In triangle RST, U is the midpoint of RS, V is the midpoint of ST, and W is the midpoint of TR. Use the triangle diagram to answer the question.
1. What is the length of RS?
A. 12
B. 6
C. 22
D. 24
2. What is the value of x?
A. 6.5
B. 6
C. 11
D. 5.5
3. What is the value of y?
A. 15.9
B. 11
C. 5.3
D. 3.7
4. What is the length of UW?
A. 11
B. 6
C. 7.95
D. 22
5. What is the length of UV?
A. 11
B. 6
C. 7.95
D. 12
Answers
(1)
we are given
U is the midpoint of RS
and we have
[tex]RU=12[/tex]
so, we can use formula
[tex]RS=2RU[/tex]
we can plug values
[tex]RS=2\times 12[/tex]
[tex]RS=24[/tex]............Answer
(2)
V is the midpoint of ST
so, we get
[tex]SV=VT[/tex]
now, we can plug values
[tex]2x=11[/tex]
divide both sides by 2
[tex]x=5.5[/tex].........Answer
(3)
now, we can find y
W is the midpoint of TR
so, we get
[tex]RW=WT[/tex]
we can plug value
[tex]15.9=3y[/tex]
divide both sides by 3
[tex]y=5.3[/tex]
(4)
we can see that
triangles URW and RST are similar
so, their sides ratios must be equal
so, we get
[tex]\frac{RW}{RT} =\frac{UW}{ST}[/tex]
we can plug values
[tex]\frac{15.9}{2\times 15.9} =\frac{UW}{2VT}[/tex]
[tex]\frac{15.9}{2\times 15.9} =\frac{UW}{2\times 11}[/tex]
[tex]UW=22\times \frac{15.9}{2\times 15.9}[/tex]
[tex]UW=11[/tex]...........Answer
(5)
we can see that
triangles SUV and RST are similar
so, their sides ratios must be equal
so, we get
[tex]\frac{SU}{SR} =\frac{UV}{RT}[/tex]
now, we can plug values
[tex]\frac{12}{2\times 12} =\frac{UV}{2\times 15.9}[/tex]
[tex]UV=2\times 15.9\times \frac{12}{2\times 12}[/tex]
[tex]UV=15.9[/tex].............Answer
1. The length of RS is 24 units.
2. The value of [tex]x[/tex] is 5.5.
3. The value of [tex]y[/tex] is 5.3.
4. The length of UW is 11.
5. The length of UV is 15.9.
According to the given figure-
[tex]\triangle RST \sim \triangle URW[/tex]
1. U is the mid-point of RS so, the length of UR and US are equal.
Hence, the length of RS is 24 units.
2. V is the mid-point of ST so, the length of VS and VT are equal.
So,
[tex]2x=11\\x=\dfrac{11}{2}\\x=5.5[/tex]
Hence, the value of [tex]x[/tex] is 5.5.
3. W is the mid-point of RT so, the length of WR and WT are equal.
So,
[tex]3y=15.9\\y=\dfrac{15.9}{3}\\y=5.3[/tex]
Hence, the value of [tex]y[/tex] is 5.3.
4. As, [tex]\triangle RST \sim \triangle URW[/tex]
So, the length of the sides is proportional.
[tex]\dfrac{RT}{RW}=\dfrac{ST}{UW}\\\dfrac{2\times 15.9}{15.9}=\dfrac{11\times 2}{UW}\\UW=11[/tex]
Hence, the length of UW is 11.
5. As, [tex]\triangle RST \sim \triangle URW[/tex]
So, the length of the sides is proportional.
[tex]\dfrac{SU}{SR}=\dfrac{UV}{RT}\\\dfrac{12}{2\times 12}=\dfrac{UV}{2\times 15.9}\\UV=15.9[/tex]
Hence, the length of UV is 15.9.
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Related Questions
Solve each equation over the set of complex numbers.
1. 2x^4-3x^3-24x^2+13x+12=0
2. x^3-7x^2+17x-15=0
Answers
Answer:
1. x= 4, 1, -1/2, -3
2. x= 3, 2+i , 2-i
Find the value of x .... need help ASAP
Answers
We know: The sum of the angles of each quadrilateral is 360°.
