Answer:
True
Step-by-step explanation:
I did it
60%of the fans at a hockey game were wearing red if there were 6040 how many were wearing red? On a double line
We can claim that after answering the above question, the Therefore, equation there were 3624 fans wearing red at the hockey game.
What is equation?In mathematics, an equation is a statement that states the equality of two expressions. An equation is made up of two sides separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" contends that the sentence "2x + 3" equals the value "9". The purpose of equation solving is to identify the value or values of the variable(s) that will make the equation true. Simple or complex equations, regular or nonlinear, with one or more factors are all possible. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are utilized in many areas of mathematics, including algebra, calculus, and geometry.
Let's start by setting up a proportion:
[tex]60/100 = x/6040\\100x = 60 * 6040\\x = (60 * 6040) / 100\\x = 3624[/tex]
Therefore, there were 3624 fans wearing red at the hockey game.
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Write the equation in standard form for the circle that has a diameter with endpoints (-4, 9) and (-4, 3)
The equation in standard form for the circle is (x + 4)² + (y - 6)² = 9.
The midpoint of the diameter is the center of the circle. Therefore, we can first find the midpoint:
Midpoint = [(x1 + x2)/2, (y1 + y2)/2] = [(-4 + (-4))/2, (9 + 3)/2] = [-4, 6]
The distance from the center to either endpoint of the diameter is the radius of the circle. In this case, the distance is:
r = |9 - 6| = 3
So we have the center (-4, 6) and the radius 3. Using the standard form equation of a circle, we can write:
(x - (-4))² + (y - 6)² = 3²
Simplifying and expanding, we get:
(x + 4)² + (y - 6)² = 9
Therefore, the equation in standard form for the circle is (x + 4)² + (y - 6)² = 9.
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Leveled Practice In 7-12, find the area of each trapezoid or kite.
7.
6 cms
21 cm
A=
8 cm
Trapezoid:
9 cm
+
+
Each triangle:
A = 2bh
D D
11
11
12
cm2
X
]
cm²
x8
Rectangle:
A = tw
=
x8
cm²
Mul
Thus, the area of the given shape of trapezoid is obtained as: 120 sq. ft.
What is meant by shape of trapezoid?Rectangle, rhombus, and square are the names given to parallelograms with particular characteristics like right angles as well as all congruent sides (or both).
The second set of parallel sides, that transforms a specific trapezium into a parallelogram, is the only unique characteristic of a trapezium that is given its own distinguishing name. Similar to how triangles with two equivalent sides (other than the base) are referred to as isosceles triangles, the term "isosceles trapezium" is used to describe a trapezium when two sides (as well as their bases) are the same length.Area of trapezoid = 1/2 * (sum of parallel sides) * height
Area of trapezoid = 1/2 * (21 + 9) *8
Area of trapezoid = 120 sq. ft.
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54 is what percent of 90? Question 9 options: 60% 65% 55% 52%
Answer:
The answer to your problem is, A. 60%
Step-by-step explanation:
54 of 90 can be written as: [tex]\frac{54}{90}[/tex]
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
[tex]\frac{54}{90} * \frac{100}{100}[/tex]
= [tex]\frac{( 54 * 100)}{90} * \frac{1}{100} = \frac{60}{100}[/tex]
Thus the answer to your problem is, A. 60%
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Answer:
x = 60%
Step-by-step explanation:
Let the unknown percentage be x.
We can make an expression using the given information.
[tex]\sf90*\frac{x}{100} =54[/tex]
Solve for x to find the percentage.
[tex]\sf\frac{90x}{100} =54\\90x=54*100\\\\90x=5400\\\\\frac{90x}{90}=\frac{5400}{90}\\\\ x=60[/tex]
determine the percentage of children who experience relief for less than four hours if the relief time follows a lognormal distribution.
Around 0.13% or 0.0013 of children find relief for less than four hours.
The percentage of children who experience relief for less than four hours if the relief time follows a lognormal distribution is determined as follows:
Step 1: Define the parameters of the problem. Assume that relief times are normally distributed with a mean of μ = 5.5 hours and a standard deviation of σ = 0.5 hours. We want to find the percentage of children who experience relief for less than four hours.
Step 2: Convert the normal distribution to the standard normal distribution using the formula: z = (x - μ) / σwhere x is the relief time in hours.
