Final answer:
This answer explains how to prove that angle KAL is 90 degrees in a parallelogram using angle bisectors.
Explanation:
To prove: m∠KAL = 90°
Given: KLMN is a parallelogram, KA - angle bisector of ∠K, LA - angle bisector of ∠L.
Proof:
Since KA and LA are angle bisectors in parallelogram KLMN, m∠K = m∠L.In a parallelogram, consecutive angles are supplementary, so m∠K + m∠L = 180°.Substitute m∠K for m∠L in the above equation: m∠K + m∠K = 180°, which simplifies to 2m∠K = 180°, giving m∠K = 90°.Proved that the measure of angle KAL is 90 degrees, which means that angle KAL is a right angle.
To prove that [tex]\( m\angle KAL = 90^\circ \)[/tex], we need to use the properties of angle bisectors and parallelograms.
Step 1: Identify the properties of a parallelogram.
In a parallelogram, opposite sides are equal in length, and opposite angles are equal. Also, adjacent angles are supplementary, meaning they add up to 180 degrees.
Step 2: Apply the properties to parallelogram KLMN.
Since KLMN is a parallelogram, we have:
[tex]\[ m\angle K + m\angle L = 180^\circ \][/tex]
[tex]\[ m\angle K = m\angle M \][/tex]
[tex]\[ m\angle L = m\angle N \][/tex]
Step 3: Use the properties of angle bisectors.
An angle bisector divides an angle into two equal parts. Therefore, we have:
[tex]\[ m\angle KAK = m\angle KAA \][/tex]
[tex]\[ m\angle LAL = m\angle LAA \][/tex]
Step 4: Express the angles in terms of the bisected angles.
Since KA is the angle bisector of [tex]\( \angle K \)[/tex], we can express [tex]\( m\angle KAK \)[/tex]and [tex]\( m\angle KAA \)[/tex] as half of [tex]\( m\angle K \)[/tex]:
[tex]\[ m\angle KAK = m\angle KAA = \frac{1}{2}m\angle K \][/tex]
Similarly, since LA is the angle bisector of [tex]\( \angle L \)[/tex], we can express [tex]\( m\angle LAL \)[/tex] and [tex]\( m\angle LAA \)[/tex] as half of [tex]\( m\angle L \)[/tex]:
[tex]\[ m\angle LAL = m\angle LAA = \frac{1}{2}m\angle L \][/tex]
Step 5: Use the supplementary angle relationship.
Since [tex]\( \angle K \)[/tex] and [tex]\( \angle L \)[/tex] are supplementary, we have:
[tex]\[ m\angle K + m\angle L = 180^\circ \][/tex]
Dividing both sides by 2, we get:
[tex]\[ \frac{1}{2}m\angle K + \frac{1}{2}m\angle L = 90^\circ \][/tex]
Step 6: Substitute the expressions for the bisected angles.
[tex]\[ m\angle KAK + m\angle LAL = 90^\circ \][/tex]
[tex]\[ \frac{1}{2}m\angle K + \frac{1}{2}m\angle L = 90^\circ \][/tex]
Step 7: Recognize that [tex]\( m\angle KAL \)[/tex] is the sum of [tex]\( m\angle KAK \)[/tex]and[tex]\( m\angle LAL \)[/tex].
[tex]\[ m\angle KAL = m\angle KAK + m\angle LAL \][/tex]
Step 8: Substitute the values from Step 6 into the equation from Step 7.
[tex]\[ m\angle KAL = \frac{1}{2}m\angle K + \frac{1}{2}m\angle L \][/tex]
[tex]\[ m\angle KAL = 90^\circ \][/tex]
Action wheels manufacturers models of antique cars for collectors. In August , it manufactured 300 model cars. In September, action wheels manufactured 5% fewer model cars than in August . What is the difference in the numbers of cars manufactured in August and September?
The difference in the number of cars manufactured in August and September is 15 cars.
The difference in the number of cars manufactured in August and September can be calculated as follows:
In August, Action Wheels manufactured 300 model cars.In September, they manufactured 5% fewer cars than in August, which means they made 95% of the cars they made in August.Calculating the number of cars manufactured in September: 300 * 0.95 = 285 cars.Therefore, the difference in the numbers of cars manufactured in August and September is 300 - 285 = 15 cars.For the first four months of the year , rain fell as follows : 2 1/2 inches , 3 1/4 inched , 1 1/8 inches and 1 1/2 inches . What was the total rainfall for these four months ?
Use euler's theorem to find a number x between 0 and 28 with x85 congruent to 6 modulo 35.
