For the given passengers per month 6,000 paying $200 each with $1 increase in the ticket price with 100 lose passengers , then the number of passengers per month N as a function of the ticket price x :
N(x) = 26,000 - 100x where x ≥ 200.
As given in the function,
Number of passengers carried by airlines per month = 6,000
Price of ticket of each passenger = $200
For each $1 increase in the ticket price lose of 100 passengers
Let N(x) be the function representing the number of passengers
And x represents the price of the ticket where x ≥ 200.
Required function to represent the number of passengers is given by :
N(x) = 6,000 -100 ( x -200)
⇒ N(x) = 6,000 -100x + 20,000
⇒ N(x) = 26,000 -100x where x ≥ 200
Therefore, for the given passengers per month 6,000 paying $200 each with $1 increase in the ticket price with 100 lose passengers , then the number of passengers per month N as a function of the ticket price x :
N(x) = 26,000 - 100x where x ≥ 200.
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At 6 AM today, you purchased 1 MW of electricity contract for 12 PM at a price of 100 pounds/MWh. Two hours later, the forecast for solar generation for 12 PM has changed from 4 GW to 4.5 GW. The market is currently bid at 95 pounds/MWh and offered at 105 pounds/MWh. What would you do, and why?
After 2 hours the plan needs to be changed, and purchase solar for the cost effect.
What is unit conversion?It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.
It is given that:
At 6 AM today, you purchased 1 MW of electricity contract for 12 PM at a price of 100 pounds/MWh.
Total cost = 6x100 = 600 pounds
Total cost for 2 hours = 200 pounds
Two hours later, the forecast for solar generation for 12 PM has changed from 4 GW to 4.5 GW.
Total cost for this:
From 8 AM to 12 PM = Number of hours 4 hours
4.5 GW = 4500 MW
= 105 pounds/MWh
Total cost for 4 hours = 630 pounds for 4500 MW per hour
Thus, after 2 hours the plan needs to be changed, and purchase solar for the cost effect.
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is 160,80,40,20 a arithmetic sequence or a geometric sequence or neither
The given sequence160,80,40,20 is the geometric sequence.
In an Arithmetic sequence, the difference between the two consecutive terms is equal.
In a Geometric sequence, the common ratio of the two consecutive terms is equal.
The given sequence is 160, 80, 40, 20
Now,
[tex]T_{1} = 160\\T_{2} = 80\\T_{3} = 40\\T_{4} =20[/tex]
Subtracting the consecutive terms to calculate the common difference,
[tex]d = T_{2} -T_{1} = 80 -160 = -80[/tex]
[tex]T_{3} -T_{4} = 40 -80 = -40[/tex]
So, [tex]T_{2} -T_{1} \neq T_{3} -T_{4}[/tex]
So, the given sequence is not an arithmetic sequence.
Now, Calculating the common ratios,
[tex]r = \frac{T_{2} }{T_{1} } = \frac{80}{160} = \frac{1}{2}[/tex]
and, [tex]r =\frac{T_{3} }{T_{2} } = \frac{40}{80} = \frac{1}{2}[/tex]
Hence, the ratio is the same for consecutive terms.
So, the given sequence is the geometric sequence.
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Identify the domain and range of each graph
0/1
3. At the carnival, there is a game with 600 ducks. If 25% of the ducks have stars on the
bottom, how many ducks have stars? Make sure to label your answer in ducks
8
Is it possible for a number to be a product of 2, a product of 5,
and a product of 10? Explain.
Yes, it is possible for a number to be a product of 2, 5, and 10.
All multiples of 10 such as 10, 20, 30, 40, 50, 60, ,,,, are a product of 2, 5, and 10.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
A number that is a product of 2, 5, and 10.
Example:
10 = 2 x 5
10 = 5 x 2
10 = 10 x 1
20
20 = 2 x 10
20 = 5 x 4
20 = 10 x 2
100
100 = 2 x 50
100 = 5 x 20
100 = 10 x 10
We see that all multiples of 10 are a product of 2, 5, and 10.
