A) r(t) =[tex]c_{1}[/tex]×e^(∧×t)[tex]v_{1}[/tex]+ [tex]c_{2}[/tex] × e^(∧²×t)[tex]v_2[/tex] ; B) r(t) = X×e^(∧×t)c ; C) [tex]r_1[/tex](t) = [tex]c_{1}[/tex](-1×[tex]e^{3t}[/tex])×cos(t) -1×[tex]e^{3t}[/tex]×sin(t) -4×[tex]e^{3t}[/tex], [tex]r_2[/tex](t) = [tex]c_2[/tex](-1×[tex]e^{3t}[/tex]×cos(t) -1×[tex]e^{3t}[/tex]×sin(t) + 4i×[tex]e^{3t}[/tex].
A) The solution to the linear equation in eigenvalue/eigenvector form:
r(t) = [tex]c_{1}[/tex]×e^(∧×t)[tex]v_{1}[/tex]+ [tex]c_{2}[/tex] × e^(∧²×t)[tex]v_2[/tex]
B) The solution to the linear equation in fundamental matrix form:
r(t) = X×e^(∧×t)c
C) As two equations: The solution to the linear system can also be written as two equations as follows:
[tex]r_1[/tex](t) = [tex]c_1[/tex] ×e^(∧²×t)[tex]v_1[/tex] = [tex]c_{1}[/tex](-1×[tex]e^{3t}[/tex])×cos(t) -1×[tex]e^{3t}[/tex]×sin(t) -4×[tex]e^{3t}[/tex]
[tex]r_2[/tex](t) = [tex]c_2[/tex]×e^(∧² ×t)[tex]v_2[/tex] = [tex]c_2[/tex](-1×[tex]e^{3t}[/tex]×cos(t) -1×[tex]e^{3t}[/tex]×sin(t) + 4i×[tex]e^{3t}[/tex]
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do the following: a) find the real and imaginary parts, and sketch each with a stem plot. b) find the magnitude and phase, and sketch each with a stem plot. g
a) To find the real and imaginary parts of a complex number, we can use the equation z = x + iy, where x is the real part and y is the imaginary part.
To sketch a stem plot, we need to plot the real part on the x-axis, and the imaginary part on the y-axis. For example, for the complex number z = 4 + 3i, the real part is x = 4 and the imaginary part is y = 3. Therefore, the stem plot would be (4, 3).
b) To find the magnitude and phase of a complex number, we can use the equation z = |z|e^(iθ), where |z| is the magnitude and θ is the phase. To sketch a stem plot, we need to plot the magnitude on the x-axis, and the phase on the y-axis. For example, for the complex number z = 4 + 3i, the magnitude is |z| = 5 and the phase is θ = arctan(3/4). Therefore, the stem plot would be (5, arctan(3/4)).
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which of the following is the solution to the compound inequality? 3x+5> or -2x-7>5
The solution of the compound inequality 3x + 5 > -1 or -2x-7 > 5 is x > -2 or x < -6.
How to solve compound inequality?Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.
A compound inequality is an inequality that combines two simple inequalities.
Therefore,
3x + 5 > -1 or -2x-7 > 5
Let's solve the inequality individually
3x + 5 > -1
3x > -1 - 5
3x > -6
x > -6 / 3
x > -2
Therefore,
-2x - 7 > 5
-2x > 5 + 7
-2x > 12
x > 12 / -2
x < -6
Hence,
x > -2 or x < -6
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5. how much are you willing to pay to play the following game? you start with $1. you flip a fair coin. if it lands on heads, you double your winnings and flip again. if it lands on tails, the game is over and you collect the money you've won. you continue playing until you land on tails. (asked by point72)
I'm willing to pay up to $1 to play the game. If I get lucky and the coin lands on heads multiple times, I could potentially win more than $1.
