The perimeter of triangle A"B"C" is found as 43.78.
How do we calculate?
We first determine length of each side:
The distance formula has that :
AB = √[(4 - (-4))² + (8 - 0)²]
= √128
= 8√2
BC = √[(8 - 4)² + (-12 - 8)²]
= √320
= 8√5
CA = √[(-4 - 8)² + (0 - (-12))^²]
= √320
= 8√5
cos(ABC) = (AB² + BC² - CA²) / (2 * AB * BC)
cos(ABC) = (128 + 320 - 320) / (2 * 8√2 * 8√5)
cos(ABC) = 1 / (4√2)
ABC = [tex]cos^{-1}[/tex](1 / (4√2))
ABC = 78.46°
A"B" = AB = 8√2
B"C" = BC = 8√5
C"A" = CA = 8√5
We then find the perimeter of triangle A"B"C" is:
A"B" + B"C" + C"A"
= 8√2 + 8√5 + 8√5
= 8√2 + 16√5
= 43.78
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Amazon purchases an office chair for $63, and marks it up 28%.
Which equation can be used to find the selling price of the office chair?
$63 + ($63 · 0.28) = $80.64
[tex]f = p + pm[/tex] where:
[tex]f[/tex] = final price: $80.64,
[tex]p[/tex] = original price: $63,
and [tex]m[/tex] = markup percent (in decimal): 28% → 0.28.
The diameter of a circle measures 28 cm. What is the circumference of the circle? Use 3.14 for pi, and do not round your answer. Be sure to include the correct unit in your answer.
The circumference of the circle with the measure of diameter as 28 cm is 87.92 cm.
Given a circle.
Also given that,
Diameter of the circle = 28 cm
We know that, radius of a circle is half the measure of the diameter of the circle.
Radius of the circle = 28 / 2 = 14 cm
The formula to find the circumference of the circle is,
Circumference = 2 πr
Here r is the radius of the circle.
Substituting the given,
Circumference = 2 π (14)
= 28π
= 28 × 3.14
= 87.92 cm
Hence the circumference is 87.92 cm.
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What is the area of this figure
Answer: i believe it’s 68
Step-by-step explanation:
My knowledge
Owen and Genesis are making fruit salads for a picnic. Owen mixes 14 cups of melon and 3 cups of apple and Genesis mixes 6 cups of melon and 1 cup of apple. Use owen and Genesis’s percent of melon to determine whose fruit salad will taste more melony.
15. The volumes of two similar solids are 857.5 mm^3 and 540 mm^3. The surface area of the smaller solid is 108 mm^2. What is the surface area of the larger solid?
The required surface area of the larger solid is approximately 147 mm². Option A is correct.
We know that,
The surface area of any form is the area of the shape that is fronted.
The surface area of a 3D object is the amount of area covering the outside.
Let's say the surface area of the bigger solid S.
Since the two solids are similar, their volumes have a ratio of (side length)³.
Let's say the ratio of the side lengths of the larger to the smaller solid as k. Then,
⇒ k³ (540 mm³) = 857.5 mm³
Simplifying the above equation, we get:
⇒ k = 7/6
So, the larger solid is about 7/6=1.183 times bigger than the smaller solid in terms of side length.
Since the surface area has a ratio of (side length)²,
we can find the surface area of the larger solid by:
⇒ (1.83²)(108 mm³)
≈ 174 mm³
Therefore, the surface area of the larger solid is approximately 147 mm².
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(a) In the figure below, m AB = 106° and m CD =66. Find mAEB
Answer:
[tex]\huge\boxed{\sf \angle AEB=86 \textdegree}[/tex]
Step-by-step explanation:
Given:arc AB = 106°
arc CD = 66°
Statement:According to angles of intersecting chords theorem, the measure of angle formed by two intersecting chords is half the sum of arcs intercepted by the angle.Mathematical form:[tex]\displaystyle \angle AEB=\frac{1}{2} (arc \ AB+arc \ CD)[/tex]
Solution:Put the given data in the above formula.