Thus,
All multiples of 10 are a product of 2,5, and 10.
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011 (part 1 of 2) 10.0 points
Young David, who slew Goliath, experi- mented with slings before tackling the gi- ant. He found that with a sling of length 0.566 m, he could revolve the sling at the rate of 10.7 rev/s. If he increased the length to 0.87 m, he could revolve the sling only 7.7 rev/s.
a) What is the larger of the two linear speeds?Answer in units of m/s.
part 2
b) Using the sling length 0.87 m, what is the centripetal acceleration at 7.7 rev/s?
Answer in units of m/s2.
this is physics
The 0.566 meter, 0.87 meter, 10.7 rev/s and 7.7 rev/s radii and respective rotational speeds of young David's slings indicates.
a) The larger linear speed is 42.09 m/s
b) The centripetal acceleration of the sling at 7.7 rev/s is approximately 2,036.39 m/s²
What is a linear speed?A linear speed is a measure of the rate at which the distance traveled by an object in rotary motion changes with time.
When the length of the sling = 0.566 m, The rate of revolving of the sling = 10.7 rev/s
When the length of sling = 0.87 m, the rate of revolving the sling = 7.7 rev/s
Linear speed = Angular speed ×Radius length
The angular speed when the length of the is 0.566 m, ω₁, is found as follows;
One complete 360° rotation = 2·π radians
ω₁ = 10.7 rev/s × 2·π ≈ 67.23 rad/s
The linear speed is; v₁ ≈ 67.23 rad/s × 0.566 m ≈ 38.05 m/s
The angular speed when the length is increased to 0.87 meters is therefore;
ω₂ = 7.7 rev/s × 2 × π ≈ 43.38 rad/sec
The linear speed is; v₂ ≈ 43.38 rad/s × 0.87 m ≈ 42.09 m/sThe larger of the two linear speed is approximately 42.09 m/s
Part 2: The centripetal acceleration, [tex]a_c[/tex], is found using the following formula;
[tex]a_c = \dfrac{v^2}{r}[/tex]
When the radius is r = 0.87 meters, the linear speed v₂ ≈ 42.09 m/s, which indicates;
[tex]a_c=\dfrac{42.09^2}{0.87} \approx 2,036.39[/tex]
The centripetal acceleration is approximately [tex]a_c[/tex] ≈ 2,036.39 m/s²
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Frank makes $320 a week. If he works more than 8 hours in a day, he gets paid $10 for each hour of overtime. What did Frank earn if he worked 9 hours on 3 days last week?
Answer:
$55.71
Step-by-step explanation:
$320/7=$45.71 per day
45.71/8=5.71 per hour
45.71+10=$55.71 for 9 hours of work
45.71+ 45.71+55.71 =$147.13 for 3days +1 hour overtime
What’s equivalent to 11:1 answer
Answer:
11
Step-by-step explanation:
11:1 = [tex]\frac{11}{1}[/tex] = 11
Answer: 11, 22:2, 33:3, etc.
Step-by-step explanation:
A ratio is dividing.
11/1 = 11.
This means that numerous ratios can be used, to the point where the answers are infinite.
Draw and label the following figure.
Scalene Right triangle RGH.
The scalene right triangle RGH is given by the image shown at the end of the answer.
What are the classification of triangles?There are two classifications of triangles, either regarding the side lengths or the angles.
Regarding the side lengths, the classifications are given as follows:
Scalene: Three different side lengths.Isosceles: Two equal side lengths.Equilateral: Three equal side lengths.Regarding the measure of the greatest angle, the classifications are given as follows:
Acute: The greatest angle has a measure that is less than 90º.Straight: The greatest angle has a measure that is exactly 90º.Obtuse: The greatest angle has a measure that is greater than 90º.In this problem, RGH is a scalene right triangle, hence:
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Jane bought 4 paintbrushes for $7
The ratio of paintbrush to follar is 7-4
The ratio if dollars to paintbrushes is 7:11
The ratio of dollars to paintbrushes is 7:4
The ratio of paintbrushes to dollars is 4-7
The ratio of dollars to paintbrushes is 4 to 11
The ratio of paintbrushes to dollars is 4:7
The ratio of dollars to paintbrushes is 7:4
What is a ratio?A ratio expresses the number of times one value is contained in another value.
