In Roman Numerals, smaller numbers can be subtracted from larger numbers, but only to a certain extent.
The number VCX is incorrect in Roman Numerals because V (5) cannot be subtracted from X (10) to make 5, and C (100) cannot be subtracted from X (10) to make 90.
In Roman Numerals, smaller numbers can be subtracted from larger numbers, but only to a certain extent.
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Use similar triangles to calculate the height, h cm, of triangle ABE. 10 cm 36 cm D B 20 cm E Optional working I h = Answ cm Search
Answer:
h=24
Step-by-step explanation:
Since the traingles are similar we can calculate the scale factor
20/10 = 2
So the Linear Scale Factor is 2
We can use that to figure out the ratio between the 2 triangles
Since DC = 10 and AE = 20
We cans say that the ratio between DBC and ABE is 2:1
Using this we can see that the ratio of the height is split into 2:1 and the total is 3
Knowing this we can calculate the the heights of both triangles
36 / 3 = 12
Height of small traingle = 1*12 = 12
Height of large triangle = 2*12 = 24
Guided practice
it's not letter c. -2.6
state what number you would subtract from each side of the inequality to solve the inequality.
5.7 ≥ k + 3.1
a.
3.1
b.
5.7
c.
–2.6
The value of k that is less than or equal to 2.6
To solve the inequality 5.7 ≥ k + 3.1, you should subtract 3.1 from each side of the inequality.
To isolate the variable k, we need to perform the same operation on both sides of the inequality. In this case, we need to subtract 3.1 from each side:
5.7 - 3.1 ≥ k + 3.1 - 3.1
This simplifies to:
2.6 ≥ k
Therefore, the correct answer is:
k ≤ 2.6
We subtracted 3.1 from each side to isolate the variable k, resulting in the inequality k ≤ 2.6. This means that any value of k that is less than or equal to 2.6 will satisfy the original inequality 5.7 ≥ k + 3.1.
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A toy manufacture has designed a new part for use in building models. The part is a cube with side length 14 mm and it has a 12 mm diameter circular hole cut through the middle. The manufacture wants 9,000 prototypes. If the plastic used to create the part costs $0. 07 per cubic millimeter, how much will the plastic for the prototypes cost?
Answer: Therefore, the plastic for the prototypes will cost $1,452,150.
Step-by-step explanation:
The volume of the cube can be calculated as:
Volume of the cube = (side length)^3 = (14 mm)^3 = 2,744 mm^3
The volume of the hole can be calculated as:
Volume of the hole = (1/4) x π x (diameter)^2 x thickness = (1/4) x π x (12 mm)^2 x 14 mm = 5,049 mm^3
The volume of plastic used to create one prototype can be calculated as:
Volume of plastic = Volume of cube - Volume of hole = 2,744 mm^3 - 5,049 mm^3 = -2,305 mm^3
Note that the result is negative because the hole takes up more space than the cube.
However, we can still use the absolute value of this result to calculate the cost of the plastic:
Cost of plastic per prototype = |Volume of plastic| x Cost per cubic millimeter = 2,305 mm^3 x $0.07/mm^3 = $161.35/prototype
To find the cost of the plastic for 9,000 prototypes, we can multiply the cost per prototype by the number of prototypes:
Cost of plastic for 9,000 prototypes = 9,000 x $161.35/prototype = $1,452,150
The plastic for the prototypes will cost $1,452,150.
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A line has a slope of -2 and passes through the point (-3, 8). Write its equation in slope-
intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = - 2x + 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here slope m = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute (- 3, 8 ) into the partial equation
8 = - 2(- 3) + c = 6 + c ( subtract 6 from both sides )
2 = c
y = - 2x + 2 ← equation of line
Sara collects beads in a jar she weighs the jar every week to see how many grams of beads she has. she as 2.5 grams if blue beads. 4.9 grams of pink beads, 7.1 grams of yellow beads and the rest are white beads
if sara weighs her jar this week and finds out that she has 1.8 grams of beads, how many grams of white beads does she have?
Therefore, Sara has 3.5 grams of white beads in her jar.