[tex]\displaystyle \angle AEB=\frac{1}{2} (106 + 66)\\\\\angle AEB=\frac{1}{2} (172)\\\\\angle AEB=86 \textdegree \\\\\rule[225]{225}{2}[/tex]
stered comsident p43336280840
Save the expression by solating the variable Hemember to balance the equation in each step you take
2
0-6
The result of the expression 20 - 6 is 14.
To solve the given expression, 20 - 6, and isolate the variable, we need to clarify whether there is an equation involved. However, in this case, the expression does not contain any variable to isolate, and it is not an equation that needs balancing. It is a straightforward arithmetic expression.
Step 1: Start with the given expression, 20 - 6.
Step 2: Evaluate the subtraction operation: 20 - 6 = 14.
Step 3: The simplified expression is now 14. However, since there is no variable present, there is no need to isolate any variable.
This means that when you subtract 6 from 20, the answer is 14. Remember that isolating a variable and balancing an equation are relevant when dealing with equations that involve variables. In this case, the expression is a simple subtraction operation, yielding a constant value of 14 as the answer.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
your credit card has a balance of $3600 and an annual interest rate of 16%. you decide to pay off the balance over three years. if there are no further purchases charged to the card, you must pay $126.59 each month, and you will pay a total interest of $957.24. assume you decide to pay off the balance over one year rather than three. how much more must you pay each month and how much less will you pay in total interest?
You will need to pay $261.76 more each month if you want to pay off the balance in one year instead of three. However, you will save a total of $953.24 - $576 = $377.24 in interest by paying off the balance in one year instead of three.
If you decide to pay off the balance over one year instead of three, the payment amount will be higher, but the total interest paid will be lower due to the shorter repayment period.
First, let's calculate the total interest paid over three years. The total payment made over three years will be the monthly payment of $126.59 times 36 months, which is $4,553.24. The total interest paid is the difference between the total payment made and the initial balance of $3600, which is $953.24.
Now, let's consider paying off the balance over one year. The total payment made over one year will be the monthly payment of $126.59 times 12 months, which is $1,519.08. To calculate the interest paid, we can use the formula:
Total interest paid = Balance × Annual interest rate × Time
where the time is expressed in years. Plugging in the values, we get:
Total interest paid = $3600 × 0.16 × 1 = $576
Therefore, if you decide to pay off the balance over one year instead of three, you will pay an additional amount each month equal to the difference between the monthly payment for one year and the monthly payment for three years, which is:
Additional monthly payment = ($4,553.24/12) - ($1,519.08/12) = $261.76
This means that you will need to pay $261.76 more each month if you want to pay off the balance in one year instead of three. However, you will save a total of $953.24 - $576 = $377.24 in interest by paying off the balance in one year instead of three.
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You have a bag of 12 blue marbles (numbered 1-12) and 12 red marbles (numbered 1-12). So you have 24 marbles in total (half blue and half red) with each of the numbers 1-12 appearing twice (once in each color). You draw one marble at random, replace it to the bag, mix up the marbles, and draw a second marble. Determine each of the following probabilities. P ( first marble is blue and second marble is red ) =
The probability that the first marble drawn is blue and the second marble drawn is red is 1/4 or 0.25, which can also be expressed as 25%.
To determine the probability of drawing a blue marble on the first draw and a red marble on the second draw, we need to consider the total number of marbles and the number of blue and red marbles in the bag
In this case, we have a bag with 12 blue marbles and 12 red marbles, making a total of 24 marbles.
When drawing the first marble, there is a 12/24 probability of selecting a blue marble since there are 12 blue marbles out of the total 24 marbles in the bag.
After replacing the first marble back into the bag and mixing up the marbles, the probability of drawing a red marble on the second draw is also 12/24, as there are still 12 red marbles remaining out of the total 24 marbles.