The number of paintbrushes Jane bought for $7 is 4
From the question, 4 paintbrushes can be bought with $7 (7 Dollars), therefore, seven dollars gives 4 paintbrushes
The ratio of dollars to paintbrushes is therefore 7 to 4, while the ratio of paintbrushes to dollars is 4 to 7
The expression for ratio is the colon symbol ':'
Ratios can also be expressed using the word 'to'.
A ratio can also be expressed using the hyphen '-'
The ratio of paintbrushes to dollars can be expressed as 4:7 or 4 to 7 or 4-7.
The correct option is therefore;
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Answer:
The ratio of paintbrushes to dollars is 4 to 7.
The ratio of dollars to paintbrushes is 7:4.
The ratio of paintbrushes to dollars is 4:7.
Step-by-step explanation:
it just is
Housing value are appreciating at a rate of 11.3% a year how much will your 810,000 house be worth in 5 years if this rate of appreciation continues
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &810000\\ r=rate\to 11.3\%\to \frac{11.3}{100}\dotfill &0.113\\ t=\textit{years}\dotfill &5\\ \end{cases} \\\\\\ A=810000(1 + 0.113)^{5} \implies A=810000(1.113)^5\implies A \approx 1383441.63[/tex]
Draw and label the following figure.
Isosceles obtuse triangle with the obtuse vertex is angle T.
The Isosceles obtuse triangle in which the obtuse vertex is angle T is represented with the attached diagram.
What is an isosceles obtuse triangle?An isosceles obtuse triangle is a type of triangle which is formed by two equal sides of the triangle.
The vertex angle, which will be the obtuse one (x) can be x > 90°.The sum of the two base angles, y1 and y2, can be represented by y1 + y2 < 90 degrees.As long as the measures of the angles add up to 180°, it is an isosceles obtuse triangle.
An obtuse angle is an angle greater than 90 degrees but less than 180 degrees.
A triangle is a polygon with three sides and three angles. There are different types of triangle, which includes:
Equilateral triangleScalene triangleObtuse triangleIsosceles triangleRight angle triangleSo therefore, an isosceles obtuse triangle is formed by having two equal sides of a triangle.
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I’m really stuck on how to answer this question I need help
2) Bethany, a pilot with a commercial airline, flew from NY to Pittsburgh and back. It took % hours to get to
Pittsburgh. With the help of the jet stream, the return trip took only 4/5 the time. How long was the round trip?
Total time taken by Bethany to make a round trip of NY to Pittsburgh as per given conditions is equal to 1 (7/ 20)hours.
As given in the question,
Time taken by Bethany to flew from NY to Pittsburgh is equal to 3/4 hours
Now using jet stream ,
Time taken by airlines from Pittsburgh to NY is (4/5) th of (3/4) hours
= (4/5) × (3/4) hours
= 3/5 hours
Total time taken by airlines to make a round trip from NY to Pittsburgh is given by:
= [(3/4) + (3/5)] hours
= [(15 +12)/20] hours
= 27/20 hours
= 1 7/20 hours
Therefore, total time taken by Bethany to make a round trip of NY to Pittsburgh as per given conditions is equal to 1 (7/ 20)hours.
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9) A shark descends from the surface of the water at a rate of 15 feet each minute. What is the depth of the shark
after 5 minutes?
Answer:
75
Step-by-step explanation:
1 minute=15
2 minutes=30
3 minutes=45
4 minutes=60
5 minutes=75
A trucking company has 5 trucks and 4 drivers available when requests for 3 trucks are received. How many different ways are there of selecting the trucks and the drivers to meet these requests?
