Answers
The correct proportion used to prove that HJ || KL is [tex]\frac{GK}{HK} = \frac{GL}{LJ}[/tex].
What is the proportion theorem of two similar lines?
According to this theorem, if you draw a line parallel to one side of a triangle that divides the other sides into two separate points, the line will proportionally divide the other sides. In addition, a line is parallel to the third side if it divides any two triangle sides in the same ratio.
We have,
HJ || KL
If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.
And in the given triangle, HJ is parallel to KL, So HJ divided the two sides in proportion, that is
[tex]\frac{GK}{HK} = \frac{GL}{LJ}[/tex]
The correct option is the fourth option.
So, The correct proportion could be used to prove that HJ || KL
[tex]\frac{GK}{HK} = \frac{GL}{LJ}[/tex]
Hence, the correct proportion used to prove that HJ || KL is [tex]\frac{GK}{HK} = \frac{GL}{LJ}[/tex].
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Related Questions
Prove that a line parallel to one side of a triangle divides the other two sides proportionally. Be sure to create and name the appropriate geometric figures.
Answers
A line parallel to one side of a triangle divides the other two sides proportionally.
What is triangle?
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
Let ΔADE and ΔABC are two triangles.
Given: DE∥BC
To prove: DB/AD = EC/AE
ΔADE and ΔAC share ∠A
∠A ≅∠A reflexive property
DE∥BC is given
∠ADE ≅ ∠B because they are corresponding angles when transversal
AB cuts parallel lines DE and BC
ΔADE ∽ ΔABC a pair of angles in each are congruent.
AB / AD = AC / AE
because corresponding sides of similar triangle's are proportional.
Now subtract 1 from each side
AB / AD - 1 = AC / AE - 1
Combining fractions,
(AB - AD) / AD = (AC - AE) / AE
⇒ DB / AD = EC / AE
Hence, a line parallel to one side of a triangle divides the other two sides proportionally.
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Geometric figure:
Are the triangles congruent, if so which triangles?
S
3 in
AD
Q
4 in
R
X
3 in
4 in
O Yes, A RSQ =A XÚC
O Yes, AUXC = AQRS
O Yes, A XCU A SRQ
O No, these triangles are not congruent
O Yes, AUXCAQSR
Answers
Answer:
Yes, [tex]\triangle UXC \cong \triangle QRS[/tex]
Step-by-step explanation:
The triangles are congruent by SAS.
I need help completing the proving Statement
Answers
This looks like a fill-in the blanks question for a two column proof :]
3. CPCTC
The reasoning for this is that because triangle ABC and EDC are congruent, their corresponding parts are also congruent, (CPCTC; Corresponding Parts of Congruent Triangle are Congruent) or AC = EC
4. ACE
Because AC = EC, triangle ACE is isosceles
5. Base Angles Theorem
The base angles of a isosceles triangle are congruent
:]
Select the correct answer.
What is the y-intercept of f(x) = 3x+2?
Ο Α.
OB.
O C.
OD.
(9, 0)
(0, 9)
(0, -9)
(9,-9)
4
Answers
Answer:
C, (0, 9)
Step-by-step explanation:
The y-intercept is when the x-value is 0. We pug in 0 for x, getting f(0) = 3^2=9. The x-coordinate must be 0, and the y-value is 3^2, or 9. The correct answer is (0, 9)
Bob invested $2,500 in an account earning 3.4% annual interest that is compounded semi-annually. How long will it take the investment to triple?
(Round your answer to the nearest hundredth.)
Answers
We can conclude that it will take Bob 10 years and 10 months to triple his investment when the compounding is happening semi-annually.
What is compounding?Compounding is the method through which interest is added to both the principal balance already in place and the interest that has already been paid.
Thus, compounding can be thought of as interest on interest, with the result that returns on interest are magnified over time, or the so-called "magic of compounding."
So, the time that will be taken to make the investment triple is:
Amount invested: $2500
Interest rate: 3.4%
Compounding: Semiannually
Now, consider a period of 2 years:
3.4 * 6/12 = 1.7%
The interest rate that is effective will be 1.7%.
