 1)
(pls let me know if I'm wrong and if I am I'm very sorry.)
QUICK QUICKQUICK QUICKQUICK QUICKQUICK QUICKPLEASE PELASE QUICK QUICKQUICK QUICKQUICK QUICKQUICK QUICKQUICK QUICKQUICK QUICK
Answer:
x ∈ {6, 7, 8, 9, 10}
Step-by-step explanation:
You want possible values of whole number x such that ...
4 ≤ √3 +√x < 5
SolutionWe can solve this inequality by first subtracting √3 from all sides:
4 -√3 < √x < 5 -√3
Squaring these positive numbers does not change their order:
19 -8√3 < x < 28 -10√3
5.14 < x < 10.67
The value of x may be any whole number in the range 6–10, inclusive.
The diameter of a circle is 170 inches. The circle has two chords of length 26 inches. What is the distance from each chord to the center of the circle?
the distance from each chord to the center of the circle is 85 inches.
what is chord ?
In geometry, a chord is a line segment that connects two points on the circumference of a circle. It is the straight line that intersects a circle at two points. In other words, a chord is a line segment that lies entirely inside the circle and connects two points on the circle.
In the given question,
If we draw a diagram of the circle with diameter 170 inches, we can see that the chords of length 26 inches divide the circle into two regions. We are interested in finding the distance from each chord to the center of the circle.
To solve this problem, we can use the following formula:
distance from chord to center = 1/2 * √(4r² - c²)
where r is the radius of the circle and c is the length of the chord.
First, we need to find the radius of the circle. The radius is half of the diameter, so:
r = 1/2 * diameter = 1/2 * 170 = 85 inches
Next, we can use the formula above to find the distance from each chord to the center of the circle. Plugging in the values we have:
distance from chord to center = 1/2 * √(4r² - c²)
distance from chord to center = 1/2 * √(4(85)² - 26²)
distance from chord to center = 1/2 * √(28,900)
distance from chord to center = 1/2 * 170
distance from chord to center = 85
Therefore, the distance from each chord to the center of the circle is 85 inches.
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messages are sent over a communications channel using two different signals. one signal requires 2 microseconds for transmittal, and the other signal requires 3 microseconds for transmittal. each signal of a message is followed immediately by the next signal. a) find a recurrence relation for the number of different signals that can be sent in n microseconds. b) what are the initial conditions of the recurrence rela?tion in part (a)? c) how many different messages can be sent in 12 microseconds?
a) A recurrence relation, aₙ = aₙ₋₂ + aₙ₋₃
is for the different signals that can be sent in n microseconds.
b) Initial conditions are a₀ = 0, a₁ = a₂ = 1
c) The number of messages sent in 12 microseconds are equal to 16.
A recurrence relation is an equation form for nth term of a sequence of numbers which is equal to some combination of the previous terms. We have a messages are sent over a communications channel using two different signals. Let an be different number of messages that can be transmitted in n microseconds. In case of First signal, it required 2 microsecondes time to tramissmit the signals. So, the different number of signals that can be transmitted in 2 microseconds are [tex]a_{n - 2} [/tex]
In case of second signal , Time required by second signal to to transmit signal = 3
microsecondes
So, different number of messages that can be transmitted in 3 microseconds are
[tex]a_{n - 3} [/tex]
Each signal of a message is transmitted one by one.
a) A recurrence relation for the number of different signals that can be sent in n microseconds is written as
[tex]a_n = a_{n - 2} + a_{n - 3}[/tex]
hat is an us sum of different signals transmitted by each signals.
b) recurrence relation is
[tex]a_n = a_{n - 2} + a_{n - 3}[/tex]
so, the initial conditions of the recurrence relation in part (a) is n = 3 , [tex]a_3 = a_1 + a_0 [/tex]
a₀ = 0, a₁ = 1 , a₂ = 1
c) Different messages can be sent in 12 microseconds is determined by plugging the value in recurrence relation, a₃
= a₁ + a₀ = 1 + 0 = 1
a₄ = 1 + 1 = 2
a₅ = 1 + 1 = 2
a₆ = 2 + 1 = 3
a₇ = 2 + 2 = 4
a₈ = 3 + 2 =5
a₉= 4 + 3 = 7
a₁₀= 5 + 4 = 9
a ₁₁ = 7 + 5 = 12
a₁₂ = 9 + 7 = 16
Hence, required value is 16.