To find the overall probability, we multiply the probabilities of each event since they are independent events:
P(first marble is blue and second marble is red) = P(first marble is blue)[tex]\times[/tex]P(second marble is red)
[tex]= (12/24) \times (12/24)[/tex]
[tex]= (1/2) \times (1/2)[/tex]
= 1/4.
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Fill in the table using this function rule.
y=-2x+3
x
-2
-1
0
1
y
0
1
0
10
X
Ś
The domain and range of the given function y = -2x + 3 are
Domain = 0, 1, 2, ,3 , 4, 5, 6
Range = 3, 1, -1, -3, -5, -7, -15
The table is given below.
We have,
y = -2x + 3
We can have domain as:
x = 0, 1, 2, 3, 4, 5, 6
For x = 0,
y = -2 x 0 + 3 = 3
For x = 1,
y = -2 x 1 + 3 = -2 + 3 = 1
For x = 2,
y = -2 x 2 + 3 = -4 + 3 = -1
For x = 3,
y = -2 x 3 + 3 = -6 + 3 = -3
For x = 4,
y = -2 x 4 + 3 = -8 + 3 = -5
For x = 5,
y = -2 x 5 + 3 = -10 + 3 = -7
For x = 6,
y = -2 x 6 + 3 = -18 + 3 = -15
The range are 3, 1, -1, -3, -5, -7, -15.
The table can be assumed as:
x y = -2x + 3
0 3
1 1
2 -1
3 -3
4 -5
5 -7
6 -15
Thus the domain and range of the given function y = -2x + 3 are
Domain = 0, 1, 2, ,3 , 4, 5, 6
Range = 3, 1, -1, -3, -5, -7, -15
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I dont get this question equation
y=0.5 (6) - 4
I know that 0.5 is equivalent to 1/2 but I just don’t get this question
Answer
[tex]\pink\sf{y=-1}[/tex]
Step-by-step explanation
I'm assuming that this exercise is asking us to simplify the equation [tex]\sf{y=0.5(6)-4}[/tex].
We know that 0.5 (6) means 0.5 multiplied by 6. That is the same as 6 divided by 2, which is 3:
[tex]\sf{y=3-4}[/tex]
And now we just simplify the last part:
[tex]\sf{y=-1}[/tex]
∴ answer: y = -1
A sensor is used to monitor the performance of a nuclear reactor. The sensor accurately reflects the state of the reactor with a probability of .97. But with a probability of .02, it gives a false alarm (by reporting excessive radiation even though the reactor is performing normally), and with a probability of .01, it misses excessive radiation (by failing to report excessive radiation even though the reactor is performing abnormally).
What is the probability that a sensor will give an incorrect report, that is, either a false alarm or a miss?
To reduce costly shutdowns caused by false alarms, management introduces a second completely independent sensor, and the reactor is shut down only when both sensors report excessive radiation. (According to this perspective, solitary reports of excessive radiation should be viewed as false alarms and ignored, since both sensors provide accurate information much of the time.) What is the new probability that the reactor will be shut down because of simultaneous false alarms by both the first and second sensors?
Being more concerned about failures to detect excessive radiation, someone who lives near the nuclear reactor proposes an entirely different strategy: Shut down the reactor whenever either sensor reports excessive radiation. (According to this point of view, even a solitary report of excessive radiation should trigger a shutdown, since a failure to detect excessive radiation is potentially catastrophic.) If this policy were adopted, what is the new probability that excessive radiation will be missed simultaneously by both the first and second sensors?
1. The probability that the sensor will give an incorrect report is 0.03 or 3%.
2. The probability that the reactor will be shut down because of simultaneous false alarms by both sensors is 0.0004 or 0.04%.
3. The probability that excessive radiation will be missed simultaneously by both sensors is 0.0001 or 0.01%.
1. Probability of the sensor giving an incorrect report (false alarm or miss):The probability of a false alarm is 0.02.
The probability of a miss is 0.01.
