Since the triangle was rotated by 30 degrees, the angle AOA' is 30 degrees, as is the angle A'OC. Thus, m/AOC is equal to 60 degrees. To demonstrate that BD is perpendicular to CD, OB = OC, angles AOB and COA are both 60 degrees, and angles BOD and COD are both 60 degrees. BD and CD are both perpendicular to the diameter through A.
What is an equilateral triangle?A triangle is said to be equilateral if all three of its sides are the same length and all three of its angles are exactly 60 degrees. It has three regular sides and is a polygon. When dividing an equilateral triangle into two congruent 30-60-90 triangles, the altitude, median, and angle bisector from any vertex are also the same line.
5. Let's identify the circle's intersection points as the equilateral triangle's A, B, and C. All angles in a triangle that is equilateral are 60 degrees. Point A will change locations when the triangle is rotated by 30 degrees; let's designate this new position A'. Since O is the centre of the circle, the angle AOC remains at 60 degrees. Since the triangle has been turned by 30 degrees, the angle AOA' is 30 degrees, as is the angle A'OC. Thus, m/AOC is equal to 60 degrees.
6. The center of the circle is O, and D is the point where the diameter through B intersects the diameter through C. To demonstrate that BD is perpendicular to CD, the center of the circle, OB = OC, and angles AOB and COA are both 60 degrees, so angle BOC is 120 degrees. Angle BOD is a right angle, and angle OBD is half of angle BOC, so it is 60 degrees. Angle COD is also a right angle, and angle OCD is half of angle BOC, so it is also 60 degrees. Since angles OBD and OCD are both 60 degrees, and they are angles in a triangle, the third angle (angle BDC) must also be 60 degrees.
Therefore, triangle BDC is equilateral, and BD = CD. Since BD and CD are both perpendicular to the diameter through A, BD is perpendicular to CD.
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A group of people were asked if they had run a red light in the last year. 220 responded "yes", and 209 responded "no".
Answer:
[tex]\frac{20}{19}[/tex] or ≈ 1.053
Step-by-step explanation:
We Know
220 responded 'yes', and 209 responded 'no'
Find the probability that if a person is chosen at random, they had run a red light in the last year.
The probability is: [tex]\frac{220}{209}[/tex] = [tex]\frac{20}{19}[/tex] ≈ 1.053
So, the answer is [tex]\frac{20}{19}[/tex] or ≈ 1.053
Help with this question
Answer:
(x - 4)(x - 7)
Step-by-step explanation:
x² - 11x + 28
consider the factors of the constant term (+ 28) which sum to give the coefficient of the x- term (- 11)
the factors are - 4 and - 7 , since
- 4 × - 7 = + 28 and - 4 - 7 = - 11
then
x² - 11x + 28 = (x - 4)(x - 7) ← factored form
Linearise cos^5(x). Help asap please
detailed answer (so much details are needed)
the answer should be:
[tex]\frac{1}{16} *(cos5x +5cos3x+10cosx)[/tex]
The final answer for linearizing the function f(x) = cos^5(x) around a = 0 is:
f(x) ≈ 1.
What is linearizing?Linearizing a function is the process of approximating the behavior of a function by a linear function (i.e., a function of the form y = mx + b) in a certain region around a specific point.
Linearization is useful because linear functions are easy to work with mathematically, and they can provide a good approximation of the original function near the point of interest. By linearizing a function, we can simplify calculations and make predictions about the behavior of the function in the vicinity of the point of interest.
In the given question,
To linearize the function f(x) = cos^5(x) around a point a, we can use the first two terms of the Taylor series expansion:
f(x) ≈ f(a) + f'(a)(x - a)
where f'(a) is the first derivative of f evaluated at x = a.
In this case, we want to linearize around a = 0, so we have:
f(x) ≈ f(0) + f'(0)(x - 0)
To find f(0) and f'(0), we need to evaluate the function and its derivative at x = 0:
f(x) = cos^5(x)
f(0) = cos^5(0) = 1
f'(x) = 5cos^4(x)(-sin(x))
f'(0) = 5cos^4(0)(-sin(0)) = 0
Therefore, the linearization of f(x) = cos^5(x) around a = 0 is:
f(x) ≈ 1 + 0(x - 0) = 1
So the linearization is simply the constant function f(x) = 1. This means that for small values of x, the function cos^5(x) can be approximated by the constant function 1. The accuracy of this approximation depends on how small x is and how far away x is from 0.
