If ∠4 ≅ ∠14, then the lines that must be parallel are a and b and so we can say that; a∥b, Converse of the Alternate Interior Angles Theorem
What are Interior Angles?Interior angles are basically the pair of angles created on the inner side of the parallel lines and right on the opposite sides of the transversal when two parallel lines are intersected by a transversal .
We are told that ∠4 ≅ ∠14, which lines,
If a transversal connects two parallel lines, we know that the corresponding angles and vertically opposite angles are equivalent.
Thus, angle 4 is congruent to angle 14.
Therefore, we can deduce the following;
Angle 15 is a corresponding angle to angle 3 and so we can write that;
∠15 ≅ ∠3
Angle 15 is a vertically opposite angle to angle 13 and so we can write that; ∠15 ≅ ∠13
By transitive property of equality, we can say that;
∠3 ≅ ∠13 [Alternate interior angles]
Thus, we have ∠4 ≅ ∠14
Therefore, we conclude that a∥b, Converse of the Alternate Interior Angles Theorem.
Hence, the correct answer would be an option (B).
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The proof below may or may not be correct. If the proof is incorrect, determine the
first step number that is not justified and the reason it is not justified.
Answer:
Step-by-step explanation: step 5
they have not proved the ASA postulate i.e. they the are missing a step to proove angle BEF = angle CED (Verticle angles)
so, correct answer is step number 5 and reason 'missing prior step'
3) Justin made some cookies for the holiday. She baked 10 sugar cookies, 18 chocolate chip cookies, and 15 ginger cookies. What is the ratio of sugar cookies to ginger cookies in simplest form?
You visit the Grand Canyon and drop a penny off the edge of the cliff. The distance the penny will fall is 32ft for the first second, 62ft the next second, 92ft the third second, and so on. How far will the penny have traveled after 7 seconds?
Answer:
212 feet fallen after 7 seconds
Step-by-step explanation:
You visit the Grand Canyon and drop a penny off the edge of the cliff. The distance the penny will fall is 32ft for the first second, 62ft the next second, 92ft the third second, and so on. How far will the penny have traveled after 7 seconds?
if 32 ft for 1 second
if 62 ft for 2 second
if 92 ft for 3 second
We see that the penny from second 1, falls an addition 30 ft/s.
equation: 32 + 30 (t - 1)
when t = 7 seconds:
32 + 30 (7 - 1)
32 + 30 (6)
32 + 180
= 212 feet fallen after 7 seconds
PAGE 6
7. Maymont Middle School is selling tickets for the winter musical. Adult tickets cost $5 each and child
tickets cost $3 each.
a. Write a mathematical equation that represents the total cost, t, for a adult tickets and c child tickets.
b. Ciera has $28. Could she buy 2 adult tickets and 7 child tickets? Use your equation from part a. to show
your work.
c. Jaylen has $22. If he buys 2 adult tickets, how many child tickets can he buy? Show your work.
C2022 Iluminate Education, Inc.
Question
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Question 7b
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a) A mathematical equation that represents the total cost, t, for a adult tickets and c child tickets is t = $5a + $3c.
b)No, she cannot buy 2 adult tickets and 7 child tickets.
Define equation.Mathematical equations are relationships between two expressions that are equal on both sides of the equal to sign. An equation is, for instance, 3y = 16.
Given,
Maymont Middle School is selling tickets for the winter musical. Adult tickets cost $5 each and child tickets cost $3 each.
a) Mathematical equation:
represents the total cost, t, for a adult tickets and c child tickets
t = $5a + $3c
A mathematical equation that represents the total cost, t, for a adult tickets and c child tickets is t = $5a + $3c.
b) Ciera has $28.
a = 2 c = 7
Equating values in equation,
= $5(2) + $3(7)
= $10 + $27
= $37
No, she cannot buy 2 adult tickets and 7 child tickets.
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PLEASE PLEASE HELP ME WITH THIS QUESTION Two systems of equations are given below.
For each system, choose the best description of its solution.
If applicable, give the solution.
When y=9, the value of y² - 1 is
2.356 in expanded form
Answer: 2 + 0.3 + 0.05 + 0.006
Step-by-step explanation: You just have to technically un add the stuff of you understand it that way.
Hope i helped you
Have a great day Darling
One leg of a right triangle is 7 units long, and its hypotenuse is 16 units long. What is the length of the other leg? Round to the nearest whole number.
Answer:
7^{2} + x^{2} = 16^{2}
49+x^2=256
x^2=207
x=14.387=14
Answer:
14 units
Step-by-step explanation:
To find the length of the other leg of a right triangle, where one leg is 7 units long and the hypotenuse is 16 units long, use Pythagoras Theorem.