The game is quite simple. I start with $1 and then flip a fair coin. If I get heads, I double my winnings and flip the coin again. I will keep flipping the coin until I get tails, at which point the game is over and I collect the money I have won. Depending on how lucky I get, I could potentially win more than $1. Therefore, I am willing to pay up to $1 to play the game. The expected value of this game is $1.50. This is because, on average, I will get heads 50% of the time and tails 50% of the time. So, if I get heads every time, I will double my winnings each time and end up with $2. If I get tails every time, I will end up with $1. Therefore, the expected value is the average of these two outcomes, which is $1.50. There is also some risk involved in this game. If I get unlucky and get tails on my first flip, then I will only get my money back and not make any profit. Therefore, I have to be willing to take on some risk if I want to try and make a profit. It is important to note that this game does not guarantee a profit. The expected value may be $1.50, but I could end up making less or more than that depending on how lucky I get. Therefore, I have to be willing to accept some uncertainty if I want to play this game.
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what property states that if two sides are congruent, then the angles opposite to them are congruent as well?
The converse of the Pythagorean Theorem states that if two sides of a triangle are congruent, then the angles opposite to them are also congruent. This property is known as the Corresponding Angles Postulate.
The Pythagorean Theorem states that the sum of the squares of the lengths of the two sides of a right triangle are equal to the square of the length of the hypotenuse. The theorem is written as a^2 + b^2 = c^2. The converse of the Pythagorean Theorem states that if two sides of a triangle are congruent, then the angles opposite to them are also congruent. This property is known as the Corresponding Angles Postulate. To prove this postulate, we can start with an arbitrary triangle ABC. If we extend the side AC to D, then we can create a line parallel to BC, creating two similar triangles, ABC and ADC. Since similar triangles have corresponding angles that are congruent, then angle A = angle D. Since side AC is congruent to side AD, then angle A is also congruent to angle B. This proves the Corresponding Angles Postulate.
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aisha, benoit, and carleen are each thinking of a positive integer. aisha's number and benoit's number have a common divisor greater than 1. aisha's number and carleen's number also have a common divisor greater than 1. benoit's number and carleen's number also have a common divisor greater than 1. is it necessarily true that the greatest common divisor of all three numbers is greater than 1? if it is necessarily true, explain how you know it's true. if it isn't necessarily true, convince us by showing us three numbers for which it's false -- in other words, show us three integers such that every pair have a common divisor greater than 1, but all three numbers don't have a common divisor greater than 1. hint(s):
No, it is not true that GCD(A, B, C).
What is the greatest common divisor?
The greatest common factor (GCF) that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor is another name for it (HCF). For instance, since both 15 and 10 can be divided by 5, 5 is the biggest common factor between both.
Here, we have
Given: Aisha's number and Benoit's number have a common divisor greater than 1. Aisha's number and Carleen's number also have a common divisor greater than 1. Benoit's number and Carleen's number also have a common divisor greater than 1.
We have to determine if is it necessarily true that the greatest common divisor of all three numbers is greater than 1.
Here, we solve this with an example.
A = 6 = 2*3,
B = 14 = 2*7,
C = 21 = 3*7
There is no GCD greater than 1 that divides all of A, B and C.
Hence, No, it is not true that GCD(A, B, C).
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43.How's the economy? A poll conducted by the American Research Group asked individuals their views on how the economy will be a year from now. Respondents were given four choices: Better than today, Same as today, Worse than today, and Undecided. Are these choices nominal or ordinal?
It is nominal because they all mean the same thing
angle bisector altitude median centroid orthocenter circumcenter incenter find missing values worksheet
Two straightforward equations are all that are left for us to solve. Therefore, the x and y values determine the coordinates of the orthocenter.
What is angle?When two rays or straight lines intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points meet. The Latin word "angulus," which means "corner," is where the term "angle" first appeared.
Its coordinates are determined using the orthocenter formula. Let's take a look at the triangle ABC in the illustration above. AD, BE, and CF are the perpendiculars that are drawn from the vertices A(x1,y1), B(x2,y2), and C(x3,y3), respectively. The three elevations come together at point O.
The slope of the triangle's sides must first be determined using the following formula:
m = y2 - y1/x2 - x1
The slope of the triangle ABC's altitudes will now be the line's perpendicular slope.