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[Maximum mark: 5] The diagram shows a sector AOB of a circle with centre O and radius r. The triangle AOB is equilateral and has perpendicular height 5 cm.
a) show that the radius of the sector is 10√3/3 cm.
b) find in terms of π, the perimeter P of the sector.
Answer:
Step-by-step explanation:
In (b) you may be more used to the formula for arc length: [tex]P=\frac{\theta }{180} \times \pi r[/tex].
The result is the same.
Can anyone help me answer this? the question is given below?
For the second attachment was the question
The average rate of change of the function is 3.
How to find the average rate of change of a function?The average rate of change of a function is given by the formula:
average of change = (f(b) - f(a)) / (b - a)
Where [a, b] is the interval of the function
f(x) = x³ + 2x; [-1, 1]
average rate of change = ([ 1³ + 2(1)] - [ (-1)³ + 2(-1)]) / (1 - (-1))
average rate of change = (3 - (-3))/(1 + 1)
average rate of change = 6/2
average rate of change = 3
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Which quadrilateral has one, and only one, line of symmetry?
rectangle square isosceles trapezoid or parallelogram?
URGENT: Describes the relationship between the line that passes through (7,1) and (10,5) and the line that passes through (-8,5) and (-5,9)
The relationship between the lines are they have same slope and they are parallel.
What is slope?
If [tex](x_1,y_1) \: and \: (x_2,y_2) [/tex] are two points on line then slope of the line will be [tex]m= \frac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]
To determine the relationship between the two lines, we need to find out if they are parallel, perpendicular, or neither.
First, we can find the slope of the line passing through (7,1) and (10,5) using the slope formula:
[tex]m_1 = \frac{(y_2 - y_1)}{(x_2 - x_1)} \\ m_1 = \frac{ (5 - 1)}{(10 - 7)} \\ m_1 = \frac{4}{3} [/tex]
Similarly, we can find the slope of the line passing through (-8,5) and (-5,9):
[tex]m_2 = \frac{ (y_2 - y_1) }{ (x_2 - x_1)} \\ m_2 = \frac{(9 - 5) }{(-5 - (-8))} \\ m_2 = \frac{4}{3} [/tex]
Since both lines have the same slope of 4/3, they are parallel to each other.
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9. Evaluate if p =-7, q = -2.
a. p + q
b. p - q
c. q - p
d.-p - q
Answer:
d
Step-by-step explanation:
trust me bro im a math teacher
The radius of a sphere is 10 units. Find the volume of the sphere. Write your answer in terms of pi. The volume is __cubic units
Answer:
4000/3 * π
Step-by-step explanation:
The formula for the volume of a sphere is;
V = (4/3) * π * r^3
Where;
r = the radius of the sphere
Substituting the given value, we get;
r = 10
V = (4/3) * π * (10)^3
= (4/3) * π * 1000
= 4000/3 * π
Therefore the volume of the sphere is (4000/3)π cubic units.
Rick has been collecting stamps. After one week, he had collected 6 stamps and each week following, he collected 3 more.
How many stamps will he have after 10 weeks?
[tex]Step-by-step-explanation-& Answer[/tex]
Well if our friend Rick continues the pattern that is shown in the question then the answer is at the bottom
Lets do some addition:
(6+3) * 5 ( 5 x 2 = 10 )
First find the parenthesis, 6 + 3 = 9
Next multiply, 9 x 5 = 45
Thus the answer to your problem is:
[tex]\left[\begin{array}{ccc}A&N&S\\=&=&=\\4&5&!\end{array}\right][/tex]
Type your response in the box.
Think about the impact on the consumer as you read these scenarios. Then answer the question that follows.
Scenario 1
Carlos is doing his weekly grocery shopping and needs to buy cereal. He turns his cart into the cereal aisle at the store. He sees many different cereals within his price range but notices that some are priced higher than others. He chooses a cereal he recognizes from a TV commercial, even though it’s slightly more expensive than he expected.
Scenario 2
Evelyn wants to purchase a plane ticket to visit her sister in London. She’s been checking prices frequently the past few days and notices that prices aren’t falling as she anticipated. She also notices that despite five airlines flying to London from the city she lives in, the prices of the tickets are all the same. She eventually decides not to go because the prices are too high for her budget.
