Answers
z = [tex]\frac{13}{20}+\frac{19}{20}i[/tex] is in the form z = a+ ib, where a = 13/20 and b = 19/20
Exact value of |z| = 1.151
Argument of z = 55.6197
Consider the complex number z = (2+7i)/(6+2i)
6a. Here z is in a rational form and we need to simplify it to represent it in the form a+ ib.
Multiplying and dividing the conjugate of the denominator to z, we get,
z = [tex]\frac{2+7i}{6+2i} \times \frac{6-2i}{6-2i}[/tex]
⇒ z = [tex]\frac{12 +38i +14}{6^2+2^2}[/tex]
⇒ z = [tex]\frac{26+38i}{40}[/tex]
⇒ z = [tex]\frac{13}{20}+\frac{19}{20}i[/tex]
is in the form z = a+ ib, where a = 13/20 and b = 19/20
6b.modulus of z = |z| = √(a²+b²)
= [tex]\sqrt{\frac{13^2}{20^2} +\frac{19^2}{20^2} }[/tex]
= [tex]\sqrt{\frac{530}{400}}[/tex]
= √(53/40)
= 1.151
6c. Argument of z = tan⁻¹(b/a)
= tan⁻¹((19/20)/(13/20))
= tan⁻¹(19/13)
= 55.6197
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Related Questions
4 Given the table below, which student wrote a correct equation between the number of horses, x, and the cost of boarding, y? # of Horses Cost O C. Tori only 37 4 99 TORI 31x - 2y = 74 J A. Both Laquita and Tori go to 6 go to 1 8 161 10 192 12 223 LAQUITA y = 15.5x +37 B. Neither Laquita nor Tori D. Laquita only go to 9 go to 8
Answers
Both Laquita and Tori wrote a correct equation which is the correct answer would be an option (A).
Let the required line would be as
⇒ y - y₁ = [(y₂ - y₁)/(x₂ -x₁ )](x - x₁ )
Here x₁ = 0 and y₁ = 37
x₂ = 4 and y₂ = 99
The equation of the line is obtained by substituting these values into the above equation;
⇒ y - 37 = (62/4)x
⇒ y - 37 = 15.5x
⇒ y = 15.5x +37
This equation is written by Laquita.
Multiply by 2 both sides of the equation,
⇒ 2y = 31x + 74
⇒ 31x - 2y = 74
This equation is written by Tori.
Therefore, both Laquita and Tori wrote a correct equation.
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Need to find the mean, median, mode, and midrange.
Answers
The science of statistics focuses on creating and researching strategies for gathering, analyzing, interpreting, and presenting empirical data.
Explain about mean median mode?A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When a data collection is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.
Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean. An average is most frequently used to refer to this. The value that appears the most frequently on the list is the mode.
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in a random sample of 45 endangered species, 12 are categorized as vulnerable, 11 are categorized as endangered, and 22 are categorized as critically endangered. what is the probability that a randomly selected species from this sample is vulnerable or critically endangered? group of answer choices
Answers
The probability that the randomly selected sample is vulnerable or critically endangered is equal to 0.76
The probability can be determined using the following formula;
probability = number of desired events or outcomes ÷ total number of events or outcomes
The total is known to be 45, the favorable or desired outcomes can be calculated as follows;
number of desired outcomes = number of vulnerable species + number of critically endangered species
number of desired outcomes = 12 + 22
number of desired outcomes = 34
Now we calculate the probability by using the above formula;
probability = 34 ÷ 45
probability = 0.76
Therefore, 0.76 is the probability that the randomly selected species is vulnerable or critically endangered.
Although a part of your question is missing, you might be referring to this question:
In a random sample of 45 endangered species, 12 are categorized as vulnerable, 11 are categorized as endangered, and 22 are categorized as critically endangered. what is the probability that a randomly selected species from this sample is vulnerable or critically endangered? group of answer choices
11/45
0.24
0.83
0.76
12/45
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10
-90+30+(−10)+ +... n = 16
3
Answers
−
90
+
30
+
(
−
10
)
+
+
...
n
=
163
1
0
−
9
0
+
3
0
+
(
−
1
0
)
+
+
.
