For the three random tosses, there are only 4 potential values out of 8 possible combinations.
The sample space for W is thus:
HHH, W = 3-0 = 3
HHT, W= 2-1=1
HTH, W= 2-1=1
THH, W=2-1 =1
HTT, W= 1-2=-1
THT, W= 1-2=-1
TTH, W=1-2=-1
TTT, W=0-3 = -3
In this instance, W is defined as the random variable that captures the difference between the number of heads and tails in three coin flips.
W = the number of heads minus the number of coins.
We have 3 coin tosses, which gives us 2*2*2=8 outcomes. The outcomes and accompanying values for W can be listed as follows:
HHH, W = 3-0 = 3
HHT, W= 2-1=1
HTH, W= 2-1=1
THH, W=2-1 =1
HTT, W= 1-2=-1
THT, W= 1-2=-1
TTH, W=1-2=-1
TTT, W= 0-3 = -3
Describe probability.
Probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
Which four forms of probability are there?
There are four primary forms of probability, which is the area of mathematics that concerns with the possibility of a randomized incident occurring: classical, empirical, random, and essential
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Write the slope-intercept form of the line containing the
point (5, −3) and is parallel to: = − 2/5 − 3/4
The slope-intercept form of the line containing the point (5, −3) and is parallel to y = − 2/5x − 3/4 is y = -2/5x - 1.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given, line containing the point (5, −3) and is parallel to: y = − 2/5x − 3/4
The slope-intercept form of the equation of a line
y=mx+b,
where m is the slope
b is the y-intercept
In our case Line is parallel to the Line y = − 2/5x − 3/4,
So the slope would be the same.
m = -2/5
Thus, the equation of the line:
y = -2/5x + b
Since the line passes through the point (5, -3)
-3 = -2/5 * 5 + b
b = -1
Thus the final equation of a line:
y = -2/5x - 1
Therefore, The slope-intercept form of the line containing the point (5, −3) and is parallel to y = − 2/5x − 3/4 is y = -2/5x - 1.
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ve the following problems.
ven: AAFD,
m/F=90°,
AD = 14,
mZD=30°
d: Area of AAFD
A
F
D
W
If ∆AFD, m ∠F = 90° AD = 14, m ∠D = 30° .The Area of ∆AFD is 49 square units.
What is area?To find the area of triangle AFD, we can use the formula for the area of a triangle given its base and height. In this case, the base is AD, and the height can be found by constructing an altitude from F to AD.
First, we will find the length of FD. Since m ∠D = 30°, we can use the trigonometric function sine to find the length of FD. Using the sine formula:
FD = AD * sin(∠D) = 14 * sin(30°) = 14 * 1/2 = 7
Next, we will find the length of A.F. Since m ∠F = 90°, FD is the height of the triangle. So, the area of triangle AFD is given by:
Area = (AD * FD) / 2 = (14 * 7) / 2 = 49 square units
Therefore the area of ∆AFD is 49 square units.
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Benita graphed point G on the coordinate grid at (2, −4)
. She also plotted point H on the grid 3 units to the left of point G.
BTW THE WHOLE GRAPH IS NOT INNNNNNNNN
The coordinates of point H are (2 - 3, -4) = (-1, -4).
What do you mean by graph?In mathematics, a graph is a visual representation of a relationship between two variables. It is usually represented as a set of points on a coordinate plane, where the horizontal axis represents one variable and the vertical axis represents the other variable. The points are plotted based on their corresponding values for the two variables, and a line or curve is drawn through the points to show the relationship between the two variables.
Graphs are often used to represent mathematical functions and equations, as they provide a quick and easy way to visualize the relationship between the input and output values. They can also be used to represent data in fields such as science, economics, and social sciences, where they provide a way to analyze and interpret data trends and patterns.
