Answers
Answer (with explanation):
1. Given
2. UY ≅ WY
3. Definition of Midpoint
4(statement). ∠UYX ≅ ∠VYW
4(reason). Side-Angle-Side SAS
5. Vertical Angle Theorem
in most proofs, (almost ALL the proofs) the first reason is always given.
you need given before you do anything.
on 2., the reason is Definition of Midpoint so you can tell it's UY is congruent to WY (uses the theorem)
on 3., it's the other way around and similar to 2. so the answer is definitely Definition of a Midpoint
on 4. statement and reason, you're side UY, angle Y, and side YX to prove that side VY, angle Y, and side YW are congruent. so, use the ∠UYX ≅ ∠VYW with the SAS
and on 5., you use vertical angles to say that ∠UYX reflects to ∠VYW so they are the same (aka congruent)
Answer:
[tex]\large\begin{array}{|l|l|}\cline{1-2}\sf Statement&\sf Reason\\\cline{1-2}1.\;\textsf{$Y$ is the midpoint of $UW$ and $VX$}&1.\;\sf Given\\\cline{1-2}2.\;UY \cong WY & 2.\; \sf De\:\!finition\;of\;a\;midpoint\\\cline{1-2}3.\;VY \cong XY&3.\; \sf De\:\!finition\;of\;a\;midpoint\\\cline{1-2}4.\;\angle UYX \cong \angle VYW&4.\; \sf Vertical\;Angle\;Theorem\\\cline{1-2}5.\; \triangle UYX \cong \triangle VYW &5.\;\sf Side-Angle-Side\;(SAS)\\\cline{1-2}\end{array}[/tex]
Step-by-step explanation:
Midpoint
The point that is halfway between the endpoints of the line segment.
Side-Angle-Side (SAS) Congruence Theorem
If two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, the triangles are congruent.
Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
[tex]\large\begin{array}{|l|l|}\cline{1-2}\sf Statement&\sf Reason\\\cline{1-2}1.\;\textsf{$Y$ is the midpoint of $UW$ and $VX$}&1.\;\sf Given\\\cline{1-2}2.\;UY \cong WY & 2.\; \sf De\:\!finition\;of\;a\;midpoint\\\cline{1-2}3.\;VY \cong XY&3.\; \sf De\:\!finition\;of\;a\;midpoint\\\cline{1-2}4.\;\angle UYX \cong \angle VYW&4.\; \sf Vertical\;Angle\;Theorem\\\cline{1-2}5.\; \triangle UYX \cong \triangle VYW &5.\;\sf Side-Angle-Side\;(SAS)\\\cline{1-2}\end{array}[/tex]
Related Questions
Last week Len spent $18 to bowl 4 games. This week he spent $27 to bowl 6 games Len owns his bowling ball and shoes, so he only has to pay for each game that he bowls. If each of these bowling games costs the same amount of money, what is the constant of proportionality between the money spent and the number of games played?
Answers
The constant of proportionality in both situations is 4.5
Constant of ProportionalityThe constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship. Other names for the constant of proportionality include the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.
The equation of constant of proportionality is given as
y = kx
k = constant of proportionalityLet's take the variable and substitute them
18 = k(4)
k = 18 / 4
k = 4.5
The constant is 4.5
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Fill in the blanks to complete the equation that describes the diagram
Answers
Answer:
-9
Step-by-step explanation:
From the scores on the diagram we can tell that the arrow first stand on the point -3 and then on the point -6.
If we add -6 to -3 the product will be:
(-3) + (-6) = -9
The answer in blocks will be (-3) and (-6)
If we add -6 to -3 the product will be:
(-3) + (-6) = -9
Given,
In the question:
Fill in the blanks to complete the equation that describes the diagram.
Now, According to the question:
From the scores on the diagram we can tell that the arrow first stand on the point -3 and then on the point -6.
If we add -6 to -3 the product will be:
(-3) + (-6) = -9
What is Number line ?
A number line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, for example, plotting a point.
Hence, The answer in blocks will be (-3) and (-6)
If we add -6 to -3 the product will be:
(-3) + (-6) = -9.
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Examine the following graph (need asap)
Answers
The slope is 3. The line is going up 3 and right 1. If it were the other way around, up 1 and right 3, that would be a slope of 1/3.