Currently, the future value of the compounded rate at 1.7% for a period of 65 factors equals 2.9913.
Consequently, the value will be $2,500 2.9913 = 7,478.25.
65 months divided by six years equals 10.833 years in total.
0.833 * 12 makes up 10 months a year.
Therefore, we can conclude that it will take Bob 10 years and 10 months to triple his investment when the compounding is happening semi-annually.
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Solve the following inequality and graph the solution:
(x-4)(x-5)<0
Choose test values and indicate whether the inequality is true or false in each region.
Enter the test values from smallest to largest.
Draw the solution above.
Write the solution as a compound inequality
4
Answers
The solution to the inequality (x - 4)(x - 5) < 0 is given as follows:
4 < x < 5.
The test values are given as follows:
x < 4 -> x = 3: false.4 < x < 5 -> x = 4.5: true.x > 5 -> x = 6: false.The graph of the inequality is given by the image shown at the end of the answer.
How to solve the inequality?The inequality in this problem is given as follows:
(x - 4)(x - 5) < 0
The inequality is a product, meaning that there is two cases for when it is negative, which are:
x - 4 > 0 and x - 5 < 0.x - 4 < 0 and x - 5 > 0.For the first case, the solution is given as follows:
x > 4 and x < 5 -> 4 < x < 5 (intersection).
For the second case, the solution is given as follows:
x < 4 and x > 5 (impossible).
Hence the compound inequality that gives the solution is of:
4 < x < 5.
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At the school fair, students used a scatter plot to compare the number of T-shirts sold
with the number of jars of jam sold. What can you conclude about the relationship
between the sales of the T-shirts and the jars of jam?
Answers
Answer: The jars of jam sales and the T-shirt sales have a positive correlation, but neither may cause the other.
Step-by-step explanation:
The correlation is a positive slope but selling T-Shirts and Jam shouldn't correlate to each other.
A cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one-half gallon of water is needed, and for every 6 scoops of mix, one and one-half gallons of water are needed. Part A: Find the constant of proportionality. Show every step of your work. (4 points) Part B: Write an equation that represents the relationship. Show every step of your work. (2 points) Part C: Describe how you would graph the relationship. Use complete sentences. (4 points) Part D: How many gallons of water are needed for 10 scoops of drink mix? (2 points)
Answers
a) The constant of proportionality of the given problem is; 4
b) An equation that represents the relationship is; y = 4x
c) The graph is as attached.
d) The gallons of water that are needed for 10 scoops of drink mix is; 2.5 gallons
How to find the proportional relationship?The general equation for the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope of line which tells us the unit rate of change of y with respect to x
c is the y - intercept
Now, it is pertinent to note that y = mx also represents direct proportionality. Making m the subject gives;
m = y/x
Thus, with proportion, we can say;
y₁/x₁ = y₂/x₂
The proportional relationship will be written as;
y = kx
where k is constant of proportionality
From the question, we can say that;
2 scoops require 0.5 gallon of water
6 scoops require 1.5 gallon of water
a) Thus;
k = 2/0.5
k = 2/(1/2)
k = 2 * 2 = 4
b) Equation that represents the relationship can be written as;
y = 4x + c
Since 2 scoops require 0.5 gallon of water, then;
2 = (4 * 1/2) + c
2 = 2 + c
c = 0
The equation will be; y = 4x.
c) Graph of y = 4x is attached at the end.
d) For 10 scoops of water;
10 = 4x
x = 2.5 gallons of water required.
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You are playing a game that involves tossing a single die. If you roll a one, you win $50.
If you roll a 2, you win $25. If you roll anything else, you lose $15. What are you expected winnings?