The different ways that are there of selecting the trucks and the drivers to meet these requests is 240 ways.
How to calculate the number of ways?Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects.
Combination formula
ⁿCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time.
The number of ways to select 3 trucks will be:
= ⁵C₃ = 10
The number of ways to select 3 drivers will be:
= ⁴C₃ = 4
Number of ways to arrange them = 3! = 3 × 2 = 6
Therefore the total number of ways will be:
= 10 × 4 × 6
= 240 ways
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All families in a given nation with four children were asked to report the sexes of the children.
What percent of families would be expected to have children who are all boys? Write your answer as an exact percentage.
The percent of families would be expected to have children who are all boys is 6.25%
How to calculate percentage?The following can be illustrated:
all 4 boys BBBB 1 1/16
3 boys 1 girl BBBG,GBBB,BGBB,BBGB 4 4/16
2 boys 2 girl BBGG,BGBG,GBGB,BGGB,GBBG, GGBB 6 6/16
1 boy 3 grisl BGGG,GBGG,GGBG,GGGB 4 4/16
all 4 girls GGGG 1 1/16
Therefore, the percent of families would be expected to have children who are all boys will be:
= All boys × 100
= (1/16)*100
= 6.25%
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What is the leading coefficient of the following polynomial function have?
ƒ (x) = 5x² + 3x³ + 2x^5 + 3x
Answer:
Step-by-step explanation:
2
Answer:
The leading coefficient is 2.
Step-by-step explanation:
Leading coefficients are the numbers with the highest degree or exponent.
A light bulb consumes 8400 watt-hours in 3 days and 12 hours. How many watt-hours does it consume per day?
Answer:
2400Watt Hours isn't it A Right Answer?
A copy machine makes 32 copies per minute. How long does it take to make 136 copies?
Answer:
4.25 minutes
Step-by-step explanation:
[tex]\frac{32 \:copies}{1\:min} = \frac{136\: copies}{x \: min} \\\\x\: min = \frac{136 \: copies}{32 \: copies} \\\\x=4.25 \: min[/tex]
Answer: 4 mins 15 seconds (4.25 mins)
Step-by-step explanation:
136 copies/32 copies per minute = 4.25 minutes
So we know it will take 4.25 mins. 4.25 mins is equal to 4 mins and 15 seconds.
Identify the function shown in this graph.
A. y= 3x - 3
B. y= -3x + 3
C. y= -3 x- 3
D. y= -1/3x + 3
The graph shows the percentage of citizens in a certain country who trust in their government. Complete parts a through c below.
Could someone please explain how to do part B. and C. in depth, thanks.
If the given equation is y-25=-0.92(x-4). The equation in the slope-intercept form is y=-0.92x+28.68.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The given equation is,y-25=-0.92(x-4)
The slope-intercept form of the equation is,
y=mx+c
m is the slope and c is the intercept.
Thus if the given equation is y-25=-0.92(x-4). The equation in the slope-intercept form is y=-0.92x+28.68.
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The length of a rectangle is 10, the width 3, and the height x. The surface area and the volume are equal. What is the value of x?
Answer:
x = 15
Step-by-step explanation:
Please refer photo
A 5 foot woman stands 3 feet from a lamppost and casts a 9 foot shadow
as shown. What is the height of the lamppost, rounded to the nearest tenth
of a foot?
O A) 6.5
OC) 6.9
O E) 6.7
O B) 6.8
OD) 6.6
Answer: e) 6.7
Step-by-step explanation:
This is a Similarity of Triangles problem (geometry)
if x is the height of the lamp post, then:
x/5 = (3 + 9) / 9
x (9) = (12) (9)
x = 60/9 = 6.7
...........................................PLEASE HELP ME
Answer:
They should pay AED 180 as interest.