To find a number x between 0 and 28 with x ≡ 6 (mod 35) using Euler's theorem, we can use Euler's totient function to find the power x^24 that is congruent to 1 (mod 35). The value x = 1 satisfies the congruence, so it is a possible solution.
Explanation:To use Euler's theorem to find a number x between 0 and 28 with x ≡ 6 (mod 35), we need to find the value of x that satisfies the congruence. Euler's theorem states that if a and n are coprime positive integers, then a^φ(n) ≡ 1 (mod n), where φ(n) is the Euler's totient function of n. In this case, we need to find x such that x^φ(35) ≡ 1 (mod 35). The Euler's totient function of 35 is φ(35) = φ(5) * φ(7) = 4 * 6 = 24. Therefore, we need to find x such that x^24 ≡ 1 (mod 35).
We can start by examining the powers of x modulo 35:
x ≡ x (mod 35)
x2 ≡ x² (mod 35)
x³ ≡ x³ (mod 35)
...
x^24 ≡ 1 (mod 35)
From this, we can see that x = 1 satisfies the congruence x^24 ≡ 1 (mod 35).
Therefore, a possible value of x between 0 and 28 that satisfies x ≡ 6 (mod 35) is x = 1.
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Jorge wants to find the most popular way for teens to volunteer in the community. He cannot decide between two methods. Option 1: He will ask every fifth person on each English class roster. Option 2: He will attend a walkathon to ask teen participants about the ways they volunteer.
Answer: option 2
Step-by-step explanation:
Answer:
Option 2 is biased
Step-by-step explanation:
Option 2 is biased
Three student teams collected 65 books for the school library. The first team collected 10 fewer books than the second team and the third team collected 30% of the number of books collected by first and second teams together. How many books did each team collect?
Fiona is serving iced tea and lemonade at a picnic. She has only 44 cups in which to serve the drinks. If x represents the number of glasses of iced tea and y represents the number of glasses of lemonade, which equation represents the number of glasses of iced tea she can serve?
Answer:
[tex]x=44-y[/tex]
Step-by-step explanation:
Let x represents the number of glasses of iced tea .
Let y represents the number of glasses of lemonade.
Now we are given that She has only 44 cups in which to serve the drinks
Since y is the number of glasses of lemonade out of 44 glasses
So, remaining glasses = [tex]44-y[/tex]
So, remaining glasses is for iced tea .
So, No. of iced tea glasses = [tex]x=44-y[/tex]
Hence She can serve [tex]x=44-y[/tex] number of glasses of iced tea serve.
What term is used in the ending terminal symbol of a function flowchart?
In a function flowchart, the ending terminal symbol is typically labeled 'End' or 'Stop', and it signifies the conclusion of the process represented within the flowchart.
Explanation:The term used in the ending terminal symbol of a function flowchart is typically 'End' or 'Stop'. A flowchart is a type of diagram that represents an algorithm or process, showing the steps as various kinds of boxes (nodes) and their order by connecting them with arrows. The terminal symbols, which are usually represented by rounded rectangles or ovals, indicate the start and end of the process.
In designing a flowchart, the starting point is marked with a terminal symbol labeled as 'Start,' and the ending of the flowchart is similarly marked with a terminal symbol labeled as 'End' or 'Stop'. This indicates the flow of control reaching the end of the predefined process or function within the flowchart.
Use the distributive property to create an equivalent expression to 42+6x
The expression 42 + 6x is already in its simplest form and does not have a common factor to apply the distributive property to simplify it. However, factoring out 6 would rewrite it as 6(7 + x), albeit without further simplification.
To create an equivalent expression to 42 + 6x using the distributive property, we need to factor out a common term from both parts of the expression. However, this expression does not have a common factor available in both terms. The distributive property typically comes into play when you have an expression in the form of a(b + c), where you would then distribute a to both b and c. The expression 42 + 6x is simplified as much as possible, given that one term is a constant and one term is a multiple of a variable. There is no factor that can be distributed to simplify the expression further.
However, if we wanted to factor out a number to potentially simplify the expression, we might choose to factor out 6, which would change the expression to 6(7 + x), although this does not simplify it further since the original expression is already in its simplest form.
It takes 212121 minutes for 555 people to paint 777 walls. How many minutes does it take 333 people to paint 555 walls?