But the slope is 3.
The slope is x = 3
Explanation:
Because when you look at the graph, between each point, the line moves 3 units up and 1 unit to the right.
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answers
As per the given angle of elevation, the height of the building is 368.5 ft.
Angle of elevation:
Basically, an angle between the horizontal plane and line of sight from the observer's eye to some object above is known as angle of elevation.
Given,
The angle of elevation to the top of a Building in New York is found to be 2 degrees from the ground at a distance of 2 miles from the base of the building.
Here we need to find the height of the building and round to the tenths.
Here we know that the angle of elevation of the building in New York is written as,
=> θ = 2°
And the distance of observation point from the building is given as,
=> l = 2 miles
Here we know that, 1 miles = 5280 feet
So, the value of l in feet is,
=> l = 2 x 5280
=> l = 10560
Now, it is required to calculate the height of the building. Use the concept of trigonometry to find the height,
So, the height is calculated as,
=> tan θ =h/l
Apply the values on the formula, then we get,
=> tan 2° = h/10560
=> 0.0349 = h/10560
=> h = 0.0349 x 10560
=> h = 368.5 feet.
Therefore, the height of the building is 368.5 ft.
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Can someone please help me.
Answers
Proved that ΔXYW ≅ ΔZYW
Consider the two triangles triangle XYW and triangle ZYW
According to SAS congruent rule if 2 sides and one angle of the one triangle is equal to the 2 sides and one angles of the another triangle, then both the triangles are congruent
The length of the side XY = The length of the side ZY
The line YW bisect the angle XYZ
Then the measure of angle XYW = The measure of angle ZYW
The length of the YW is common
Therefore the 2 sides and one angle of the triangle XYW is equal to the 2 sides and one angle of the triangle ZYW
Then the triangles XYW and triangle ZYW are congruent
Hence, proved that ΔXYW ≅ ΔZYW
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In a certain Algebra 2 class of 27 students, 11 of them play basketball and 13 of them play baseball. There are 5 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball? [tex]help\\[/tex]
Answers
Answer:
?? There are 27 students!
11+13 = 24 students play those sports
How can there be 5 students who play neither sport! I'm kind of confused!
Step-by-step explanation:
Answer:
22 / 27
Step-by-step explanation:
See Venn diagarm below
72km = 90 mins. how many km = 40 mins?
Answers
Answer: 32 km
Step-by-step explanation:
Set the unknown value as x and use proportions to find the answer:
[tex]\frac{72}{90} =\frac{x}{40} \\\\90x=72*40\\\\x=\frac{72*40}{90} =32[/tex]
Quinn makes pies at her bakery. She can make 6 pies with 4 cups of sugar. How
much sugar will she need to make 18 pies?
Answers
Answer:
She can make 12 cups of sugar for 18 pies
Step-by-step explanation:because 6x3=18 so you multiply 4x3 to get 12, she need 12 cups of sugar for 18 pies or 18 pies with 6 cups of sugar
Tell me if it is wrong in the comment
Thank you.
A student solved the equation and determined that the solution was -2. Find the error and correct it. 1.5x-2=-2+1.5x -2=-2
Answers
The student solved the equation and determined that the solution was -2. This is wrong as the solution is 0.
What is an equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
This will be illustrated as:
1.5x - 2 = -2
Collect like terms
1.5x = - 2 + 2
1.5x = 0
Divide
x = 0/1.5
x = 0.
Therefore, the student is wrong.
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The Bay purchases an armchair with MSRP $780 less a trade discount of 30%. The Bay sells the armchair at the MSRP. What is the markup amount?
Answers
The markup amount of the purchase is $1114
How to determine the markup amount?From the question, we have the following parameters that can be used in our computation:
Discount = 30%
Selling price = $780
The markup amount is calculated using the following equation
Selling price = Markup amount * (1 - discount)
Make the markup the subject
Markup = Selling price/(1 - discount)
Substitute the known values in the above equation, so, we have the following representation
Markup = 780/(1 - 30%)
Evaluate
Markup = 1114
Hence, the markup is $1114
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What is the approximate area of a circle with radius 6 cm?