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Please answer the questions in the picture below and show work
The value of the variables as identified from the reciprocal function are;
a = 5
h = -6
k = 7
2. The correct option is Option A
What is a reciprocal function?A reciprocal function is a mathematical function that can be represented as f(x) = 1/x, where x ≠ 0.
The graph of a reciprocal function is a hyperbola with two branches that approach the x and y axes, but never touch them.
From the information given, we have the function as;
y = a/x - h + k
Given that the function with numbers is written as;
y = 5/x + 6 + 7
To determine the values of a, h and k, we get;
The variable, a = 5
The variable, k = 7
The variable, h = -(6) = -6
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A large Ferris wheel has a diameter of 90 meters and the top of the wheel is 102 meters above the ground. The Ferris wheel has 36 passenger capsules spaced evenly along the wheel. The diagram below shows 10 of the Ferris wheel capsules arranged such that the center of the wheel is at point C, the capsule at point M is at the same height as the center of the wheel, and the capsule at point T is at the very top of the wheel.
The height of the center of the Ferris wheel 51 m.
The height of capsule M is 51 m and the height of capsule T is 102 m.
What is the height of the wheel?
Using this information, we can calculate the height of the center of the Ferris wheel, the height of capsule M, and the height of capsule T.
Height of the center of the Ferris wheel:
The center of the Ferris wheel is the midpoint of its diameter. Therefore, the height of the center of the Ferris wheel is half of the height of the top of the wheel above the ground.
Height of center of Ferris wheel = 102 meters / 2 = 51 meters.
Height of capsule M:
Since capsule M is at the same height as the center of the Ferris wheel, the height of capsule M is also 51 meters.
Height of capsule T:
Since capsule T is at the very top of the Ferris wheel, its height above the ground is equal to the height of the top of the Ferris wheel above the ground.
Height of capsule T = 102 meters.
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One cubic foot of a chemical weighs 50 pounds. How many pounds of the chemical can a container with the dimensions shown hold?
The container can contains 3,000 pounds of chemicals.
How many pounds can the container hold?One cubic foot of a chemical weighs 50 pounds which means 1 ft³ of chemical = 60 pounds
We must find how many pounds in the container whose dimension 6 ft, 4 ft and 2.5 ft. So, the l = 6 ft, b = 4 ft and h = 2.5 ft.
Volume of box = L*B*H
Volume of box = 6 x 4 x 2.5
Volume of box = 60 ft³
From 1 ft³ of chemical = 60 pounds; then, the 50 ft³ of chemical will be:
= 50 x 60
= 3,000 pounds
Full question "One cubic foot of a chemical weighs 60 pounds. How many pounds of the chemical can a container with the dimensions shown hold? The base is 6, the width is 4, and the height is 2.5"
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1. Complete the table and determine the rule for this transformation.
Answer:
the table is analysis swap around
Step-by-step explanation:
like if the input is (3,1) the output will be (1,3)
Eric needs to read 5 novels each month. Let n be the number of novels Eric needs to read in m months. write you equation and graph it.
The price of the daily dinner special at Deb’s Dinner increases from $7.00 to $8.75. By what percent does the price of the dinner special increase?
The percent increase for the dinner is 25%
The first step is to calculate the increase
The price rose from $7 to $8.75
Increase= 8.75-7
= 1.75
Therefore the percent increase can be calculated as follows
1.75/7 × 100
= 0.25 × 100
= 25
Hence the percent increase is 25%
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what two numbers multiply to 21 and add to -10
Answer: brainliest ?
-3 and -7
Step-by-step explanation:
What are the steps to finding out 4. 25 - 7. 06?
The result of subtracting 7.06 from 4.25 is -2.81.
