Use rigid motions to explain whether the triangles in the figure are congruent. Be sure to describe specific rigid motions in your explanation.
Answers
In the case above, ΔDWP is presumed to be congruent to ΔMJS. Rigid motions involved here are translation and rotation.
In translation, you are basically sliding/moving the figure. ΔDWP is moved five (5) units down then one (1) unit to the left. Thereby, coinciding point W of ΔDWP and point J of ΔMJS.
Next rigid motion used is rotation. The figure is simply rotated approximately 90 degrees thereby coinciding all points of ΔDWP to ΔMJS.
To check for congruency by just merely looking on the plane, compare the lengths of the sides of the triangles.
side DW = side MJ = 2 units
side WP = side JS = 4 units
side PD = side SM = 5 units
Therefore, we can say that ΔDWP is congruent to ΔMJS.
In mathematics, congruence of triangles is determined using rigid motions. If one can be made to coincide with the other through translation, rotation, and reflection, then the triangles are congruent.
Explanation:In mathematics, congruence of triangles is determined using rigid motions. Rigid motions include translation, rotation, and reflection. These motions maneuver a figure without altering its shape or size, hence the term 'rigid'.
To determine if two triangles are congruent by rigid motions, you could move one triangle using a combination of these rigid motions to check if it can overlap perfectly with the other triangle. For example, you may need to translate (or slide) the triangle a certain distance in a certain direction, rotate it around a point by a certain angle, and possibly reflect it across a line.
If you can make one triangle coincide with the other through these rigid motions, then the triangles are congruent. Otherwise, they are not congruent. This is basically the idea behind the congruence of triangles through rigid motions.
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Related Questions
2. At the grocery store checkout, you watch at the register as it rings up your purchases and coupons. The prices are as follows:
$2.95
$1.19
$4.61
$1.74
$3.04
$8.83
$1.16
− $0.75 (coupon)
− $1.00 (coupon)
The register gives your total bill as $21.77.
(a) Round each price and coupon to the nearest dollar and then estimate the total amount of the bill.
(b) Using your estimate, determine whether the total on the register is reasonable. Justify your answer.
Answers
-$3
-$1
-$5
-$2
-$3
-$9
-$1
- $1 off (coupon)
- $1 off (coupon)
Rounded Total: $22
Exact Total: $21.77
B) The total on the register is reasonable because even with the rounded price at the end, it is only 23 cents off, which is good.
Answer and explanation:
Given : At the grocery store checkout, you watch at the register as it rings up your purchases and coupons.
The register gives your total bill as $21.77.
To find :
(a) Round each price and coupon to the nearest dollar and then estimate the total amount of the bill.
The prices are as follows:
$2.95 estimated to $3 as (9>5)
$1.19 estimated to $1 as (1<5)
$4.61 estimated to $5 as (6>5)
$1.74 estimated to $2 as (7>5)
$3.04 estimated to $3 as (0<5)
$8.83 estimated to $9 as (8>5)
$1.16 estimated to $1 as (1<5)
− $0.75 (coupon) estimated to -$1 as (7>5)
− $1.00 (coupon) estimated to -$1 as (0<5)
The total amount bill is $3+$1+$5+$2+$3+$9+$1-$1-$1=$22.
So, Estimated total amount of the bill is $22.
(b) Using your estimate, determine whether the total on the register is reasonable. Justify your answer.
The register gives your total bill as $21.77.
The total on the register is reasonable because even with the rounded price at the end the price became same which is reasonable.
As 21.77 estimated to 22 as (7>5).
what is the preimter and area of a rectangle that is 30 inchs long and 39 inchs wide
Answers
30 x 2 = 60
39 x 2 = 78
60 + 78 = 138
And never forget to label your units!
The perimeter of the rectangle is 138 inches.
To get the area, multiply the sides by each other.
30 x 39 = 1170
The area of the rectangle is 1170 inches^2, or 1170 inches squared.
Area is 1170 (30*39)
Carlos purchased an antique chair for $15 he later so this year for $27 to an antique dealer what was the percent markup of the chair
Answers
Answer: The required percent markup is 80%.
Step-by-step explanation: Given that Carlos purchased an antique chair for $15 and later he sold it this year for $27 to an antique dealer.
We are to find the percent markup of the chair.
The markup price of the chair is given by
[tex]m_p=\$(27-15)=\$12.[/tex]
Since Carlos purchased the chair for $15, so the markup percent is given by
[tex]\dfrac{m_p}{15}\times100\%\\\\\\=\dfrac{12}{15}\times100\%\\\\\\=\dfrac{4}{5}\times100\%\\\\=80\%.[/tex]
Thus, the required percent markup is 80%.
0.12 or 1.2% which is greater
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0.12% isn’t a full percent, the decimal determines the greatness of the two
1.2% is the larger number
1.2% is the greater percentage than 0.12
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
We need to find 0.12 or 1.2% which is greater
0.12 isn’t a full percent, the decimal determines the greatness of the two number.
1.2% is the larger number.