Pythagoras Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the legs.
Let the legs of the right triangle be "a" and "b", and the hypotenuse be "c". Therefore:
[tex]\begin{aligned}a^2+b^2&=c^2\\a^2+7^2&=16^2\\a^2+49&=256\\a^2+49-49&=256-49\\a^2&=207\\\sqrt{a^2}&=\sqrt{207}\\a&=14.3874945...\\a&=14\;\sf(nearest\;whole\;number)\end{aligned}[/tex]
Therefore, the length of the other leg is 14 units (rounded to the nearest whole number).
a homeowner wants to fence in a rectangular space in her yard along one side of her house for her dogs. the total area she can fence in is 650 square feet.
write an expression to find the area of the fenced region.
The required expression for the fenced region is lw = 650.
Given that,
A homeowner wants to fence in a rectangular space in her yard along one side of her house for her dogs. the total area she can fence in is 650 square feet.
What is a rectangle?
The rectangle is 4 sided geometric shape whose opposites are equal in length and all angles are about 90°.
Here,
Let the length of the area be l and the width of the area be w,
The total area she can fence in is 650 square feet.
lw = 650
Thus, the required expression for the fenced region is lw = 650.
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an important issue facing americans is the large number of medical malpractice lawsuits and the expenses that they generate. in a study of 1228 randomly selected medical malpractice lawsuits, it is found that 856 of them were later dropped or dismissed (based on data from the physician insurers association of america). construct a 99% confidence interval estimate of the proportion of medical malpractice lawsuits that are dropped or dismissed.
About [0.7479, 0.8091] of medical malpractice cases are abandoned or dismissed, according to the estimate with a 95% confidence level.
A confidence interval is a method for estimating a population parameter, such as the population proportion, at a given level of confidence, using the sample statistic, such as the sample proportion, and the confidence coefficient, such as the critical value.
arbitrary sample size, n = 1228
number of those who were dropped or dismissed, x = 856
The sample percentage of later discarded or dropped, p = 956 / 1228 ≅ 0.7785
Level of confidence = 0.99
Level of significance α = 0.01
The population proportion's 99% confidence interval estimate is calculated as follows:
p ± [tex]z_{a/2}[/tex] * [tex]\sqrt\frac{p (1 - p)}{n}[/tex]
Using the Excel function or the z-distribution table for calculation
[tex]z_{a/2} = z_{0.01/2} = z_{0.005}[/tex]
=NORMSINV(0.05)
[tex]z_{0.01/2}[/tex] ≅ ±2.58
The interval's computation is as follows:
0.7785 ± 2.58 * [tex]\sqrt\frac{0.7785 (1 - 0.7785)}{1228}[/tex]
= 0.7785 ± 2.58 * 0.0118
= = 0.7785 ± 0.0306
(0.7479, 0.8091)
As a result, the estimate of the proportion of medical malpractice claims that are withdrawn or dismissed at a 99 percent confidence interval is roughly [0.7479, 0.8091].
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Can anyone answer question 8?
Which sentence describes a benefit that short-term disability insurance offers a policyholder?
A. It provides 30% to 40% of the policyholder’s income for up to one year.
B. It provides 10% to 25% of the policyholder’s income for up to two years.
C. It provides 50% of the policyholder’s income for up to one year.
D. It provides 40% to 60% of the policyholder’s income for up to one year.
The sentence that describes a benefit of short-term disability insurance is D. It provides 40% to 60% of the policyholder’s income for up to one year.
What is short-term disability insurance?Short-term disability insurance is meant to cover a portion of a person's wages in the event that they get injured such that they are unable to work and earn a salary in that time.
The short-term disability insurance policies these days generally cover about 40% to 60% of the income that the policyholder would have made in one year and so has less premiums.
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2.2(s + 1) 14.7 = 5.1
Answer:-454/539
Step-by-step explanation:32.34(s+1)=5.1
32.34s+32.34=5.1
32.34s=5.1-32.34
32.34s=-27.24
s=-454/539
a passenger train traveled 240 miles in the same amount of time it took a freight train to travel miles. the rate of the freight train was miles per hour slower than the rate of the passenger train. find the rate of the passenger train.
The rate of the passenger train is 60mph.
We know that,
Speed = Distance / Time
Time = Distance / Speed
s = speed of passenger train
speed of freight train = (s - 20)
T = 240 / s
T = 160 / (s-20)
240 / s = 160 / (s-20)
240(s - 20)/s(s - 20) = 160s/s(s - 20)
240(s - 20)/s(s - 20) - 160s/s(s - 20) = 0
240(s - 20) - 160s = 0s(s - 20)
240s - 4800 - 160s = 0
80s - 4800 = 0
80s = 4800
Hence the speed of the freight train is 40mph, while the speed of the passenger train is 60mph.