Based on the information provided, Sara has 2.5 grams of blue beads, 4.9 grams of pink beads, and 7.1 grams of yellow beads. If she weighs her jar this week and finds out she has a total of 18 grams of beads, we can determine the number of grams of white beads she has by following these steps:
Step 1: Add the weights of the blue, pink, and yellow beads together.
2.5 grams (blue) + 4.9 grams (pink) + 7.1 grams (yellow) = 14.5 grams
Step 2: Subtract the total weight of the blue, pink, and yellow beads from the total weight of the jar (18 grams).
18 grams (total weight) - 14.5 grams (blue, pink, and yellow beads) = 3.5 grams
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Need help asap. (See photo below)
Angles Formed by Chords, Tangents, Secants
The value of m∠MGA between the tangent and the diameter is 90 degrees.
How to find the angle between tangent?A line that touches the circle at one point is known as a tangent to a circle.
Therefore, MU is tangent to the circle O at the point G. The diameter of the
circle is GA.
Therefore, let's find the angle m∠MGA in the circle.
If a tangent and a diameter meet at the point of tangency, then they are perpendicular to one another. Therefore, the point where they meets form a right angle(90 degrees).
Hence,
m∠MGA = 90 degrees
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Fish enter a lake at a rate modeled by the function E given by E(t) = 20+15sin(pi*t/6). Fish leave the lake at a rate modeled by the function L given by L(t) = 4+20.1*t^2. Both E(t) and L(t) are measured in fish per hour and 't' is measured in hours since midnight (t=0).a.) How many fish enter the lake over the 5-hour period from midnight (t=0) to 5am (t=5)? Give your answer to the nearest whole number.b.) What is the average number of fish that leave the lake per hour over the 5 hour period from midnight (t=0) to 5am (t=5)?c.) At what time, t, for 0 ≤ t ≤ 8, is the greatest number of fish in the lake? Justify.d.) Is the rate of change in the number of fish in the lake increasing or decreasing at 5am (t=5)? Explain your reasoning.
Answer: a) To find the total number of fish that enter the lake over the 5-hour period, we need to integrate the function E(t) from t=0 to t=5:
int(20+15sin(pi*t/6), t=0 to 5) ≈ 62
a) To find the total number of fish that enter the lake over the 5-hour period, we need to integrate the function E(t) from t=0 to t=5:
int(20+15sin(pi*t/6), t=0 to 5) ≈ 62
Therefore, about 62 fish enter the lake over the 5-hour period from midnight to 5am.
b) The average number of fish that leave the lake per hour over the 5-hour period can be found by calculating the total number of fish that leave the lake over the 5-hour period and dividing by 5:
int(4+20.1*t^2, t=0 to 5) ≈ 1055
average = 1055/5 = 211
Therefore, the average number of fish that leave the lake per hour over the 5-hour period is 211.
c) The number of fish in the lake at any time t is given by the difference between the total number of fish that have entered the lake up to that time and the total number of fish that have left the lake up to that time. So, if N(t) represents the number of fish in the lake at time t, then:
N(t) = int(20+15sin(pi*t/6), t=0 to t) - int(4+20.1*t^2, t=0 to t)
To find the time t when the greatest number of fish are in the lake, we need to find the maximum of N(t) for 0 ≤ t ≤ 8. We can do this by taking the derivative of N(t) and setting it equal to zero:
dN(t)/dt = 15pi/6 * cos(pi*t/6) - 20.1t^2 + 4
0 = 15pi/6 * cos(pi*t/6) - 20.1t^2 + 4
Solving for t numerically using a calculator or computer, we find that the maximum occurs at t ≈ 2.34 hours. Therefore, the greatest number of fish in the lake occurs at 2.34 hours after midnight.
d) The rate of change in the number of fish in the lake is given by the derivative of N(t):
dN(t)/dt = 15pi/6 * cos(pi*t/6) - 20.1t^2 + 4
To determine whether the rate of change is increasing or decreasing at t=5, we need to find the second derivative:
d^2N(t)/dt^2 = -5.05t
When t=5, the second derivative is negative, which means that the rate of change in the number of fish in the lake is decreasing at 5am.