Step-by-step explanation:
Simple interest:
P = The amount borrowed = AED 3000
R = rate of interest = 3% per year
t = time = 24 months = 24 ÷ 12 = 2 years
[tex]\sf \boxed{Interest = PRt}[/tex]
Substitute the values,
[tex]\sf = 3000 * \dfrac{3}{100}*2\\\\ = 30*3*2\\\\=AED \ 180[/tex]
What equation is graphed in this figure?
Responses
y−4=−13(x+2)
y minus 4 equals negative fraction 1 over 3 end fraction open parenthesis x plus 2 close parenthesis
y−3=13(x+1)
y minus 3 equals fraction 1 over 3 end fraction open parenthesis x plus 1 close parenthesis
y+2=−3(x−1)
y plus 2 equals negative 3 left parenthesis x minus 1 right parenthesis
y−5=3(x−1)
y minus 5 equals 3 left parenthesis x minus 1 right parenthesis
Number graph ranging from negative four to four on the x and y axes. A line is drawn on the graph that passes through begin ordered pair negative one comma four end ordered pair and begin ordered pair one comma negative two end ordered pair
The linear equation shown in the graph is the one in the third option.
y + 2 = -3*(x - 1)
What is the equation graphed?Here we have a graph, and there we can see a linear equation, on that graph, we can see that:
The y-intercept is y = 1.
For each horizontal unit, the line goes 3 units down, then the slope is -3.
Then the linear equation is:
y = -3*x + 1
If now we add 2 in both sides, we get:
y + 2 = -3x +1 + 2
y + 2 = -3x + 3
y + 2 = -3*(x - 1)
So the correct option is the third one.
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A light bulb consumes 2100 watt-hours in 3 days and 12 hours. How many watt-hours does it consume per day?
Answer:
below
Step-by-step explanation:
12 hours is .5 day so a total of 3.5 days
2100 w-h / 3.5 d = 600 w-h per day
If 49% of the people in a community use the emergency room at a hospital in one year, a sample of 11 people use the emergency room. Find the probability of more than 5 people use the emergency room.
The probability of more than 5 people using the emergency room is 0.4729
How to find the probability of more than 5 people who use the emergency room?Since 49% of the people in a community use the emergency room at a hospital in one year, a sample of 11 people use the emergency room. To find the probability of more than 5 people use the emergency room, we use binomial probability.
What is binomial probability?
We find that the binomial probability of x is P(X = x) = ⁿCₓpˣ(1 - p)ⁿ⁻ˣ
where
n = number of total trialsp = probability of event andx = number of required trialsSince
n = 11, p = 49% = 0.49 and x = 5,Let us now find the probability of x ≤ 5.
So, P(X ≤ 5) = ¹¹C₀p⁰(1 - p)¹¹⁻⁰ + ¹¹C₁p¹(1 - p)¹¹⁻¹ + ¹¹C₂p²(1 - p)¹¹⁻² + ¹¹C₃p³(1 - p)¹¹⁻³
+ ¹¹C₄p²(1 - p)¹¹⁻⁴ + ¹¹C₅p⁵(1 - p)¹¹⁻⁵
So, substituting the values of the variables into the equation, we have
= ¹¹C₀(0.49)⁰(1 - 0.49)¹¹ + ¹¹C₁(0.49)¹(1 - 0.49)¹⁰ + ¹¹C₂(0.49)²(1 - 0.49)⁹ + ¹¹C₃(0.49)³(1 - 0.49)⁸
+ ¹¹C₄(0.49)⁴(1 - p)⁷ + ¹¹C₅(0.49)⁵(1 - 0.49)⁶
= (1)(1)(0.51)¹¹ + (11)(0.49)(0.51)¹⁰ + (55)(0.49)²(0.51)⁹ + (165)(0.49)³(0.51)⁸
+ (330)(0.49)⁴(0.51)⁷ + (462)(0.49)⁵(0.51)⁶
= 0.0006071 + (11)(0.49)(0.0011904) + (55)(0.2401)(0.0023341) + (165)(0.117649)(0.0045768)
+ (330)(0.0576480)(0.0089741) + (462)(0.0282475)(0.0175963)
= 0.0006071 + 0.0064163 + 0.0308230 + 0.0888452
+ 0.1707218 + 0.2296378
= 0.5270512
≅ 0.5271
So, P(X ≤ 5) = 0.5271, we see that the binomial probability of more than 5 people is P(X ≥ 5) = 1 - P(X ≤ 5)
So, substituting the value of the variable into the equation, we have
= 1 - 0.5271
= 0.4729
The probability is 0.4729
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NO LINKS!! Please help me with this graph
=========================================================
Explanation:
The three points are at these locations:
A = (10, 6)B = (1,-3)C = (-5, 3)The notation "d(A,C)" means "the distance from A to C". It's equivalent to saying "the length of segment AC".