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I need help understanding domain and range better. I am in algebra 1 in high school freshmen
The domain and the range of a function have the concepts given as follows:
Domain: input values of a function/relation.Range: output values of a function/relation.What are the domain and range of a function?The domain of a function or of a relation is the set that contains all possible input values. Hence, among possible representations, we have that:
In a graph, the domain is composed by the values of x.In a relation of points (x,y), the domain is also composed by all the values of x.For a function, the domain is composed by all values that respect the restrictions of a function. For example, in a fraction, the domain is composed by all values for which the denominator is not zero.The range of a function or of a relation is the set that contains all possible output values. Hence, among possible representations, we have that:
In a graph, the domain is composed by the values of y.In a relation of points (x,y), the domain is also composed by all the values of y.For a function, the range is composed by all the numeric values assumed by the function inside it's domain.More can be learned about the domain and the range of a function or of a relation at https://brainly.com/question/10197594
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1. Name a plane parallel to plane WXT
2. Name two segments parallel to VU.
3. Name two segments parallel to SW.
4. Name two segments skew to XY.
5. Name two segments skew to VZ.
The plane which is parallel to the line WXT is UVZW
two segments parallel to VU is ST and WX
two segments skew to XY is UT
two segments skew to VZ is YU and TX
What are parallel lines ?Lines that are always the same distance apart in a plane are said to be parallel. Lines that are parallel never cross. Lines that cross at a straight angle (90 degrees) are said to be perpendicular.
Given : The quadrilateral prism
Parallel lines means lines which does not interact and run parallel meaning they have equal distance between them.
The plane which is parallel to the line WXT is UVZW
two segments parallel to VU is ST and WX
two segments skew to XY is UT
two segments skew to VZ is YU and TX
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what's the answer to
m + 6n; use m = 6, and n = 6
Answer:
Step-by-step explanation:
1. Put the variable as numbers in the computation. m=6 and n=6
SO:
6+6*6
2. Compute using Pemdas( Parentheses, exponets,multiplication, division, addition, subtraction)! Or order of operations!
6+36= 42
Answer: 42
By increasing the pendulum's mass and releasing the pendulum from a greater height the maximum potential energy
will increase and the maximum kinetic energy will decrease.
Answer: False
Step-by-step explanation:The potential energy will decrease and the kinetic will increase
Tom is applying for a visa.
He has to pay £2,300 for the visa as well as a 7% charge on the visa price for an on-the-day service.
If Tom has 1 year to save, how much money should he save per month to be able to cover his costs?
Round your answer to the nearest £10.
What are the domain and range of the function f(x)=3/4x+5?
Answer:
domain: [tex](-\infty, \infty)[/tex]
range: [tex](-\infty, \infty)[/tex]
Step-by-step explanation:
You can put any real number into [tex]x[/tex] and get any real number out oft the function [tex]f(x)[/tex]
in a class of 150 students the ratio of boys to girls is 3 2 how many more boys than girls are in the class
The number of boys and girls in a class of 150 students is 90 and 60 respectively.
RATIO:
Comparing two quantities of the same units and determining the ratio tells us how much of one quantity is in the other.
i.e., it shows how many times a number contains another.
Total number of students = 150
ratio of boys to girls = 3 : 2
B:G = 3 : 2
now
3x + 2x = 150
5x = 150
x = 30
the number of boys = 3x = 3 X 30 = 90 boys.
the number of girls = 2x = 2 X 30 = 60 girls.
The number of boys and girls in a class of 150 students is 90 and 60 respectively.
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Paul is a keen cyclist. the chart shows the distance he cycled each day of last week. a)How much further did Paul cycle on Friday than on Monday? b)what is the total distance cycled by Paul on the three days he cycled the most?
Answer:
a) 6 km
b) 66 km
Step-by-step explanation:
a) According to the graph:
Paul cycled about 22 km on Friday.Paul cycled about 16 km on Monday.To find how much further, subtract the distance cycled those two days:
22 - 16 = 6 km
b) The three days he cycled the most are the three days with the highest lines on the graph, so that would be:
Saturday, about 24 km.Friday, about 22 km.Wednesday, about 20 km.Add them all up to find the total distance cycled:
24 + 22 + 20 = 66 km
Forty students in the second grade class listed their hair and eye colors in the table below:
Brown hair Blonde hair Total
Blue Eyes 5 12 17
Brown Eyes 16 7 23
21 19 40
Are the events “blonde hair” and “brown eyes” independent?