Step 3: Find the z-score corresponding to the value of x = 4:z = (4 - 5.5) / 0.5 = -3
Step 4: Use a standard normal distribution table to find the percentage of the area under the curve to the left of z = -3. This is equivalent to the percentage of children who experience relief for less than four hours.
Using the standard normal distribution table or calculator, we get that the percentage of children who experience relief for less than four hours is approximately 0.13% or 0.0013.
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The list below represents the number of novels written
by each of Amir's 10 favorite authors.
1 3 3 4 5 7 8 10 12 23
What is the interquartile range of the number of novels
written by each of Amir's 10 favorite authors?
The interquartile range of the number of novels
written by each of Amir's 10 favorite authors would be = 7
How to calculate the interquartile range of the novels?The total number of the novels written by the 10 favorite authors of Amir = 1 +3 +3 +4+ 5 +7+ 8+ 10+ 12+ 23 = 76
The interquartile range of the number of novels = Q3-Q1
Where Q3 = median of second half = 10
Q1 = median of the first half = 3
The interquartile range of the number of novels = 10-3 = 7
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16. Movie tickets for an adult and three children cost $29. An adult's
ticket is $3 more than a child's ticket. Find the cost of an adult's ticket.
rent-a-reck incorporated finds that it can rent cars if it charges for a weekend. it estimates that for each price increase it will rent three fewer cars. what price should it charge to maximize its revenue? how many cars will it rent at this price?
Rent-A-Reck Incorporated should charge $95 to maximize its revenue and the company will rent 45 cars at a price of $95.
To determine the price that will maximize Rent-A-Reck Incorporated's revenue, we need to consider the relationship between the price of renting a car and the number of cars that are rented.
Based on the information provided, we know that the demand for rental cars decreases as the price increases. Specifically, for each $5 increase in price, two fewer cars will be rented.
Let's denote the price of renting a car as P and the number of cars rented as Q. Then we can express the relationship between price and quantity as:
Q = 60 - 2(P - 80)/5
This equation tells us that as the price P increases, the number of cars rented Q decreases. We can also use this equation to find the price that will maximize revenue. Revenue is calculated by multiplying the price by the number of cars rented, so we can write the revenue function as:
R = P(Q) * Q
= P * (60 - 2(P - 80)/5)
To find the price that maximizes revenue, we need to find the value of P that makes R as large as possible. One way to do this is to take the derivative of R with respect to P and set it equal to zero:
dR/dP = (60 - 2(P - 80)/5) - 2P/5 = 0
Solving for P, we get:
P = $95
To find the number of cars that will be rented at this price, we can substitute P = $95 into the demand equation:
Q = 60 - 2($95 - $80)/5
= 45
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Complete question is:
Rent-A-Reck Incorporated finds that it can rent 60 cars if it charges $80 for a weekend. It estimates that for each $5 price increase it will rent two fewer cars. What price should it charge to maximize its revenue? How many cars will it rent at this price?
Could someone help me? Please.
The solution of the system of equations is (2, 1).
How to solve the system of equations graphically?Here we have the system of equations:
y = 2x - 3
y = -x + 3
To solve the system of equations graphically, we need to graph both of these lines in the same coordinate axis and then find the point where the lines intersect.
That point will be the solution of the system.
On the image at the end you can see the graph of the system of equations, there we can see that the solution is (2, 1).
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SOMEONE HELP I WILL GIVE U BRAINLEST PLS 1-10
Answer:
7/4
Step-by-step explanation:
if you divide 7/4, you will get 1.75 which is greater than 1.43.
Answer:
Hi, your answer is 7/4
Step-by-step explanation:
Hope this helps :D
Brainly what is the volume of a cylinder with a base radius 3 and height 6
Answer:
about 169.65
Step-by-step explanation:
The formula for the volume of a cylinder is [tex]\pi r^2h[/tex].
All you have to do is plug the numbers in.
[tex]V=\pi (3)^2(6)[/tex]
Then use a calculator to evaluate.
The volume of the cylinder is approximately 169.56 cubic units.
The formula for the volume of a cylinder is:
V = πr^2h
where V is the volume, r is the radius of the base, and h is the height.
Substituting the given values, we get:
V = π(3)^2(6)
V = π(9)(6)
V = 54π
Therefore, the volume of the cylinder is 54π cubic units. If you need an approximate numerical value, you can use the approximation 3.14 for π and calculate:
V ≈ 54 x 3.14
V ≈ 169.56
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The correct question is :
What is the volume of a cylinder with a base radius of 3 units and height of 6 units?