Graphs can be drawn by hand, using graph paper and a ruler, or they can be generated using software, such as spreadsheet programs, mathematical software, and graphing calculators. In addition to helping to visualize the relationship between two variables, graphs can also be used to estimate values, find maximum and minimum points, and make predictions.
The coordinates of point H can be determined by subtracting 3 from the x-coordinate of point G. Therefore, the coordinates of point H are (2 - 3, -4) = (-1, -4). So, point H is located 3 units to the left of point G on the x-axis.
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a woman is traveling in her car at 25 miles per hour. how far will that woman travel in thirty minutes? (distance
In 30 minutes, the woman will travel 12.5 miles.
This is due to the fact that the rate (25 mph) times the time equals the distance traveled. Mathematically, this can be expressed as d = rt, where d represents the distance, r represents the rate (speed), and t represents the time. In this instance, the distance can be calculated as d = 12.5 miles by multiplying d = 25 mph by 30 minutes/60 minutes.
The distance between two points is measured in distance. The rate, or the amount of distance traveled per unit of time, is the speed at which a person or vehicle travels. The woman in the car is traveling at a rate of 25 miles per hour (mph).
In this instance, the time is. The formula d = rt can be used to determine the distance traveled by multiplying her rate by the time. Given the rate and duration of travel, this formula can be used to determine the distance traveled by any object or person.
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A store buys 15 sweaters for $90 and sells them for $405. If p represents the total profit in dollars and cents when the store buys any number of sweaters, s, write a proportional equation for p in terms of s that matches the context.
If p represents the total profit in dollars and cents when the store buys any number of sweaters, s, then the proportional equation for p in terms of s is, p = $21 x s
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Let's call the selling price of each sweater "sp".
The store buys 15 sweaters for $90, so each sweater must cost
=$90 / 15
= $6
The store sells each sweater for
= $405 / 15
= $27,
so sp = $27
The total profit is equal to the selling price minus the buying price, so the equation for the total profit, p, in terms of the number of sweaters sold, s, is:
p = sp x s - $6 x s
We can simplify this equation to:
p = ($27 - $6) x s
p = $21 x s
So, the proportional equation for the total profit in dollars and cents when the store buys any number of sweaters, s, is:
p = $21 x s
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find the parametric equation of the line through a parallel to b, using t as the parameter!
The parametric equations of a line can be determined using a point on the line and a direction vector. To find the parametric equation of a line that passes through a point A and is parallel to a direction vector b, we can use the following formula:
x = x0 + tbx
y = y0 + tby
z = z0 + tbz
where (x0, y0, z0) is the position vector of point A, (bx, by, bz) is the direction vector, and t is the parameter that varies along the line.
What is equation?An algebraic equation, also known as a polynomial equation, is a mathematical equation of the form P=0, where P is a polynomial with coefficients in some field, most commonly the field of rational numbers. An algebraic equation is a mathematical statement that sets two expressions equal to each other. An algebraic equation is typically made up of a variable, coefficients, and constants.
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Let sets A and B be defined as follows.
A is the set of integers greater than or equal to -9 and less than or equal to - 3
B=1-29, -26, -23, 30}
(a) Find the cardinalities of A and B.
n(A) =
n (B) =
The cardinalities:
n(A) = 3
n (B) = 1.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Let sets A and B be defined as follows.
A is the set of integers greater than or equal to -9 and less than or equal to - 3
Set A can be expressed as,
A = {n ≥ -9 or n ≤ -3}
And set B is given,
B = {1-29, -26, -23, 30}
Simplifying,
B = {-28, -26, -23, 30}
The cardinalities:
n(A) = 3
n (B) = 1.
Therefore, n(A) = 3 and n (B) = 1.
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Evaluate:
10³ +5² +2²=
A. 10,029
B. 1,029
C. 10,254
D. 129
Answer:
B
Step-by-step explanation:
10*10*10 =1000
5*5 =25
2*2 =4
1000+25+4 =1029
the weights, in pounds, for 15 1515 horses in a stable were reported, and the mean, median, range, and standard deviation for the data were found. the horse with the lowest reported weight was found to actually weigh 10 1010 pounds less than its reported weight. what value remains unchanged if the four values are reported using the corrected weight?