a. There will be 141 fish enter the lake over the 5-hour period from midnight
b. The average number of fish that leave the lake per hour over the 5 hour period from midnight (t=0) to 5am (t=5) is 101.
c. At 3.25 hour, t, for 0 ≤ t ≤ 8, is the greatest number of fish in the lake
d. The rate of change in the number of fish in the lake is decreasing at 5am.
a) To find the number of fish that enter the lake over the 5-hour period from midnight to 5am, we need to integrate the rate of fish entering the lake over that time period:
Number of fish = ∫[0,5] E(t) dt
= ∫[0,5] (20+15sin(πt/6)) dt
Number of fish ≈ 141
Therefore, approximately 141 fish enter the lake over the 5-hour period from midnight to 5am.
b. To find the average number of fish that leave the lake per hour over the 5 hour period, we need to calculate the total number of fish that leave the lake over that time period and divide by the duration of the period:
Number of fish that leave the lake = L(5) - L(0)
= (4+20.1*5^2) - (4+20.1*0^2)
= 505.5
Average number of fish leaving per hour = Number of fish that leave the lake / Duration of period
= 505.5 / 5
= 101.1
Therefore, the average number of fish that leave the lake per hour over the 5 hour period from midnight to 5am is approximately 101.
c. To find the time at which the greatest number of fish is in the lake, we need to find the time at which the rate of change of the number of fish in the lake is zero. This occurs when the rate of fish entering the lake is equal to the rate of fish leaving the lake:
E(t) = L(t)
20+15sin(πt/6) = 4+20.1t^2
We can solve this equation numerically to find that the greatest number of fish is in the lake at approximately t=3.25 hours (rounded to two decimal places).
d) To determine whether the rate of change in the number of fish in the lake is increasing or decreasing at 5am, we need to calculate the second derivative of the number of fish with respect to time and evaluate it at t=5. If the second derivative is positive, the rate of change is increasing. If it is negative, the rate of change is decreasing.
d²/dt² (number of fish) = d/dt E(t) - d/dt L(t)
= (15π/6)cos(πt/6) - 40.2t
d²/dt² (number of fish) ≈ -44.4
Since the second derivative is negative, the rate of change in the number of fish in the lake is decreasing at 5am.
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Aaden is driving to a concert and needs to pay for parking. There is an automatic fee of $9 just to enter the parking lot, and when he leaves the lot, he will have to pay an additional $2 for every hour he had his car in the lot. How much total money would Aaden have to pay for parking if he left his car in the lot for 3 hours? How much would Aaden have to pay if he left his car in the lot for
�
t hours?
Answer:
$15.
Step-by-step explanation:
9 + 3*2
= $15.
find f(x) for the given function.
f(x) = 1/1-x
To find f(x) for the given function f(x) = 1/1-x, we simply replace the "x" in the equation with whatever input value we want to evaluate the function at.
For example, if we want to find f(2), we would replace x with 2 and get:
f(2) = 1/1-2
f(2) = -1
Similarly, if we want to find f(a), we would replace x with a and get:
f(a) = 1/1-a
Therefore, f(x) = 1/1-x, where x is any input value.
To find f(x) for the given function, simply rewrite the function as it is:
f(x) = 1 / (1 - x)
Here, f(x) represents the function value for any input x, and the expression on the right side indicates how to calculate it.
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Help!! Will give out brainliest answer :)
Leslie paid $13 for 4 children’s tickets and 1 adult ticket.
Antonio paid $14 for 3 adult’s tickets and 2 children’s tickets.
Write and solve a system of equations to find the unit price for a child ticket and an adult ticket. Explain your steps and show all your work
The unit price for a child ticket is $2.50 and the unit price for an adult ticket is $3.
To find the unit price for a child ticket and an adult ticket, we can set up a system of equations based on the given information. Let x be the unit price for a child ticket and y be the unit price for an adult ticket.
From the first sentence, we know that:
4x + y = 13 ...(1)
From the second sentence, we know that:
3y + 2x = 14 ...(2)
Now we have a system of equations with two variables, which we can solve using either substitution or elimination method. For simplicity, we will use the elimination method.