Therefore we have equation:
x + 3x + 4x + 2x = 360
10x = 360 |:10
x = 36
or inequalities. Greater Than, >, and Less Than, <, mean the solution does NOT contain the number. So would you use and open circle or a closed circle to graph on a number line ___________________ For inequalities. Greater Than or Equal TO, >, and Less Than or Equal TO, <, mean the solution does contain the number. So would you use and open circle or a closed circle to graph on a number line?____________________
Answers
In case of inequalities we have following two rules.
Rule 1:
If we have just greater than > or less than < sign , then we would use open cirlce.
An open dot means the function has no definition at the specific point
Greater Than, >, and Less Than, <, mean the solution does NOT contain the number
Rule 2:
For inequalities. Greater Than or Equal TO, >, and Less Than or Equal TO, <, mean the solution does contain the number.
So in that case we will use closed circle.
Hope that helps.
Closed circle for the first one
Open circle for the second one
I need help with these 3 questions. 25 points!!!
1. Andrew is renting a camera that cost d dollars per day for 8 days. He can only spend $3,000. Make a inequality that Andrew can use to find all values of d within his budget
2. The movie camera shoot 24 frames per second. The scene is 4 minutes long. How many frames are there in that scene?
3. Filmmakers shoot much more film than they eventually use. The ratio of film shot to film used is called the footage ratio. Andrew shot 9 hours of film for his movie that is 1 hour and 30 minutes long. What is his footage ratio?
Answers
1. The inequality 8d ≤ 3000 when Andrew is renting a camera that cost d dollars per day for 8 days. He can only spend $3,000.
2. There are 5760 frames in that scene.
3. Andrew's footage ratio is 6, meaning he shot 6 times more film than what was eventually used in his 1 hour and 30-minute movie.
1. Let's create an inequality to represent Andrew's budget for renting the camera. The cost of renting the camera per day is represented by "d" dollars. He wants to rent it for 8 days, and his budget is $3,000.
The total cost of renting the camera for 8 days is 8d dollars. Andrew's budget is $3,000.
So, the inequality would be:
8d ≤ 3000
This inequality ensures that the total cost of renting the camera (8d) does not exceed his budget of $3,000.
2. To find the number of frames in a scene, we need to multiply the frame rate (frames per second) by the duration of the scene (in seconds).
Given:
Frame rate = 24 frames per second
Duration of the scene = 4 minutes
First, convert the duration to seconds since the frame rate is given in frames per second:
4 minutes * 60 seconds per minute = 240 seconds
Now, multiply the frame rate by the duration:
Number of frames = 24 frames/second * 240 seconds = 5760 frames
So, there are 5760 frames in that scene.
3. To find the footage ratio, we need to compare the amount of film shot to the amount of film used.
Film shot = 9 hours
Film used = 1 hour and 30 minutes
First, convert the film used to hours:
1 hour and 30 minutes = 1.5 hours
Now, divide the film shot by the film used:
Footage ratio = Film shot / Film used
Footage ratio = 9 hours / 1.5 hours
Footage ratio = 6
So, Andrew's footage ratio is 6, meaning he shot 6 times more film than what was eventually used in his 1 hour and 30-minute movie.
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Cost of 10 oranges is one dollar what is the cost of five
Answers
5 oranges = $?
To get from 10 to 5 you divide by 2 so that’s what you do with the $1 so it would be $0.50
Greg drove 660 miles in 12 hours. At the same rate, how long would it take him to drive 495 miles?
Answers
This one has two parts, first we have to find out the speed to drive 660 miles in 12 hours. Divide 660 by 12 to get the speed of 55 miles per hour, that is your rate for the next part.
Next we need to find out how long it will take to drive 495 miles at the same pace of 55 mph.
Do the same thing 495/55. That will give you your final answer.
495/55= 9
It will take him 9 hours to drive 495 miles at a rate of 55 mph.
Final answer:
Greg drives at a speed of 55 miles per hour. To drive 495 miles at this rate, it would take him 9 hours.