Let's see how these steps apply to the problem at hand:
4.25
-7.06
In this case, we don't need to borrow because the top number 4.25 is already smaller than the bottom number 7.06.
Starting from the rightmost column, we subtract 5 from 6. Since 6 is larger than 5, we can subtract 5 from 6 and get 1. We write down 1 in the hundredths column.
Next, we move to the tenths column and subtract 2 from 0. We can't do this, so we need to borrow 1 from the digit in the ones column. The 4 in the ones column becomes 3, and the 2 in the tenths column becomes 12.
Now we can subtract 2 from 12, which gives us 10. We write down 0 in the tenths column and carry 1 to the ones column.
In the ones column, we have 3 - 7 - 1 (the borrowed 1) = -5. Since we can't have a negative number in this position, we need to borrow again from the digit in the tens column. The 2 in the tens column becomes 12, and we bring down the borrowed 1 to the ones column.
Now we can subtract 7 from 12, which gives us 5. We write down 5 in the ones column.
Step 4: Bring down any digits that have not been used.
We don't have any digits left to bring down, so we have finished the subtraction.
Therefore, the result of subtracting 7.06 from 4.25 is -2.81.
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A cylinder has a volume of 490 pi inches squared and a height of 10 inches what is the length of the radius
The length of the radius of the cylinder with a volume of 490π cubic inches and a height of 10 inches is 7 inches.
The formula for the volume of a cylinder is V = πr²h,in which r= radius , h= cylinder height. Now we can rearrange formula by equating for r which gives the following formula:
V = πr²h
r² = V/(πh)
r = √(V/(πh))
By putting the values in the formula we can get:
r = √(490π/(π*10))
r = √49
r = 7
Therefore, the length of the radius is 7 inches.
Cylinder's volume can be viewed as the area that it takes up. It is computed by dividing the cylinder's height by the base's area, which is a circle. In this instance, we are informed that the height is 10 inches and the capacity is 490 cubic inches.
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The angle of elevation to a nearby tree from a point on the ground is measured to be 32^{\circ}
∘
. How tall is the tree if the point on the ground is 71 feet from the tree? Round your answer to the nearest tenth of a foot if necessary.
The height of the tree is 44.4 feet.
What is height?Height is the vertical distance between two points.
To calculate the height of the tree, we use the formula below
Formula:
h = dtan∅.................... Equation 1Where:
h = height of the treed = Distance from the point on the ground to the tree∅ = Angle of elevationFrom the question,
Given:
d = 71 feet∅ = 32°Substitute these values into equation 1
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which integer conversion specifier would display the hexadecimal digit a? a) H b) h c) Xd) x
The integer conversion specifier that would display the hexadecimal digit "a" is "x".
d) x
To display the hexadecimal digit "a" using an integer conversion specifier.
The "x" specifier is used for displaying an integer value in hexadecimal format with lowercase letters (i.e., a, b, c, etc.), while "X" would display the value in uppercase letters (i.e., A, B, C, etc.).
Options "H" and "h" are not standard integer conversion specifiers for displaying hexadecimal values.
Hence d) x is correct.
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A grocery store finds that the number of boxes of new cereal sold increases each week. In the 1st week, 24
boxes of cereal were sold. In the 2nd week, 39 boxes of cereal were sold and in the 3rd week 54 boxes of
cereal were sold. The number of boxes of cereal sold each week represents an arithmetic sequence.
A) Write the explicit rule in simplified form for the arithmetic sequence that defines the number of boxes
of cereal sold in week n. Make sure to show all steps
B) Use this rule to calculate how many boxes of cereal will be sold during the 10th week.
Answer: a)159 boxes of cereal will be sold during the 10th week, b) an = 15n + 9
Step-by-step explanation:
Boyle's Law states that the pressure exerted by a gas held at a constant temperature varies inversely with the volume of the gas. At a volume of 4 L the pressure of a gas is 112 kPa. If the volume of the gas is 16 Lwhat would be the pressure of the gas in kPa? (Write your answer as a whole number)
Answer:
the pressure of the gas at a volume of 16 L would be 28 kPa.