.
.
=
1
6
3
Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply.
For any value of x, g(x) will always be greater than h(x).
For any value of x, h(x) will always be greater than g(x).
g(x) > h(x) for x = -1.
g(x) < h(x) for x = 3.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).
Answers
Correct option are C,D, E. g(x) > h(x) for x = -1, For positive values of x, g(x) > h(x), For negative values of x, g(x) > h(x).
What are functions?A function is a type of rule that produces one output for a single input. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.
They have the same value if x=0.
The first and second choices are not viable
for x=-1
g(-1)=1
h(-1)=-1
3. is accurate
4th , false G(x)>H for all values other than zero (x)
the proper ones are
For x=-1, g(x) exceeds h(x).
G(x) > h for positive values of x. (x).
G(x) > h for negative values of x (x).
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Simplify the function f (x) = one-third (81) Superscript StartFraction 3 x Over 4 EndFraction. Then determine the key aspects of the function.
Answers
The function is f(x) = 1/3(27)ˣ, the key aspects are domain: -oo < x < oo and range: y ≥ 1/3
How to simplify the equation of the function?From the question, the equation of the function is given as
f (x) = one-third (81) Superscript StartFraction 3 x Over 4 EndFraction
Rewrite the equation properly
So, we have
f(x) = 1/3(81)³/⁴ˣ
Express 81 as 3 exponent 4
So, we have the following equation
f(x) = 1/3(3⁴)³/⁴ˣ
Evaluate the exponents
f(x) = 1/3(3)³ˣ
Further, evaluate the exponents
f(x) = 1/3(27)ˣ
Next, we calculate the key aspects i.e. the domain and the range
The above function is an exponential function.
The domain of an exponent is the set of all real values
Set the radicand to 1, to calculate the range
So, we have
y = 1/3 * 1
Evaluate
y = 1/3
Since the coefficient, this value is a minimum
So, the range is
y ≥ 1/3
Hence, the simplified function is f(x) = 1/3(27)ˣ
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Answer:
1/3
27
all real numbers
y > 0
or B. C. D. B.
Step-by-step explanation:
hope I could help
Which of the following values "completes the square," or creates a perfect square trinomial, for x2 + 6x + ___?
1
3
6
9
Answers
Answer:
+ 9
Step-by-step explanation:
x² + 6x
to complete the square
add ( half the coefficient of the x- term )² to x² + 6x
x² + 2(3)x + 3²
= x² + 2(3)x + 9
= (x + 3)² ← a perfect square
on a piece of paper, graph the system of equations. Find the solution to the system. y=2x-1 y=x+5
Answers
The solution to the system is 6 and 11.
What is 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. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" symbol and terms on both sides must always be present when writing an equation.
Given equation:
y=2x-1 .....(1)
y=x+5....(2)
Now solving equation 1 and 2, we get
2x -1 = x + 5
2x - x= 5 +1
x = 6
and, y= 2x-1
y= 2(6)-1
y= 12 -1
y= 11
Hence, the value of x is 6 and y is 11.
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Find the value of x.
Answers
Answer:
x=15
Step-by-step explanation:
You can set up the equation like this
60 =3x+15
Get x by itself
45=3x
Divide both sides by 3
x=15
if you want to just give me the answer that would be fine. i just want to make sure i’m correct.
Answers
Okay, here we have this:
Considering that if the graph of the line rises from left to right, then it means that the slope is positive. On the other hand, if the graph of the line falls from left to right, the slope will be negative.
So, according with this finally we obtain that the correct answer is that the slope is negative.
Answer:
Negative
Step-by-step explanation:
Because MATH
Each number in a list of numbers can be found using the expression 6 − 23(n − 1), where n is a positive integer that gives the position of the number in the list. What is the thirteenth number in the list? A. −8 B. −2 C. 8 D. 13
Answers
The solution is Option A.