Explanation:
The question asks how long it would take Greg to drive 495 miles if he drove 660 miles in 12 hours. To solve this, we need to find his driving speed and then calculate how long it would take to drive 495 miles at that same speed.
First, we find the speed by dividing the distance traveled by the time:
Speed = Distance ÷ Time
Speed = 660 miles ÷ 12 hours = 55 miles per hour
Now that we know Greg drives at a speed of 55 miles per hour, we can calculate the time it would take him to drive 495 miles:
Time = Distance ÷ Speed
Time = 495 miles ÷ 55 miles per hour = 9 hours
Therefore, it would take Greg 9 hours to drive 495 miles at the same rate of speed.
You have saved $342 and want to go shopping for a few things. You buy a pair of shoes for $73, a pair of jeans for $38$38, and a watch for $64. How much money do you have left?
Answers
First I added $73+$38+$64=175 then I subtracted $342-$175=$167.
I hope this helps.
Answer:
167
Step-by-step explanation:
I did my math check and got 167 hope its right :)
Pls make me brainliest
Rachel says that she ran 115 yards she went farther then Beth who only ran 327 feet.Is Rachel corect
Answers
yes rachel is correct.
1 yd=3 ft. 115*3=345 ft
345>327 so rachel is correct.
Hope this helps!
Yes, Rachel is correct.
What is Measurement unit?
A measurement unit is a standard quality used to express a physical quantity.
Given that;
Rachel says that she ran 115 yards.
And, She went farther then Beth who only ran 327 feet.
Since, 1 yards = 3 feet
Then, 115 yards = 115 × 3 feet
=345 feet
Now, Rachel ran 345 feet.
And, Beth run 327 feet.
Since, 345 > 327
Hence, Rachel went farther then Beth.
So, Rachel is correct.
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__:14=15:21 is a question for ratio. The_ is the answer needed
Answers
See the attcahment
Answer: The required missing number is 10.
Step-by-step explanation: We are given to find the missing number in the following proportion :
[tex]?:14=15:21.[/tex]
Let the missing number be represented by x.
Then, according to the given information, we have
[tex]x:14=15:21\\\\\Rightarrow \dfrac{x}{14}=\dfrac{15}{21}\\\\\\\Rightarrow \dfrac{x}{14}=\dfrac{5}{7}\\\\\\\Rightarrow x=\dfrac{5}{7}\times14\\\\\Rightarrow x=10.[/tex]
Thus, the required missing number is 10.
The sales tax for a certain state can be found by multiplying the purchase price by 1/2. What is the sales tax on an item that is $25.60? Express your answer as a decimal.
Answers
$12.80
sales tax = [tex]\frac{1}{2}[/tex] × $25.60 = $12.80
Answer:
the answer is:12 4/5=$12.80
Step-by-step explanation:
sales tax = 1/2 × 25 3/5 = $12.80
25.60 12 4/5
Help with algebra please
Answers
1.) A - Rational Numbers
2.) C - Natural (Counting) Numbers
3.) B - Integer Numbers
3:
B-7
because it must be between 5 and 8 not including 5 and 8.
[tex]Q2.\\\\1.\ \text{All real numbers}\ \mathbb{R}\\\\2.\ \{1,\ 2,\ 3,\ ...\}\ \mathbb{N}\\\\3.\ \{...,\ -3,\ -2,\ -1,\ 0,\ 1,\ 2,\ 3,\ ...\}\ \mathbb{Z}[/tex]
[tex]Q3.\\5\ not\ \text{because it's not true}\ 5 < 5\ \text{and}\ 5 > 8\\\\7\ not\ \text{because it's not true}\ 7 < 5\ \text{and}\ 7 > 8\\\\8\ not\ \text{because it's not true}\ 8 < 5\ \text{and}\ 8 > 8\\\\9\ yes\ \text{because it's true}\ 9 > 8[/tex]
Two buses go from Sacramento to San Diego. The express bus makes the trip in 6.8 hours and the local bus takes 10.2 hours for the trip. The speed of the express bus is 25 mph faster than the speed of the local bus. Find the speed of both buses.