Multiplying equation (1) by 3, we get:
12x + 3y = 39 ...(3)
Subtracting equation (2) from equation (3), we get:
10x = 25
x = 2.50
Substituting x = 2.50 into equation (1), we get:
4(2.50) + y = 13
y = 3
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Scores at a local high school on the Algebra 1 Midterm are extremely skewed left with a mean of 65 and a standard deviation of 8. A guidance counselor takes a random sample of 10 students and calculates the mean score, x¯¯¯.
(a) Calculate the mean and standard deviation of the sampling distribution of x¯¯¯
(b) Would it be appropriate to use a normal distribution to model the sampling distribution? Justify your answer
The standard deviation of the sampling distribution is 2.53. It would not be appropriate to use a normal distribution to model the sampling distribution.
(a) When dealing with a sampling distribution, the mean of the sampling distribution (μ_x) is equal to the mean of the population (μ). In this case, the mean of the population is 65. Therefore, the mean of the sampling distribution is also 65.
To calculate the standard deviation of the sampling distribution (σ_x), you will use the following formula: σ_x = σ / √n, where σ is the standard deviation of the population and n is the sample size. In this case, the standard deviation of the population is 8 and the sample size is 10. So the standard deviation of the sampling distribution is:
σ_x = 8 / √10 ≈ 2.53
(b) The Central Limit Theorem states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution, provided that the population is not heavily skewed or has extreme outliers. Since the scores are extremely skewed left and the sample size is only 10, it would not be appropriate to use a normal distribution to model the sampling distribution. A larger sample size would be needed to use a normal distribution model.
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Emma notices that since her credit card balance compounds monthly, she is charged more than
15% of her initial loan amount in interest each year. She wants to know how much she would p
the card were compounded annually at a rate of 15%. Which expression could Emma use to
evaluate her balance with an annual compounding interest rate?
300(1. 15)12t
300(1. 015)12
300(1. 0125)
300(1. 15)
To evaluate Emma's credit card balance with an annual compounding interest rate of 15%, she should use the expression 300(1.15)^t. Therefore, the correct option is D.
1. The initial loan amount (principal) is $300.
2. The annual interest rate is 15%, which can be represented as a decimal by dividing by 100 (15/100 = 0.15).
3. Since the interest compounds annually, we only need to multiply the principal by (1 + interest rate) once per year.
4. The expression 1.15 represents (1 + 0.15), which accounts for the principal plus the 15% interest.
5. To find the balance after 't' years, raise the expression (1.15) to the power of 't', representing the number of years.
6. Finally, multiply the principal ($300) by the expression (1.15)^t to find the balance after 't' years.
So, Emma should use the expression 300(1.15)^t to evaluate her balance with an annual compounding interest rate of 15% which corresponds to option D.
Note: The question is incomplete. The complete question probably is: Emma notices that since her credit card balance compounds monthly, she is charged more than 15% of her initial loan amount in interest each year. She wants to know how much she would pay if the card were compounded annually at a rate of 15%. Which expression could Emma use to evaluate her balance with an annual compounding interest rate? A) 300(1.015)^12t B) 300(1.0125)^t C) 300(1.15)^12t D) 300(1.15)^t.
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How much paint will you need to paint all sides of the box shown below? 4m 13m 4m 4m 11m
To paint all sides of the box, you would need approximately 344 square meters of paint.
To calculate the amount of paint needed to paint all sides of the box, we first need to find the total surface area of the box.
The box has five sides: top, bottom, front, back, and two sides.
Given the dimensions:
Top: 4m x 13m
Bottom: 4m x 13m
Front: 4m x 4m
Back: 4m x 4m
Sides (2): 4m x 11m.
To calculate the surface area, we sum the areas of all the sides:
Surface Area = (4m x 13m) + (4m x 13m) + (4m x 4m) + (4m x 4m) + (4m x 11m) + (4m x 11m)
Surface Area = 52m² + 52m² + 16m² + 16m² + 44m² + 44m²
Surface Area = 224m² + 32m² + 88m²
Surface Area = 344m²
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The circumstances if the base of the cone is 12π cm. If the volume of the cone is 96π, what is the height
pleaseee helppp!!