The events “blonde hair” and “brown eyes” are not independent.
What are independent events?
The term "independent events" refers to those whose occurrence is not reliant on another event.
When two events A and B are independent then the intersection of the two events is equal to zero. i.e. They do not have any element in common.
But from the given table we can see that the intersection of the events of "blonde hair" and "brown eyes" exists.
Therefore, the events "blonde hair" and "brown eyes" are not independent.
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how to find the vertex
Answer: To find the vertex: use formula x= -b/2a.
plug x into the given equation to find y value.
now you have (h,k)
find a point on the graph and plug in to the vertex form equation to find "a"
Step-by-step explanation:
Use remainder theorem for x^3+8x^2+11x-20 by (x+4)
Answer:
x^3 + 64 + 11x - 20bxy - 80by
(if I am wrong, apologies)
Answer:
x^2+4x-5
Step-by-step explanation:
x^3+8x^2+11x-20/x+4=x^2+4x-5
Frances owns a landscaping business. She has 425 plants and is placing an equal number of plants into 47 yards. After planting, how many plants will she have left to take home and plant in her own yard?
A. 0 plants
B. 1 plant
C. 2 plants
D. 3 plants
Triangle FGH has vertices F(-3, 4), G(2, 0), and H(-1, -2). Graph AFGH and its image after a rotation of 180° about (-3, -6).
Answer:
Im gonna assume its counter clockwise (excuse the bad drawing)
Step-by-step explanation:
The vertices of triangle F'G'H' after a rotation of 180° about (-3, -6) are F'(0, 10), G'(5, 6) and H'(2, 4).
What is rotation?Rotations are transformations that turn a shape around a fixed point. To rotate a shape we need: a centre of rotation. an angle of rotation (given in degrees) a direction of rotation – either clockwise or anti-clockwise.
Given that, triangle FGH has vertices F(-3, 4), G(2, 0), and H(-1, -2).
180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).
So, (x, y) → (x+3, y+6)
F(-3, 4) → (-3+3, 4+6) → F'(0, 10)
G(2, 0) → (2+3, 0+6) → G'(5, 6)
H(-1, -2) → (-1+3, -2+6) → H'(2, 4)
Therefore, the vertices of triangle F'G'H' after a rotation of 180° about (-3, -6) are F'(0, 10), G'(5, 6) and H'(2, 4).
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A 12 pack of sodas is priced at $5.40 and a 16 pack of sodas is priced at $6.72. Which is a better buy?
Answer:
Step-by-step explanation:
5.40/12= 0.45
6.72/16=0.42
Answer:
The 16 pack
Step-by-step explanation:
Pack 1: $5.40 for 12
Find the price per soda by dividing the price by 12: $5.40 / 12 = $0.45 per canPack 2: $6.72 for 16
Find the price per soda by dividing the price by 16: $6.72 / 16 = $0.42Therefore the 16 pack is the better buy because you purchase an extra 4 sodas for $0.03 less.
n how many ways can a math team of 14 students be chosen from a math club which consists of 15 seniors and 11 juniors if the team must consist of 8 seniors and 6 juniors?
Using Combination formula, total 2,24,070 ways to make a math team of 14 selected students in which consist of 8 seniors and 6 juniors.
We have following information,
total number of seniors in math club = 15
total number of juniors in math club = 11
total number of students in math club = 26
A math team of 14 students be choosen from maths club such that it consists 8 seniors and 6 juniors .
Number of ways to choose 8 seniors out of 15 seniors = ¹⁵C₈ = 485
Number of ways to choose 6 juniors out of 11 juniors = ¹¹C₆ = 462
Number of ways to select/choose a math team of 14 students consists 8 seniors and 6 juniors
= 485 × 462 = 2,24,070
Hence, the number of ways to select/choose a math team of 14 students consists 8 seniors and 6 juniors is 2,24,070..
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there are 5 major sea islands in the queen elizabeth islands of canada that you are interested in visiting. there are 12 major lakes in saskatchewan, canada that you would also like to visit. (a) if you are planning a trip to visit one of these islands, followed by one of these lakes, how many different trips could you make?
The person can make 60 trips.
Let us say that A indicates the major sea Islands and B indicates the major lakes. Taking both the cases as events, we will use multiplication principle. Based on the information, the event A occurs in m ways and the event B will occur in n ways. So, the two events will occur in m×n ways.
Thus, A × B = 5 × 12
Performing multiplication on Right Hand Side of the equation to find the number of trips
Total number of trips = 60
Hence, there are 60 trips that could be made.
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