Answers
Answer: Speed of local bus is 50 mph and speed of express bus is 75 mph
Step-by-step explanation:
let say speed of local bus = x
so speed of express bus = x + 25
Distance = Speed × Time
Distance traveled by local bus = x × 10.2 = 10.2x
Distance traveled by express bus = (x + 25) × 6.8
since Distance traveled by local bus is same as Distance traveled by express bus
⇒10.2x = (x + 25) × 6.8
⇒ 10.2x = 6.8x + 170
⇒ 10.2x - 6.8x = 170
⇒ x = 170/3.4 = 50
So Speed of local bus = x = 50 mph
and Speed of express bus = x + 25 = 50 + 25 = 75 mph
Final answer:
The speed of the local bus is 50 mph and the speed of the express bus is 75 mph.
Explanation:
Let's define the speed of the local bus as 'x'.
The speed of the express bus is 25 mph faster than the speed of the local bus, so the speed of the express bus can be represented as 'x + 25'.
We know that the time taken by the express bus is 6.8 hours and the time taken by the local bus is 10.2 hours.
Using the formula Speed = Distance / Time, we can set up two equations:
Distance / 6.8 = x + 25 (equation 1)
Distance / 10.2 = x (equation 2)
Since the distance is the same for both buses (Sacramento to San Diego), we can equate the distances in equation 1 and equation 2:
x + 25 = (10.2/6.8) * x
x + 25 = 1.5x
0.5x = 25
x = 50
Substituting the value of x in equation 1, we can find the speed of the express bus:
Distance / 6.8 = (50 + 25)
Distance = 6.8 * 75
Speed of the express bus = Distance / 6.8 = 75
So, the speed of the local bus is 50 mph and the speed of the express bus is 75 mph.
Saul recorded the number of different types of pets his friends have in the table shown below: Cats 3 Dogs 2 Rabbits 1 Guinea Pigs 2 Which of the following plots represents the data in the table? A line with 4 tick marks labeled Cat, Dog, Rabbit, and Guinea Pig. Cat has 3 crosses, Dog has 2 crosses, Rabbit has 3 crosses, and Guinea Pig has 2 crosses. The line is labeled Number of Pets, and title of graph is Pet Owners. A line with 4 tick marks labeled Cat, Dog, Rabbit, and Guinea Pig. Cat has 1 cross, Dog has 2 crosses, Rabbit has 1 cross, and Guinea Pig has 2 crosses. The line is labeled Number of Pets, and title of graph is Pet Owners. A line with 4 tick marks labeled Cat, Dog, Rabbit, and Guinea Pig. Cat has 2 crosses, Dog has 1 cross, Rabbit has 0 crosses, and Guinea Pig has 1 cross. The line is labeled Number of Pets, and title of graph is Pet Owners. A line with 4 tick marks labeled Cat, Dog, Rabbit, and Guinea Pig. Cat has 3 crosses, Dog has 2 crosses, Rabbit has 1 cross, and Guinea Pig has 2 crosses. The line is labeled Number of Pets, and title of graph is Pet Owners.
Answers
The answer to this is the last option
Answer:
The correct answer is:
A line with 4 tick marks labeled Cat, Dog, Rabbit, and Guinea Pig. Cat has 3 crosses, Dog has 2 crosses, Rabbit has 1 cross, and Guinea Pig has 2 crosses. The line is labeled Number of Pets, and title of graph is Pet Owners.
Step-by-step explanation:
The survey is given as:
Pet Frequency
Cats 3
Dogs 2
Rabbits 1
Guinea Pigs 2
When we will draw a line plot where the horizontal axis denote the pet and the cross above the pet represent the number of pets.
Hence, as the frequency of cat is three so there will be three cross above cat.
Similarly as the frequency of dogs is two so there will be two cross above dogs.
the frequency of rabbits is one so there will be one cross above rabbit.
the frequency of Guinea Pigs is two so there will be two cross above Guinea Pigs.