The only value that remains unchanged is the standard deviation.
The mean, median, range, and standard deviation will all change once the corrected weight is used to calculate the data. The mean is calculated by adding all the weights and dividing by the total number of horses. Therefore, the mean will be recalculated using the corrected weight of 1005 and the new value will be lower than the previous mean. The median is the midpoint of the data set, so it will also decrease with the updated weight. The range is the difference between the highest and lowest values, so it will also decrease with the corrected weight. Lastly, the standard deviation is a measure of the spread of the data and will also decrease when the corrected weight is used. Therefore, the only value that remains unchanged is the standard deviation.
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in the 1908 19081908 olympic games, the olympic marathon was lengthened from 40 4040 kilometers to approximately 42 4242 kilometers. of the following, which is closest to the increase in the distance of the olympic marathon, in miles? ( 1 (1(, 1 mile is approximately 1.6 1.61, point, 6 kilometers. ) )
The closest answer to the increase in the distance of the Olympic marathon is 1.50 miles. Hence the correct answer is option C.
In order to find the increase in the distance of the Olympic marathon, we will find the difference between the old distance (40 km) and the new distance (42 km) and then convert it to miles.
40 km - 42 km = -2 km
Converting -2 km to miles, we get:
-2 km x 1.6 miles/km = -3.2 miles
However, since the marathon was lengthened, the actual increase in the distance is:
-3.2 miles = 3.2 miles
Rounding to the nearest 0.25 miles, we get,
3.2 miles = 3.25 miles ≈ 3.25 miles
So the closest answer to the increase in the distance of the Olympic marathon is 1.50 miles.
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The complete question is -
In the 1908 Olympic Games, the Olympic marathon was lengthened from 40 kilometers to approximately 42 kilometers. Of the following, which is closest to the increase in the distance of the Olympic marathon, in miles? (1 mile is approximately 1.6 kilometers.)
A) 1.00
B) 1.25
C) 1.50
D) 1.75
A product is currently made in a process-focused shop, where fixed costs are $9000 per year and variable cost is $50 per unit. The firm is considering a fundamental shift in process, to repetitive manufacture. The new process would have fixed costs of $90,000, and variable costs of $5. What is the crossover point for these processes?
Every year, 1800 units crossover point. The process focus is less expensive for volumes over 1800.
What is the crossover point?When all tax credits have been used up by a limited partnership and the limited partners are left with a tax burden, that moment is known as the crossover point.
When both projects have positive values, the crossover point is formed by the intersection of two IRR curves.
The weighted average cost of capital, also known as the crossover rate, is the rate of return at which the net present values (NPV) of two projects are equal.
The rate of return at which the net present value profiles of two projects cross each other is what this term denotes.
So, annual crossover sales are 1800 units.
Process emphasis is less expensive and less important for volumes under 1800 units; repeated manufacturing concentration is less expensive and less important for volumes exceeding 1800 units.
Fixed cost ÷ variable cost
$90000÷50 =$1800
$9,000÷5=$1800
Therefore, every year, 1800 units cross over. The process focus is less expensive for volumes over 1800.
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Correct question:
A product is currently made in a process-focused shop, where fixed costs are $9,000 per year and variable costs are $50 per unit. The firm is considering a fundamental shift in process, to repetitive manufacturing. The new process would have fixed costs of $90,000, and variable costs of $5. The cross over is at 1800 units annually. for volumes over 1800, the process focus is cheaper.
a diamond ring was purchased ten years ago for 300. the value of the ring increased by 7% each year. what is the value of the ring today
Answer:
Below
Step-by-step explanation:
Value will be original value * ( 1 + i)^n i = decimal annual interest
n = years
Value = 300 ( 1 + .07)^10 = 590.15 (dollars ?)
why does it require less work to raise one end of a log to shoulder height than to raise the whole log to the same height?