Why isn't x^4+4x-21 factorable?
Answer:
The polynomial expression x^4 + 4x - 21 cannot be factored into linear factors with rational coefficients. This can be shown using the rational root theorem, which states that any rational roots (zeros) of the polynomial must be of the form p/q, where p is a factor of the constant term (in this case, 21) and q is a factor of the leading coefficient (1). The only possible rational roots of this polynomial are ±1, ±3, ±7, and ±21. However, plugging in each of these values does not give a zero of the polynomial, meaning it has no rational roots. Therefore, it cannot be factored into linear factors with rational coefficients. It may still be factorable using complex numbers, but it is not factorable using only real numbers.
Eight avocados cost $4. How much is 1 avocado?
The cost of one avacado is equal to 0.5$ and it is found by the use of division method.
One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. an a person who knows what I mean by just calling it what they do when they just want to go to the store. Just call it what they call it, whatever ites. Really, whatever it is, these are the same people. It is a mathematical operation used for equal distribution and equal grouping.
One of the fundamental mathematical operations is division, which involves breaking a larger number into smaller groups with the same number of items.
We are given the cost of 8 avacados= $4.
The cost of 1 avacado= 1/8 * 4 = 1/2 = 0.5.
Hence, the cost of one avacado is equal to $0.5.
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midpoint of 0 and 2/7
Answer: 0, 4.5
Step-by-step explanation:
The answer in decimal form is 0 and 4.5. :)
he tapes the edge with special tape.how much tape will each coaster required
Answer: 5% Of Tape
there is going to be 5% of tape for the coaster
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. A tank contains 15,000 L of brine with 22 kg of dissolved salt. Pure water enters the tank at a rate of 150 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. Exercise (a) How much salt is in the tank after t minutes? Click here to begin! Exercise (b) How much salt is in the tank after 10 minutes? Click here to begin! Need Help? Read It Talk to a Tutor
Answer:
a) 22e^-0.01t kilograms
b) about 19.906 kilograms
Step-by-step explanation:
You want an equation for the amount of salt in a 15 kL brine tank initially containing 22 kg of salt if 150 L/min of the contents is replaced by pure water.
(a) Remaining saltThe quantity of salt s(t) in kilograms can be described by the differential equation ...
s(0) = 22; s'(t) = -150/15000·s(t)
The solution can be found by separation of variables.
[tex]\displaystyle\dfrac{ds}{dt}=-0.01s\\\\\int{\dfrac{1}{s}}\,ds=-0.01\int{}\,dt\\\\\ln{s}=-0.01t+c_1\\\\s=c_2\cdot e^{-0.01t}\qquad\text{where $c_2$ is $s(0)=22$}\\\\\boxed{s(t)=22e^{-0.01t}}[/tex]
(b) s(10)The amount of salt remaining after 10 minutes is ...
s(10) = 22·e^(-0.01·10) = 22·e^-0.1
s(10) ≈ 19.906 . . . . kilograms
There is about 19.906 kg of salt in the tank after 10 minutes.
__
Additional comment
The initial rate of change of the amount of salt is -22/100 kg/min, so after 10 minutes, we expect an approximate reduction by 2.2 kg to 19.8 kg. Since the rate slows as salt is removed, the value 19.9 kg after 10 minutes is reasonable.
There are a couple of places where the integration constant can be put in the equation for the salt quantity. As a multiplier of the exponential function, its value is found in a straightforward way.
What is the measure of each interior angle of a regular 20-gon?