Answers
Answer:
the answer is: 01111001 01101111 01110101 00100000 01101000 01100001 01110110 01100101 00100000 01101000 01100001 01110110 01100101 00100000 00110011 00110000 00100101 00100000 01100011 01101000 01100001 01101110 01100011 01100101 00100000 01101111 01100110 00100000 01110111 01101001 01101110 01101110 01101001 01101110 01100111 00100000 01100001 01110011 01110011 01110101 01101101 01101001 01101110 01100111 00100000 01110100 01101000 01100101 00100000 01100100 01101001 01100011 01100101 00100000 01101000 01100001 01110011 00100000 00110110 00100000 01110011 01101001 01100100 01100101 01110011 00101110 . do a bit of work decoding it to get the right answer
Step-by-step explanation:
Jonah ran 1 Taps on Monday, 21 laps on Tuesday, and 6 laps on Wednesday.
How much farther did he run on Wednesday than on the other two days
combined? Show your work.
Answers
Jonah runs 2 (19/20) laps more than the remaining two days
Adding Fractions:The fractions that have the same denominator are like fractions, to add like fractions directly, But if the denominators are not the same then we need to change their denominators to the same then we can add the fractions.
To make denominators as same we need to take the LCM of denominators of two fractions.
Here we have
Jonah ran 1(3)/(4) laps on Monday
=> 1 3/4 = 7/4 laps
On Tuesday he ran 2(3)/(10) laps
=> 2 3/10 = 23/10 laps
On Wednesday he ran 6(1)/(5) laps
=> 6 1/5 = 31/5 laps
The total number of laps ran combining Monday and Tuesday
= 7/4 laps + 23/10 laps
= (35 + 46)/20 [ take Lcm of 4, 10 i.e 20 ]
= 81/20
From the above calculations,
Jonah ran 81/20 laps on combining Monday and Tuesdays
The difference between Wednesday's counted laps and Monday, and Tuesday's counted laps
= 31/5 - 81/20
= (140 - 81)/20 [ Take Lcm of 5, 20 i.e 20 ]
= 59/20
= 2 (19/20)
Therefore,
Jonah runs 2 (19/20) laps more than the remaining two days
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Complete Question:
Jonah ran 1(3)/(4) laps on Monday, 2(3)/(10) laps on Tuesday, and 6(1)/(5) laps on Wednesday. How much farther did he run on Wednesday than on the other two days combined? Show your work.
Fill in the blanks below in order to justify whether or not the mapping shown represents a function.
The mapping diagram above a function since
in where there
Answers
Answer:
This is a function
Step-by-step explanation:
For every input there is only one output.
Simplify: 3/8(4a-5)-5/12(3a-4)=1/6
Answers
Answer:
Step-by-step explanation:
3/8(4a-5)-5/12(3a-4)=
9/24(4a-5)-10/24(3a-4)=1/6 | x24
9*(4a-5)-10(3a-4)=4
36a-45-30a+40=4
6a=9
a=3/2
Determine the probability: It will definitely turn dark tonight.
a. 0.5
b. 1
c. 0.30
d. 0.67
Answers
The probability of 'It will definitely turn dark tonight' would be 1.
So option (B) is correct.
What is a probabilty?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
If by "likelihood" probability, the word definitely implies the probability would be 1, certainty.
Because definitely after daylight, the light will turn dark at the night.
So the probability would be 100% or 1.
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2. Determine the theoretical probability of rolling a two with one standard die. Write this probability in three equivalent forms: as a fraction, a decimal (rounded to three places), and a percentage (rounded to one decimal place).