Line slope perpendicular to the plane is -1/m
Let mAC be the slope of the AC. Hence,
mAC = y3 - y1/x3 - x1
Similarly, mBC = (y3 - y2)/(x3 - x2)
Now, the corresponding altitudes' slopes are as follows:
BE slope: mBE = -1/mAC
AD slope: mAD = -1/mBC
Now, in order to determine the equations of the lines that coincide with BE and AD, we will use the slope point form equation of a straight line.
Hence,
mBE = (y - y2)/(x - x2)
mAD = (y - y1)/(x - x1)
As a result, we are left with two equations that are simple to answer. The orthocenter's coordinates are thus determined by the values of x and y.
The complete question is :
The orthocenter of a triangle is the point where the perpendicular drawn from the vertices to the opposite sides of the triangle intersect each other.
For an acute angle triangle, the orthocenter lies inside the triangle.For the obtuse angle triangle, the orthocenter lies outside the triangle.For a right triangle, the orthocenter lies on the vertex of the right angle.Take an example of a triangle ABC.
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If 25% of a number is 60 and 90% of the same number is 216, find 65% of that number.
65 percent of the number 240 is 156, as 25% and 90% of 240 will give 60 and 216 respectively.
How to calculate for the percentageWe shall represent the number with the letter x so that we evaluate for the 25 and 90 percent respectively as follows:
25 percent of x;
25x/100 = 60
x = (60 × 100)/25 {make x the subject}
x = 240
90 percent of x;
90x/100 = 216
x = (216 × 100)/90 {make x the subject}
x = 240
Therefore, 65 percent of the number 240 is derived as:
(65 × 240)/100
15600/100
156.
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Not all visitors to a certain company's website are customers,. In fact, the website administrator estimates that about 12% of all visitors to the website are looking for other websites. Assuming that this estimate is correct, find the probability that, in a random sample of 5 visitors to the website, exactly 2 actually are looking for the website
This question involves the binomial probability distribution. The probability of exactly 2 successful outcomes (in this case, visitors who are looking for the website) in 5 trials (visitors to the website) can be calculated using the formula:
P(X = 2) = (5C2)(0.12)^2(0.88)^3
Where C represents the binomial coefficient and 0.12 and 0.88 represent the probability of a successful outcome (looking for the website) and unsuccessful outcome (not looking for the website), respectively.
Calculating this gives:
P(X = 2) = (5C2)(0.12)^2(0.88)^3 = 100.01440.4712 = 0.066
So the probability that, in a random sample of 5 visitors to the website, exactly 2 are looking for the website is 0.066 or about 6.6%.
Which of the following correlation coefficients indicates the strongest relationship between two variables?
a. -.90 b. -.50 c. +.80 d. +.25
c. +.80 is correct.
lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
Solve for the indicated variable.
H = kx - kx0 for x
Answer:
5.0 if you love life
Step-by-step explanation:
for a nrw musical adult tickets cost 5 dollars and students cost three 56 tickets were sold for a total of 232
Answer: We can set up a system of equations to represent the given information:
Let x be the number of adult tickets sold
Let y be the number of student tickets sold
x + y = 56 (the total number of tickets sold is 56)
5x + 3y = 232 (the total amount of money made is 232 dollars)
To find the number of adult and student tickets sold, we can use the first equation to solve for one of the variables in terms of the other, and then substitute that into the second equation.
x + y = 56
x = 56 - y
Now we can substitute this value of x into the second equation:
5(56 - y) + 3y = 232
280 - 5y + 3y = 232
280 = 8y
y = 35
So, 35 student tickets were sold, and 56 - 35 = 21 adult tickets were sold.
Step-by-step explanation:
the accompanying sketch represents a maze of oneway streets in a city in the united states. the traffic volume through certain blocks during an hour has been measured. suppose that the vehicles leaving the area during this hour were exactly the same as those entering it.
Based on the sketch, it appears that the traffic flow in the city would remain the same during the hour. All of the vehicles entering the area would leave it, meaning that the same number of vehicles would remain in the area for the entire hour.
1. The sketch shows a maze of one-way streets in a city in the United States.
2. The traffic volume through certain blocks during an hour has been measured.
3. Suppose that the vehicles leaving the area during this hour were exactly the same as those entering it.
4. This means that the same number of vehicles would remain in the area for the entire hour, as the vehicles entering the area would be the same as those leaving it.