P(false alarm or miss)
= P(false alarm) + P(miss)
= 0.02 + 0.01 = 0.03
Therefore, the probability that the sensor will give an incorrect report is 0.03 or 3%.
2. Probability of simultaneous false alarms by both sensors:
P(false alarm by both sensors)
= P(false alarm by sensor 1) * P(false alarm by sensor 2)
= 0.02 * 0.02
= 0.0004
Therefore, the probability that the reactor will be shut down because of simultaneous false alarms by both sensors is 0.0004 or 0.04%.
3. Probability of missing excessive radiation by both sensors:
P(miss by both sensors)
= P(miss by sensor 1) * P(miss by sensor 2)
= 0.01 * 0.01
= 0.0001
Therefore, the probability that excessive radiation will be missed simultaneously by both sensors is 0.0001 or 0.01%.
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Sally had 52 more stickers than Joe after Joe gave 1/5 of his stickers to her. if they both had a total of 260 stickers, how many stickers did Sally have to start?
There are 125 stickers did Sally have to start.
We have to given that,
Sally had 52 more stickers than Joe after Joe gave 1/5 of his stickers to her.
Let us assume that,
Joe had x stickers to start with.
Since, After Joe gave 1/5 of his stickers to her.
He have 4/5 of his original amount left.
That is, 4/5x
Since, Sally had 52 more stickers than Joe
Hence, We get;
4/5x + 52 = 1/5x + y .. (i)
where y is the number of stickers Sally had to start with.
Here, they both had a total of 260 stickers,
Hence,
x + y =260 .. (ii)
From (i) and (ii);
y = 125
Thus, There are 125 stickers did Sally have to start.
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On first down, Savannah threw a 29-yard pass.
On the next play, she threw a 13-yard pass. How
feet did Savannah throw in all?
many
A. 42 feet
B. 96 feet
C. 126 feet
D. 128 feet
Answer: 126 feet
Step-by-step explanation: Convert yards into feet. IF we are given different units then you must convert it.
To convert yards into feet, MULTIPLY by 3
29 yards * 3= 87 feet
13 yards * 3= 39 feet
Now, key word= THROWS IN ALL= addition
87 + 39 is 126
Complete the work to solve for y: 2 5 ( 1 2 y + 5 ) − 4 5 = 1 2 y − 1 + 1 10 y 1.Distributive property: 1 5 y + 2 − 4 5 = 1 2 y − 1 + 1 10 y 2.Combine like terms: 1 5 y + 6 5 = 3 5 y − 1 3.Subtraction property of equality: 6 5 = 2 5 y − 1 Addition property of equality: 11 5 = 2 5 y 4.Division property of equality: What is the value for y?
The value of y is 4.4.
Let's go through the steps to solve for y:
Distributive property:
[tex]1/5y + 2 - 4/5 = 1/2y - 1 + 1/10y[/tex]
Combine like terms:
[tex]1/5y + 2 - 4/5 = 1/2y - 1 + 1/10y[/tex]
Simplify the equation by getting rid of fractions. To do this, we can multiply every term by the least common denominator (LCD) of 10:
[tex]10 * (1/5y + 6/5) = 10 * (3/5y - 1 + 1/10y)[/tex]
Simplifying further:
[tex]2y + 12 = 6y - 10 + y[/tex]
Now, let's combine like terms again:
[tex]2y + 12 = 7y - 10[/tex]
Next, let's isolate the variable y. Subtract 2y from both sides and add 10 to both sides:
[tex]12 + 10 = 7y - 2y[/tex]
Simplifying:
22 = 5y
Finally, divide both sides by 5 to solve for y:
y = 22/5
Note: It's important to check our solution by substituting y = 4.4 back into the original equation to ensure it satisfies the equation.
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Answer:
11/2
Step-by-step explanation:
11/5 = 2/5y
11 = 2y
y = 11/2
Given the net, what is the surface area of the rectangular prism below?
