The number of ways to choose 6 letters from a set of 13 is given as follows:
a) Order does not matter: 1716.
b) Order matters: 1,235,520.
When to use permutation and when to use combination?A combination is used when the order does not matter, hence, for item a, the number of ways is obtained as follows:
C(13,6) = 13!/(6!7!) = 1716.
A permutation is used when the order matters, hence, for item b, the number of ways is obtained as follows:
P(13,6) = 13!/7! = 1,235,520.
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Rate of change In gallons of gas per year from 1995 to 1997???!?
The rate of change In gallons of gas per year from 1995 to 1997 is: C. Δg/Δt = 4 gal/year.
How to calculate the rate of change?In Geometry, the rate of change of the data in this table can be calculated by using this mathematical equation;
Rate of change (slope), m = (Change in y-axis, Δg)/(Change in x-axis, Δt)
Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)
From the information provided in the graph above, we can logically deduce the following data points located on the line:
Points on the x-coordinate = (1995, 1997).Points on the y-coordinate = (530, 538).Substituting the given data points into the rate of change formula, we have the following;
Rate of change (slope), Δg/Δt = (y₂ - y₁)/(x₂ - x₁)
Rate of change (slope), Δg/Δt = (538 - 530)/(1997 - 1995)
Rate of change (slope), Δg/Δt = 8/2
Rate of change (slope), Δg/Δt = 4 gallon/year.
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review the select balance sheet and income statement for apple, inc. (found in the 10-k). for the account assigned to you (see below on assignments), identify assertions that you think are relevant for the assigned accounts.
The assertions relevant for Trade and other receivables are existence, rights and obligations, completeness, and valuation.
Account Assigned: Trade and other receivables
The assertions relevant for Trade and other receivables are existence, rights and obligations, completeness, and valuation.
Existence assertion means that the receivables must exist and they must be recorded in the books of Apple Inc. Rights and obligations assertion means that the receivables must be legally enforceable, and Apple Inc. must have the right to receive the payment from its customers. Completeness assertion means that all the receivables must be recorded in the books of Apple Inc. Valuation assertion means that the receivables must be recorded in Apple Inc.’s financial statements at the correct amount. Valuation can be measured by calculating the amount of receivables as a percentage of total revenue. For example, if the total revenue is $100 million and the total receivables are $20 million, then the receivables are 20% of total revenue.
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1 to 11 for 100 points (serious answers or report and 1 star)
Based on isosceles trapezoid base angle theorem the sides AD and BC demonstrated that corresponding parts are congruent.
What is isosceles trapezoid base angle theorem?It is a 2-dimensional geometry defined as a quadrilateral with four sides, two of which are parallel to each other.
We provided a trapezoid in which:
BA ≅ CD
It is necessary to demonstrate BD ≅ CD
We can demonstrate this by doing the following:
ABCD is a trapezoidal shape (given)
BA ≅ CD (given) (given)
ABCD is a trapezoid with isosceles angles (definition of isosceles trapezoid)
AD ≅ AD (by using reflexive property) (by using reflexive property)
Angle BAD is congruent to Angle CDA = 5) theorem of base angles
BAD angle CDA angle (base angle theorem)
BD ≅ CA (corresponding parts of congruent triangles are congruent) (corresponding parts of congruent triangles are congruent)
As a result, AD ≅ BC has demonstrated that corresponding parts of congruent triangles are congruent.
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help me white this for brainliested
Answer:
please take a better picture
Step-by-step explanation:
What does x equal???
here is ur answer seeee now
In a certain bag, the ratio of red to green to blue marbles is 1:2:3 . There are 5 red marbles. How many blue marbles are there?
Explanation
The ratio 1:2:3 refers to the idea we could have: 1 red, 2 green, 3 blue. The order of the colors is important. Follow the order mentioned in the 1st sentence of the instructions. That order being red:green:blue.