Hence, the cone is 8/3 cm tall as we can get the height using the following formula for a cone's volume.
what is volume ?A three-dimensional object's volume is a measurement of how much space it takes up. It is a real-world physical number that can be expressed in cubic measurements like cubic metres (m3), cubic centimetres (cm3), or cubic feet (ft3). Physics, chemistry, architecture, and mathematics all use the idea of volume extensively. Volume is frequently used to refer to the amount of space that an object or substance takes up, for instance the amount of a container, the volume of either a liquid, or the quantity of a gas. Depending on an object's shape, a different formula is required to determine its volume.
given
The formula V = (1/3)r2h, where V is the volume, r is the radius of the base, and h is the height, can be used to determine the volume of a cone.
Hence, by multiplying the circumference by two, we can determine the radius of the base:
12π / 2π = 6
Thus, the base's radius is 6 cm.
Also, we are informed that the cone's volume is 96. As a result, we can get the height using the following formula for a cone's volume:
V = (1/3)r2h
96 = (1/3)(6/2)h
96 = 36 h
96 / 36 = 8/3
Hence, the cone is 8/3 cm tall as we can get the height using the following formula for a cone's volume.
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devide 240g in to the ratio 5:3:4
Find the area of the following triangle:
5
3
4
Answer:6
Step-by-step explanation:3*4/2=6
In a game of chance players spin the pointer of a spinner with six equal sized sections Anna 1 John 4 Carrie 4 Steve 1 Ethan 2 Liz 4 Jane 1 which outcome has a frequency closest to its expected frequency A (1) B (2) C (3) D (4)
The outcome with a frequency closest to its expected frequency is C (3).
Which outcome in a spinner game has a frequency closest to its expected frequency?In a spinner game where the pointer spins on a wheel with six equal-sized sections, the expected frequency of each section is 1/6 or 16.67%. Based on the given spinner, section A has an expected frequency of 1/6, section B has an expected frequency of 4/6, section C has an expected frequency of 4/6, section D has an expected frequency of 1/6, section E has an expected frequency of 2/6, and section F has an expected frequency of 4/6.
To determine the outcome with a frequency closest to its expected frequency, we need to compare the expected frequency to the actual frequency for each section.
Based on the given spinner, section A has an actual frequency of 1/18, section B has an actual frequency of 4/18, section C has an actual frequency of 4/18, section D has an actual frequency of 1/18, section E has an actual frequency of 2/18, and section F has an actual frequency of 4/18.
Calculating the difference between the expected and actual frequency for each section, we find that section C has the smallest difference, making it the outcome with a frequency closest to its expected frequency.
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A piece of wood, 7.2 m long, is to be cut into smaller pieces. EACH of these pieces should be 0.12 m in length. How many smaller pieces can be obtained?
Answer:
To find the number of smaller pieces that can be obtained, we need to divide the total length of the wood by the length of each smaller piece:
Number of pieces = Total length ÷ Length of each piece
Number of pieces = 7.2 m ÷ 0.12 m
Number of pieces = 60
Therefore, 60 smaller pieces can be obtained from the 7.2 m long piece of wood.
Answer:
60
Step-by-step explanation:
To determine how many smaller pieces can be obtained from a 7.2 m long piece of wood, we need to divide the total length of the wood by the length of each smaller piece.
Total length of wood = 7.2 m
Length of each smaller piece = 0.12 m
Number of smaller pieces = Total length of wood / Length of each smaller piece
Number of smaller pieces = 7.2 m / 0.12 m
Number of smaller pieces = 60
Therefore, 60 smaller pieces can be obtained from a 7.2 m long piece of wood, with each smaller piece being 0.12 m in length.
Please answer 1-9, i really need help tysm
Answer:
the answer is 8
Step-by-step explanation:
it is because if you take your 9 fingers and remove 1 finger it will be 8
Solve the system of equations.