Based on the sketch, it appears that the traffic flow in the city would remain the same during the hour. All of the vehicles entering the area would leave it, meaning that the same number of vehicles would remain in the area for the entire hour.
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Which of the following conditions or set of conditions must be met for a parallelogram to be a rectangle?
A. Diagonals are perpendicular.
B. Diagonals are congruent.
C. All sides are congruent.
D. The length of a diagonal is equal to the length of a side.
A parallelogram can only be a rectangle if the following conditions are satisfied: B) The diagonals must be congruent, and A) the diagonals must be congruent and perpendicular.
What is meant by parallelogram?A unique kind of quadrilateral known as a parallelogram is defined by having both pairs of its opposite sides parallel and equal. The opposing sides of a parallelogram are all parallel and of equal length. a quadrilateral parallelogram. Rhombus: An equal-length parallelogram with four sides. A parallelogram is a square. Always. This is accurate. A square is a quadrilateral with two sets of parallel sides, four right angles, and four congruent sides.Since not all parallelograms have equal sides, not every parallelogram is a rhombus. The opposite is true, though, when every rhombus is a parallelogram.Every rectangle is a parallelogram, but not every parallelogram is a rectangle, is the correct statement.Therefore,
One feature of a parallelogram is that its diagonals are divided in half. A rectangle also has congruent diagonals.
In addition to being congruent, the diagonals in a square are perpendicular to one another.
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arundel company disclosed the following information for its recent calendar year. income statement data selected year-end balance sheet data revenues $ 100,000 accounts receivable decrease $ 24,000 expenses: purchased a machine for cash 10,000 salaries expense 84,000 salaries payable increase 18,000 utilities expense 14,000 interest payable decrease 8,000 depreciation expense 14,600 interest expense 3,400 net loss $ (16,000) prepare the operating activities section of the statement of cash flows using the indirect method. (amounts to be deducted should be indicated with a minus sign.)
The operating activities section of the statement of cash flows for the company using the indirect method showed a net cash used by operating activities of $(4,400).
Net Loss $(16,000)
Adjustments to Reconcile Net Loss to Net Cash Used by Operating Activities:
Depreciation Expense 14,600
Decrease in Accounts Receivable 24,000
Increase in Salaries Payable (18,000)
Decrease in Interest Payable (8,000)
Net Cash Used by Operating Activities $(4,400)
The operating activities section of the statement of cash flows for the company using the indirect method showed a net cash used by operating activities of $(4,400). This was calculated by adjusting the net loss of $(16,000) with depreciation expense, decrease in accounts receivable, increase in salaries payable, and decrease in interest payable.
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After giving a test to a group of students, below is the summary of grades by gender. A B C Total Male 16 17 11 44 Female 14 6 3 23 Total 30 23 14 67 If a student is randomly chosen, find the probability that the student is female or earned grade C. Leave your answer as a reduced fraction.
The probability that the student is female or earned grade C is 0.6
How to find the probability?You should recall that probability is the chance of occurrence of an event E
P(E) = (Number of required outcome)/(number of possible outcomes)
The given parameters are
We'll use this table (below) to answer the questions
A B C Total
Male 16 17 11 44
Female 14 6 3 23
Total 30 23 14 67
Total number of female = 23Total number in grace C = 14Total number of students = 67Pr(E) = 23/67 + 14/67
Simplifying the fractions to have
37/67 = 0.55
Therefore this is approximately rounded to 1 decimal place as 0.6
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1. Jeremy's father is paying for a $30 meal. He has a 20% off coupon for the meal. How much money will the coupon save Jeremy's dad?
2. Jeremy's father is paying for a $30 meal. He has a 20% off coupon for the meal. After the discount, a 6% sales tax is applied. How much will Jeremy's father pay in sales tax?
3. Jeremy's father is paying for a $30 meal. He has a 20% off coupon for the meal. How much in total did Jeremy's father pay for the meal (including tax)?
1. The coupon will save: $6.
2. The sales tax is of: $1.44.
3. The total price paid for the meal is of: $25.44.
How to obtain the total cost?The total cost is obtained applying the proportions in the context of this problem.