Work is defined as the product of force and distance, and can be calculated using the equation W = F * d, where W is work, F is force, and d is distance.
When lifting the whole log, the force required is equal to the weight of the log, and the distance over which the force is applied is the distance from the ground to the height of the shoulder.
When lifting one end of the log, the force required is still equal to the weight of the log, but the distance over which the force is applied is reduced. This is because the lever arm (the distance from the axis of rotation, which is the shoulder joint, to the point where the force is applied, which is the end of the log) is reduced.
So the equation for work done in lifting the whole log would be W = m * g * h, where m is the mass of the log, g is the acceleration due to gravity, and h is the height from the ground to the shoulder. The equation for work done in lifting one end of the log would be W = (m/2) * g * h', where h' is the reduced height.
It can be seen that the work done in lifting one end of the log is equal to half the work done in lifting the whole log, because the force applied is the same, but the distance over which it is applied is reduced.
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in exercises 1 and 2 rewrite the expression in rational exponent form
Rewrite expression in rational exponent form
[tex]a) \: \: \: \: \sqrt[5]{ (- 53) ^{4} } \\ b) \: \: \: \: \: \: \sqrt[4]{(110) {}^{7} } [/tex]
the rational exponent form :
a)
[tex] { - 53}^{ \frac{4}{5} } [/tex]
b)
[tex]110 { }^{ \frac{7}{4} } [/tex]
About Exponential numberExponential numbers are a form of mathematical abbreviation that allow us to write complex mathematical expressions more succinctly. An exponential number is a number that is repeatedly multiplied by itself.
Exponential is written with numbers and letters to the right of certain mathematical expressions called bases. While exponential numbers are often also called powers. Properties of exponential numbers
Exponential numbers have their own special properties as follows:
a¹ =a mathematical expression with an exponential of 1 or to the power of one, the result is always a mathematical expression itself. Example: 2¹ = 2, 67¹=67, and 700¹=700. aº=1 , when the exponent is zero, then regardless of the number, the expression will always equal one. Example: 2º=1 In addition to one and zero exponentials which are often referred to as powers of one and powers of zero, the following are the properties of exponentials in multiplication, division, multiple powers, as well as exponential fractions:Learn more about exponent at
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What is the lateral surface area of the rectangular prism below?
72 cm²
3 * ( 6+2+2) + 2 * (2 * 6) + 6 * 3
11) show all ur equation steps
The number of solutions that the system has is
One Solution
How do we solve the equations?To solve the system algebraically, we can substitute the first equation into the second equation to eliminate one of the variables. We'll use y:
x=2y-5
7x-14y=10
Substitute x=2y-5 into 7x-14y=10:
7(2y-5)-14y=10
Expand the left side:
14y-35-14y=10
Combine like terms:
-35=10
Solve for y:
y = -7.5
Substitute y = -7.5 back into x=2y-5:
x = 2(-7.5) - 5
Solve for x:
x = -10
So the solution to the system of equations is (x, y) = (-10, -7.5).
Since there is one unique solution, the system has One Solution.
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Solve for arc x
Thxs and hurry
The value of arc x is solved to be 120 degrees
How to find the value of arc xThe Arc x is solved using the knowledge of linear pair
A linear pair of angles forms a straight line, and the two angles are said to be "linear" because they are next to each other and their measures add up to 180 degrees.
Applying this we have that
60 + x = 180
x = 180 - 60
x = 120 degrees
hence we can say that x is 120 degrees
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How much of a radioactive kind of neodymium will be left after 44 days if the half-life is
11 days and you start with 120 grams?
There will be left 7.5 grams of the radioactive kind of neodymium after 44 days, with half life of 11 days.
What is half life?Half-life is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential decay.