Solution: We are given that:
5 people can paint 7 walls in 21 minutes
Therefore, 1 person can paint 7 walls in [tex] 21 \times 5=105 [/tex] minutes
Which means 1 person can paint 1 wall in [tex] \frac{105}{7} =15 [/tex] minutes
Now, 3 people can paint 1 wall in [tex] \frac{15}{3} =5 [/tex] minutes
Therefore, 3 people can paint 5 walls in [tex] 5 \times 5=25 [/tex] minutes
Answer:
25 :)
Step-by-step explanation:
A stop sign is a regular octagon. Each side of the sign is 12.6 in. long. The area of the stop sign is 770 in.^2. What is the length of the apothem to the nearest whole number?
Final answer:
To determine the length of the apothem of a regular octagonal stop sign given its side length and area, use the formula for the area of a regular polygon, solve for the apothem, and then calculate it to be approximately 15 inches when rounded to the nearest whole number.
Explanation:
The student is asking how to find the length of the apothem of a regular octagonal stop sign with side lengths of 12.6 inches and a total area of 770 square inches. The apothem of a regular polygon is a line from the center to the midpoint of one of its sides and is also the radius of the inscribed circle within the polygon.
To find the apothem's length, we can use the formula for the area of a regular polygon: Area = (1/2) × Perimeter × Apothem. The perimeter (P) of the octagon is the length of one side multiplied by 8 (since an octagon has eight sides). Therefore, the perimeter is 12.6 in × 8 = 100.8 in.
We can rearrange the area formula to solve for the apothem (a): Area = (1/2) × P × a becomes a = Area × 2 / P. Substituting the known values, we get: a = 770 in² × 2 / 100.8 in, which calculates to an apothem length of approximately 15.24 inches. Round this to the nearest whole number to get an apothem length of 15 inches.
the number of sentence is an example of which multiplication property
9xa+9xb write as a product
To write the expression 9xa+9xb as a product, factor out the common factor 9x to get 9x(a+b), which is the simplified product form.
The student has presented an algebraic expression: 9xa+9xb and is requesting to rewrite it as a product. To simplify this expression, we can factor out the common factor which is present in both terms. The common factor here is 9x. When we factor out 9x, we combine the terms within the parentheses.
Here is the step-by-step simplification:
Identify the common factor in both terms, which is 9x.Factor out the 9x, resulting in 9x(a+b).This is the simplified product form of the given expression.what is the gcf of the numerator and denominator of the rational expression
3x-15/x^2-x-20
A: x-5
B: x+4
C: 4
D: 5
The mean of people in the sample of households of 7th-grade students is 4.3. The mean of people in the sample of households for 8th-grade students is 4.5. What might Principal Coleman infer or predict about the entire population based on the data?
Answer:
The mean of something is the "average"
For example, if the mean of people in the households of 7th-grade students is 4.3, this means that if you go to a random house of a 7th-grade student, you can expect around 4 people in there.
Now, for the 7th-grade students, the mean is 4.5, just a 0.2 bigger. (This means that, on average, there is more people in the 8th-grade student's households)
So Principal Coleman can infer that the amount of people in the households of 7th-grade students and 8th-grade students is almost the same, wherein the 8th-grade students there is a small chance of finding more people, but this difference is almost depreciable.
Find f '(0.3) for f of x equals the integral from 0 to x of the arccosine of t, dt
By the fundamental theorem of calculus,
[tex]\displaystyle\frac{\mathrm d}{\mathrm dx}\int_0^x\cos^{-1}t\,\mathrm dt=\cos^{-1}x[/tex]
so that
[tex]f'(0.3)=\cos^{-1}0.3\approx1.266[/tex]
find d for the arithmetic series with S17=-170 and a1=2
How many possible outcomes exist when Louisa spins the spinner below twice? The spinner is numbered from 1-8.
Answer:
The total number of possible outcomes are:
64
Step-by-step explanation:
It is given that:
Louisa spins the spinner below twice.
The spinner is numbered from 1-8.
Now, on spinning the spinner twice we obtain the sample space as:
(1,1) (1,2)....................(1,8)
(2,1) (2,2)...................(2,8)
(3,1) (3,2)..................(3,8)
(4,1) (4,2)..................(4,8)
(5,1) (5,2)..................(5,8)
(6,1) (6,2)..................(6,8)
(7,1) (7,2)..................(7,8)
(8,1) (8,2)..................(8,8)
Hence, the total number of outcomes is equal to the number of elements in sample space.
Hence, the total number of possible outcomes are:
64
glenn raced his motorcycle 30 times last season. he finished first 12 times, second 5 times and crashed in 9 races. what percent of races did he crash? set up a proportion and solve.
Final answer:
Glenn crashed in 30% of the races.
Explanation:
To find the percentage of races Glenn crashed, you can set up a proportion. A proportion is an equation that states that two ratios are equivalent. Since Glenn raced 30 times and crashed 9 times, the ratio of crashes to total races is 9 crashes out of 30 races.