Answers
The theoretical probability of rolling a two with one standard die in three equivalent form is 1/6, 0.167 and 16.7%
How to determine the theoretical probability?From the question, we have the following parameters that can be used in our computation:
The rolling of a standard die
In this case, we assume that the standard die is a fair die
i.e. the faces have equal chance of appearing
This means that the sample space of the die is
Sample space = {1. 2. 3. 4. 5. 6}
In this sample space, we have
Number of occurrence of 2 = 1
Number of items in the sample space = 6
The theoretical probability of 2 is then calculated as
Probability = Number of occurrence of 2/Number of items in the sample space
Substitute the known values in the above equation, so, we have the following representation
Probability = 1/6 --- in fraction
Evaluate the quotient
Probability = 0.167 -- in decimal
Express as percentage
Probability = 16.7%
Hence, the probability is 16.7%
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X
Y
If L=4, Y=30 and Z=14. Solve for X. (round to 2 decimal places)
L
N
Answers
Answer:
Y+Z/Z = X/L
X= (44/14)4 = 12.57(nearest 2 decimal
what is the area of a circle with a radius of 2 cm anda circle with a radius of 4 cm
Answers
Answer:
Step-by-step explanation:
area = pi * r^2
area = pi * 2^2
area = 4pi
area = pi * 4^2
area = 16pi
Anita Jacobs could deposit R600 every 3 months in her credit union which pays 12% interest compounded quarterly. How much more would she have in her account at the END of 4 years if she deposited the R600 at the BEGINNING of each quarter rather than at the END of each quarter?
Answers
Answer: 1890
Step-by-step explanation:
a recipe calls for 5 teaspoons of seasoning for every 6 batches of chilli if you have 102 batches of chilli how many teaspoons of seasoning will you need
Answers
For 102 batches of chilli, 85 number of teaspoons of seasoning needed.
What do you mean by fraction?
Fraction represents a part of a whole, or more generally, any number of equal parts. In everyday English, fractions represent how many parts of a particular size are there.
For positive common divisors, the numerator and denominator are natural numbers. The numerator represents the number of equal parts and the denominator shows the number of parts that make up the unit or whole. A zero part can never make up a whole, so the denominator is never zero.
It is given that a recipe calls for 5 teaspoons of seasoning for every 6 batches of chilli.
For 6 batches of chilli, number of teaspoons of seasoning needed = 5
For 1 batch of chilli, number of teaspoons of seasoning needed = 5/6
For 102 batches of chilli, number of teaspoons of seasoning needed = [tex]\frac{5}{6}\times 102[/tex] = 85
Therefore, For 102 batches of chilli, 85 number of teaspoons of seasoning needed.
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Find how long it takes a person to drive 260 miles on a highway if she merges onto a highway at 7 p.m. and drives nonstop with her cruise control set on 80 mph.
Answers
When time is also known, distance—the measurement of how far something has travelled in a straight line—can be used to determine speed.
Step-by-step explanation:Speed can be calculated using distance—the amount of distance something has travelled in a straight line—when time is also known.Distance, D = 260 miles
Velocity, V = 80 miles/hour
Time taken, t = distance/velocity
= D/V
= 260/80
= 3.25 hours
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2. Find the 72nd term in the arithmetic sequence 2,
-8, -18, -28, ..
Answers
Answer:
The 72nd term is -708
Step-by-step explanation:
Shelby and Aisha baked homemade dog treats to sell. They baked 116 dog treats in all.
Shelby baked 3 times as many treats as Aisha.
4) How many dog treats did Aisha bake?
Answers
Answer:
87
Step-by-step explanation:
If Shelby and Aisha baked a total of 116 dog treats to sell, and Shelby baked 3 times as many dog treats that Aisha, then we need to figure out what 3/4 of 116 dog treats is.
116 ÷ 4 = 29
29 × 3 = 87
Shelby baked 87 dog treats.
Business Information System (BIS)A combination of hardware, software, data, people, and procedures employed to pursue an organization's objective.
Answers
A system of hardware, software, information, people, and used to further an organization's goal is known as a business information system (BIS).
Given that,
What is Business Information System?Students can prepare for a range of positions in business, industry, government, and the military with a Bachelor of Business Administration with a major in Business Information Systems (BIS). Business information systems, often utilising computer systems and technology, provide information that firms utilise to govern themselves successfully and efficiently. Hardware, software, data, procedures (design, development, and documentation), and people make up the bulk of business information systems. Students majoring in BIS will learn how to use technology and information systems to enhance corporate processes and decision-making.