Given that, a radioactive kind of neodymium have the half-life is 11 days, and with 120 grams
We need to find the remaining after 44 days,
The formula to calculate half life =
[tex]N(t) = N(1/2)^\frac{t}{t_{1/2} }[/tex]
N(t) = quantity of the substance remaining
N = initial quantity of the substance
t = time elapsed
t{1/2} = half life of the substance
N(t) = 120(1/2)⁴⁴/₁₁
= 120(1/2)⁴
= 120(1/16)
= 7.5
Hence, there will be left 7.5 grams of the radioactive kind of neodymium after 44 days, with half life of 11 days.
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PLS HELP ASAP I NEED IT PLS PLS PLS
I WILL MARK BRAINLIST AND SET THIS 100 POINTS BUT PLS ANSWER CORRECTLY.THIS IS GRADED OUT OF 100% I need 80% to pass for an A- PLS YALL!
Answer:
x=105
Step-by-step explanation:
The angles of a triangle add up to 180 degrees.
[tex]180 = 30 +45+x[/tex]
[tex]x=105[/tex]
∠X and ∠Y are supplementary angles. The measure of ∠X=3n−18 . The measure of ∠Y=2n−27
The measure of the supplementary angles is:
∠X = 117°
∠Y = 63°
How to find the measures of the angles?Here we know that angles ∠X and ∠Y are supplementary angles. Remember that two angles are supplementary if their measures add up to 180°.
Here we know that the measures are:
∠X = 3n − 18
∠Y = 2n − 27
We can write:
∠X + ∠Y = 180°
(3n - 18) + (2n - 27) = 180
Then we can solve that for n.
3n + 2n - 18 - 27 = 180
5n = 180 + 45
n = 225/5 = 45
Then the measures of tha angles are:
∠X = 3n − 18 = 3*45 - 18 = 117°
∠Y = 2n − 27 = 2*45 - 27 = 63°
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Ted is designing a miniature railroad station layout as shown below. The missing portions of the track represent the arcs of two congruent circles. Each circle has a radius of 10 inches. The central angles of these sectors are 75º and 85º.How many inches of curved track will Ted need to complete the missing part of his model station layout if he rounds the length to the nearest inch?
Ted needs 47 + 53 = 100 inches of curved track to complete the missing parts of his model station layout.
How do we get the value?First, we need to find the length of each arc. To do this, we'll use the formula:
arc length = circumference * central angle / 360
The circumference of a circle with radius 10 inches is 2 * pi * 10 = 20 * pi inches.
So, for the 75º sector:
arc length = 20 * pi * 75 / 360 = 15 * pi inches
And for the 85º sector:
arc length = 20 * pi * 85 / 360 = 17 * pi inches
Rounding pi to 3.14, we get:
arc length = 15 * 3.14 = 47.1 inches (rounded to 47 inches)
arc length = 17 * 3.14 = 53.4 inches (rounded to 53 inches)
So, Ted needs 47 + 53 = 100 inches of curved track to complete the missing parts of his model station layout.
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a local bank branch employs three tellers who can each help a customer on average in 6 minutes, with a standard deviation of 3 minutes. on average, 24 customers arrive at this bank per hour (in a random fashion). how long would customers have to wait if we do pool the employees? that is, we make one line to lead to all three servers. group of answer choices
Customers have to wait for d) approximately 12 minutes if we do pool the employees.
This can be found by calculating the average waiting time per customer, which is the average service time divided by the average number of customers.
In this case, the average service time is 6 minutes (with a standard deviation of 3 minutes) and the average number of customers is 24. So, the average waiting time per customer is 6/24 = 0.25 hours = 15 minutes.
To ensure that customers do not have to wait any longer than necessary, it is best to have three separate lines for the three tellers. This way, customers are served in the order they arrive, rather than having to wait for one teller to serve all the customers.
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During the ceremony, a printing
company received a very large order to
carry out the production of campaign
material. It was estimated that the 3
machines would take 24 hours to
perform the entire service. Assuming
that one of these machines breaks
down before starting the service, how
long will it take to meet this demand?