Step-by-step explanation:
Using Boyle's Law:
P1V1 = P2V2
Where:
P1 = 112 kPa (initial pressure)
V1 = 4 L (initial volume)
V2 = 16 L (final volume)
Solving for P2:
P2 = (P1 x V1) / V2
P2 = (112 kPa x 4 L) / 16 L
P2 = 28 kPa
Therefore, the pressure of the gas at a volume of 16 L would be 28 kPa.
Object 1: Cereal Box 3D shape: Rectangular Prism Dimensions: length = 12 inches width = 8 inches height = 1.75 inches
find the Formula for area and the base area
Answer:
Great, based on the provided dimensions for Object 1 (the cereal box), here are the formulas and calculations for:
Area of the entire rectangular prism:
A = lw + lh + wh
A = 128 + 121.75 + 8*1.75
A = 96 + 21 + 14 = 131 square inches
Base area:
The base of a rectangular prism is a rectangle. So the base area formula is:
Base area = Length * Width
= 12 inches * 8 inches = 96 square inches
So the formulas are:
Area (entire prism): A = lw + lh + wh
Base area: Base area = Length * Width
In this case:
Length = 12 inches
Width = 8 inches
Height = 1.75 inches
Step-by-step explanation:
Jordan reads a comic book at a rate of 21 pages in 6 minutes. At this rate, how many pages does he read each minute?
Answer:
x = 3.5 pages per minute
Step-by-step explanation:
We make the relationship
21 pages ------ 6 min
x pages -------- 1 min
So x= (21x1)/(6)
x = 3.5 pages per minute
In circle H with m/GHJ = 46 and GH = 4 units find area of sector GHJ. Round
to the nearest hundredth.
G
1
H
rann
Area of sector GHJ ≈ 2.04 square units
Area of sector calculation.
Since we are given the central angle GHJ in degrees and the radius GH of circle H, we can find the area of sector GHJ using the formula:
Area of sector GHJ = (θ/360) × πr^2
where θ is the central angle in degrees and r is the radius.
Substituting the given values, we get:
Area of sector GHJ = (46/360) × π(4)^2
= (0.1278) × 16π
= 2.0448 square units
Rounding to the nearest hundredth, we get:
Area of sector GHJ ≈ 2.04 square units
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Use the image to determine the type of transformation shown.
Reflection across the x-axis
90' clockwise rotation
Horizontal translation
Vertical translation
C
B
Which scatter plot shows a positive linear association? A. Scatter plot graph in quadrant 1 of a coordinate plane. 11 points are plotted approximated at (2, 5), (1.5, 11.5), (3.1, 6.1), (4, 9), (5.9, 12.5), (7, 6), (7.5, 8.5), (8, 11), (8.9, 4.1), (9, 8), and (11, 10). B. Scatter plot in quadrant 1 of a coordinate plane. 14 points are plotted at (3, 11), (3, 12), (4, 11), (4.2, 11), (5, 10.8), (5.5, 12), (6, 10), (6.5, 11), (7, 9), (7.1, 6), (7.1, 7.5), (7.5, 9), (8, 7.5), and (8.1, 6.1). C. Scatter plot graph in quadrant 1 of a coordinate plane. 10 points are plotted at (2, 11), (2.5, 9), (3, 10), (4, 8), (5, 8.2), (5.5, 6.5), (6.5, 7), (6.5, 5), (8, 5.8), and (9, 4). D. Scatter plot graph in quadrant 1 of a coordinate plane. 10 points are plotted at (2, 3), (2.8, 4.2), (3.8, 3.2), (4, 4.7), (4, 6), (5, 5), (6, 8), (7, 7), (7.8, 9.2), and (8.9, 9.1).
So, from the given options, the scatter plot that shows a positive linear association is option B.
What is scatter plot?A scatter plot is a type of graph that displays the relationship between two variables. Each data point in the scatter plot represents a pair of values for the two variables being plotted, with one variable on the x-axis and the other on the y-axis. Scatter plots are used to examine the correlation or relationship between the variables. If the points on the scatter plot form a pattern that slopes upwards as you move from left to right, it indicates a positive linear association between the variables. If the pattern slopes downwards, it indicates a negative linear association. If there is no pattern or trend, it indicates no correlation between the variables.