What affected the purchasing decisions in these two scenarios?
The purchasing decisions in both scenarios were affected by the prices of the products/services being considered.
What is meant by budget?
In general, a budget is a financial plan or estimate that outlines the expected income and expenses over a specific period.
The purchasing decisions in both scenarios were affected by the prices of the products/services being considered.
In scenario 1, Carlos chose a more expensive cereal because he recognized it from a TV commercial, which may have influenced his perception of its quality or desirability.
In scenario 2, Evelyn decided not to purchase a plane ticket because the prices were too high for her budget, despite there being multiple airlines offering flights to London.
Therefore,The purchasing decisions in both scenarios were affected by the prices of the products/services being considered.
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I’m a certain magnetic field the cross-sectional area is 0.5 meter square and the flux is 1500 uwb what is the flux density
The flux density is 3000 uT.
Flux density (B) is a measure οf the strength οf a magnetic field in a given regiοn.
Hοw tο calculate flux density fοr the given prοblem?It is defined as the amοunt οf magnetic flux () that passes thrοugh a unit area (A) perpendicular tο the magnetic field's directiοn.
The flux density (B) can be calculated using the fοrmula:
B = Φ / A
where 'Φ' is -> flux and A is the -> crοss-sectiοnal area.
Plugging in the values given, we get:
B = 1500 uWb / 0.5 m²
B = 3000 uT (micrοtesla)
Therefοre, the flux density is 3000 uT.
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IFA has made a football of diameter 14 cm from leather. 3% leather is wasted. If the cost of leather including labo er sq.cm, find the total cost of leather purchased to make
the total cost of leather purchased to make the football is $30.79.
how to find volume of football?The volume of a football can be calculated using the formula for the volume of a sphere:
V = (4/3)πr³
Where r is the radius
Given that the diameter of the football is 14 cm and the radius is half of the diameter, so radius is 7 cm.
So, the volume of the football is:
V = (4/3)π(7 cm)³
= 1437.33 cm³
Now, we know that 3% of the leather is wasted,
so the amount of leather to make the football is:
(100% - 3%) = 97% of the total leather purchased.
Therefore, the amount of leather used to make the football is:
0.97 × 1437.33 cm³ = 1394.19 cm³
To find the total cost of the leather purchased, we need to know the cost of leather per square centimeter. Let's assume that the cost of leather including labor is $0.05 per square centimeter.
The surface area of a sphere can be calculated using the formula:
A = 4πr²
So, the surface area of the football is:
A = 4π(7 cm)²
= 615.75 cm²
the total cost of the leather:
Cost of leather = Cost per square centimeter × Surface area of the football
= $0.05/cm² × 615.75 cm²
= $30.79
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(f+g)(x)= f(x) * g(x)
true or false
Answer:
true
Step-by-step explanation:
Please help with solving this problem
Answer:
Step-by-step explanation:
Answer:
the first car drove 30 miles and the second drove 35
Step-by-step explanation:
1. add how many mile they can travel together.
15+20=35
2. subtract 35 from 65 and whats left is how youll determine which car drove how many the lower number goes to the lower miled vehicle.
POSSIBLE POINTS: 18.18
A sequence of transformations is applied to a polygon. Which of the following statements represent a sequence of transformations where the
resulting polygon is similar to the original polygon but has a smaller area than the original polygon? Select TWO that apply.
a reflection over the y-axis followed by a translation of 10 units down and a dilation about the origin by a scale factor of 2
a dilation about the origin by a scale factor of 2/3 followed by a rotation of 90° counterclockwise about the origin and a translation 5
units left
a rotation of 180° counterclockwise about the origin followed by a dilation about the origin by a scale factor of 5/2
a dilation about the origin by a scale factor of 5/7 followed by a reflection over the y-axis and a dilation about the origin by a scale
factor of 3/4
Answer:
C, D
Step-by-step explanation:
Any rigid transformation (rotation, translation, reflection) will result in a congruent polygon. To make a similar (smaller) polygon, a dilation by a factor less than 1 must be used.