Then writing [tex]\left[d(A,C)]^2[/tex] means we'll square that distance.
Use the distance formula to get...
[tex]A = (x_1,y_1) = (10,6) \text{ and } C = (x_2, y_2) = (-5,3)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(10-(-5))^2 + (6-3)^2}\\\\d = \sqrt{(10+5)^2 + (6-3)^2}\\\\d = \sqrt{(15)^2 + (3)^2}\\\\d = \sqrt{225 + 9}\\\\d = \sqrt{234}\\\\[/tex]
This is the exact length of segment AC. That value squares to 234.
[tex]d = \sqrt{234} \ \to \ d^2 = (\sqrt{234})^2 = 234\\\\[/tex]
The square root and squaring operation cancel each other out. Think of it like fire vs water.
So we really only care about what's under the square root; rather than the entire square root expression itself. Which is nice because we don't have to worry about pesky things like decimal values.
This is why 234 is typed into the first box.
---------------------
Next, use the distance formula to find how far it is from A to B. Square the result to get what you see below.
[tex]A = (x_1,y_1) = (10,6) \text{ and } B = (x_2, y_2) = (1,-3)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(10-1)^2 + (6-(-3))^2}\\\\d = \sqrt{(10-1)^2 + (6+3)^2}\\\\d = \sqrt{(9)^2 + (9)^2}\\\\d = \sqrt{81 + 81}\\\\d = \sqrt{162}\\\\d^2 = (\sqrt{162})^2\\\\d^2 = 162\\\\[/tex]
This is the value of [tex]\left[d(A,B)\right]^2[/tex]
Now find the distance from B to C, and square the result.
[tex]B = (x_1,y_1) = (1,-3) \text{ and } C = (x_2, y_2) = (-5,3)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-(-5))^2 + (-3-3)^2}\\\\d = \sqrt{(1+5)^2 + (-3-3)^2}\\\\d = \sqrt{(6)^2 + (-6)^2}\\\\d = \sqrt{36 + 36}\\\\d = \sqrt{72}\\\\d^2 = \left(\sqrt{72}\right)^2\\\\d^2 = 72\\\\[/tex]
Add this to the previous squared value and we get 162+72 = 234, which matches exactly with the 234 found up toward the top.
We'll write 234 in the 2nd box as well.
This shows that [tex]\left[d(A,C)\right]^2 = \left[d(A,B)\right]^2+\left[d(B,C)\right]^2[/tex] is a true statement. By the converse of the Pythagorean theorem, we have confirmed this is a right triangle.
In other words, we've shown that [tex]a^2+b^2 = c^2[/tex] is a true statement (a,b,c are the sides of the right triangle such that c is the hypotenuse).
---------------------
Recall that we found these segment lengths:
[tex]AB = \sqrt{162} = \text{leg1}\\\\BC = \sqrt{72} = \text{leg2}\\\\AC = \sqrt{234} = \text{hypotenuse}\\\\[/tex]
The legs of a right triangle represent the base and height, in either order. This is because the legs are perpendicular to one another. They form a right (aka 90 degree) angle.