Then the instructions mention that there are actually 5 red (instead of 1 red). This means we multiply each part of the ratio by 5
1*5 = 5 red2*5 = 10 green3*5 = 15 blueThe ratio 1:2:3 scales up to 5:10:15
We see that there are 15 blue marbles
what is the y intercept
x y
34 -52
51 -65
68 -78
Answer:
y- intercept = - 26
Step-by-step explanation:
to find the y- intercept, obtain the equation of the line in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (34, - 52) and (x₂, y₂ ) = (68, - 78) ← 2 ordered pairs from the table
m = [tex]\frac{-78-(-52)}{68-34}[/tex] = [tex]\frac{-78+52}{34}[/tex] = [tex]\frac{-26}{34}[/tex] = - [tex]\frac{13}{17}[/tex] , then
y = - [tex]\frac{13}{17}[/tex] x + c
to find c substitute any of the ordered pairs into the equation and solve for c
using (51, - 65 ) , then
- 65 = - [tex]\frac{13}{17}[/tex] (51) + c = - 39 + c ( add 39 to both sides )
- 26 = c
then y- intercept = - 26
What is the following difference?? PLSS help
The simplified expression is ab∛ 3ab².
The correct option is (C).
What are Exponents and Power?Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.
For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.
Given:
2ab (∛192ab²) -5(∛81 [tex]a^4b^5[/tex])
Now, factorizing the terms as
192ab² = 2 x 2 x 2 x 2 x 2 x 2 x 3 x a x b x b
81 [tex]a^4b^5[/tex] = 3 x 3 x 3 x 3 x a x a x a x a x b x b x b x b x b
So, 2ab (∛192ab²) -5(∛81 [tex]a^4b^5[/tex])
= 2ab (∛2 x 2 x 2 x 2 x 2 x 2 x 3 x a x b x b) -5(∛3 x 3 x 3 x 3 x a x a x a x
a x b x b x b x b x b)
= 2ab ( 2 x 2 ∛ 3 x a x b x b) -5( 3 x a x b ∛3 x a x b x b )
= 8ab ∛ 3ab² - 15ab∛ 3ab²
= -7ab ∛ 3ab²
Hence, the simplified expression is ab∛ 3ab².
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Find the missing coordinate of P, using the fact that P lies on the unit circle in the given quadrant.
Coordinates Quadrant
P( , -5/7) IV
The missing coordinate of P, using the fact that P lies on the unit circle in the given quadrant is √(2/7) or √(2/7)
The unit circle is a circle with a radius of 1 centered at the origin (0,0) on a coordinate plane. If a point P lies on the unit circle, then the distance from the origin to P is 1.
We can use the distance formula to find out the missing coordinate of P.
The distance formula: [tex]d = \sqrt((x2 - x1)^2 + (y2 - y1)^2)[/tex]
where (x1, y1) is origin and (x2, y2) is the point P.
Given in the problem that P is in Quadrant IV, then the (x, y)-coordinate is negative.
So we can use the given information and the distance formula to find out the missing coordinate.
[tex]d = \sqrt((x2 - 0)^2 + (y2 - 0)^2) = 1[/tex]
x2 = -5/7, y2 = -5/7
[tex]d = \sqrt((-5/7 - 0)^2 + (-5/7 - 0)^2) = \sqrt((-5/7)^2 + (-5/7)^2) = \sqrt(25/49 + 25/49) = \sqrt(50/49) = \sqrt(2/7) = 1[/tex]
Therefore, the missing x coordinate of P is √(2/7) or √(2/7)
P = (-5/7,√(2/7))
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Question 5 Piecewise graphs. Graph each of the given functions. Be sure to clearly indicate possible points that may be significant. 2 (a) f(x) = x^2 +1
The function f(x) = x^2 + 1 can be graphed using the coordinates (x, y) where x is the x-coordinate, and y is the y-coordinate.
This function can be written as y = x^2 + 1. Using this equation, we can plot the graph of the function. To plot the graph, we need to plot points on the x-axis and y-axis. The x-axis is the horizontal line and the y-axis is the vertical line.
For example, let us take a point x = 0. Substituting x = 0 in the equation f(x) = x^2 + 1, we get y = 0^2 + 1, which is equal to 1. So, we can plot the point (0,1) on the graph. Similarly, we can plot the point (1,2), (2,5), (3,10), (4,17), (5,26), and so on.