PLS HELP ASAP WILL MARK BRAINLIST
Answer:
Step-by-step explanation:
I'm sorry, but I cannot answer your question without a visual representation or description of the rectangular prism. Please provide more information or a picture so that I can assist you accurately.
Answer:
72 cm 2?? THERE Isn't anything bellow I am sorry?
Step-by-step explanation:
A rental company charges $75 a day and 25 cents a mile for renting a truck. Michael rents a truck for 2 days, and his bill came to $243. How many miles did he drive?
The calculated total distance he drive is 372 miles
How many miles did he drive?From the question, we have the following parameters that can be used in our computation:
Charges $75 a day25 cents a mileSo, we have
Total charges = 75 * days + 0.25 * miles
For 2 days and total ot 243. we have
75 * 2 + 0.25 * miles = 243
So, we have
miles = 372
Hence, the total distance he drive is 372 miles
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What is the surface area of the cylinder? Approximate using π = 3.14 and round to the nearest square meter.
a cylinder with a radius labeled 2.3 meters and height labeled 6.9 meters
336 square meters
133 square meters
84 square meters
73 square meters
The surface area of the cylinder is 133 square meters.
The formula for the surface area of a cylinder is given by:
Surface Area = 2πrh + 2πr²
Given that the radius (r) is 2.3 meters and the height (h) is 6.9 meters, we can substitute these values into the formula:
Surface Area =2 x 3.14 x 2.3 x 6.9 + 2 x 3.14 x 5.29
= 2 x 3.14 x 15.87 + 33.925
= 132.8848 square meter.
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Answer: B 133
Step-by-step explanation:
A(2, 50°) is a point in a polar coordinate plane. Let O be the pole. 2 If B is another point in the same polar coordinate plane such that OA LOB and OB = 3 units, write down one possible answer for the coordinates of B.
Given statement solution is:- The coordinates of point B is (3, 50°).
In the given scenario, we have point A with polar coordinates (2, 50°) and the pole O. We need to find point B such that OA is parallel to OB and OB has a length of 3 units.
Since OA and OB are parallel, they have the same angle with the positive x-axis. Therefore, the angle between OB and the positive x-axis would also be 50°.
To find the coordinates of point B, we can use the polar coordinates system, where the distance from the pole is denoted by r and the angle with the positive x-axis is denoted by θ.
Since OB has a length of 3 units, the distance from the pole (r) would be 3. The angle between OB and the positive x-axis is also 50°. Therefore, the coordinates of point B would be (3, 50°).
So, one possible answer for the coordinates of point B is (3, 50°).
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An alcohol was made by mixing 6fl. oz. of a 20% alcohol solution and 4fl. oz. of a 5% alcohol solution. What is the concentration of the mixture?
The concentration of the mixture made by mixing 6 fl. oz. of a 20% alcohol solution and 4 fl. oz. of a 5% alcohol solution will be; 14%
Consider that x represents the concentration of the mixture, hence:
(6 x 20%) + (4 x 5%) = x (4 + 6)
1.2 + 0.2 = 10x
x = 0.14 = 14%
The concentration of the mixture is made by mixing 6 fl. oz. of a 20% alcohol solution and
Thus 4 fl. oz. of a 5% alcohol solution = 14%
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A picture framing business designs two types
of pictures -- matted and unmatted.
The company employees can complete 36
pictures each day using up to 80 total man-
hours of labor. It takes 4 man-hours to complete
one matted and framed picture, and 2 man-hours
to complete one unmatted and framed picture.
How many of each type of picture should be
made daily to maximize the company's profit,
if the profit on a matted picture is $40 and the
profit on an unmatted picture is $35?
To determine the optimal number of matted and unmatted pictures to maximize the company's profit, we can set up a linear programming problem.
