Without using the triangle sum theorem, the proof that shows that m∠G + m∠K + m∠GHK = 180° is proved below.
What is the Triangle Angle Sum Theorem?Based on the triangle angle sum theorem, all the interior angles in a triangle will add up to the sum of 180 degrees.
The complete proof that shows that m∠G + m∠K + m∠GHK = 180 degrees is explained below.
Statement Reason
1. GK║HJ 1. Given
2. ∠G ≅ ∠IHJ 2. Corresponding angles theorem
3. ∠K ≅ ∠JHK 3. Alternate interior ∠s theorem
4. m∠IHK = m∠IHJ + m∠JHK 4. Additive property of angle measure
5. m∠IHK = m∠G + m∠K 5. Substitution
6. m∠IHK + m∠GHK = 180° 6. Angles forming a linear pair sum of 180°
7. m∠G + m∠K + m∠GHK = 180° 7. Substitution
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Points L and M on the side YZ of a triangle XYZ are drawn so that L is between Y and M. Given that XY = XZ and YXL = MXZ, prove that YL = MZ
We prove that \(YL = MZ\).
It is given that,
Points \(L\) and \(M\) on the side \(YZ\) of a triangle \(XYZ\) are drawn so that \(L\) is between \(Y\) and \(M\).
According to given details the figure of the triangle is
Given that:
\(XY = XZ\)
\(YXL = MXZ\)
Then we have to prove that \(YL = MZ\).
As given that
\(XY = XZ\)
\(\angle YXL =\angle MXZ\)
So according to SAS Postulate
SAS Postulate means Side Angle Side. The two triangles are congruent if we can prove that two sides and the included angle of one triangle are congruent with two sides and the included angle of another triangle.
So \(XL=XM\)
\(\triangle YXL \cong\triangle MXZ\)
So \(YL = MZ\)
Hence, we prove that \(YL = MZ\).
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what is the measure of angle OAC
Answer:
60
Step-by-step explanation:
2. If D is the midpoint of segment AB, explain using transformations why AC = BC. Use complete sentences. (10 points)
AC is equal to BC by the corresponding side of a congruent triangle.
What is a line segment?
A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).
The midpoint of a line segment means a point that lies in the mid of the given line segment.
If D is the midpoint of segment AB, then AD = BD.
So in a triangle ACD and BCD
AD = BD (by midpoint D)
angle ADC = angle BDC = 90
CD = CD (common)
Therefore, triangle ACD and BCD are congruent.
Hence, AC = BC by the corresponding side of a congruent triangle.
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TRUE/FALSE. if january has 31 days, then 7 is an even number.
Answer: False
Step-by-step explanation:
7 is not an even number, and it never will be.
Even though january has 31 days, 7 is an odd number.
False. 7 is an odd number. This is because an even number is a number which can be divided by 2 without a remainder. 7 cannot be divided by 2 without a remainder, so it is an odd number.
To calculate this, we can use the remainder operator. This operator is represented by the percentage sign (%). When using this operator, the result is the remainder of a division operation. For example, if we divide 7 by 2, the result is 3 with a remainder of 1. If we write this as an equation, it will be 7 % 2 = 1. This means that 7 is not evenly divisible by 2, and is thus an odd number.
Therefore, even though january has 31 days, 7 is an odd number.
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-0.8°C < _____ < -0.1 °C
Do not include units (°C) in your answer.
Select one:
-0.89
-0.61
-2
-0.95
Answer:
0.61 °C
Step-by-step explanation:
1. You look at all the tenths in the degrees
2.You figure out which one of the tenths fits between -0.8 and -0.1
The function y = f (x) is linear.