By plotting all these points, we can get the graph of the function f(x) = x^2 + 1. This graph is a parabola with vertex at (0,1). It is an increasing function, which means that as the value of x increases, the value of y also increases. The graph is also symmetric about the y-axis.
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The cost of manufacturing a particular videotape is C(x) = 9000 + 9x, where x is the number of tapes produced. The average cost per tape, denoted by overbar(C)(x), is found by dividing C(x) by x. Find (x→9000) is under (lim)overbar(C)(x).
The average cost per tape is 10.
What is average cost?The average cost is the ratio of the total of cost of all the products to the total number of products. We can calculate the average cost by dividing the total cost by the total output quantity.
The cost of manufacturing a particular videotape is :
C(x) = 9000+9x
Where
x is the number of tapes produced.
We need to find the value of average per tape i.e. lim x →9000 C (x)
C (x) = 9000 + 9x
x
= 9000 + 9
x
Lim n→ 9000 C (x) = 9000 +9
9000
= 1 + 9
= 10
So, the average cost per tape is 10
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2. The table shown below shows some values for functions f(x) and g(x). What is/are the solution(s)
when f(x) = g(x)? Explain your answer
Answer: x= -3 and x= -1
Step-by-step explanation:
We can see from table that when x= -3, the f(x) have the same y with g(x). Also when x= -1, the f(x) have the same y with g(x).
A spaceship approaches the Moon along a parabolic trajectory which is almost tangent to the Moon's surface. At the moment of the maximum approach the brake rocket was fired for a short time interval, and the spaceship was transferred into a circular orbit of a Moon satellite. Find how the spaceship velocity modulus increased in the process of braking.
The spaceship's velocity modulus increased due to the firing of the brake rocket in order to transfer the spacecraft into a circular orbit of the Moon satellite.
When approaching the Moon, a spacecraft follows a parabolic trajectory which is almost tangent to the Moon's surface. At the moment of maximum approach, the brake rocket is fired for a short time interval. This causes a decrease in the spacecraft's velocity and an increase in its centripetal force. This, in turn, causes the spacecraft to move away from the Moon and into a circular orbit of a Moon satellite. The increased centripetal force causes the spacecraft to accelerate, and thus its velocity modulus increases. The magnitude of this increase in velocity modulus depends on the duration and power of the brake rocket. In conclusion, the velocity modulus of the spacecraft increases due to the firing of the brake rocket.
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Consider a pool of six I/O buffers. Assume that any buffer is just as likely to be available or occupied as any other. Compute the probabilities associated with the following events:
A = At least two but no more than five buffers occupied.
B = At least three but no more than five buffers occupied.
C = All buffers available or an even number of buffers occupied.
D = At least one of the events A, B, and C occurs.
The associated probabilities are A = At least two but no more than five buffers occupied.
There are a total of 2^6 = 64 possible outcomes when rolling 6 dice.
To find the probability of event A, we need to find the number of outcomes where at least two but no more than five buffers are occupied.
This can be done by summing the probabilities of each individual outcome where two, three, four, or five buffers are occupied and subtracting the probabilities where six or zero buffers are occupied.
The probability of two buffers being occupied is (6 choose 2)(1/64) = 15/64
The probability of three buffers being occupied is (6 choose 3)(1/64) = 20/64
The probability of four buffers being occupied is (6 choose 4)(1/64) = 15/64
The probability of five buffers being occupied is (6 choose 5)(1/64) = 6/64
So the probability of event A is (15/64) + (20/64) + (15/64) + (6/64) = 56/64.
B = At least three but no more than five buffers occupied.
To find the probability of event B, we need to find the number of outcomes where at least three but no more than five buffers are occupied.
This can be done by summing the probabilities of each individual outcome where three, four, or five buffers are occupied and subtracting the probability where six buffers are occupied.
The probability of three buffers being occupied is (6 choose 3)(1/64) = 20/64
The probability of four buffers being occupied is (6 choose 4)(1/64) = 15/64
The probability of five buffers being occupied is (6 choose 5)*(1/64) = 6/64
So the probability of event B is (20/64) + (15/64
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Let us choose some number t and consider a point A(2t+3,24t+1).Prove that all such points make a line.What is the slope and the y intercept of this line?