Let's denote:
- x: the number of matted pictures
- y: the number of unmatted pictures
The objective is to maximize the profit, which can be expressed as:
Profit = 40x + 35y
We need to consider the following constraints:
1) The number of pictures completed each day cannot exceed 36:
x + y ≤ 36
2) The total man-hours of labor cannot exceed 80:
4x + 2y ≤ 80
3) The number of pictures cannot be negative:
x, y ≥ 0
Now we can solve this linear programming problem to find the optimal values for x and y.
First, let's graph the feasible region defined by the constraints:
```
x + y ≤ 36
4x + 2y ≤ 80
x, y ≥ 0
```
The feasible region is the area of the graph that satisfies all the constraints.
Next, we need to evaluate the objective function (Profit = 40x + 35y) at the vertices of the feasible region to find the maximum profit.
We can use different methods such as the corner-point method or the simplex method to determine the vertices and evaluate the profit at each vertex.
Thus, once we find the vertex that yields the maximum profit, we will have the optimal values for x and y.
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Si un editor pone un precio de S/ 16 a un libro, se venderán 10,000 copias. Por cada dólar que aumente al
precio se dejarán de vender 300 libros. ¿Cuál debe ser el precio al que se debe vender cada libro para
generar un ingreso total por las ventas de S/ 129200?
Answer:
Step-by-step explanation:
Math
82°F
Algebra 1 CC.20 Checkpoint: Quadratic equations NXG
2
x² - y + x = 16
y = 3x + 2
3x² - y + 32 = 22x
y = 2x - 16
Language arts
Decide whether each system of equations has two real solutions, exactly one real solution, or
no real solutions.
y = -x² + 6x + 12
y = -x +3
Answer:
x² - y + x = 16 is 1 real solution
3x² - y + 32 = 22x is 2 real solutions
y = -x² + 6x + 12 is 1 real solution
Step-by-step explanation:
sorry i am unsure about rest, they do not have a value. good luck :)
6. Julie went to a family reunion at a restaurant. In total there were 8 families that attended. The bill at the restaurant was $1,060.32. How much does each family need to pay if they split the bill evenly? (WITHOUT TIP!)
Answer:
$132.54
Step-by-step explanation:
$1060.32 / 8 families = $132.54 / family
5. 49% of adults say cashews are their favorite kind of nut. You randomly select 19 adults and ask
each to name his or her favorite nut. Find the probability that the number who say cashews are
their favorite nut is exactly four. (Round to the nearest thousandth as needed.)
6. According to the website nationalbikeregistry.com, at UCLA only 3% of stolen bikes are returned
to owners. If there are 335 bikes stolen at UCLA what is the probability that 12 or more stolen
bikes will be returned? (Round to the nearest thousandth as needed.)
The probability that exactly four out of 19 adults say cashews are their favorite nut is approximately 0.251.
The probability that 12 or more stolen bikes will be returned is approximately 0.026 (rounded to the nearest thousandth).
To solve both of these probability problems, we can use the binomial probability formula:
P(X = k) = (n C k) × p^k × (1 - p)^(n - k)
where:
P(X = k) is the probability of getting exactly k successes
n is the total number of trials
k is the number of desired successes
p is the probability of success in a single trial
(1 - p) is the probability of failure in a single trial
(n C k) represents the binomial coefficient, calculated as n! / (k! x (n - k)!)
Let's solve each problem separately:
The probability that exactly four out of 19 adults say cashews are their favorite nut can be calculated as:
P(X = 4) = (19 C 4) ⁴(0.49⁴) (0.51¹⁵)
Using the binomial probability formula, we can calculate:
P(X = 4) ≈ 0.251
Therefore, the probability that exactly four out of 19 adults say cashews are their favorite nut is approximately 0.251.
To find the probability that 12 or more stolen bikes will be returned out of 335 stolen bikes, we can use the binomial probability formula. Let's denote the probability of a stolen bike being returned as p = 0.03, the number of trials as n = 335, and the number of desired successes as k = 12 or more.