Here,
A scatter plot that shows a positive linear association is one where the points on the graph form a pattern that goes upward and to the right.
In option A, the data points do not show a clear upward trend, so this scatter plot does not show a positive linear association.
In option B, there is a clear upward trend in the data points as you move from left to right, so this scatter plot does show a positive linear association.
In option C, the data points do not show a clear upward trend, so this scatter plot does not show a positive linear association.
In option D, the data points do not show a clear upward trend, so this scatter plot does not show a positive linear association.
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Which of the following sets of parametric equations represents (x - 1)2 + (y + 4)2 = 9?
the sets of parametric equation that represents (x-1)²+(y+ 4)² = 9 is:
x = 1 + 3 cosθ
y = -4 + 3 sinθ
How to the sets of parametric equation?( x -1)^2 = (r cosθ)^2
x - 1 = r cosθ
= 3 cosθ
x = 1 + 3 cosθ
y + 4 = 3 sinθ
= y = -4 + 3 sinθ
There, the sets of parametric equation that represents (x-1)²+(y+ 4)² = 9 is:
the sets of parametric equation that represents (x-1)²+(y+ 4)² = 9 is:
x = 1 + 3 cosθ
y = -4 + 3 sinθ
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The question is incomplete, see missing part in the attached image.
A useful computational shortcut for the ANOVA test is expressed asa. dfw = dfb + SST
b. SSB SSW-SST
c. SST = SSB/SSW
d. SSW SST-SSB
The correct answer is (b). SSB = SST - SSW
The ANOVA (analysis of variance) test is a statistical method used to compare the means of two or more groups. One useful computational shortcut for this test is expressed as SSB = SST - SSW, where SSB is the sum of squares between groups, SST is the total sum of squares, and SSW is the sum of squares within groups.
The useful computational shortcut for the ANOVA test is expressed as:
SSB = SST - SSW
where SSB is the sum of squares between groups, SST is the total sum of squares, and SSW is the sum of squares within groups.
Option (b) is the closest, but it has a typo. It should be:
SSB = SST - SSW
Therefore, the correct answer is (b).
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The useful computational shortcut for the ANOVA test is SSW = SST - SSB
therefore,option d. SSW = SST - SSB is correct.
ANOVA (Analysis of Variance) is a statistical test used to analyze differences between group means.
The test involves partitioning the total variation into two components:
variation between groups (SSB, sum of squares between) and variation within groups (SSW, sum of squares within).
The total sum of squares (SST) represents the overall variability in the dataset.
The computational shortcut for ANOVA states that the sum of squares within groups (SSW) can be calculated by
subtracting the sum of squares between groups (SSB) from the total sum of squares (SST).
So, SSW = SST - SSB.
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Ryan has 2,000 grams of Flerovium-289, which has a half life of 30 seconds. Use
the formula y = ab* to figure out how much Flerovium-289 you will have after
5 minutes. (Hint: x is the the total number of half lives in 5 minutes)
(.5)_
a.) 62.5 grams
b.) 1.95 grams
c.) 353.55 grams
d.) 1,000 grams
y =____
Kendrick attends a private school where he must wear a uniform. Last year, the price of the uniform was $52. This year's uniform price was $65. What is the percent of increase in the cost of the uniform?
The percent increase in the cost of the uniform from last year to this year is 25%.
What is the percent of increase in the cost of the uniform?To find the percent increase in the cost of the uniform from last year to this year, we need to calculate the difference between the two prices, divide it by the original price, and then multiply by 100 to express the result as a percentage.
The difference between this year's price and last year's price is:
$65 - $52 = $13
The original price (last year's price) is $52.
So the percent increase in the cost of the uniform is:
percent increase = (difference / original price) x 100
percent increase = ($13 / $52) x 100
percent increase = 0.25 x 100
percent increase = 25%
Therefore, the percent increase in the cost of the uniform from last year to this year is 25%.