The parametric vector represents a line, whose slope and intercept are 12 and - 35, respectively.
How to analyze and interpret parametric functions
Parametric functions are multi-dimensional functions in terms of a variable t that is a real number. In this problem we find a parametric function with coordinates, that is, a vector of the form (x, y) = (f(t), g(x)) and we are supossed to determine the rectangular form of such function, that is, a function of the form:
y = f(x)
The rectangular form of the function is a line if and only if the resulting expression is of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variabley - Dependent variableFirst, write the components of the parametric functions:
x = 2 · t + 3
y = 24 · t + 1
Second, clear variable t in each parametric expression:
t = (x - 3) / 2
t = (y - 1) / 24
Third, eliminate parameter t by transitive property:
(x - 3) / 2 = (y - 1) / 24
Fourth, obtain the equation of the line:
24 · (x - 3) = 2 · (y - 1)
24 · x - 72 = 2 · y - 2
24 · x - 70 = 2 · y
y = 12 · x - 35
Fifth, determine the slope and intercept of the equation of the line:
m = 12, b = - 35
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What is the inverse of function f? f(x) = √x + 7
The inverse of the given function is [tex]f^{-1}(x) = (x-7)^2[/tex].
What is inverse of function?A function that may reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y.
Given that the equation of the function is:
f(x) = √x + 7
Covert the given function into an equation:
y = √x + 7
Interchange the variables in the equation:
x = √y + 7
Isolate the value of y.
Subtract, 7 from both sides of the equation:
x - 7 = √y + 7 - 7
x - 7 = √y
Take square on both sides of the equation:
(x-7)² = (√y)²
(x-7)² = y
Replace, y with [tex]f^{-1}(x)[/tex].
[tex]f^{-1}(x) = (x-7)^2[/tex]
Hence, the inverse of the given function is [tex]f^{-1}(x) = (x-7)^2[/tex].
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Write the polynomial that represents the perimeter of the figure pictured below.
The polynomial that represents the perimeter of the figure is 3x
How to determine the perimeter of the triangleFrom the question, we have the following parameters that can be used in our computation:
Side length = x
Triangle type = equilateral triangle
See attachment for the figure
The perimeter of an equilateral triangle can be calculated as
P = 3 * side length
substitute the known values in the above equation, so, we have the following representation
P = 3 * x
So, we have the following representation
P =3x
Hence, the perimeter expression is 3x
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How to Use a Graphing Calculator to Solve a Word Problem Involving a Local Extremum of a Polynomial Function.
The graphing calculator was used to identify the coordinates of the local extremum point of the polynomial function. This allowed us to find the solution to the word problem by finding the x and y coordinates of the extremum point.
Using a Graphing Calculator to Find the Local Extremum of a Polynomial FunctionBegin by entering the polynomial function into your graphing calculator.Set the calculator to graph the function by pressing the appropriate keys.Observe the graph and locate any local extremum points.Using the calculator’s zoom feature to better view the graph, identify the x-coordinate of the local extremum point.Enter the x-coordinate of the local extremum point into your calculator and press the “Evaluate” key.The calculator will display the y-coordinate of the local extremum point. This is the solution to the word problem.Learn more about Graphing Calculator: https://brainly.com/question/28969437
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75% of Benny's toy vehicles are trucks if he has 45 trucks how many toy vehicles does Benny have not picked the model that represents the problem how many toy vehicles does Benny have enough
Answer:
Bottom model and has 60 toys in all
Step-by-step explanation:
Hannah makes 5 out of 8 attempted free-throws! What is the average waiting time for Hannah to make her first basket, and what is the probability that she will make a basket on or before her last attempt within her average waiting time?
The probability that she will make a basket on or before her last attempt within her average waiting time are 1/8 and 2/8
How can we interpret probability?Probability of an event is a measurement of how likely an event can occur as an outcome of a random experiment.
Probability ranges from 0 to 1, both inclusive. Events whose probability is closer to 0 are rarer to occur than those whose probabilities are closer to 1 (relatively).
When converted to percentage, we just need to multiply its decimal representation by 100. In percentage form, the probability ranges from 0% to 100%.