Answer:
162°
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 20 , then
sum = 180° × (20 - 2) = 180° × 18 = 3240°
The interior angles of a regular polygon are congruent
then each interior angle = 3240° ÷ 20 = 162°
a) use these data to estimate the mean wrist extension for people using this new mouse design using a 90% confidence interval. (round your answers to three decimal places.) , (b) what assumptions are required in order for it to be appropriate to generalize your estimate to the population of students at this university? yes, the assumption would have to be made that the 24 students in the study formed a random sample of people in the country. no, we can generalize the estimate to the population of students at this university. yes, the assumption that the 24 students in the study formed a random sample of students at all universities. yes, the assumption would have to be made that the 24 students in the study formed a random sample of students at this university. no, we cannot generalize the estimate to any population as we have less than 30 students. to the population of all university students? no, we cannot generalize the estimate to any population as we have less than 30 students. yes, the assumption would have to be made that the 24 students in the study formed a random sample of people in the country. yes, the assumption would have to be made that the 24 students in the study formed a random sample of students from this university. no, we can generalize the estimate to the population of all university students. yes, the assumption that the 24 students in the study formed a random sample of students at all universities. (c) based on your interval from part (a), do you think there is reason to believe that the mean wrist extension for people using the new mouse design is greater than 20 degrees? explain why or why not. no, the entire confidence interval is below 20, so the results of the study would be very likely if the population mean wrist extension were greater than 20. no, the confidence interval contains 20, so the results of the study would be very likely if the population mean wrist extension were greater than 20. yes, the confidence interval contains 20, so the results of the study would be very unlikely if the population mean wrist extension were as low as 20. yes, the entire confidence interval is above 20, so the results of the study would be very unlikely if the population mean wrist extension were as low as 20.
The random sample of [tex]24[/tex] students has a mean of [tex]1.9149[/tex], and the data suggests that the mean is [tex]20^{0}[/tex].
How to Use the Sample Mean Formula to Determine the Sample Mean?x = (xi) / n is the general solution for computing the sample mean. Thus, xi refers to all X sample values, xi represents the sampling distribution, and n is the total number of specimen terms inside the data collection.
What does sample in statistics mean?The statistic known as the sampling distribution is created by arithmetically averaging the values of the variables in a group. The sample mean is an estimate of the anticipated value if the sample is taken from probabilistic with a common expected value.
(a) Sample mean [tex]= (17 + 21 + 20 + 19 + 23 + 22 + 20 + 20 + 18 + 21 + 19 + 24 + 22 + 20 + 19 + 20 + 19 + 20 + 21 + 22 + 23 + 21 + 18 + 22)/24 = 20.5[/tex]Sample standard deviation [tex]= 1.9149[/tex]
Next, we can use a t-distribution with [tex]23[/tex] degrees of freedom
Confidence interval [tex]= (20.5 - 0.8277, 20.5 + 0.8277) = (19.6723, 21.3277)[/tex]
b) The assumption required in order to generalize the estimate to the population of students at this university is that the [tex]24[/tex] students in the study formed a random sample of students at this university.
(c) There is not enough evidence to suggest that the mean wrist extension for people using the new mouse design is greater than [tex]20^{0}[/tex].
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how many feet are in 300.0 inches? type in your numerical answer only, do not include units. do not use scientific notation.
There are 25 feet in 300.0 inches.
What is conversion?Conversion is a numerical quantity that enables you to convert one unit to another. There are various units for measurements such as length, weight, mass, and so on.
The conversion factor between inches and feet is important to understand when performing this type of calculation. As I mentioned earlier, there are 12 inches in one foot, which can be expressed as:
1 foot = 12 inches
This means that to convert a measurement in inches to feet, we need to divide the number of inches by 12.
300.0/12 = 25
Therefore, 300.0 inches is equivalent to 25 feet.
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The following graph represents a function.
-8-6-4
39
8
Domain: [Select]
6
P
P
-2-
-4
-6
-8
2019 StrongMind
What are the domain and range of the function?
The domain of the function is: Domain = {-8, -6, -4, -2, 1, 2} and range of the function is :- Range = {-8, -6, -4, -2, 0}.
Define function?A function is a rule that maps each element in one set, called the domain, to a unique element in another set, called the range.
It is a relation between two sets where each input in the domain corresponds to a unique output in the range.
Functions are often represented by equations, graphs, or tables, and they are used to model real-world phenomena and solve mathematical problems in various fields such as science, engineering, economics, and more.
The domain of the function is the set of all possible input values, which in this case are the x-coordinates of the given points on the graph. So, the domain is:
Domain = {-8, -6, -4, -2, 1, 2}
The range of the function is the set of all possible output values, which in this case are the y-coordinates of the given points on the graph. So, the range is:
Range = {-8, -6, -4, -2, 0}
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Which of the following shows an example of two irrational numbers being multiplied to get a rational number?
Responses
3×9
0×5√
2√ ×8√
2√×3√
Step-by-step explanation:
Which of the following shows an example of two irrational numbers being multiplied to get a rational number?
Responses
option c
Nicholas and three other members from the Culinary Team had 100 fliers to post
around the school. Last week, they posted 1/4 of them. This week, they posted 2/4
of the remaining fliers. How many fliers have they still not posted?