[tex]\text{area} = \frac{1}{2}*\text{base}*\text{height}\\\\\text{area} = \frac{1}{2}*\text{AB}*\text{BC}\\\\\text{area} = \frac{1}{2}*\sqrt{162}*\sqrt{72}\\\\\text{area} = \frac{1}{2}*\sqrt{162*72}\\\\\text{area} = \frac{1}{2}*\sqrt{11664}\\\\\text{area} = \frac{1}{2}*108\\\\\text{area} = 54\\\\[/tex]
Here are some alternative methods you can follow to find the area of this triangle.
Pick's TheoremShoelace TheoremCreate a bounding box around the triangle. Make the box as small as possible. Find the area of the whole box, and subtract off the smaller pieces outside the triangle.Heron's FormulaAs for verifying the answers, you can use a tool like GeoGebra.
Answer:
[tex][d(A,C)]^2=\boxed{234}[/tex]
[tex][d(A,B)]^2+[d(B,C)]^2=\boxed{234}[/tex]
[tex]\sf Area=\boxed{54}\; units^2[/tex]
Step-by-step explanation:
From inspection of the given diagram:
A = (10, 6)B = (1, -3)C = (-5, 3)If ΔABC is a right triangle, the sum of the squares of the two shorter sides will equal the square of the longest side. This is the definition of Pythagoras Theorem.
Use the distance formula to find the length of each side of the triangle.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
[tex]\begin{aligned}d[(A,C)]&=\sqrt{(x_C-x_A)^2+(y_C-y_A)^2}\\&=\sqrt{(-5-10)^2+(3-6)^2}\\&=\sqrt{(-15)^2+(-3)^2}\\&=\sqrt{225+9}\\&=\sqrt{234}\end{aligned}[/tex]
[tex]\begin{aligned}d[(A,B)]&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(1-10)^2+(-3-6)^2}\\&=\sqrt{(9)^2+(-9)^2}\\&=\sqrt{81+81}\\&=\sqrt{162}\end{aligned}[/tex]
[tex]\begin{aligned}d[(B,C)]&=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\&=\sqrt{(-5-1)^2+(3-(-3))^2}\\&=\sqrt{(-6)^2+(6)^2}\\&=\sqrt{36+36}\\&=\sqrt{72}\end{aligned}[/tex]
Therefore:
The longest side of the triangle is line segment AC.The two shorter sides of the triangle are line segments AB and BC.[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
Therefore, the triangle is a right triangle if:
[tex][d(A,B)]^2+[d(B,C)]^2=[d(A,C)]^2[/tex]
Substitute the found side lengths into the formula:
[tex]\implies [\sqrt{162}]^2+[\sqrt{72}]^2=[\sqrt{234}]^2[/tex]
[tex]\implies162+72=234[/tex]
[tex]\implies 234=234[/tex]
Hence proving that ΔABC is a right triangle.
To find the area of a right triangle, half the product of the two shorter sides:
[tex]\begin{aligned}\implies \sf Area &= \dfrac{1}{2}bh\\&=\dfrac{1}{2} \cdot [d(A,B)] \cdot [d(B,C)]\\&=\dfrac{1}{2} \cdot \sqrt{162} \cdot \sqrt{72}\\&=\dfrac{1}{2} \cdot \sqrt{162 \cdot 72}\\&=\dfrac{1}{2} \cdot \sqrt{11664}\\&=\dfrac{1}{2} \cdot \sqrt{108^2}\\&=\dfrac{1}{2} \cdot 108\\&=54 \sf \; units^2\end{aligned}[/tex]
Michael was assigned math problems to complete for his weekly homework. So far, he has completed 28 problems, which is of the total number of math problems he was assigned. How many 2/7 total math problems was Michael assigned for homework?
Michael was assigned a total of 98 task which a fraction of 2/7 is 28
FractionsA fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.
Data;
Fraction completed = 2/7Number completed = 28Number of problem = xWe can find the number of problem as
28 = 2/7 * x
7 * 28 = 2x
x = 98
The number of task assigned is 98.
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