Given;
Hannah makes 5 out of 8 attempted free-throws
Now,
The average waiting time of hannah to make her first basket=5/8
The probability of hannah making basket at her last attempt=1/8
The probability of hannah making basket before her last attempt= 2/8
Therefore, the probabilty will be 1/8 and 2/8.
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help pls A rational expression has been simplified below.
(x-2)(x+6)/7(x+6) = x-2/7
For what values of x are the two expressions equal?
O A. All real numbers except 2
OB. All real numbers
O C. All real numbers except -6
O D. All real numbers except -6 and 2
All real numbers, with the exception of -6 , are the solution to a rational equation. The quotient of two polynomials is the definition of a rational expression.
What do you meant by rational expression ?[tex]$\frac{(x-2)(x+6)}{7(x+6)}=\frac{x-2}{7} \quad: \quad x \neq-6$[/tex]
[tex]$\frac{(x-2)(x+6)}{7(x+6)}=\frac{x-2}{7}$[/tex]
Simplify
[tex]$\frac{(x-2)(x+6)}{7(x+6)}: \quad \frac{x-2}{7}$[/tex]
[tex]$\frac{x-2}{7}=\frac{x-2}{7}$[/tex]
Seven times both sides
[tex]$\frac{x-2}{7} \cdot 7=\frac{x-2}{7} \cdot 7$[/tex]
Simplify
[tex]$x-2=x-2$[/tex]
There is equality between the two sides.
For every x Verify Solutions, true
Search for ill-defined (singularity) points: [tex]$x=-6$[/tex]
Because -6, the equation is undefined.
[tex]x \neq -6[/tex]
Therefore the correct answer is option C ) All real numbers except -6 .
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an object starts from rest at time t = 0.00 s and moves in the +x direction with constant acceleration. the objects travels 14.0 m from time t = 1.00 s to time t = 2.00 s. What is the acceleration of the object?
The acceleration of this object is equal to: d) 9.33 m/s^2.
How to calculate the acceleration of this object?In order to calculate the acceleration of the object, we would apply the second equation of motion. Mathematically, the second equation of motion is given by this mathematical expression:
S = ut + ½at²
Where:
S represents the distance travelled or covered.t represents the time.u represents the initial velocity.a represents the acceleration.At time, t = 1.00 seconds, the position is given by:
x₁ = 0 + 1/2(1²)a
x₁ = ¹/₂(a)
At time, t = 2.00 seconds, the position is given by:
x₂ = 0 + 1/2(2²)a
x₂ = 0 + 4a/2
x₂ = 2a
Therefore, the change in position is given by;
Change in position, Δx = x₂ - x₁
Change in position, Δx = 14
From the second equation of motion, the acceleration of this object is given by:
14 = 2a - 1/2(a)
14 = 3a/2
3a = 28
a = 9.33 m/s².
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Complete Question:
An object starts from rest at time t = 0.00 s and moves in the +x direction with constant acceleration. The object travels 14.0 m from time t = 1.00 s to time t = 2.00 s. What is the acceleration of the object?
a) 5.20 m/s^2 b) 10.4 m/s^2 c) 8.67 m/s^2 d) 9.33 m/s^2 e) 12.1 m/s^2
f(x) 2x + 7 and g(x) = 3x - 12, find f(g(-4))
Step-by-step explanation:
g(-4) = 3(-4)-12
= -24
f(g(-4)) = f(-24)
f(-24) = 2(-24)+7
= -41
i don't know it is true i'm just trying:)
Marcus bought 4 packets of baseball cards and 4 packets of animals cards.Write an algebraic expression for the total number of cards Marcus bought.
Answer: How many cards are in a packet?
Step-by-step explanation:
Please help me, I need this.
Answer:
Slope = 4/3
Step-by-step explanation:
The coordinates are,
→ x1 = 6, y1 = 0
→ x2 = 0, y2 = -8
Formula we use,
→ Slope(m) = (y2 - y1)/(x2 - x1)
Now required slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (-8 - 0)/(0 - 6)
→ m = (-8)/(-6)
→ m = 8/6
→ [ m = 4/3 ]
Hence, the slope is 4/3.