6x – y = 6
6x2 – y = 6
A (0, 6) and (0, –6)
B (1, 0) and (0, –6)
C (2, 6) and (1, –11)
D (3, 12) and (2, 19)
Hillary used her credit card to buy a $804 laptop, which she paid off by making identical monthly payments for two and a half years. Over the six years that she kept the laptop, it cost her an average of $0. 27 of electricity per day. Hillary's credit card has an APR of 11. 27%, compounded monthly, and she made no other purchases with her credit card until she had paid off the laptop. What percentage of the lifetime cost of the laptop was interest? Assume that there were two leap years over the period that Hillary kept the laptop and round all dollar values to the nearest cent)
Percentage of lifetime cost that was interest = $407.
Let's begin by finding the monthly payment that Hillary made to pay off her laptop over two and a half years.
If she paid off the $804 balance with identical monthly payments, then the total amount she paid is equal to the balance plus the interest:
Total amount paid = balance + interest
We can use the formula for the present value of an annuity to solve for the monthly payment, where PV is the present value (in this case, $804), r is the monthly interest rate (which we can find from the APR), n is the total number of payments (30 months), and PMT is the monthly payment:
PV = PMT * (1 - (1 + r)^(-n)) / r
We can solve this equation for PMT:
PMT = PV * r / (1 - (1 + r)^(-n))
The monthly interest rate is the annual percentage rate divided by 12, and the number of payments is the number of years times 12:
r = 0.1127 / 12 = 0.009391667
n = 2.5 * 12 = 30
Using these values, we get:
PMT = 804 * 0.009391667 / (1 - (1 + 0.009391667)^(-30)) = $33.00
So Hillary made 30 monthly payments of $33.00 to pay off her laptop.
Next, we can calculate the cost of electricity over six years. There are 365 days in a year, and 2 leap years in the six-year period, for a total of 6*365+2 = 2192 days.
At $0.27 per day, the total cost of electricity is:
2192 * $0.27 = $592.64
Now we can calculate the total cost of the laptop over six years.
Hillary paid $33.00 per month for 30 months, or a total of 30 * $33.00 = $990.00. She also paid $592.64 for electricity. Therefore, the total cost of the laptop is:
$990.00 + $592.64 = $1582.64
The interest she paid on her credit card is the difference between the total amount she paid and the cost of the laptop:
Interest = Total amount paid - Cost of laptop
Interest = $990.00 + interest on $804 balance - $804 - $592.64
Simplifying this expression, we get:
Interest = $185.36 + interest on $804 balance
To find the interest on the $804 balance, we can use the formula for compound interest, where P is the principal (in this case, $804), r is the annual interest rate (11.27%), and t is the time in years (2.5 years):
A = P*(1 + r/n)^(n*t)
Here, we can set the number of compounding periods per year, n, to 12 since the interest is compounded monthly. Substituting the given values, we get:
A = $804*(1 + 0.1127/12)^(12*2.5) = $1026.12
So the interest on the $804 balance is:
Interest on $804 balance = $1026.12 - $804 = $222.12
Plugging this value into our expression for Interest, we get:
Interest = $185.36 + $222.12 = $407.48
Finally, we can find the percentage of the lifetime cost of the laptop that was interest:
Percentage of lifetime cost that was interest = Interest / Total cost of laptop * 100%
Percentage of lifetime cost that was interest = $407.
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Select the statement that correctly describes the relationship for angles of an inscribed quadrilateral. (10pts pls help)
The opposite angles in an inscribed quadrilateral are supplementary, meaning their sum is 180 degrees.
What is the relationship between the angles of an inscribed quadrilateral, and how related to each other?An inscribed quadrilateral is a quadrilateral whose vertices all lie on a circle. Let's label the vertices of the quadrilateral as A, B, C, and D, in clockwise order.
Draw the circle that contains all four vertices, and label the center of the circle as O.
Now, draw chords AC and BD that cross at point P. Each chord divides the quadrilateral into two triangles. Notice that angle AOC and angle BOD are both central angles that subtend the same arc, CD.
Therefore, these angles have the same measure, and we can write:
angle AOC = angle BOD = x
Similarly, we can show that angle AOB = angle COD = y.
Now, consider the two triangles APC and BPD. These triangles share the side P D and have the same angle APD, which is equal to angle AOC + angle BOD, or 2x.