The value of the 13th number from the equation A = ( -2/3 ) ( n - 1 ) is A = -8
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
A = ( -2/3 ) ( n - 1 ) be equation (1)
On simplifying the equation , we get
The thirteenth number in the list is n = 13
So , when n = 13
A = ( -2/3 ) ( n - 1 )
A = ( -2/3 ) ( 13 - 1 )
On further simplification , we get
A = ( -2/3 ) ( 12 )
A = ( -2 ) x 4
So , the value of A = -8
Hence , the thirteenth number in the list is A = -8
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Ms. Gartland bought x number of shirts for the new members of her chorus. The cost for x number of shirts, including $3.99 shipping, was $77.49. Each shirt cost $12.25. There was no sales tax on this purchase. Which equation could be used to find x?A. 3.99(+12.25)=77.49B. 3.99+12.25=77.49C. 12.25(+3.99)=77.49D. 12.25+3.99=77.49
Answers
the expression for the given situation is given as follows,
12.25x + 3.99 = 77.49 $
here, x = no. of shirt
so the correct answer is option D
Help! 100 points! Evaluate the function at: x=3
Answers
Answer: When x=3 y=-3
Step-by-step explanation:
Use the values In 8 ≈ 2.08 and In 1000≈6.91 to find the approximate value of log8 1000
Answers
The approximate value of log₈1000 is 0.30.
What are logarithms?The inverse of power is a logarithm. When you take the log of a number, you reverse the exponent.Logarithms normally use a base of 10 (but a different value can be provided), whereas natural logs always use a base of e. Use the following calculation to convert between logarithms and natural logs.[tex]log_{10}x[/tex] [tex]= ln(x) / ln(10)[/tex]
The given values are:
In 8 ≈ 2.08 and In 1000 ≈ 6.91
To find the approximate value of log₈1000,
log₈1000 = In 8/In 1000
= 2.08/6.91
≅ 0.30
Therefore, the approximate value of log₈1000 is 0.30.
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g(x)=3/4f(x) graphed
Answers
The function g(x) is a dilated form of f(x) and the dilation scale factor [K] in this case is (3/4). The graphs f(x) and g(x) are attached with the answer.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is the following equation-
g(x) = 3/4 f(x)
Since, the functions are not given, we will assume them by ourselves. You can use the same procedure for any pair of functions of the form -g(x) = n f(x)
Assume that -
f(x) = 2x + 1
Now -
g(x) = (3/4) f(x)
g(x) = (3/4)(2x + 1)
g(x) = (3/2)x + 3/4
Now, both the graphs f(x) and g(x) are attached below. In general, g(x) is a dilated form of f(x) and the dilation scale factor [K] in this case is (3/4).
Therefore, the function g(x) is a dilated form of f(x) and the dilation scale factor [K] in this case is (3/4). The graphs f(x) and g(x) are attached with the answer.
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A piece of artwork, purchased for $1500, increases in value by 8% each year,11) (3pt) Write an exponential function to represent the value of the artworkafter z number of years.12) (2pt) What will the artwork be worth in 10 years?
Answers
Let's begin by listing out the information given to us:
Cost (c) = $1500, interest (r) = 8% /annum
The equation for this is given by:
[tex]\begin{gathered} y=c\cdot(1+r)^z\Rightarrow y=c(1+0.08)^z \\ c=\text{ \$1500, }r=0.08 \\ y=c(1.08^z)^{}=1500\cdot1.08^z \\ \\ z=10 \\ y=1500\cdot1.08^{10} \\ y=\text{ \$}3238.39 \end{gathered}[/tex]11. The exponential function is given by: y = c * 1.08^z
12. The artwork is worth $3238.39
finishing a long race, a runner puts on a burst of speed 15 meters from the finish line. two seconds later, she comes to a stop 3 meters past the finish line. what was her average speed during those two seconds?
Answers
The average speed during the two seconds in which the runner moved from 15 meters from the finish line to 3 meters past the finish line is 9 m/s
The average speed of the runner can be determined by using the following formula;
speed = distance ÷ time
As she moved from 15 meters from the finish line to 3 meters past the finish line in 2 seconds, the total distance covered in these 2 seconds by her can be calculated as follows;
distance = 15 meters + 3 meters
distance = 18 meters
Now substituting the values for distance and time in the formula;
speed = 18 / 2
speed = 9 m/s
Hence the average speed of the runner during the two seconds is calculated to be 9 m/s.