Given f-¹ (0) = 3 and f (1) = - 4, find the formula of
f (x) and f-¹ (x)
Answer:
\(f(x)=2x-6\)
\(f^{-1}(x)=\dfrac{x+6}{2}\)
Step-by-step explanation:
Using slope-intercept form of linear function: \(y = mx + b\)
\(\implies f(x)=mx+b\)
\(\textsf{if} \ \ f(1) = -4\)
\(\implies m + b=-4\)
\(\implies b = -4-m\)
Find inverse of slope-intercept form:
swap x and y: \(x = my + b\)
Make y the subject:
\(\implies x - b = my\)
\(\implies y = \dfrac{x-b}{m}\)
\(\implies f^{-1}(x) = \dfrac{x-b}{m}\)
\(\textsf{if} \ \ f^{-1}(0) = 3\)
\(\implies \dfrac{0-b}{m}=3\)
\(\implies b=-3m\)
\(\textsf{equation 1:} \ \ b = -4-m\)
\(\textsf{equation 2:} \ \ b=-3m\)
Equate the equations and solve for \(m\):
\(\implies b=b\)
\(\implies -4-m=-3m\)
\(\implies -4=-2m\)
\(\implies m=2\)
Substitute found value for \(m\) into one of the equations and solve for \(b\):
\(b = -4-2=-6\)
Substitute found values of \(m\) and \(b\) into equations for \(f(x)\) and \(f^{-1}(x)\):
\(f(x)=2x-6\)
\(f^{-1}(x)=\dfrac{x+6}{2}\)
PLS HELP FAST
A plane in which the coordinates of a point are its distances from two intersecting perpendicular lines called axes.
Which term is defined in the above statement?
Question 6 options:
Air Plane
Coordinate Plane
Quadrant
Ordered Pair
Answer:
Coordinate plain
Step-by-step explanation:
airplane... i think you know what that is, and quadrant is the squares sectored off by a coordinate plane.
Suppose that 3 balls will be randomly put into 3 buckets, with each ball being equally likely to be put into each of the buckets, independently of which buckets are chosen for any of the other balls. (E.g., the first ball is equally likely to be put into any of the 3 buckets, and then regardless of which bucket the first ball is placed in, the second ball is equally likely to be put into any of the 3 buckets.) What is the probability that all of the balls will be put into the same bucket
Answer:
\(\frac{1}{27}\)
Step-by-step explanation:
Since there are a total of three buckets and only one can be chosen at a time, this would mean that the probability of a ball being placed in a bucket is 1/3. Since each ball has the same probability of being placed into any bucket regardless of the where the previous ball landed, it means that each ball has the same 1/3 probability of a bucket. In order to find the probability that all three land in the same bucket, we need to multiply this probability together for each one of the balls like so...
\(\frac{1}{3} * \frac{1}{3} * \frac{1}{3} = \frac{1}{27}\)
Finally, we see that the probability of all three balls landing in the same bucket is \(\frac{1}{27}\)
Lucy reads 450 words in 3 minutes.
This is an equation that can be used to
find w, the number of words Lucy can
read in 20 minutes if she continues to
read at the same rate?
Answer:
3000 words
Step-by-step explanation:
450 words in 3 minutes is 150 words in 1 minute. 20 minutes = 1 times 20.
1 minute = 150 words so 150 words times 20 minutes = 3000 words.
16. Find the perimeter of the triangle. (Perimeter is the distance AROUND the shape)
(x+6) + (×+4) + x
The perimeter of the triangle is 3x + 10
How to find the perimeter of the triangle.From the question, we have the following parameters that can be used in our computation:
Side lengths = (x+6) and (x+4) and x
The perimeter is the distance AROUND the shape
Using the above as a guide, we have the following:
Perimeter = x + 6 + x + 4 + x
Evaluate the like terms
Perimeter = 3x + 10
HEnce, the perimeter is 3x + 10
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2. The grocery store is about 0.72 of a mile from Allen's house. What is the value of this distance as a fraction?
The distance from Allen's house as a fraction is 18/25.
What is the fraction?A decimal is used to denote integers and non-integers. The integers are separated from the non-integers by a point known as the decimal point. An example of a decimal is 0.71.
A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 1/2.
In order to change a decimal to a fraction, divide the value of the fraction by the value of the digit in the decimal.
Division is the process that is used to calculate the quotient of a number. Division is the process of grouping a number into equal parts using another number.