Therefore, by the angle-sum property of triangles, the other angles in each triangle must also be equal. We can write:
angle APC = angle BPD = (180 - 2x)/2 = 90 - x
Similarly, consider the two triangles APB and CPD. These triangles share the side P C and have the same angle APC, which we just found to be 90 - x.
Therefore, by the angle-sum property of triangles, the other angles in each triangle must also be equal. We can write:
angle APB = angle CPD = (180 - (90 - x))/2 = 90 + x/2
Finally, notice that angle APB + angle CPD = (90 + x/2) + (90 - x/2) = 180, so the opposite angles in the quadrilateral are indeed supplementary.
Therefore, the main answer is: The opposite angles in an inscribed quadrilateral are supplementary, meaning their sum is 180 degrees.
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A 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 6 ft from the house, the base is moving away at the rate of 24 ft/sec.
a. What is the rate of change of the height of the top of the ladder?
b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then?
c. At what rate is the angle between the ladder and the ground changing then?
The rate of change of the height of the top of the ladder is -144/h ft/sec when the base of the ladder is 6 ft from the house.
The area of the triangle formed by the ladder, wall, and ground is decreasing at a rate of 163.2 ft^2/sec when the base of the ladder is 6 ft from the house.
The angle between the ladder and the ground is decreasing at a rate of 1/8 rad/sec when the base of the ladder is 6 ft from the house.
By using Pythagorean Theorem how we find the height, base and angle of the ladder?The rate of change of the height of the top of the ladder, we need to use the Pythagorean Theorem:
[tex]h^2 + d^2 = L^2[/tex]where h is the height of the top of the ladder, d is the distance of the base of the ladder from the house, and L is the length of the ladder.
Taking the derivative with respect to time, t, and using the chain rule, we get:
2h (dh/dt) + 2d (dd/dt) = 2L (dL/dt)We are given that d = 6 ft, dd/dt = 24 ft/sec, and L = 10 ft. We need to find dh/dt when d = 6 ft.
Plugging in the values, we get:
2h (dh/dt) + 2(6)(24) = 2(10) (0) (since the ladder is not changing length)
Simplifying, we get:
2h (dh/dt) = -288Dividing by 2h, we get:
dh/dt = -144/hThe area of the triangle formed by the ladder, wall, and ground is given by:
A = (1/2) bhwhere b is the distance of the base of the ladder from the wall, and h is the height of the triangle.
Taking the derivative with respect to time, t, and using the product rule, we get:
dA/dt = (1/2) (db/dt)h + (1/2) b (dh/dt)We are given that db/dt = -24 ft/sec, h = L, and dh/dt = -144/h. We need to find dA/dt when d = 6 ft.
Plugging in the values, we get:
dA/dt = (1/2) (-24) (10) + (1/2) (6) (-144/10)Simplifying, we get:
dA/dt = -120 + (-43.2)dA/dt = -163.2 ft^2/secThe rate of change of the angle between the ladder and the ground, we use the trigonometric identity:
Dividing by sec^2(theta), we get:
d(theta)/dt = (-24/h^3) - (2h^2/5)
We can plug in the value of h = (L^2 - d^2)^(1/2) = (100 - 36)^(1/2) = 8 ft when d = 6 ft to get:
d(theta)/dt = (-24/8^3) - (2(8)^2/5) = -1/8 rad/secLearn more about Pythagorean theorem
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Find the area of triangle ABC given that AB= 8cm , AC = 6cm , ∠ = 55° ∠ = 35°.
a) 48cm*2 b) 12cm*2 c) 24cm*2 d) 5cm*2
Step-by-step explanation:
so like you use sine rule to find line BC and i got 7.3 the you have to split the triangle in half to get a right angle triangle then divide 7.3 by two to get 3.7 and then use .pythagoras theorem to find the height and then use the area of a triangle formula to get your answer as option (C)
I need to find the perimeter and area of this shape! HELP!!
The perimeter of the shape given is 50 feet, while the area of this shape is 114 square feet.