The initial fee for the meal is of:
$30.
With the coupon of 20% off, the amount paid is of:
0.8 x 30 = $24.
Meaning that the amount saved is of:
30 - 24 = $6.
After the sales tax, the total price is of:
1.06 x 24 = $25.44.
Meaning that the tax is of $1.44.
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Regina bought a handmade quilt at original cost $120 to sale in her quilt store. She marked the price of 55%. What is the amount of markup
A grandmother is now 48 years older than her grandson. 14 years ago she was thirteen times as old as her grandson. How old is the grandmother? How old is the grandson?
Let's call the grandmother's current age G and the grandson's current age S.
From the first piece of information given, we know that:
G = S + 48
From the second piece of information given, we know that:
G - 14 = 13S
We can use the first equation to substitute for G in the second equation:
(S + 48) - 14 = 13S
S + 34 = 13S
34 = 12S
S = 34/12
S = 2.8 years
So the grandson is 2.8 years old.
Now we can use this information to find the grandmother's age:
G = S + 48
G = 2.8 + 48
G = 50.8 years
So, the grandmother is 50.8 years old and the grandson is 2.8 years old.
Select all the correct locations on the image. Identify which functions have complex roots by selecting the function names on the provided coordinate plane.
Out of the given functions, a ,b, c, d , the function with complex roots are b and d.
What are complex roots?
Complex roots, also known as non-real roots, are roots of an equation that are not real numbers but instead are complex numbers. Complex roots are usually represented in the form of a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.
The functions which have complex roots are b and d.
hence, out of the given functions, a ,b, c, d , the function with complex roots are b and d.
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Select the correct answer.
Rita is reviewing her electricity bills for the past year. The monthly bills were:
$92, $98, $90, $99, $96, $91, $89, $106, $95, $102, $96, $99.
Which measure should Rita use to find the average monthly bill for the year?
A.
range
B.
interquartile range
C.
median
D.
mean
I'm pretty sure the answer is D.mean absolute deviation.
I hope it'll help you.
Solve for the indicated value, and graph the situation showing the solution point. The formula for measuring sound intensity in decibels D is defined by the equation D=10log(II0) using the common (base 10) logarithm where I is the intensity of the sound in watts per square meter and I0=10−12
is the lowest level of sound that the average person can hear. How many decibels are emitted from a jet plane with a sound intensity of 8.1⋅102
watts per square meter?
Round your answer to three decimal places.
The jet plane emits ___ decibels at 8.1⋅102 watts per square meter.
149.0848502 decibels are emitted from a jet plane with a sound intensity of 8.1*10²
How to find the number of decibels?Decibels are units for expressing the ratio between two physical quantities, usually amounts of acoustic or electric power, or for measuring the relative loudness of sounds.
Number of watts per square meter
d = 10*log(I/IO)
IO = 10⁻¹²
Therefore: d = 10 * log(I/10⁻¹²
jet plane has a sound intensity of 8.1*10² watts per square meter.
Therefore: d = 10*log((8.1*10²) / 10⁻¹²)
10²/10⁻¹² = 10²⁽⁻¹²⁾ = 10⁽²⁺¹²⁾ = 10¹⁴
Therefore: d = 10 * log(8.1 * 10¹⁴)
log(8.1 * 10¹⁴) = 14.90848502
10 * that = 149.0848502 decibels
That's the value of d.
In conclusion, 149.0848502 decibels are emitted from a jet plane with a sound intensity
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One numbe is 5 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 513 . Find the numbers
Answer:
x = 56
First number = 56
Second number = 280
Third number = 156
Total 331
Step-by-step explanation:
Last year, The Lakewood Times had a total of 4,770 subscribers. This year, after the paper
was bought out, it had 6,201 subscribers. What is the percent of increase in the number of
subscribers?
%
The Lakewood Times had a 30.4% increase in the number of subscribers after it was bought out.
What is the percentage increase?
Percent increase is a way of measuring how much something has increased relative to its original value. It is expressed as a percentage, and it is calculated by taking the difference between the new value and the original value, and then dividing that difference by the original value, and then multiplying by 100.