If one of the three machines breaks down before starting the service, it would take the remaining two machines longer to meet the demand. If each machine can produce the same amount of material, it would take each machine 24 hours / 3 machines = 8 hours to perform the entire service.
So, with two machines working, it would take each machine 8 hours / 2 machines = 4 hours to complete the job. Thus, the total time to meet the demand would be 4 hours * 2 machines = 8 hours.
Find 3 ratios that are equivalent to the given ratio 7 over 6
Write the following expression using the fewest possible terms.
(−5x − 12) + (14 + 7x)
2x + (−2)
2x + 2
17x + (−26)
17x + 26
The expression which can be used to represent the given using the fewest possible terms is 2x + 2
The correct answer choice is option B.
How to write expression using fewest possible terms?(−5x − 12) + (14 + 7x)
open parenthesis
-5x - 12 + 14 + 7x
collect like terms
-5x + 7x - 12 + 14
2x + 2
In conclusion, 2x + 2 is the expression which represents the fewest possible terms of (−5x − 12) + (14 + 7x)
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Answer:
its C
Step-by-step explanation:
other guy wasn't reasonable and chose the actual shortest one possible instead of the one that made sense
Step by step please and thank you……
Answer:
Answer is in attached photo.
Step-by-step explanation:
SolutionThe solution is in the attached photo, do note that this question requires the concept on Pythagoras' Theorem.
Help..please!!!
Hfurbrurbrurhgedhvudbeyrb FB yd
3a.) The number of calories at 24 minutes would be = 60 calories
3b.) The time at 280 calories = 42 minutes.
4a.) The height in feet after 4 minutes = 24 feet
4b.) The time when the height is 48 minutes = 8 mins.
Hone to calculate calories per unit time?There are two main graphs represented above which include the following details:
The first graph: Calories was plotted in y-axis against time in x-axis.
The second graph : Height was plotted in y-axis against time is X axis.
When an imaginary straight line is drawn from the origin of the graph, the following values can be derived:
3a) The number of calories at 24 minutes would be = 60 calories.3b.) The time at 280 calories = 42 minutes.4a.) The height in feet after 4 minutes = 24 feet. This is because the point created by the interception of x-axis on the imaginary line drawn from the origin is at 24 feet on the y-axis.4b.) The time when the height is 48 minutes = 8 mins. This is because the point created by the interception of y-axis on the imaginary line drawn from the origin is at 8 mins on the x-axis.Learn more about graph here:
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a box contains six green dice, three red dice and three white dice. a die is selected at random from the box. the die's colour is noted and it is not replaced. this experiment is repeated four times. find the probability that a green die is selected fewer than three times.
The die's color is noted and it is not replaced. This experiment is repeated four times. The probability that a green die is selected fewer than three times is 8/11.
A box contains six green dice, three red dice and three white dice.
Total dice = Green Dice + Red Dice + White Dice
Total dice = 6 + 3 + 3
Total dice = 12
The probability that a green die is selected fewer than three times = P(G'G'G'G') + P(G'G'G'G) + P(G'G'GG') + P(G'GG'G') + P(GG'G'G') + P(GGG'G') + P(GG'GG') + P(GG'G'G) + P(G'GGG') + P(G'GG'G) + P(G'G'GG)
Here G represents that the dice is green while G' represents as the dice is not green.
The probability that a green die is selected fewer than three times = 6/12×5/11×4/10×3/9 + 6/12×6/11×5/10×4/9 + 6/12×6/11×5/10×4/9 + 6/12×5/11×6/10×4/9 + 6/12×5/11×4/10×6/9 + 6/12×5/11×6/10×5/9 + 6/12×6/11×5/10×5/9 + 6/12×6/11×5/10×5/9 + 6/12×6/11×5/10×5/9 + 6/12×6/11×5/10×5/9 + 6/12×5/11×6/10×5/9
The probability that a green die is selected fewer than three times = 360/11880 + 720/11880 + 720/11880 + 720/11880 + 720/11880 + 900/11880 + 900/11880 + 900/11880 + 900/11880 + 900/11880 + 900/11880
The probability that a green die is selected fewer than three times = 8640/11880
The probability that a green die is selected fewer than three times = 8/11
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Which of the following is NOT a solution to the system of inequalities in the given graph?