Using the complement rule, we can calculate the probability of not getting 11 or fewer successes:
P(X ≥ 12) = 1 - [P(X = 0) + P(X = 1) + ... + P(X = 11)]
To perform the calculation, summing up individual probabilities can be time-consuming. However, using statistical software or a binomial probability calculator can provide a convenient solution.
Using such a calculator, we find that the probability of 11 or fewer stolen bikes being returned is approximately 0.974. Therefore, the probability of 12 or more stolen bikes being returned is:
P(X ≥ 12) = 1 - 0.974 ≈ 0.026
Thus, the probability that 12 or more stolen bikes will be returned is approximately 0.026 (rounded to the nearest thousandth).
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100 Points! Algebra question. Photo attached. Find the amplitude, if it exists, and period of the function. Then graph the function. Thank you!
The amplitude and the period of the function f(x) = cos(5θ) are 1 and 2π/5
How to determine the amplitude and period of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = cos(5θ)
A sinusoidal function is represented as
f(x) = Acos(B(x + C)) + D
Where
Amplitude = APeriod = 2π/BSo, we have
A = 1
Period = 2π/5
Evaluate
A = 1
Period = 2π/5
Hence, the amplitude is 1 and the period is 2π/5
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100 Points! Algebra question. Graph the function. Photo attached. Thank you!
The functions have the following
Domain: (-∞, -1) ∪ (-1, ∞)
Range: (-∞, -∞) excluding -5
Vertical Asymptote: x = -1
Horizontal Asymptote: y = -5
We have,
Domain:
The domain of a function refers to the set of all possible input values (x) for which the function is defined.
In this case, the function f(x) is defined for all real numbers except when the denominator (x + 1) is equal to zero.
The domain is all real numbers except x = -1.
So, the domain is (-∞, -1) ∪ (-1, ∞).
Range:
The range of a function refers to the set of all possible output values (y) that the function can produce.
In this case, we can observe that as x approaches -1 from either side, the function approaches negative infinity.
The range is (-∞, -∞) excluding -5.
Vertical Asymptote:
A vertical asymptote occurs when the function approaches infinity or negative infinity as x approaches a certain value.
In this case, the vertical asymptote occurs when the denominator (x + 1) is equal to zero, which is x = -1.
Horizontal Asymptote:
To determine the horizontal asymptote, we need to examine the behavior of the function as x approaches positive or negative infinity.
As x approaches positive or negative infinity, the term 1/(x + 1) becomes negligible compared to -5.
The horizontal asymptote is y = -5.
Thus,
The functions have the following
Domain: (-∞, -1) ∪ (-1, ∞)
Range: (-∞, -∞) excluding -5
Vertical Asymptote: x = -1
Horizontal Asymptote: y = -5
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find the value of x and y
The values of x and y in the figure are 3√2 and 3, respectively.
Identities in trigonometryThe diagram shown is a right triangle with a 45-degree acute angle.
The values of variables x and y must be determined.
Using the trigonometry identity, we get:
opposite/hypotenuse = sin 45
sin45 = 3/x
x = 3/sin45
x = 3(1/√2)
x = 3√2
Likewise,
tan 45 = opposite/adjacent
tan 45 = 3/y
1 = 3/y
y = 3
As a result, the values of x and y in the figure are 32 and 3, respectively.
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Can I get help, please
Answer:
see attached
Step-by-step explanation:
You want the areas of the four triangles in the figure.
Triangle areaThe area of a triangle is given by the formula ...
A = 1/2bh
where b is the base of the triangle, and h is its height perpendicular to the base.
Triangles A, B, C are right triangles, so their areas are easy to figure. Triangle D will be the difference between the area of the square and the areas of the other triangles.
The calculations are shown in the first attachment. Confirmation is provided by a geometry program in the second attachment.
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Additional comment
If all you have are the coordinates of the vertices of triangle D, this method of finding its area is as good as any. There are other methods that can also be used, but they can be more trouble.
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