C. a dilation about the origin by a scale factor of 2/3 followed by a rotation of 90° counterclockwise about the origin and a translation 5 units left
D. a dilation about the origin by a scale factor of 5/7 followed by a reflection over the y–axis and a dilation about the origin by a scale factor of 3/4
A point in the table for the transformed function is
Answer:
linear function
Step-by-step explanation:
straight line then add up
suzie lives in dauphin manitoba. she wants to buy a new truck. the base price is $27 280. she has $2450 for a down payment. she must pay the extra changes at the right. how much must suzie pay on delivery
Suzie must pay $27,864 on delivery for the new truck. To determine how much Suzie must pay on delivery, we need to add the extra charges to the base price of the truck and subtract the down payment she already made.
Let's first list the extra charges:
Freight and PDI: $1,650
Air Tax: $100
Tire Tax: $20
GST (Goods and Services Tax): 5%
To calculate the extra charges, we can use the following formula:
Extra charges = Freight and PDI + Air Tax + Tire Tax + (GST x Base Price)
Substituting the given values, we get:
Extra charges = 1650 + 100 + 20 + (0.05 x 27280)
Extra charges = 1650 + 100 + 20 + 1364
Extra charges = 3134
Therefore, the total cost of the truck, including extra charges, is:
Total cost = Base price + Extra charges - Down payment
Total cost = 27280 + 3134 - 2450
Total cost = 27864
Thus, Suzie must pay $27,864 on delivery for the new truck.
It's important to note that the amount Suzie will actually pay will depend on the financing and payment options available to her. She may be able to spread out the payments over a longer period of time or negotiate a different down payment amount. It's always a good idea to research and compare different financing options before making a major purchase like a new vehicle.
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Ruth has $4,942 in an account that earns 12% interest compounded annually.
To the nearest cent, how much will she have in 1 year?
Ruth will have the principal is approximately $5,534.04 in 1 year at earns 12% interest compounded annually.
What is principal?
To find how much Ruth will have in 1 year, we can use the formula for compound interest:
A = [tex]P(1 + r/n)^{n*t}[/tex]
where A is the amount after t years, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years.
Plugging in the given values, we get:
A = [tex]$4,942(1 + 0.12/1)^{1*1}[/tex]
A = $4,942(1.12)
A = $5,534.04
Therefore, Ruth will have approximately $5,534.04 in 1 year.
What is an interest?
Interest is the amount of money charged by a lender to a borrower for the use of money over a period of time. It is typically calculated as a percentage of the amount borrowed or invested, and is often expressed as an annual percentage rate (APR). Interest can be simple or compound, depending on whether it is calculated only on the principal amount or on both the principal and accumulated interest. Interest is an important concept in finance and economics, and is used in a wide range of financial transactions, including loans, investments, and savings accounts.
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Jose bought 100 shares of stock at 17 5/8 and sold it for 21 1/4. What was his profit in dollars
Answer: 3.625 or 3 5/8
Step-by-step explanation:
So I personally would turn everything into decimals and subtract.
21.250 -17.625
And using our handy calculator, you get
3.625
2% of what number is 91 ?
Answer:
4550
Step-by-step explanation:
Answer:
4,550
Step-by-step explanation:
4,550 x 2% = 91
Consider the set K = (triangle upsidedown triangle square rectangle)
Let inversion be defined on K as a physical act of turning a member of K upside down. What is triangle?
If inversion be defined on K as a physical act of turning a member of K upside down. Then it will be the upside-down triangle.
consider the set K = (triangle, upside-down triangle, square, rectangle). Inversion is defined on K as the act of turning a member of K upside down.
To determine which shape is the triangle, follow these steps:
1. Identify the properties of each shape in set K:
- Triangle: 3 sides and 3 angles
- Upside-down triangle: same properties as a triangle, but inverted
- Square: 4 sides, all equal in length, and 4 right angles
- Rectangle: 4 sides, opposite sides equal in length, and 4 right angles
2. Analyze the effect of inversion on each shape:
- Triangle: Inverting a triangle results in an upside-down triangle.
- Upside-down triangle: Inverting an upside-down triangle results in a regular triangle.
- Square: Inverting a square does not change its appearance.
- Rectangle: Inverting a rectangle does not change its appearance.
3. Identify the shape that becomes a triangle after inversion:
- The upside-down triangle becomes a regular triangle after inversion.
So, the shape in set K that corresponds to the triangle after applying inversion is the upside-down triangle.