Formula: % increase = (new value - original value) / original value x 100
To find the percent increase, you can use the formula:
% increase = (new value - old value) / old value x 100
In this case, the percent increase would be:
% increase = (6201 - 4770) / 4770 x 100 = 30.4%
Hence, The Lakewood Times had a 30.4% increase in the number of subscribers after it was bought out.
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I WILL GIVE BRAINLIEST!!!!
To make 4 cups of punch, David needs 3 cups of cranberry juice. David wants to make 72 cups of punch.
How many cups of cranberry juice will he need?
Work Shown:
4/3 = 72/x
4x = 3*72
4x = 216
x = 216/4
x = 54
Explanation:
Each fraction in the first step is of the form A/B, where A is the amount of punch and B is the amount of cranberry juice. Both measured in cups. In the 2nd step, I cross multiplied. Afterward, divide both sides by 4 to isolate x.
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 3, 5, 7, 9}, B = {2, 4, 6, 8, 10}, and C = {1, 2, 3, 4, 7, 8}. List the elements of each set. (Enter your answers using roster notation. Enter EMPTY or ∅ for the empty set.) (a) AC $$ Incorrect: Your answer is incorrect. (b) B ∪ C (c) C ∪ CC
The elements of each set are given as follows:
a) A and C: {1, 3, 7}.
b) B U C = {1, 2, 3, 4, 6, 7, 8, 10}
c) C U C' = U.
How to realize the operations with sets?The intersection operation between two sets is composed by the elements that belong to both sets, hence:
A and C: {1, 3, 7}.
(as the elements 1, 3 and 7 belong to both of the sets).
The union operation between two sets is composed by the elements that belong to at least one of the sets, hence:
B U C = {1, 2, 3, 4, 6, 7, 8, 10}
The union between a set and it's complement is always the universal set, hence:
C U C' = U.
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in a survey collecting data about the salaries earned by recent college graduates, li found that her salary was in the 78th percentile. that means that 78% of recent college graduates earn less than or equal to what li does. [1 point]
Li earns more than 78percentage of recent college graduates, and is in the 78th percentile of salaries earned.
1. Calculate the total number of recent college graduates surveyed: Multiply the total number of responses to the survey by 100 to get the total number of graduates surveyed.
2. Calculate the number of recent college graduates who earn less than or equal to Li's salary: Multiply the percentile (78%) by the total number of graduates surveyed to get the number of graduates who earn less than or equal to Li's salary.
3. Calculate the percentage of recent college graduates who earn less than or equal to Li's salary: Divide the number of graduates who earn less than or equal to Li's salary by the total number of graduates surveyed to get the percentage of graduates who earn less than or equal to Li's salary. The result will be 78%.
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what is the unit rate of 6/11 1/6
Answer:
Step-by-step explanation:
Answer:
36/11 or 3.2727
Step-by-step explanation:
A unit rate is a rate with 1 in the denominator.
Since you didn't specify, I assume 6/11 per 1/6 rate.
Divide 6/11 by 1/6
[tex]\frac{6}{11} /\frac{1}{6}[/tex]
Multiply the reciprocal:
[tex]\frac{6}{11} *\frac{6}{1}=\frac{36}{11}[/tex]
Which graph represents a proportional relationship? Explain
Graph A.
Proportional relationships have to go through the origin, (0,0).
given a pair of similar triangles find the missing length x and the missing angles a,b,c
Angles of similar triangles are always congruent a: 63, b: 88, c: 29 and x = 53.75
Find the missing length?Based on the information available, there are numerous equations for calculating the area of a triangle. As indicated in the calculator above, please use the Triangle formula for additional information and equations for calculating the area of a triangle as well as determining the sides of a triangle using whatever information is available.
find the ratio between the two triangles:
40 on the left corresponds to 50 on the right = 40/50 = 43/x
to find x:
40x = 43 × 50
40x = 215
x = 215/40
x = 53.75
"angles of similar triangles are always congruent."
a: 63
b: 88
c: 29
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Full question:
Given a pair of similar triangles, find the missing length x and the missing angles A, B, and C.