72 / 100
Divide both the numerator and denominator by 4
18 / 25
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Please help me with explanation thank you very much.
Answer:
B
Step-by-step explanation:
I did some maths
(3882+3561+3459+2587+ 2817
+2068+2516+3590+2740+2572) ÷ 10
Mean =
the gazebo in the park is an octagon. each side of the gaebo is 4 feet ong. what is the perimeter of the gazbebo
The perimeter of the gazebo can be calculated by adding up the length of all 8 sides. Since each side is 4 feet long, the perimeter is simply 8 times 4 feet, or 32 feet.
In geometry, the perimeter of a polygon is defined as the total length of its sides. For regular polygons, such as an octagon, all sides have equal length, and the perimeter is simply the product of the number of sides and the length of each side.
In this case, since each side of the gazebo is 4 feet long, we can simply multiply by 8 to get the total length of all sides, or the perimeter. Therefore, the perimeter of the gazebo is 32 feet.
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Question 3 of 10
of the way from
What is the location of the point on the number line that is
A = 5 to B = 23?
O
A. 8
B. 9
C. 10
D. 7
Answer:
B. 9
Step-by-step explanation:
solve it and u will find out
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help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The curve -3\(x^{2}\) + 18x +3 has a maximum value of 30 at x = 3
What is a maximum point?In mathematics, a point at which a function’s value is greatest. If the value is greater than or equal to all other function values, it is an absolute maximum. if it is merely greater than any nearby point, it is a relative, or local, maximum. In calculus, the derivative equals zero or does not exist at a function’s maximum point.
Differentiate f(x) = -3\(x^{2}\) + 18x +3 ,
we have dy/dx = -6x + 18.
at turning point, dy/dx = 0
-6x + 18 = 0
6x = 18
x =18/3
x = 3
to check if x = 3 is a minimum or maximum point, we take the second derivate
which is \(\frac{d^{2}y }{dx^{2} }\) = -6
since \(\frac{d^{2}y }{dx^{2} }\) < 0
F(x) is a maximum,
so maximum value of x, we substitute x = 3 into the function
f(x) = -3\((3)^{2}\) + 18(3) + 3
f(x) = 30
In conclusion, the maximum value for the function is 30 at x = 3
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You are running an experiment in class where you draw colored marbles out of a bag. There are
eight marbles in the bag, you will draw five times, and you will replace the marble each time. How many ways can you draw the marbles out of the bag?
A: 40
B: 3,360
C: 4,096
D: 32,768
Answer:
32768 ways
Step-by-step explanation:
Given
Marbles = 8 marbles
Selection = 5 (with replacement)
Required
Determine the number of ways
Because it is a selection with replacement; each selection is as follows:
\(First = 8\ marbles\)
\(Second = 8\ marbles\)
\(Third= 8\ marbles\)
\(Fourth = 8\ marbles\)
\(Fifth = 8\ marbles\)
Total number of ways is then calculated as:
\(Total = 8 * 8 * 8 * 8 * 8\)
\(Total = 32768\)
7z+9z+7-7 =180 How do
You solve this
The solution for the given linear expression is 11.25 (45/4).
Linear Expression
A linear expression can be represented by a line. The standard form for this equation is: y=mx+b , for example, y=11x+9. Where:
m= the slope.
b= the constant term that represents the y-intercept.
For the given example: m=11 and b=9.
The question gives the expression:7z+9z+7-7 =180. Then, you should find the variable z.
7z+9z+7-7 =180
16z+0=180
16z=180
z=180/16=90/8=45/4=11.25
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In the regression of textbook retail price (PRICE) on number of pages in the book (LENGTH), you estimate the following equation: PRICE = $10.40 + $0.03LENGTH What is the interpretation of the coefficient $0.03? Select one: a. As the estimated length of the book increases by one page, the estimated price increases by $0.03. b. None of the interpretations are correct c. As the length of the book increases by one page, the estimated price increases by $0.03 on average. d. As the length of the book increases by one page, the price increases by $0.03. e. As the estimated length of the book increases by one page, the price increases by $0.03.