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Trend component is easy to identify by using
A. Moving average
B. Exponential smoothing
C. Regression analysis
D. Delphi approach
Trend component is easy to identify by using Moving average, Exponential smoothing, Regression analysis. So, correct options are A, B and C.
The trend component of a time series is a long-term movement in the data that represents a gradual increase or decrease over time. It is an important component of time series analysis because it can provide insights into the overall direction of the data and help forecast future trends.
One of the easiest ways to identify the trend component of a time series is by using a moving average. A moving average is a statistical method that calculates the average of a set of data over a specified period of time. By calculating the moving average, we can smooth out the short-term fluctuations in the data and identify the underlying trend.
Exponential smoothing is another method that can be used to identify the trend component of a time series. It is a forecasting technique that assigns exponentially decreasing weights to older observations, which places greater emphasis on more recent data.
This approach can help identify the trend by smoothing out the data and highlighting the underlying pattern.
Regression analysis can also be used to identify the trend component of a time series. It involves fitting a mathematical model to the data and identifying the relationship between the independent and dependent variables.
If the independent variable represents time and the dependent variable represents the data being analyzed, then regression analysis can help identify the trend component.
The Delphi approach is not typically used to identify the trend component of a time series. It is a forecasting technique that involves gathering expert opinions and using them to make predictions about future events.
In conclusion, the methods that are most commonly used to identify the trend component of a time series are moving average and exponential smoothing. Regression analysis can also be used in certain situations.
So, correct options are A, B and C.
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Two amateur marathoners were running a marathon. The first marathoner kept a steady pace and was able to finish in four hours. The second marathoner was keeping 4 the speed of the speed of the first runner. Then he was tired and his speed for the 3
second half of the distance was only 3 4 the speed of the first runner. How much did it
take the second runner to finish the distance?
It takes the second marathoner 4 hours and 40 minutes to complete the marathon.
Let's assume the distance of the marathon is "d" miles.
The first marathoner runs at a constant speed for 4 hours, so we can find their speed as:
speed = distance / time = d / 4
The second marathoner starts by running at 4 times the speed of the first marathoner, so their speed is:
speed = 4(d / 4) = d
For the second half of the race, the second marathoner's speed drops to 3/4 of the first marathoner's speed. Let's assume it takes "t" hours for the second marathoner to complete the second half of the race. Then, we can write:
d / 2 = (3/4)(d / 4)(t)
Simplifying this equation, we get:
t = (2/3) hours
So the total time it takes the second marathoner to finish the race is:
4 + (2/3) = 4 2/3 hours = 4 hours and 40 minutes.
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Y'all I really need some help here. 100 points.
Answer:
42 degrees
Step-by-step explanation:
So, first to find <QUT, which is a vertical angle, we have to figure out either QUR or TUS. So:
9x+3=11x-27
solve for x:
x=15
Then, plug it into one of the equations. Let's use 9x+3.
9(15)+3=138
So, we know that QUR is 138 degrees.
That means that TUS is ALSO 138.
138x2=276
Now we know that QUT and RUS have to equal whatever 360-276 is:
360-276=84
QUT and RUS have to equal 84 degrees, so we DIVIDE by 2.
84/2=42
So, QUT=42 degrees
Answer:
42 Degrees
Step-by-step explanation
Becuase (11x-27) and (9x+3) are vertical angles that means they are equal to each other
(11x - 27) = (9x + 3)
First you will add 27 to both sides
11x -27 = 9x +3
+27 +27
Making it to:
11x = 9x + 30
Now you need to subtract 9x from both sides
11x = 9x +30
-9x -9x
Turning it into this
2x= 30
Now Lastly, divide both sides by 2
2x = 30
2x 2x
And the answer is...... X=15
Now that you have the x value, we go back to the 11x-27 and replace the X with 15
11(15) -27 = 138 degress
Now because angle QUT and 138 degrees make a straight line that means together they will be 180 degress so you will subtract 180 by 138
Giving you the final answer of
42 Degrees