The number of fliers that Nicholas and three other Culinary Team members have not still posted is 37 fliers.
How is the number determined?The remaining number of fliers not yet posted is a function of mathematical operations.
Basically, mathematical operations involve addition, subtraction, division, and multiplication.
The total number of fliers, Nicholas and three other Culinary Team members are posting around the school = 100
The fraction posted last week = 1/4
= 25 fliers (100 x 1/4)
The remaining fliers after posting 25 fliers = 75 (100 - 25)
The fraction posted this week = 2/4 = 1/2
1/2 of 75 = 37.5 or 38 fliers
The remaining fliers they still have not posted = 37 (75 - 38)
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factor x^2=14x-18=-8x-2
Answer:
=(x+9)(x+5)
Step-by-step explanation:
sam wants to build a toy box in the shape of a rectangular prism that will hold 36 cubic feet. if the height needs to be 1 foot less than the width and the length is twice the width, find the height of the toy box.
The Height of the toy box is 7 feet.
The height of the toy box in the shape of a rectangular prism is calculated using the following formula:
Volume = Length * Width * Height.
In this case, Volume = 36 cubic feet, Length = 2 * Width, and Height = Width - 1.
Therefore, we can solve for the Width by substituting the values into the formula:
36 = (2 * Width) * (Width - 1)
36 = 2 * Width^2 - Width
2 * Width^2 - Width - 36 = 0
By using the quadratic formula, Width = 8.
Therefore, the Height of the toy box is 7 feet.
To summarize, the toy box in the shape of a rectangular prism has a Width of 8 feet, a Length of 16 feet, and a Height of 7 feet to hold a total of 36 cubic feet.
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higgins iced cream shop sells ice cream in cone containers. The diameter of the cone containers in 2.5 inches, and the height is 6 inches. One tub of Higgins Ice cream is 384 ounces, and 1 cubic inch is equivalent to .55. What is the maximum number of cone containers higgins ice cream shop can fill completely with one tub of ice cream?
There isn't a way we get a fractional number or cones, we roll down to the closest full amount: 28 cones. The great majority of cone boxes that Higgins Shop can fill to the brim by one ice cream tub is 28.
What does 3 + 4 represent as a fraction?or as one number followed by the other number inside a line of text, as in: 3/4. 3 out of 4 components are represented by the fraction 3/4, or three quarters. The term "numerator" refers to the higher number, 3, whereas the term "denominator" refers to the lower number, 4.
Its radius is 2.5/2 ≈ 1.25 inches because the cone container's diameter is specified as 2.5 inches. It states that the height is 6 inches.
Thus, one cone container has a volume of: V = (1/3)(1.25)2(6)V 7.35 cubic inches.
We must now determine which of these cone-shaped containers one tub of cream can fit into.
First, we must convert 1 tub of ice cream's volume from inches to cubic centimeters.
211.2 cubic inches from 384 ounces divided by 0.55 cubic inches per ounce.
Secondly, we divide a volume of a cone container by volume of an ice cream tub:
28.77 cones out of 28.12 cubic inches at 7.35 cubic inches each
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there is a population of 15,500 bacteria in a colony. if the number of bacteria doubles every 234 hours, what will the population be 936 hours from now?
If the number of bacteria doubles every 234 hours, we can use the exponential growth formula to find the population at a future time t:
N(t) = N0 * 2^(t/T)
where N(t) is the population at time t, N0 is the initial population, T is the doubling time (234 hours in this case), and t is the time elapsed.
We are given that the initial population is 15,500 bacteria. We want to find the population 936 hours from now. Therefore, we can substitute the values into the formula:
N(936) = 15,500 * 2^(936/234)
N(936) = 15,500 * 2^4
N(936) = 15,500 * 16
N(936) = 248,000
Therefore, the population of bacteria in the colony will be 248,000 after 936 hours.
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in a large population, 64% of the people have been vaccinated. if 3 people are randomly selected, what is the probability that at least one of them has been vaccinated?
The probability that at least one of three randomly selected people has been vaccinated in a large population where 64% of people have been vaccinated is 0.784.
The probability that at least one of three randomly selected people has been vaccinated in a large population where 64% of people have been vaccinated can be calculated using the binomial probability formula.
The binomial probability formula is used to calculate the probability of a given number of successes from a given number of trials when the probability of success is constant. In this case, the number of trials is 3 (i.e. the three randomly selected people) and the probability of success is 64% (i.e. the probability that each of the randomly selected people has been vaccinated).