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A shipping container will be used to transport several 120-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 14900 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine x, the number of 120-kilogram crates that can be loaded into the shipping container.
HURRY PLEASEEEEEEEEEEEEEEEEEEE!
Answers
A maximum of 105 number of 120 kilograms can be loaded in the container.
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
Weight of each crate = 120 kg
The greatest weight loaded in the container = 27500 kg
Weight already loaded in the container = 14900 kg
Now,
Since, Weight already loaded = 14900 kg
Let number of 120 kilograms loaded in the container = x.
Hence, Weight of x = 120 kg
So, After combined we get;
Weight nor be greater than the capacity of the container.
Hence, we can formulate;
14900 + 120x ≤ 27500
Subtract 14900 we get;
120x ≤ 27500 - 14900
120x ≤ 12600
x ≤ 12600 ÷ 120
x ≤ 105
Thus, A maximum of 105 number of 120 kilograms can be loaded in the container.
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What's the circumference of a circle with a diameter of 31 inches
Answers
Answer:
C≈97.39in
Step-by-step explanation:
Answer:97.39
Step-by-step explanation:
A pump fills a pool at a constant rate. At the end of 1 minute, it has filled 10 gallons of water. Which table represents the relationship between the number of minutes and the number of gallons of water in the pool?
A
\text{Time} \newline \text{ (minutes)}Time
(minutes) \text{Water} \newline \text{ (gallons)}Water
(gallons)
22 2020
44 4040
66 6060
B
\text{Time} \newline \text{ (minutes)}Time
(minutes) \text{Water} \newline \text{ (gallons)}Water
(gallons)
11 1010
22 3030
44 5050
C
\text{Time} \newline \text{ (minutes)}Time
(minutes) \text{Water} \newline \text{ (gallons)}Water
(gallons)
22 2020
44 2222
66 2424
D
\text{Time} \newline \text{ (minutes)}Time
(minutes) \text{Water} \newline \text{ (gallons)}Water
(gallons)
11 1010
22 1111
44 1313
I'm sorry this is confusing :\
Answers
The answer is A, because if one minute corresponds to 10 gallons of water, then the amount of gallons is the minutes times 10.
When you round up to a place that has a 9, you create a 10. Then you need to round up the next place to the left of the place you are rounding to.There are 198,714 people living in Belleville. What is the number of people rounded to the nearest ten thousand?a. What digit is in the ten thousands place?b. Which place is used to decide which way to round the ten thousands place?c. What is the digit in this place?d. Should you round the number in the ten thousands place up or down?e. What happens when you round up a 9?f. What do you do when the value of a place is 10 or more?g. What is the value of the ten thousands place when the number is rounded to the nearest tenthousand?h. What is 198,714 rounded to the nearest ten thousand?i. What is 302,895 rounded to the nearest thousand?j. What is 7,142 rounded to the nearest ten?k. Round 24,793 to the nearest hundred.?
Answers
198, 714
a. What digit is in the ten thousands place? - 9
b. Which place is used to decide which way to round the ten thousands place? - thousands place
c. What is the digit in this place? - 8
d. Should you round the number in the ten thousands place up or down? - UP
e. What happens when you round up a 9? - It becomes 10.
f. What do you do when the value of a place is 10 or more? - The number becomes 0 and we add 1 to the next place to the right.
g. What is the value of the ten thousands place when the number is rounded to the nearest ten thousand? 100,000
h. What is 198,714 rounded to the nearest ten thousand? - 200,000
i. What is 302,895 rounded to the nearest thousand? - 303, 000
j. What is 7,142 rounded to the nearest ten? - 7, 140
k. Round 24,793 to the nearest hundred? - 24, 800
HELP ASAP
You are working as a car salesperson. You make $13.25 per hour. You are paid biweekly (two weeks of work). Your boss encourages competition between employees by letting you know that you will receive a commission of $150 for each new car you sell.