-2+3c=2x+6+x 8th Grade Math Problem-
Answer:
3c=3x+6
Step-by-step explanation:
-2+3c=2x+6+x
-2+3c=3x+6 First combine the x on the right side.
-2+3c=3x+6
+2 +2 Add 2 to both sides to eliminate 2 on the left side.
3c=3x+6
find the range of sina(3cos2a cos4a 3sin2a sin2a cos2a) ^ tan a(sec a -sina tana) where a is not an integer multiple of 7t/2. (source: hmmt)
The range of sina(3cos2a cos4a 3sin2a sin2a cos2a) ^ tan a(sec a -sina tana) where a is not an integer multiple of 7t/2.
The range of sina(3cos2a cos4a 3sin2a sin2a cos2a) ^ tan a(sec a -sina tana) where a is not an integer multiple of 7t/2 can be calculated using the following formula:
Range = Maximum Value - Minimum Value
The expression inside the parentheses can be simplified to 3cos2a cos4a + 3sin2a sin4a and the expression inside the exponential can be simplified to tan2a (1 / cos2a - sin2a). This gives us the expression
Range = 3cos2a cos4a + 3sin2a sin4a ^ tan2a (1 / cos2a - sin2a)
To calculate the maximum and minimum values, we can use derivatives to find the critical points of the expression. Taking the first derivative with respect to a, we get
d/da (3cos2a cos4a + 3sin2a sin4a ^ tan2a (1 / cos2a - sin2a)) = 0
Solving this equation gives us the critical points of a = ±7t/6. Using these values, we can calculate the maximum and minimum values of the expression.
Maximum Value = 3cos14t/6 cos8t/6 + 3sin14t/6 sin8t/6 ^ tan4t/3 (1 / cos14t/6 - sin14t/6)
Minimum Value = 3cos22t/6 cos16t/6 + 3sin22t/6 sin16t/6 ^ tan4t/3 (1 / cos22t/6 - sin22t/6)
Finally, using the formula for the range, we can calculate the range of the expression to be
Range = 3cos14t/6 cos8t/6 + 3sin14t/6 sin8t/6 ^ tan4t/3 (1 / cos14t/6 - sin14t/6) - (3cos22t/6 cos16t/6 + 3sin22t/6 sin16t/6 ^ tan4t/3 (1 / cos22t/6 - sin22t/6))
This expression gives us the range of sina(3cos2a cos4a 3sin2a sin2a cos2a) ^ tan a(sec a -sina tana) where a is not an integer multiple of 7t/2.
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Two angles are supplementary if the sun of their measures is 180 degrees find two supplementary angles such that one is 150 degrees more than 1/5 of the others
The two supplementary angles are 155 and 25.
What are supplementary angles?Two angels whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
Given;
Two angles are supplementary
One is 150 degrees more than 1/5 of the others
Let one angle be x
Then the other angle will be x/5+150
Now,
x+ x/5+150=180
6x/5+150=180
6x/5=180-150
6x/5=30
x=150/6
x=25
Other angle= x/5+150=25/5+150
=155
Therefore, the angles will be 155 and 25.
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Find the length of midsegment of the trapezoid.
MN=?
The length of midsegment of the trapezoid is MN = 66.5 units
How to find the length of midsegment of the trapezoid?
The midsegment of a trapezoid is a line segment that connects the midpoints of the legs of the trapezoid.
The midsegment of a trapezoid is parallel to each base, and its length is one-half the sum of the lengths of the bases.
In this case, length of midsegment of the trapezoid will be:
MN = 1/2 × (76 + 57)
MN = 1/2 × (133)
MN = 66.5 units
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Label the missing angle measures and statements for this diagram.
The missing angle measure is of:
1. 25º.
The missing side length is of:
2. 12 cm.
Triangles ABC and ACD(3) are similar by the AAS theorem.
What are similar triangles?Similar triangles are triangles that share these following two features:
Congruent angle measures.Proportional side lengths.For this problem, we have that the segment SSC is the bisection of angle A, hence:
The missing angle measure is of 25º.The missing side length is of 12 cm.We have two similar angle measures, C and 25º, along with the opposite length, hence the AAS theorem is used.
More can be learned about similar triangles at brainly.com/question/14285697
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