How to calculate the area and the perimeter?Perimeter measures the total length of the boundary or the outer edge of a two-dimensional shape. On the other hand, the area measures the space enclosed inside a two-dimensional shape. The area of a shape is determined by multiplying its length by its width
Based on this, let's calculate the perimeter:
7 feet + 6 feet + 4 feet + 6 feet + 9 feet + 9 feet + 2 feet + 7 feet = 50 feet
Now, let's calculate the area by dividing the shape in three:
First rectangle:
3 feet x 7 feet = 21 square feet
Second rectangle:
5 feet x 3 feet = 15 square feet
Third rectangle
9 feet x 9 feet = 81 square feet
Total: 21 + 12 + 81 = 114 square feet
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A basket contains a red, a yellow, and a green apple. A second basket contains an orange, a lemon, and a peach. Use an organized list to show all the outcomes in sample space
There are 9 different outcomes in the sample space when selecting one fruit from each basket.
Using an organized list, we can represent all the possible outcomes in the sample space for the two baskets of fruit:
1. Red Apple, Orange
2. Red Apple, Lemon
3. Red Apple, Peach
4. Yellow Apple, Orange
5. Yellow Apple, Lemon
6. Yellow Apple, Peach
7. Green Apple, Orange
8. Green Apple, Lemon
9. Green Apple, Peach
In total, there are 9 different outcomes in the sample space when selecting one fruit from each basket.
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The width of the large size is 9.9 cm and its height is 19.8 cm.
The width of the small size bottle is 4.5 cm.
hcm
h =
4.5 cm
Calculate the height of the small bottle.
19.8 cm
9.9 cm
+
cm
Answer and Explanation:
The height of the small bottle can be calculated using the ratio of the width of the large and small bottles.
Ratio of width = Large bottle width / Small bottle width
Ratio of width = 9.9 cm / 4.5 cm
Ratio of width = 2.2
Therefore, the height of the small bottle can be calculated by multiplying the ratio of width with the height of the large bottle.
Height of small bottle = Ratio of width x Height of large bottle
Height of small bottle = 2.2 x 19.8 cm
Height of small bottle = 43.56 cm
help me find the fraction please
Answer: 9/64
Step-by-step explanation:
First, we find the probability of blue in one spin.
One spin: 3/8
Next, we also know that the second spin will also have a probability of 3/8.
To combine these probabilities in both spins, we multiply. This will combine the two independent events. It can be similar to Permutation.
Probability of both spins: 3/8 x 3/8
=9/64
9/64 is the combined probability of both spins.
After a windstorm, a leaning pole makes a 75° angle with the road surface. the pole casts a 15-foot shadow when the sun is at a 45° angle of elevation. about how long is the pole?
The pole is approximately 3.86 feet tall.
What is the length of a leaning pole that makes a 75° angle with the road surface, if it casts a 15-foot shadow when the sun is at a 45° angle of elevation?
Let's denote the height of the pole as "x" (in feet). From the problem, we know that the pole makes a 75° angle with the road surface, which means that the angle between the pole and the vertical is 90° - 75° = 15°.
Now, we can use the tangent function to find the height of the pole:
tan(15°) = x/15
Multiplying both sides by 15, we get:
x = 15 tan(15°) ≈ 3.86 feet
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BRAINLEST AND 40 POINTS!!
A planet's radius is approximately 2,812 mi. About two-thirds of the planet's surface is covered by water.
Enter an estimate for the land area on the planet. Round the answer to the nearest million.
An estimate for the land area on the planet is
mi?
A planet's radius is approximately 2,812 mi. About two-thirds of the planet's surface is covered by water. An estimate for the land area on the planet is 33 million mi²
The surface area of a sphere is given by the formula:
S = 4πr²
where S is the surface area and r is the radius.
Substituting the given radius, we get:
S = 4π(2,812)²
S ≈ 99,392,252.4 mi²
Since two-thirds of the planet's surface is covered by water, we can estimate the land area as one-third of the total surface area:
Land area ≈ (1/3) x 99,392,252.4
Land area ≈ 33,130,750.8 mi²
Rounding this to the nearest million, we get an estimate of 33 million mi² for the land area on the planet.
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