Answers
Answer:
133 m^2
Step-by-step explanation:
to find are of a circle it’s r^2 times pi
6^2 x pi
36 pi
113 m^2
Hopes this helps please mark brainliest
Answer:
Answer C is correct
Step-by-step explanation:
The formula to find the area of a circle is:
A = πr²
Here,
r => radius = 6m
Let us find the area of the circle.
A = πr²
A = 3.14 × 6 × 6
A = 113.04 m²
Approx. = 113m²
ANSWER THIS QUESTION WILL MARK BRAINLIEST
Answers
The probability that Jordan will win in three or fewer matches if they play 5 matches using binomial probability distribution is; 0.95636
How to solve Binomial probability distribution problems?The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability.
The general formula for binomial probability distribution is;
P(X = x) = nCx * p^(x) * (1 - p)^(n - x)
where;
Px = the probability of exactly x events occurring
x = the number of expected successful outcomes
n = the number of trials you perform
nCx = the number of different combinations for x items you test in n trials
We are given probability that Jordan wins the match as 1/3. Thus;
p = 1/3 = 0.333
Thus, probability that Jordan will win in three or fewer matches if they play 5 matches is;
P(X ≤ 3) = P(0) + P(1) + P(2) + P(3)
From online binomial probability calculator, we have;
P(X ≤ 3) = 0.95636
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The number of sales of cars sold from January to November are 28, 20, 49, 29, 38, 40, 45, 49, 50, 55 and 60. Find the median and modal sales.
Answers
The Median and the modal sales is 45 and 49 respectively.
What is a median?A median simply means the middle number when the number are arranged in ascending order. The mode is the number that appears most.
Since the number of sales of cars sold from January to November are 28, 20, 49, 29, 38, 40, 45, 49, 50, 55 and 60, this will be arranged as:
20, 28, 29, 38, 40, 45, 49, 49, 50, 55, 60
Therefore, the middle number is 45 and mode is 49.
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Fill in the blanks below.
Find the slope of the line passing through the points (-6, 3) and (-6, -8).
slope:
Find the slope of the line passing through the points (-3, -6) and (8,-6).
slope:
Answers
The slope of the lines are -2/9 and 14/3.Given the coordinates of two points on the line, use the slope formula to determine the slope of the line.
How do you determine a line's slope?Determine the coordinates of two points along the line that you choose.Find the difference between these two points' y-coordinates (rise).Find the difference between these two points' x-coordinates (run).Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.Given the coordinates of two points on the line, use the slope formula to determine the slope of the line. The slope of the lines are -2/9 and 14/3., is m=(y2-y1)/(x2-x1).Explanation:
m = (-8 - -6)/(3 - -6)
= -2/9.
m = (-6 - 8)/(-6 - -3)
= -14/-3 = 14/3.
The slope of the lines are -2/9 and 14/3.
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Mr. Jackson was born on January 1, 1970. His daughter Lea was born on
January 1, 1992. In what year was Mr. Jackson exactly three times as old
as Lea?
Answers
2003 - Lea would be 11, and as there is 22 years between them Mr Jackson would be 33, which is 11 X 3.
Write the domain and range for the following functions using interval notation, inequality notation, and set builder notation
Domains
Interval Notation:
Inequality Notation:
Set Builder Notation:
Range:
Interval Notation:
Inequality Notation:
Set Builder Notation:
Domain:
Interval Notation:
Inequality Notation:
Set Builder Notation:
Range:
Interval Notation:
Inequality Notation:
Set Builder Notation:
Answers
The domain and the range for each function, considering the three notations, are given as follows:
1.
Domain:
Interval Notation: (-∞, ∞).Inequality Notation: All real numbers.Set Builder Notation: {x | x ∈ R}.Range:
Interval Notation: [-4, ∞).Inequality Notation: y >= -4.Set Builder Notation: {y | y >= -4}2.
Domain:
Interval Notation: (-∞, ∞).Inequality Notation: All real numbers.Set Builder Notation: {x | x ∈ R}.Range:
Interval Notation: [-4, ∞).Inequality Notation: y >= -4.Set Builder Notation: {y | y >= -4}How to obtain the domain and the range of a function?The domain of a function is the set containing all the input values of a function, hence on the graph it is given by the values of x for which the function is defined.
The range of a function is the set containing all the output values of a function, hence on the graph it is given by the values of y which the function assumes.