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Use an identity to write the expression as a single trigonometric function or as a single number. sin 28⁰/ 1 + cos 28°
Answer: We can simplify the expression by using the identity for the tangent of half an angle:
tan(x/2) = sin(x) / (1 + cos(x))
where x is the angle in radians. We can use this identity by setting x = 56° since 2*28°= 56°.
So, we have:
sin(28°) / (1 + cos(28°)) = tan(56°/2)
We know that 56°/2 = 28°, so we have:
tan(28°)
Therefore, the expression simplifies to a single trigonometric function:
tan(28°)
Step-by-step explanation:
Given Z₁= 2+j4, and Z₂ = 3-j, determine: i Z₁+Z2 ii Z₁-Z₂ iii Z₂-Z₁ iv Show the results on an Argand diagram.
The coordinate of the complex numbers are plotted on a graph below
What are the values of the complex numbersi) Z₁ + Z₂ = (2+j4) + (3-j) = (2+3) + (j4-j) = 5 + j3
ii) Z₁ - Z₂ = (2+j4) - (3-j) = (2-3) + (j4+j) = -1 + j5
iii) Z₂ - Z₁ = (3-j) - (2+j4) = (3-2) + (-j-4j) = 1 - j5
iv) To represent these complex numbers on an Argand diagram, we plot the real part on the x-axis and the imaginary part on the y-axis.
Z₁ = 2 + j4 can be represented as a point in the complex plane with coordinates (2,4).
Z₂ = 3 - j can be represented as a point in the complex plane with coordinates (3,-1).
Using these coordinates, we can plot the results from parts (i) to (iii) as follows:
(i) Z₁ + Z₂ = 5 + j3 can be represented as a point in the complex plane with coordinates (5,3).
(ii) Z₁ - Z₂ = -1 + j5 can be represented as a point in the complex plane with coordinates (-1,5).
(iii) Z₂ - Z₁ = 1 - j5 can be represented as a point in the complex plane with coordinates (1,-5).
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Find x round to the nearest 100th
Is the slope of the line illustrated in the graph below positive or negative?
Moving from left to right, the line starts in the upper left-hand quadrant, passes through the x-axis into the lower left-hand quadrant, and then crosses the y-axis, passing into the lower right-hand quadrant.
Answer: change in y divided by change in x
Step-by-step explanation: The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run"
Triangle ABC is reflected over the line y=2 to obtain triangle A'B'C'. Then triangle A'B'C' is translated by the directed line segment from (0,0) to (3,2) to obtain triangle A"B"C".
Answer: To obtain triangle A'B'C' from triangle ABC by reflection over the line y = 2, we reflect each point of the triangle over the line. This gives us:
A' = (A_x, 4 - A_y)
B' = (B_x, 4 - B_y)
C' = (C_x, 4 - C_y)
To obtain triangle A"B"C" from triangle A'B'C' by translation by the directed line segment from (0,0) to (3,2), we add the vector (3,2) to each point of the triangle. This gives us:
A" = (A'_x + 3, A'_y + 2) = (A_x + 3, 6 - A_y)
B" = (B'_x + 3, B'_y + 2) = (B_x + 3, 6 - B_y)
C" = (C'_x + 3, C'_y + 2) = (C_x + 3, 6 - C_y)
Therefore, the vertices of triangle A"B"C" are (A_x + 3, 6 - A_y), (B_x + 3, 6 - B_y), and (C_x + 3, 6 - C_y).
Step-by-step explanation:
in exercises 1 and 2 find the scale factor. then list all pairs of congruent angles and write the ratios of the corresponding side lengths in a statement of proportionality
Answer:
Step-by-step explanation:
99+988
Which expression is a factor of 2x^2 + 10x -48
Answer choices
A : x + 3
B: x-6
C: x+8
D: x+16
Answer:
[tex]2 {x}^{2} + 10x - 48[/tex]
[tex]2( {x}^{2} + 5x - 24)[/tex]
[tex]2(x + 8)(x - 3)[/tex]
So C is correct.
20-4=5908
is it true or is it not
Answer: Not true
Step-by-step explanation:
This isn't true.
There is no way to manipulate the number 20 to get the number 5908 by subtraction or any other arithmetic operation.
Therefore, "20-4=5908" is false.