The correct answer is c.
How to interpret the coefficient?The interpretation of the coefficient $0.03 in the regression of textbook retail price (PRICE) on number of pages in the book (LENGTH) is: As the length of the book increases by one page, the estimated price increases by $0.03 on average. Therefore, the correct answer is c.
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simplify 3x(4x-5)+3 and its value for X = 3
Answer:
Step-by-step explanation:
3x ( 4x - 5 ) + 3
12x^2 - 15x + 3
12 × 3^2 - 15 × 3 + 3
12 × 9 - 45 + 3
= 108 - 45 + 3
= 66
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On a coordinate plane, 2 parallelograms are shown. Parallelogram 1 has points (0, 2), (2, 6), (6, 4), and (4, 0). Parallelogram 2 has points (2, 0), (4, negative 6), (2, negative 8), and (0, negative 2). How do the areas of the parallelograms compare? The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2. The area of parallelogram 1 is 2 square units greater than the area of parallelogram 2. The area of parallelogram 1 is equal to the area of parallelogram 2. The area of parallelogram 1 is 2 square units less than the area of parallelogram 2.
Answer:
A) The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2.
The area of parallelogram 1 is 2 square units greater than the area of parallelogram. Option 2 is correct.
What is the area?The space filled by a flat form or the surface of an item is known as the area.
The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.
A₁ is the area of parallelogram 1
A₁ is the area of parallelogram 2
l₁ is the distance between the points (2,6),(0,2)
l₂ is the distance between the points (4,0)(0,2)
b₁ is the distance between the points (2,0),(0,-2)
b₂ is the distance between the points (2,6),(4,-6)
A₁ = l₁ × b₁
A₁=4.47 ×4.47
A₁ = 19.89 sq.unit
A₂=l₂×b₂
A₂=2.82 × 6.342
A₂=17.88 sq.unit
A₁-A₂ = 19.89 sq.unit - 17.88 sq.unit'
A₁-A₂= 2.01
The area of parallelogram 1 is 2 square units greater than the area of a parallelogram.
Hence,option 2 is correct.
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Find (c. d)(x).
c(x) = 5x
d(x) = 2x
Answer: 10x
Step-by-step explanation:
c(x) = 5x
d(x) = 2x
(cod)(x)=
c(d(x))=
5(d(x))=
5(2x)=10x
For the following ODE: x'(t) = x1/3 , x(0) = x0 > 0
(a) Show that local existence and uniqueness is valid (using both Peano and Picard-Lindelof theorems)
(b) Show that this ODE is not globally unique (i.e. where does the global uniqueness argument fail for this ODE?)
Both the Peano and Picard-Lindel of theorems show local existence and uniqueness function for the given ODE, but it fails to be globally unique due to lack of Lipschitz continuity.
(a) Both the Peano and Picard-Lindelof theorems can be used to show the local existence and uniqueness of the given ODE. The Peano Theorem states that if a continuous function F is defined on a neighborhood of a point in the domain of the ODE, then there exists a unique solution in this neighborhood. The Picard-Lindelof Theorem states that if the function F is continuous and Lipschitz continuous then there exists a unique solution in the given interval. Since the given ODE is a continuous and Lipschitz continuous function, it satisfies both the Peano and Picard-Lindelof Theorems and therefore, it has a local existence and uniqueness.
(b) The global uniqueness argument for this ODE fails because the given ODE is not Lipschitz continuous in the whole domain. This means that the given ODE is not guaranteed to have a unique solution in the entire domain. The global uniqueness fails because the given ODE could have multiple solutions in some parts of the domain.
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i’m circle c, what is the value of x?
The value of x from the triangle inscribed in the circle which is the unknown angle is 22°
Angles of a semicircle Theorem.For a given triangle inscribed in a circle, it should be noted that the angle that is inscribed along the diameter of the circle will be regarded as the right angle.