In the first week, you work 25 hours and sell 3 cars.
In the second week, you work 18 hours and sell 2 cars.
How much will your total pay be at the end of these two weeks?
Answers
Total pay be the at the end of the two weeks with rate of $13.25 per hour and commission of $150 for selling each new car is $1319.75.
As given,
Rate of salesperson per hour pay = $13.25
Commission on selling each new car =$150
Amount of the pay earned by salesperson:
First week :
25 (13.25) + 3 (150)
= 331.25 + 450
= $781.25
Second week:
18 (13.25) + 2(150)
= 238.5 +300
= $538.50
Total pay of salesperson at the end of two weeks
=$(781.25 +538.5)
=$1319.75
Therefore, total pay be the at the end of the two weeks with rate of $13.25 per hour and commission of $150 for selling each new car is $1319.75.
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A large multiplex movie house has many theaters. The largest theatre has 36 rows. There are 20 seats in the first row. Each row has four seats more than the previous row. How many total seats are there in this theatre?
Answers
Answer:
2880 seats
Step-by-step explanation:
r1 r2 r3 r36
20 + 20+4 + 20+4+4 + ···+20+4×35
total seats = ((20 + 20+4×35)÷2)×36= 2880
Please help me, it is important
Answers
Answer: Your fourth point is going to be (-3,4). Hope this helps!
Step-by-step explanation:
The largest angle of a triangle measures 9degrees less than 5 times the measure of the smallest angle. The middle angle measures three times that of the smallest angle. Find the measures of the three angles.
Answers
Let the smallest angle be represented as
[tex]=x[/tex]Step 1: The largest angle of a triangle(let the largest angle =z) measures 9degrees less than 5 times the measure of the smallest angle, this statement is represented as
[tex]\begin{gathered} 5\text{ times the smallest angle gives} \\ =5\times x \\ =5x \\ 9\text{ degr}ees\text{ less will give the largest angle to be} \\ \text{largest angle =5x-}9 \\ z=5x-9 \end{gathered}[/tex]Step 2: let's calculate the middle angle (let the middle angle =y)
The middle angle measures three times that of the smallest angle, which means that
[tex]\begin{gathered} y=3\times x \\ \text{middle angle =y= 3x} \\ y=3x \end{gathered}[/tex]Recall that the total angles in a triangle give
[tex]=180^0[/tex]Therefore,
[tex]\begin{gathered} \text{largest angle + middle angle + smallest angle =180}^0 \\ z+y+x=180^0 \end{gathered}[/tex]Substituting we will have
[tex]\begin{gathered} 5x-9+3x+x=180^0 \\ \text{collect the sinmilar terms we will have} \\ 5x+3x+x=180^0+9^0 \\ 9x=189^0 \\ \text{divide both sides by 9} \\ \frac{9x}{9}=\frac{189^0}{9} \\ x=21^0 \end{gathered}[/tex]Hence,
the smallest angle is = 21 degrees
[tex]\begin{gathered} \text{The largest angle =5x-9} \\ =5\times21^0-9 \\ =105^0-9 \\ =96^0 \end{gathered}[/tex]Hence,
The largest angle = 96 degrees
[tex]\begin{gathered} \text{The middle angle=}3x \\ =3\times21^0 \\ =63^0 \end{gathered}[/tex]Hence,
The middle angle = 63 degrees
Explain in detail with at least two sentences how to represent the difference of z1 and z2 geometrically, given that z1= −7i and z2 = 4+3i. Then, give the difference z1 − z2 in rectangular form.
Answers
Given that z₁= −7i and z₂ = 4+3i, the difference z₁ − z₂ in rectangular form is; -4 - 10i
What is the Vector in rectangular form?Addition of complex numbers is basically the same thing as adding two-dimensional vectors that are located on the x-y Cartesian plane.
Now, it is pertinent to note that when doing vector addition, we denote the x-component with i^ and y-component with j^.
We should also not that when adding complex numbers, the x-component is the real part and y-component is the imaginary part.
Geometrically, we can say that the addition of complex numbers can be equated to the addition of vectors in x-y plane.