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Ben made trail mix for his camping trip that contained 8 ounces of peanuts, 6 ounces of raisins, and 10 ounces of chocolate candies. He wants to make a larger batch for his next camping trip with 28 ounces of peanuts. How many ounces of raisins will he need?
Answers
The amount of raisins that Ben will mix if he wants to make a larger batch is 21 ounces of raisins
How to determine the raisins for larger batchThe amount is determined by comparing the trial mix used
Initially, 8 ounces of peanuts, 6 ounces of raisins, and 10 ounces of chocolate candies. This has a ratio of
peanut : raisins : chocolate
8 : 6 : 10
If 8 ounces of peanuts was used with 6 ounces of raisins, 28 ounces of peanuts wall be mixed with ? raisins
8 peanuts = 6 raisins
28 peanuts = ? raisins
? = 28 * 6 / 8
? = 21 ounces of raisins
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Based on the giving information, what is the measure of the missing length, w?
Answers
The measure of the missing length of the triangle is 16 units.
According to the question,
We have the following information:
We have a figure of right-angled triangle where two sides are given.
In order to find the third side of this triangle, we will use the Pythagoras theorem.
So, we have the following expression:
[tex]AC^{2} = AB^{2} + BC^{2}[/tex]
[tex](20)^{2} = AB^{2} + (12)^{2}[/tex]
400 = [tex]AB^{2}[/tex] + 144
Subtracting 144 from both sides of the equation:
[tex]AB^{2}[/tex] = 400-144
[tex]AB^{2}[/tex] = 256
We know that the square root of 256 is 16 or in other words, the square of 16 is 256.
AB = 16 units
Hence, the measure of the missing length of the triangle is 16 units.
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Work out
198.02% of £83.02
83.02
Give your answer rounded to 2 DP
Answers
The value of 198.02 percent of £83.02 is £164.40
How to calculate the value?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.
The value will be illustrated thus:
198.02% × £83.02
= 1.9802 × £83.02
= £164.3962
= £164.40
The value is £164.40.
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TYPING Nebi has already typed 250 words. He then starts a timer and finds that he types 150 words in 3 minutes. If Nebi types at a constant rate, write a linear equation to represent the number of words w Nebi types m minutes after starting the timer.
Answers
The linear equation that represents the number of words Nebi types per minutes after the timer is started is: w = 50m + 250.
How to Write a Linear Equation?Linear equation can be written in the slope-intercept form as y = kx + b. To write this, find the values of the slope = m, and the y-intercept of starting value = b.
From the equation given, find the unit rate/slope, which is the number of words typed in one minute.
Thus, we have:
Slope/unit rate (m) = 150/3
m = 50 words per minute.
The y-intercept (b) is 250, because it is the initial/starting value.
Let w represent the total number of words, and m represents the minutes after the starting time.
To write the linear equation, substitute k = 50 and b = 250 into w = km + b:
w = 50m + 250
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How is a fraction related to its simplified form?
A) The simplified fraction is the square root of the original fraction.
B) The original fraction is larger in value than the simplified one.
C) The simplified fraction is half the value of the original fraction.
D) The simplified fraction and the original fraction have the same value
Answers
The simplified fraction and the original fraction have the same value. Option D is correct.
Given that,
To justify, how is a fraction related to its simplified form.
Fraction is defined as the number of compositions that constitute the Whole.
Here,
The value of the fraction does not change when it is brought into a simplified form.
Thus, the simplified fraction and the original fraction have the same value. Option D is correct.
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please help due tomorrow NO SILLY ANSWERS
Answers
Answer:
20-29 songs
Step-by-step explanation:
Artists with 20-29 songs had the highest total number of people in the crowd.
Solve the formula for the variable h.
f=9gh
Answers
Answer:
[tex]h=\frac{f}{9g}[/tex]
Step-by-step explanation:
Divide both sides by [tex]9g[/tex].
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Answers
Which of the following is a factor of 24x^6 - 1029y^3?
Answers
The factors of (24x⁶ - 1029y³) are 3, (2x² - 7x), (4x⁴ +14x²y+49y²)
Factors of Polynomials:When a polynomial is factored, its prime factorization is used to break it down into the product of two or more other polynomials. Polynomials may be easily simplified with the use of factoring.