This means that the angle facing the diameter line (C), i.e angle c is 90 degrees. We all know that the sum of angles in a triangle is 180 degrees. Therefore, to find the third unknown angle x, we have:
x + 68° + 90° = 180°
x + 158° = 180°
x = 180° - 158°
x = 22°
Therefore, we can conclude that the value of x which is the unknown angle is 22°
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Need to generate a recursive formula to the story problem given below. Give the recursive equation at the top of your answer (do not forget your base case(s)) and then show your thought process after. Question: How many n-letter "words" can be created from an unlimited supply of a’s, b’s, and c’s, if each word MUST contain an even number of a’s?
The recursive formula for the given problem is W(n) = W(n-1) + 2 * W(n-1), with the base case W(0) = 1. This formula calculates the number of n-letter "words" that can be created from an unlimited supply of 'a's, 'b's, and 'c's,
To derive the recursive formula, we consider two cases for the first letter of the word: either it is an 'a' or it is not. If the first letter is 'a', we need to ensure that the remaining (n-1) letters form a word with an even number of 'a's. Therefore, the number of words in this case is equal to W(n-1), as we are recursively solving for the remaining letters.
If the first letter is not 'a', we have the freedom to ch
oose from 'b' or 'c'. In this case, we have two options for each of the remaining (n-1) letters, resulting in 2 * W(n-1) possibilities. By summing these two cases, we obtain the recursive formula W(n) = W(n-1) + 2 * W(n-1), which calculates the total number of n-letter words satisfying the given criteria.
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I NEED HELP!I WILL MARK BRAINLEIST LOVES :)<3
Answer:
i think its c person :)
Step-by-step explanation:
Answer:
The correct answer is A! :)
The probability of two or more independent events occurring is calculated by multiplying the probability of each event. This is an example of ______.
The multiplication rule in probability theory states that the probability of two or more independent events occurring together is calculated by multiplying the probabilities of each individual event.
When events are independent, it means that the occurrence or non-occurrence of one event does not affect the probability of the other event. By multiplying the probabilities, we obtain the joint probability of all events happening simultaneously.
This rule is applicable when the events are independent, and it allows us to compute the overall probability of complex events by breaking them down into simpler, independent components.
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3. Line a passes through (-4, 5) and (-2, 8); Line b passes through (-6, 7) and (-3, 5).
A. parallel
B perpendicular
C neither
Of people who died in the United States in recent years, 86% were white, 12% were black, and 2% were Asian. (This ignores a small number of deaths among other races.) Diabetes caused 2.8% of deaths among white people, 4.4% among black people, and 3.5% among Asians. What is the probability that a randomly chosen death is a white person who died of diabetes? (Round your answer to three decimal places.)
The probability that a randomly chosen death is a white person who died of diabetes is 0.024 determined using the law of total probability.
The law of total probability is a fundamental rule that connects marginal probabilities to conditional probabilities and expresses the total probability of an outcome via several distinct events. The rule states that if the probability of an event is unknown, it can be calculated using the known probabilities of several distinct events. It is given by P(A ∩ B) = P(A|B)P(B)
In order to determine the probability of an event (D) with not enough information to calculate it directly, a related event, say W can be taken and use that to calculate the probability for D.
Let the events that a person from a certain race die be denoted as:
P(W) = 0.86; P(B) = 0.12; P(A) = 0.02
Let the events that a person from a certain race dies of diabetes be denoted as:
P(D/W) = 0.0.028; P(D/B) = 0.044; P(D/A) = 0.035
Probability that a randomly chosen death is a white person who died of diabetes
P(W) x P (D/W) = 0.86 x 0.028 = 0.02408 ≈ 0.024
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What is the slope of the line through the points (-2, -1) and (4, 3)?
Answer: \(\frac{2}{3}\)
Step-by-step explanation:
Answer:
m=2/3
Step-by-step explanation:
Identify the coordinates (x₁,y₁) and (x₂,y₂) . ...
Input the values into the formula. (-2,-1) (4,3) the formula is (y1-y2)/(x1-x2)
Subtract the values in parentheses to get 4/6
Simplify the fraction to get the slope of 2/3