Thus by the the parallelogram law of vector addition, we will be able to find the resultant vector.
In rectangular coordinates,
z₁ = -7i
z₂ = 4 + 3i
Then, z₁ - z₂ = -7i - (4 + 3i)
= -7i - 4 - 3i
= -4 - 10i
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Rabbit populations can double every 30
days. If there are 10 rabbits on a farm,
how many rabbits will be on the farm
after 120 days?
Future Amount = [?] rabbits
Hint: Future Amount =
←
+ r)t
(1 + r)t time
(1
periods
initial
growth
amount rate
Round to the nearest whole number.
Answers
Answer:
80
Step-by-step explanation:
→ Work out how many rabbits after 60 days
20 rabbits
→ Work out how many rabbits after 90 days
40 rabbits
→ Work out how many rabbits after 120 days
80 rabbits
What is the difference between a relation and a function? Classify each of the following as a function or not a function. State the domain and range. {(0,0),(2,22),(3,33)}
Answers
The relation given can be classified as a function as every single input corresponds to a single output value.
What is the difference between a relation and function?The difference between a relation and a function lies in the fact that a relation can have many outputs for a single input, but a function has a single input for a single output. The statement above is the distinctive property between a relation and a function.
The relation given in the task content is a function as every single input has a single output as evident in the function.
Hence, the domain of the function is; {x | x : 0, 2, 3} while the range is; {y | y : 0, 22, 33}.
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156.24 is 36% of what
Answers
Answer:
434
Step-by-step explanation:
Steps:
156.24 ÷ 36% = 156.24 ÷ 0.36 = 434
(20pts, 5pts each) The median of AMND from vertex N of the
isosceles trapezoid MNFD is 5cm. The diagonal ND is
perpendicular to the leg MN. The shorter base NF = 6cm and the
32cm².
A
MNFD
=
Find: MD, the altitude of the trapezoid h, the length of the
legs of the trapezoid and the ratio between the areas of AMND and
ANFD.
Answers
Answer:
MD = 10 cmh = 4 cmMN = FD = 2√5 cm ≈ 4.47 cmarea ratio = 5 : 3Step-by-step explanation:
Given isosceles trapezoid MNFD with short base NF = 6 cm, diagonal ND perpendicular to leg MN, and triangle MND median NX = 5 cm, you want ...
length MDaltitude h of the trapezoidlengths of MN and FDratio of areas of ∆MND and ∆NFDMDMD is the hypotenuse of right triangle MND. The median from the right angle of a right triangle is half the length of the hypotenuse, so ...
MD = 2·NX = 2·(5 cm)
MD = 10 cm
AltitudeIn the attached diagram, we see that right triangle XYN has side XY = 3 (half of NF), and hypotenuse NX = 5 (given). These are two sides of a 3-4-5 right triangle, so the remaining side, altitude h, is 4.
h = 4 cm
Side lengthsThe attache diagram shows congruent side lengths MN and FD are the hypotenuse of a right triangle with sides YM = 2 and YN = 4. The Pythagorean theorem tells us the length of side MN is ...
MN² = MY² +NY²
MN² = 2² +4² = 4 +16 = 20
MN = √20
MN = FD = 2√5 ≈ 4.47
Area ratioTriangle MND has a base length MD = 10 and a height h = 4. Triangle NFD has a base length NF = 6 and a height h = 4. The ratio of the areas of these two triangles is ...
[tex]\dfrac{A_{MND}}{A_{NFD}}=\dfrac{\frac{1}{2}\cdot10\cdot4}{\frac{1}{2}\cdot6\cdot4}=\dfrac{10}{6}=\boxed{\dfrac{5}{3}}[/tex]
The ratio between the areas is 5 : 3.
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Additional comment
We are also given the area of the trapezoid as 32 cm². That can be used to find the longer base and/or the altitude, or to check the answers we have for those values. It is redundant information.
The midpoint X of MD is the center of the circumscribing circle of the trapezoid and right triangles MND and MFD. The midpoint of the hypotenuse of a right triangle is always the circumcenter, so knowing the length NX tells us the radius of that circle, hence MX and XD.