When a polynomial is factored, its factors are expressed as the polynomial's product. Finding the zeros of the polynomial expression or the values of the variables in the supplied expression are both made possible by factoring polynomials.
Here we have
24x⁶ - 1029y³
Take 3 as common
=> 3(8x⁶ - 343y³)
As we know 8 = 2³ and 343 = 7³
=> 3[(2x²)³ - (7y)³]
From the algebraic identities
a³-b³ = (a-b)(a²+ab+b²)Take a = 2x² , b = 7y and apply above formula
=> 3[(2x² - 7x)((2x²)²+(2x²)(7y)+(7y)²)]
=> 3 [ (2x² - 7x) (4x⁴ +14x²y+49y²)]
Therefore,
(24x⁶ - 1029y³) = 3 (2x² - 7x) (4x⁴ +14x²y+49y²)
Therefore,
The factors of (24x⁶ - 1029y³) are 3, (2x² - 7x), (4x⁴ +14x²y+49y²)
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Can someone solve these math problems for me? (No explanation needed)
2/3 x (-4/5)
(-5/7) x (7/5)
(-2/39) x 39
(2/5) x (-3/4)
Answers
2. -1
3. -2
4. -3/10
Answer:
do the brackets first the solve the division then multiply both
Please help will mark Brainly
Answers
Answer:
B
Step-by-step explanation:
The distance between the lines stays constant, and they never intersect. In other words, you can translate (move) either line by that constant distance, in some direction, to get the other line. It's just like how when you change the y-intercept but keep the slope the same, you get parallel lines.
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Suppose your friend says he can solve the equation 15-(2x+6)=1/2(7x-4) by first using the multiplication property of equality to multiply each side of the equation by 2. Is he correct?
Answers
No
Explanation:
Use distribution property on the right side of the equation. The equation will be:
15-2x-6 = 7/2x-2
Solve to get x=2
Derek is writing an essay for school, He writes 1/6 page in 1/12 of an hour. How much can he write in one hour
Answers
The required number of papers he can write in one hour is 2 pages.
Given that,
Derek is writing an essay for school, He writes 1/6 page in 1/12 of an hour.
Rate of change is defined as the change in value with rest to the time is called rate of change.
Here,
Number of pages written = 1/6
Time = 1/12
Rate = 1/6 / [1 / 12]
Rate = 1/6 × 12 / 1
Rate = 2 pages per hour
Thus, the required number of papers he can write in one hour is 2 pages.
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You need a 35% alcohol solution. On hand, you have a 300 mL of a 20% alcohol mixture. You also
have 65% alcohol mixture. How much of the 65% mixture will you need to add to obtain the desired
solution?
You will need____
mL of the 65% solution
Answers
As per the concept of unitary method, there are 180.8 ml of the 65% mixture will you need to add to obtain the desired solution
Unitary method:
Basically, the way of finding out the solution of a problem by initially finding out the value of a single unit, and then finding out the essential value by multiplying the single unit value.
Given,
You need a 35% alcohol solution. On hand, you have a 300 mL of a 20% alcohol mixture. You also have 65% alcohol mixture.
Here we need to find how much of the 65% mixture will you need to add to obtain the desired solution.
Let us consider x be the amount of the 65% alcohol needed (in milliliters.
Here the amount of the resulting 65% alcohol solution will be is (x+15) milliliters.
So, the amount of the "pure" alcohol in 300 mL of the 20% alcohol solution is written as,
=> 0.20 x 300 mL.
And the amount of the "pure" alcohol in x mL of the 65% alcohol solution is written as,
=> 0.65 * x mL.
Therefore, the total amount of the "pure" alcohol in ingredients is the sum and it can be calculated as,
=> 0.20*300 + 0.65*x mL.
So, it should be equal to the amount of the "pure" alcohol in the mixture, which is written as,
=> 0.35 * (x+15) ml.
Therefore, your "pure alcohol" equation is
=> 0.65* x + 0.20 * 300 = 0.35*(x+15).
When we simplify this one then we get the value of x as,
=> 0.65* x + 0.20 * 300 = 0.35*(x+15).
=> 0.65x + 60 = 0.35x + 5.25
=> 0.3x + 54.25
=> x = 180.8
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