I do 140 miles per week and i get 17mpg , how many days do i have to fill up my tank
Answers
20m a day
20 divided by 17
1.8
about 4 days you would need to fill the tank
NEED HELP ASAP WILL MARK BRAINLIST PLEASE HURRY
Carrie and Juanita are saving up to start a slime business. They need at least $125 to cover their start-up costs.
To earn that money, Carrie decides to do sell cupcakes. She sells cupcakes for $0.50 each. Juanita decides that she would like to sell homemade cards. She will be selling the cards for $2.25 each. Juanita plans to make at least 35 cards. To make up the difference, Carrie plans to sell no less than 3 times the number of cards Juanita makes.
To earn that money, Carrie decides to do sell cupcakes. She sells cupcakes for $0.50 each. Juanita decides that she would like to sell homemade cards. She will be selling the cards for $2.25 each. Juanita plans to make at least 35 cards. To make up the difference, Carrie plans to sell no less than 3 times the number of cards Juanita makes.
Answers
$236.25 is how much money carrie got
$78.75 is how much juanita got
What is the inequality of 5(3-x)-4(2-3x)>2
Answers
5(3 - x) - 4(2 - 3x) > 2
15 - 5x - 8 + 12x > 2 distributed 5 and 4 on the left side
7 + 7x > 2 added like terms (15 and -8) and (-5x and 12x)
-7 -7
7x > -5
[tex]\frac{7x}{7} > \frac{-5}{7}[/tex]
[tex]x > \frac{-5}{7}[/tex]
Statement Justification
∠1 + ∠2 = 180 Definition of Supplementary Angles
∠1 + ∠4 = 180° Definition of Supplementary Angles
∠1 + ∠2 = ∠1 + ∠4 Transitive Property of Equality
is this wrong? please explain
Answers
Technically you should use "substitution" in place of "transitive property of equality", though they are very closely related ideas. If I were your teacher, then I would accept that answer as valid nonetheless.
-------------------
Substitution says that if a = b and c = b, then a = c. We replace the 'b' in a = b with 'c'. Think of your substitute teacher who replaces your current teacher for a temporary basis. This is how to remember the term "substitution.
On the other hand, the transitive property of equality says that if a = b and b = c, then a = c. The equations chain together and can simplify into one single equation.
Factor the perfect square trinomial completely.
7w^2-84w+252
ive got an idea how to solve it, but i need double checking
Answers
This is the result :7(x-6)(x-6)
what is the greatest number of tables you could use to serve dinner to 55 guest so that each table has a different number of guest
Answers
The greatest number of tables needed to serve dinner to 55 guests, with each table having a different number of guests, is 10 tables.
Explanation:To find the greatest number of tables needed to serve dinner to 55 guests so that each table has a different number of guests, we need to distribute the guests among the tables in a way that maximizes the number of tables. We can start by placing one guest at each table, then add one more guest to each subsequent table until there are no more guests remaining. This will result in the maximum number of tables, with each table having a different number of guests.
Let's see how this works:
After distributing the guests this way, we have used 10 tables, with each table having a different number of guests. Therefore, the greatest number of tables we could use to serve dinner to 55 guests, with each table having a different number of guests, is 10 tables.
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Solve for x: 2(x-5) = 6x - (x-8)
Answers
First you need to distribute
2x-10=6x-x+8
Add like terms
2x-10=5x+8
Subtract 8 from each side
2x-18=5x
Subtract 2x from each side
-18=3x
Divide each side by 3
X=-6
2x-10=6x-x+8
2x-10=5x+8
add 10 to both sides
2x=5x+18
subtract 5x from both sides
-3x=18
divide each side by -3
x=-6
The price of an item has been reduced by 85%. The original price is $39.What is the price of the item now?
Answers
GIVEN:- The actual price was $39. And it is reduced to 85%.
To prove :- After reducing the actual price.
SOLUTION:- Firstly we have to find 85% of $39
=> 39× 85/100
=> 39× 0.85
=> 33.15
Now the actual price after reducing is 39 - 33.15
=> 5.85
HOPE IT HELPED YOU.
To find the new price of an item that has been reduced by a certain percentage, multiply the original price by the percentage (converted to decimal form) to find the discount. Subtract this discount from the original price to get the new price. Therefore, the new price of the item originally priced at $39 and reduced by 85% is $5.85.