1.2% = 1.2/100
= 0.012
Therefore, 1.2% is the greater percentage than 0.12
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Please Troy to help me understand this example
Answers
The given value is 3 9/100
9/100 = 0.09
3 + 0.09 = 3.09.
Therefore, 3 9/100 = 3.09.
8x-3y=6-4x in linear equation
Answers
8x-3y=6-4x
-8x -8x
-3y=6-12x
/-3 /-3 /-3
y=-2+4x
y=4x-2
A constant of proportionality can also be considered a(n)
Answers
Answer: A. Unit Rate
Addition and __?___ are operations you can use to join __?____?
Answers
Answer: The correct answer is:
Addition and multiplication are operations you can use to join equal groups.
Step-by-step explanation: Confirmed correct.
Help what does this mean
Best answer I will mark as brainliest
Answers
I hope this helps!
it will cost $73 per hour to rent a sailboat and 88 per hour to rent a ski boat. how much more will it cost to rent a ski boat than a sailboat for 4 hours
Answers
If y=-7 when x=-21, what is the value of x when y=9
Answers
So then when y=9, 9=x-21.
Solve for x.
x=9+21
x=30
If y = -7 when x = -21, then y = (1/3)x, and (1/3) is the constant of proportion.
A similar truth is that x = 3(y), as -21 = 3(-7)
So, if y=9, x = 3(9) = 27
A movie theater has 24 screens. The ratio of action films to other film is 1:2 in the summer. How many action films are shown?
Answers
Answer:
8 action films being shown
Step-by-step explanation:
Great question, it is always good to ask away and get rid of any doubts that you may be having.
Based on this question we can see that the movie theater has 1 action movie for every 2 other type of movies. We can add these two numbers together and divide by 24 to find out how many action movies are playing compared to the other types of movies.
[tex]1 + 2 = 3[/tex]
[tex]24 / 3 = 8[/tex]
8 action movies : 16 other type of movies
As we can see from the adjusted ratio above, there are 8 action films being shown
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
What happens to the arrangement of water molecules as ice melts?
Molecules release enough energy to move from their fixed positions.
Molecules release enough energy to escape as vapor.
Molecules gain enough energy to move from their fixed positions.
Molecules gain enough energy to escape as vapor.
Answers
According to the school survey, 12% of the students at Rockwood Junior High School speak Spanish. There are 36 students at the school who speak Spanish. How many students were surveyed?
Answers
36=(0.12)n
n=300
300 students were surveyed.
That's the way I answer in my country but I'm not sure about this solution is correct in your school or not.
Answer:
300 students were surveyed.
Step-by-step explanation:
We are given the following information in the question:
Percentage of students at Rockwood Junior High School who speak Spanish = 12%
Number of students at Rockwood Junior High School who speak Spanish = 36
We have to find the total number of students who surveyed:
Formula:
Let x be the total number of students who were surveyed.
[tex]12\% \text{ of }x = 36\\\\\displaystyle\frac{12}{100}\times x = 36\\\\x = \frac{36\times 100}{12}\\\\x = 300[/tex]
Thus, 300 students were surveyed.
All of the following expressions have the same value, when x = -2 and y = 4, except _____.
a. x 2y
b. (-2) 2y
c. -4 x 2
d. -2 xy
Answers
-2 *2(4) = -2 *8 = -16
(-2) *2(4) = -2 *8 = -16
-4(2)*2 = -8*2 = -16
-2*(-2*4) = -2 *-8 = 16
D is the only one that is positive so D is the answer
C. -4 x^2
next time add the ^ it doesnt copy the small numbers
Rachel bought 6 1/4 pounds of dried fruit. If 1/3 of the fruit was dried apricots, how many pounds of dried apricots did she buy?
Answers
Rachel bought 6 1/4 pounds of dried fruit. If 1/3 of the fruit was dried apricots, then the pounds of dried apricots which she bought was 25/12 or 2.08pounds.
What is Arithmetic operation?This basically comprises of operations such as Addition, Subtraction, Multiplication and Division.
Operations such as 'of ' are usually represented with the multiplication sign which is ( × ). In this scenario we were told that 1/3 of the 6 1/4 pounds of dried fruit was dried apricot.
This therefore means that 1/3 of 25/4 = 1/3 × 25/4 = 25/12.
This means that 25/12 or 2.08pounds was bought by her.
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Colin drove 45 minutes to the air port. He arrived 90 minutes before his flight departed and then he spent 70 minutes in the air. Once he landed Colin spent 20 minutes gathering his language and the. He drive 35 minutes to his hotel what must be true of any expression that represents the hotel time Collin spent traveling from his house to the hotel.
Answers
Given: The time taken to do each activity from Colin's house to his hotel in given.
he drove to the airport for 45 minuteshe waited at the airport for the flight to depart for 90 minuteshis fight duration was 70 minutesupon landing, he gathered his luggage for 20 minuteshe drove to the hotel for 35 minutesTo Find: what is true of any expression that represents the total time Collin spent traveling from his house to the hotel
Solution: Any expression will involve the sum of all the durations of his various activities i.e., 260 minutes or 4 hours and 20 minutes.
Explanation:
As each of the activities described is an independent activity that does not overlap, we can easily sum up the durations of each to find the total time Collin took from his house to the hotel.