To calculate the probability that at least one of the three randomly selected people has been vaccinated, we first calculate the probability of none of them having been vaccinated:
P(none) = (1 - 0.64)^3 = 0.216
Then, the probability of at least one of them having been vaccinated is 1 - P(none) = 1 - 0.216 = 0.784.
In conclusion, the probability that at least one of three randomly selected people has been vaccinated in a large population where 64% of people have been vaccinated is 0.784.
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A white solid is known to be a chloride in which the metal ion is sodium, potassium, calcium, or aluminium.
A chemist was told to carry out a test for each metal ion that could be present in this white solid.
Describe tests to show the presence of each of these metal ions.
The reaction of ammonium hydroxide and aluminium chloride will form a white precipitate.
The presence of sodium, potassium, calcium, or aluminium chloride can be tested using a combination of physical and chemical methods. For sodium chloride, the flame test is the most common and effective way to confirm its presence. The sodium chloride compound will emit a yellowish-orange flame when exposed to heat. To test for the presence of potassium chloride, the chloride test is used. The presence of potassium chloride will cause a violet or purple color in the reaction when it is added to a silver nitrate solution. To test for the presence of calcium chloride, aqueous ammonia is added.
The formation of a white precipitate confirms the presence of calcium chloride. Lastly, to test for the presence of aluminium chloride, ammonium hydroxide is used.
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philip is making snack mix to take on his family's upcoming road trip. he mixes 2 pounds each of pretzels, peanuts, and cheese crackers. then, he splits the mix evenly among 12 bags. how many ounces of snack mix does philip put in each bag?
Philip puts 8 ounces of snack mix in each bag. To get this answer, we found the total weight of the mix by adding the weights of the three ingredients and converted it to ounces.
First, we need to find the total weight of the mix. Since Philip mixes 2 pounds of each ingredient and he has three ingredients, the total weight of the mix is:
2 pounds + 2 pounds + 2 pounds = 6 pounds
Since there are 16 ounces in a pound, the total weight of the mix in ounces is:
[6 pounds] 16 ounces/pound = 96 ounces
To find how many ounces of mix Philip puts in each bag, we divide the total weight of the mix by the number of bags:
96 ounces / 12 bags = 8 ounces per bag
Therefore, Philip puts 8 ounces of snack mix in each bag.
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In the figure, the vertices of ∆ ABC are A ( 0, 6 ), B ( 8, 0 )
and C ( 5, 8 ). If CD ⊥ AB, then find the length of altitude CD.
The length of altitude CD is 133/25 units.
What is the length if altitude?
To find the length of altitude CD, we need to find the length of the line segment CD, which is perpendicular to AB and passes through the point C.
First, let's find the equation of the line AB. We can use the two-point form:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is one of the points on the line. Using points A and B, we get:
m = (0 - 6)/(8 - 0) = -3/4
y - 6 = (-3/4)(x - 0)
y = (-3/4)x + 6
Next, let's find the slope of the line CD, which is the negative reciprocal of the slope of AB. This is because perpendicular lines have slopes that are negative reciprocals of each other. Therefore:
m_CD = 4/3
Now we can use the point-slope form to find the equation of line CD. We know that the line passes through point C (5, 8), so:
y - 8 = (4/3)(x - 5)
Simplifying, we get:
y = (4/3)x - 4/3 + 8
y = (4/3)x + 20/3
Now we need to find the intersection of line CD with line AB. We can solve the system of equations:
y = (-3/4)x + 6
y = (4/3)x + 20/3
Setting the two expressions for y equal to each other, we get:
(-3/4)x + 6 = (4/3)x + 20/3
Multiplying both sides by 12, we get:
-9x + 72 = 16x + 80
25x = -8
x = -8/25
Substituting this value of x into either equation, we get:
y = (-3/4)(-8/25) + 6 = 57/25
Therefore, the point of intersection is (-8/25, 57/25).
Finally, we can use the distance formula to find the length of CD, which is the distance between C and the point of intersection:
d = √[(5 - (-8/25))² + (8 - 57/25)²]
d = √[(125/25 + 8/25)² + (200/25 - 57/25)²]
d = √[(133/25)² + (143/25)²]
d = √(17689/625)
d = 133/25
Therefore, the length of altitude CD is 133/25 units.
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