Explanation:This is a basic percentage problem in mathematics. The phrase 'reduced by 85%' implies that we are subtracting 85% of the original price from the original price itself. To find the discount, we multiply the original price by the reduction rate (in decimal form). Then, to get the final price, we subtract the discount from the original price. So, if the original price is $39 and the item has been reduced by 85%, then the discount would be $39. The calculation would look like this:
First, calculate the discount: $39 * 0.85 = $33.15.Then, subtract the discount from the original price to find the new price: $39 - $33.15 = $5.85.So, the new price of the item is $5.85.
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Simplify the expression.
(–1 + 6i) + (–4 + 2i)
5 – 8i
–3 + 8i
–5 + 8i
3 + 8i
Answers
Answer: C
Step-by-step explanation:
Add like terms
-1 + 6i
+ -4 + 2i
-5 + 8i
What's the answer to this.
Answers
-19 < -30. You're welcome!!
The snow fell 3/4 of an inch every hour. After 12 hours pass, write an equation to represent how many inches of snow has fallen. After you have written the equation, please solve that equation.
Answers
To find the total snow fall you would multiply the amount of snow per hour by the number of hours it snows:
Total = 3/4 inch per hour x hours: Total = 3/4h
h = 12 hours:
Total = 3/4(12) = 9 inches total.
But it can also be 12 x 0.75.
Equal to 9. 12 x 0.75 = 9.
9 inches
so i’m doing a project and they want me to do a line bisector. so it’s just to cut the line, right? like i wouldn’t have to add arrows to the end or anything?
sooo like —————-
^ that
<————->
^ that
•—————•
or that?
Answers
Search up line bisector, i just wanna slap you, i know your mom thinks your a failure, such an idiot
the letters that spell Mississippi are each written on separate tiles lying face down on a table. a tile is selected at random, the litter is recorded, and then the tile is placed face down on the table. then the process repeats. What is the theoretical of choosing a tile with the letter P?
Answers
Answer: The theoretical probability of choosing a tile with letter P =0.18
Step-by-step explanation:
Given word = MISSISSIPPI
Total number of letters in given the word = 11
Number of letter P in given word = 2
Let A be a event of choosing a tile with a letter P then
P(A) =Number of tiles with letter P / Total letters in given word
= 2 /11 = 0.18
The probability of choosing a tile with the letter P from the word 'Mississippi' is 1/11.
The probability of choosing a tile with the letter P can be calculated by determining the ratio of the number of P tiles to the total number of tiles.
In the word 'Mississippi', there is only 1 letter P. The total number of letters in 'Mississippi' is 11. Therefore, the probability of choosing a tile with the letter P is 1/11.
So, the theoretical probability of choosing a tile with the letter P is 1/11.
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210 students buy milk and 196 students buy juice.How many drinks are sold that week?
Answers
196 * 5 = 980 juice
total drinks: 2,030 drinks total
The price of a technology stock has dropped to $9.54 today. Yesterday's price was $9.61 . Find the percentage decrease. Round your answer to the nearest tenth of a percent.
Answers
Yesterday's price is the original price or the old price.
[tex]Percentage \: decrease = \frac{9.61 - 9.54}{9.61} \times 100[/tex]
[tex]Percentage \: decrease = \frac{0.07}{9.61} \times 100[/tex]
[tex]Percentage \: decrease = \frac{700}{961} = 0.728[/tex]%
Rounding to the nearest tenth means round to one decimal place.
This will give us,
0.7% decrease in price.
Therefore between yesterday and today, there was a 0.7 percentage decrease in price.
Which polynomial represents the difference below
(7x^2+8)-(4x^2+x+6)
A.3x^2+x+14
B.11x^2-x+2
C.3x^2+x+14
Answers
What is the range of the function shown in this table?
x y
3 4
4 4
5 2
6 5
A. (3, 4)
B. {3, 4, 5, 6}
C. {2, 4, 5}
D. (3, 4), (4, 4), (5, 2), (6, 5)
Answers
The answer is C. Because the range is the y-axis