You can set up the proportion as follows:
Crashes / Total Races = Percentage of Crashes / 100
Plugging in the known values gives us this:
9 / 30 = Percentage of Crashes / 100
To solve for the percentage of crashes, you multiply both sides of the equation by 100:
(9 / 30)
100 = Percentage of Crashes
Simplifying gives us:
(9/3) 10 = Percentage of Crashes
Hence, the percentage of races that Glenn crashed is 30%.
witch statement best describes how to determine whether f(x) =x^3+5x+1 is an even function?
HELP PLEASE!!!!!!!
Which of the following is equal to 4 and 1 over 2 divided by 2 and 2 over 3?
4 and 1 over 2 times 2 and 3 over 2
9 over 2 times 8 over 3
9 over 2 times 3 over 8
41 over 2 times 3 over 22
Ava bought a rectangular rug for her hallway. The rug is 23 yards wide and 234 yards long. What is the area of the rug as a mixed number in simplest form?
The area of Ava's rectangular rug is 5382 square yards, calculated by multiplying the width (23 yards) and the length (234 yards).
To find the area of Ava's rectangular rug, we need to multiply its length and width:
Area = length × width
Using the given dimensions: 23 yards wide and 234 yards long:
Area = 23 × 234
First, let's perform the multiplication:
23 × 234 = 5382 square yards
Thus, the area of the rug is 5382 square yards as an improper fraction, which cannot be simplified further as a mixed number. Since the measurements are whole numbers, converting to a mixed number doesn't apply in this case.
A biologist studied the populations of common guppies and Endler's guppies over a 6-year period. the biologist modeled the populations, in tens of thousands, with the following polynomials where x is time, in years.
common guppies: 3.1x^2+6x+0.3
Endler's guppies: 4.2x^2-5.2x+1
what polynomial models the total number of common and Endler's guppies
what polynomial models the total number of common and Endler's guppies
your answer will be:
7.3x^2+0.8+1.3
Step-by-step explanation:
this answer correct for 2022
What fraction is equivalent to the fraction 0/6
Matt Miller, age 28, takes out $50,000 of straight-life insurance. His annual premium is $418.20. Using
the tables in the Business Math Handbook that accompanies the course textbook, determine the cash value
of his policy at the end of 20 years.
A. $13,250
B. $26,000
C. $30,000
D. $26,500
Explain how 3/4 and 6/8 are the same
Suppose p(x1) = .75 and p(y2 | x1) = .40. what is the joint probability of x1 and y2?
The joint probability of x1 and y2 is P (Y₂/X₁ ) = P(Y₂ ∩ X₁ )/ P (X₁) will be 0.3.
What is the probability about?In the joint probability of x1 and y2 is P (Y₂/X₁ )= P(Y₂ ∩ X₁ )/ P (X₁).
Therefore:
P(Y₂ ∩ X₁ )
=0.40 x 0.75
= 0.3
Therefore by following the law of conditional probability, the outcome of the The joint probability of x1 and y2 is P (Y₂/X₁ ) = P(Y₂ ∩ X₁ )/ P (X₁) will be 0.3.
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Marks computer weighs 35.769 pounds. What’s the weight of his computer rounded to the nearest hundredth
Answer:
35.77 pounds
Step-by-step explanation:
Which equation represents a direct linear variation?
y=1/x
y=x+2
y=x^2
y=(1/2)x
Thanks for helping. Im pretty sure its either the 2nd or the fourth but im not Sure
Answer: y=(1/2)x represents a direct linear variation.
Step-by-step explanation:
Write a while loop that adjusts uservalue while uservalue is less than 0 or greater than 80. if uservalue is greater than 80, then subtract 5 from uservalue. if uservalue is less than 0, then add 10 to uservalue.
A 'while loop' can be programmed with conditions to adjust a 'user value'. If 'user value' is greater than 80, 5 would be subtracted from it. If it is less than 0, 10 would be added to it. This loop continues until 'user value' does not meet either condition.
Explanation:The question asks for a while loop in programming that modifies a value (user value) based on these conditions: if the user value is less than 0, it should be increased by 10 and if it's greater than 80, it should be decreased by 5. Here's a representative code for that:
while(user value < 0 || user value > 80) {
if(user value > 80) {user value -= 5; } else if(user value < 0) {user valuable += 10;}
This loop will continue to execute until the user value is not less than 0 or greater than 80.
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Deposit $400 into an account that pays simple interest at rate of 4% per year how much interest will she be paid in the first 6 years