We add it as follows :
he drove to the airport for 45 minutes + he waited at the airport for the flight to depart for 90 minutes + his fight duration was 70 minutes + upon landing, he gathered his luggage for 20 minutes + he drove to the hotel for 35 minutes.
So, 45+90+70+20+35 = 260 minutes
which means it took a total of 260 minutes or 4 hours and 20 minutes from Collin's house to his hotel.
Answer:
the answer is A
Step-by-step explanation:
I got a 90 and I got it right and so will u so trust me
what is 10% as a decimal?
Answers
10% as a decimal is 0.1
To find the decimal of a percentage, just divide the percentage by 100.
10/100 = 1/10 = 0.1
I hope this helps!
A physicist working in a large laboratory has found that light particles traveling in a particle accelerator increase velocity in a manner that can be described by the linear function −4x + 3y = 9, where x is time and y is velocity in kilometers per hour. Use this function to determine when a certain particle will reach 50km/hr.
The particle will reach 50km/hr when x =
.
Answers
Answer:
x = 35.25 hr
Step-by-step explanation:
The velocity model is given by −4x + 3y = 9, where x is time and y is velocity in kilometers per hour.
Solve the equation for x
Add 4x to both sides of the equation
[tex]3y=4x+9[/tex]
Subtract 9 to both sides
[tex]3y-9=4x[/tex]
Divide both sides by 4
[tex]x=\frac{3}{4}y-\frac{9}{4}[/tex]
Now, we have to find x for y = 50
Replace y with 50
[tex]x=\frac{3}{4}\cdot50-\frac{9}{4}\\\\x=\frac{75}{2}-\frac{9}{4}\\\\x=\frac{141}{4}\\\\x=35.25[/tex]
Therefore, the particle will reach 50 km/hr when x = 35.25 hr
There are 5 flower gardens in front of the building where Eddie works. Eddie has 40 red and 80 white flowering plants to put in the gardens. How many plants will be in each garden, if he plants the same number in each?
Answers
120 / 5 = 24
24 plants will be in each garden.
A classmate believes that a triangle can have both a right angle and an obtuse angle. Which of the following statements would you pick to convince him that he is incorrect
(a) It is not possible because the sum of the angles in the triangle can’t exceed 180°
(b)It is not possible because if a triangle has an obtuse triangle, that means all the angles are obtuse angles. (c) It is not possible because if a triangle has a right triangle, that means all the angles are right angles (d)It is possible. The classmate is correct
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fill in the blanks with two rational numbers (other than 1 and -1)
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How to subtract 4/5 and 3/10 in simplest form
Answers
4/5- 3/10 = 8/10- 3/10
You can now solve this to get 5/10. This answer can then be reduced to 1/2.
Henry has a bag containing 35 letter tiles some consonants and some vowels He selects a tile without looking and then replaces it if he pull 3 consonants tiles and 4 vowel tiles which is the most likely number of consonant tile in Henry’s bag
Answers
35/7
=5
This gives you 5
You then take that 5 and multiply it by the amount of consonant vowels he pulled out, which is 3.
5x3
=15
So your answer is...
D.) 15 Tiles
I hope this helped! : )
What is the value of the function at x= -2?
Answers
Answer:
The correct answer is y = 2
Peaches are being sold for $2 per pound. If x represents the number of pounds of peaches bought and yrepresents the total cost of the peaches, which best describes the values of x and y?
Answers
2) y = total cost of the peaches
3) formula would be: y = $2x
but i don't understand what you'd want to know...
Let
x----------> represents the number of pounds of peaches bought
y----------> represents the total cost of the peaches
we know that
Peaches are being sold for [tex]2\frac{\$}{pound}[/tex]
so
the equation that best describes the values of x and y is equal to
[tex]y=2x[/tex] or [tex]x=y/2[/tex]
The relationship between the two variables, x, and y, represent a direct variation
therefore
the answer is
[tex]y=2x[/tex] or [tex]x=y/2[/tex]
a large aquarium has 6 more fish than a small aquarium. There are 19 fish in a large aquarium. How many fish are in a small aquarium
Answers
The number of fish in the small aquarium is 13 fish.
What is a word problem?A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
The number of fish in the large aquarium = 19
A large aquarium has 6 more fish than a small aquarium.
The number of fish in the small aquarium is
⇒ [tex]19-6[/tex]
⇒ [tex]13[/tex]
Hence we can conclude that the number of fish in the small aquarium is 13 fish.
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The Smiths spend 11% of their budget on entertainment. Their total budget this year is $2,000 more than last year, and this year they plan to spend $4,950 on entertainment. What was their total budget last year?
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11%= $4950
1%= $4950/ 11
= $450
100%= $450 x 100
= $45 000 (this year)
Last year= $45 000- $2000
= $43 000
Hope this helps:))
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Find the value of 3x + 2 when 7 + x =5
Answers
7 + x =5
x =5 - 7
x = -2
<6/>3(2) -2 = answer
Answer = 6 />
Hope this helps
How do you change an improper to a mixed numeral
Answers
3 1/2