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Simplify the expression below. Leave your expression in an exact form with coefficient a and radicand b so we have: a\sqrt[]{b} . Keep in mind that the coefficient a can be a product of a number and a variable. 2\sqrt[]{x^2y} Simplifies to a\sqrt[]{b} where: our coefficient a = and our radicand b =
Answers
The simplified expression of 2√x²y is 2x√y
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
2\sqrt[]{x^2y}
Rewrite properly
So, we have the following representation
2√x²y
Take the square root of x²
So, we have
2x√y
Hence, the solution is 2x√y
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What is the range of this absolute value function?
Answers
The range of this absolute value function is -∞ < y ≤ 7
What are the domain and range of a function?
The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
Consider the vertical extent of the graph along y axis.
It starts from +7 extends till -∞
So, the range is -∞ < y ≤ 7
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According to a study done by a university student, the probability a randomiy selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and
obsorve people's habits as they sneeze.
What is the probability that among 10 randomly observed individuals fewer than 5 do not cover their mouth when sneezing?
Answers
Answer:
the total number of random sample n 10
probability of is 0.267
Fill in the chart on paper,
then list the coefficient
of the "x" term.
4x
-10
3x²
-8x
+2
Enter
Answers
Answer:
2
Step-by-step explanation:
add 2 by 6 to get 02
In this activity, you will create a function from two points that satisfy it. A linear function passes through the points ( - 2 , 3 ) and ( - 3 , 5 ) . Complete the following tasks to find the equation of the function. Part A To find the equation, first find the rate of change. What is the rate of change for the linear function that passes through the two points?
Answers
The linear function would be y = -4x - 7 which passes through the points (- 2 , 3 ) and ( - 3 , 5 ).
Given that linear function passes through the points (- 2 , 3 ) and ( - 3 , 5 ).
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = -2, y₁ = 3
x₂ = -3, y₂ = 5
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute values in the equation, we get
⇒ y - 3 = (5 - 1)/(-3 - (-2))[x -(-2)]
⇒ y - 3 = (4)/(-1)[x +2]
⇒ y - 1 = -4(x +2)
⇒ y = -4x - 8 + 1
⇒ y = -4x - 7
Therefore, the linear function would be y = -4x - 7 which passes through the points (- 2 , 3 ) and ( - 3 , 5 ).
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A rectangular solar panel has a length that is 11 inches shorter than 4 times it’s width. If the perimeter of the panel is 178 inches, what are the dimensions of the panel?
The width of the panel is *blank* inches.
Answers
Answer:
The width of the panel is 20 inches----------------------
Let the width be x, then the length is 4x - 11.
The perimeter of the rectangle is:
2(x + 4x - 11) = 178Solve it for x:
2(5x - 11) = 1785x - 11 = 895x = 100x = 20Select the correct answer.
Which equation has only one unique solution?
A. -4|x|+ 1 = -3
B. 9-|12x-1|=9
C. |x-2|-7= 7
D. |13-x|= 3
Answers
Answer:
9-|12x-1|=9
Step-by-step explanation:
Solve for x over the real numbers:
9 - abs(12 x - 1) = 9
Subtract 9 from both sides:
-abs(12 x - 1) = 0
Multiply both sides by -1:
abs(12 x - 1) = 0
Eliminate the absolute value:
12 x - 1 = 0
Add 1 to both sides:
12 x = 1
Divide both sides by 12:
Answer: x = 1/12
Answer:
Answer is B
Step-by-step explanation:
If the lengths of two sides of a triangle are represented by 2x + 5 and 3x + 7 (in which x is positive), describe in terms of x the possible lengths of the third side whose
length is represented by y.
Answers
Answer:
x + 2 < y < 5x + 12
Step-by-step explanation:
given 2 sides of a triangle then the third side y is within the limits
difference of 2 sides < y < sum of 2 sides
3x + 7 - (2x + 5) < y < 3x + 7 + 2x + 5
3x + 7 - 2x - 5 < y < 5x + 12
x + 2 < y < 5x + 12