A. (-2, -4)
B. (2, 0)
C. (0, 0)
D. (1, 1)
Answer:
I think B
Step-by-step explanation:
sorry if I said wrong
Helpppppp pleaseeeee !!!
Based on each given quadrilateral, we know that:
Rectangle ABCD has:
DC = 12BC = 5DE = 6.5∠DBA = 35°∠DAC = 55°∠DEC = 110°∠CEB = 70°Rhombus FGHJ:
∠JGH = 120°∠FJH = 120°∠KFG = 30°GH = 10KG = 5F.K = 5√3FH = 10√3Square LMNO:
∠OMN = 45°PM = 8LN = 16∠OPL = 90°Let's discuss each quadrilateral we have:
ABCD is a rectangle; then:
AD // BC and AD = BCAB // CD and AB = CDAC = BD but not perpendicular to each otherAC bisects BDDC = AB = 12
BD² = BC² + CD²
13² = BC² + 12²
169 = BC² + 144
BC² = 25
BC = 5
DE = 1/2 BD
DE = 1/2 (13)
DE = 6.5
∠DBA and ∠BDC are alternate interior angles and congruent, then:
∠DBA = ∠BDC = 35°
∠DBA = ∠BAC because triangle BAE is isosceles triangle.
∠BAC is the alternate interior angle of ∠DCA; then:
∠BAC = ∠DCA = 35°
∠DAB = ∠DAC + ∠BAC
90° = ∠DAC + 35°
∠DAC = 55°
Focus on triangle DEC:
∠DEC + ∠EDC + ∠ECD = 180°
∠DEC + 35° + 35° = 180°
∠DEC = 110°
Focus on triangle CEB:
∠CEB + ∠EBC + ∠CBE = 180°
∠CEB + 55° + 55° = 180°
∠CEB = 70°
FGHJ is a rhombus; then:
All sides share the same lengthIts diagonals are perpendicular and bisect each otherIts diagonals bisect its respective anglesHave 2 pairs of opposite angles and congruentThe sum of angles is 360°∠JGH = ∠FJH = 2∠FJG
∠JGH = ∠FJH = 2(60)
∠JGH = ∠FJH = 120°
Since FGHJ is a rhombus, then:
∠JGH + ∠JHG + ∠FGH + ∠JFG = 360°
120° + ∠JHG + 120° + ∠JGH = 360°
240° + 2∠JHG = 360°
2∠JHG = 120°
∠JHG = 60°
∠KFG = 1/2∠JHG
∠KFG = 1/2 (60)
∠KFG = 30°
GH = FG = 10
To find KG, we need to focus on triangle F.KG. Under the Sines Law:
KG / sin 30 = FG / sin 90 = F.K / sin 60
KG / √3/2 = 10 / 1 = F.K / 1/2
KG = 5
F.K = 5√3
FH = 2F.K
FH = 2(5√3)
FH = 10√3
LMNO is a square, then:
All sides share the same lengthBoth diagonals are perpendicular and bisect each otherBoth diagonals share the same lengthAll diagonals bisect its respective anglesThe sum of angles is 360°All sides angle are 90°∠OMN = 45°
Please focus on triangle MNP. Under the Sines Law:
PM / sin 45 = MN / sin 90
PM / √2/2 = 8√2 / 1
PM = 8
LN = 2PM
LN = 2(8)
LN = 16
∠OPL = 90°
Learn more about Rhombus here: brainly.com/question/27870968
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