Please help!!!
Triangle ABC is similar to triangle PQR
AB = 4cm
PQ=12cm
RQ= 16.5 cm
AC = xcm
PR= ycm
(a) Calculate the length of BC
(b) Write down an expression for y in terms of x
Check the picture
Answers
Answer:
5.5
3y = x
Step-by-step explanation:
→ Find the scale factor enlargement
12 ÷ 4 = 3
→ Divide 16.5 by 3
5.5
→ Write SF in terms of x and y
3y = x
The Length of BC is 5.5 cm and equation for y in terms of x is y = 3x
What are similarity in triangles?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.
According to question
Triangle ABC ≅ triangle PQR
where,
AB = 4cm
PQ=12cm
RQ= 16.5 cm
AC = xcm
PR= ycm
According to the similarity rule
the same ratio of corresponding sides
therefore,
[tex]\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AC}{PR} \\[/tex]
(a) Calculate the length of BC
[tex]\frac{AB}{PQ} = \frac{BC}{QR}[/tex]
⇒ [tex]\frac{4}{12} = \frac{BC}{16.5}[/tex]
⇒ [tex]\frac{1}{3} = \frac{BC}{16.5}[/tex]
⇒ BC = 5.5 cm
(b) Write down an expression for y in terms of x
we know , [tex]\frac{AB}{PQ} = \frac{AC}{PR} \\[/tex]
⇒ [tex]\frac{4}{12} = \frac{x}{y} \\[/tex]
⇒ [tex]\frac{1}{3} = \frac{x}{y} \\[/tex]
⇒ [tex]y=3x[/tex]
Hence, Length of BC is 5.5 cm and equation for y = 3x
To know more about similarity in triangles here :
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Related Questions
) Which expression represents the SUM of n and 12?
Answers
the "sum of" means we add.
So the sum of n and 12 means we add n and 12:-
n+12
or
12+n (both of these expressions mean the same thing)
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)
Please help!!!
Mr. Johnson's class will study one sea animal for the next week. Which group should Mr. Johnson survey to find the type of sea animal his students should study?
A: His students
B: Teachers at his school
C: Parents of his students
D: Workers at a sea animal park
Answers
Answer:
A He should ask his students to know what they prefer
Step-by-step explanation:
James has 16 balloons. 1/4 of his balloons are red. How many red balloons does he have? Half of his red ballons pop after 10 minutes of playing with them. How many of his red ballons pop?
Answers
half of them pop
4/2=2
2 red balloons pop.
help please
on the image.
Answers
Answer:
the women won 1 fewer matches than the men
Step-by-step explanation:
In a pie chart, the fraction of the total that is represented by any sector is the ratio of the angle subtended by that sector to 360°.
__
For the men's team, the winning games represent 150°/360° = 5/12 of all games played. The men played 24 games, so they won ...
5/12 × 24 = 10 . . . . games won
__
For the women's team, the winning games represent 180°/360° = 1/2 of all games played. The women played 18 games, so they won ...
1/2 × 18 = 9 . . . . games won
The number of matches won by the men is larger than the number of matches won by the women. (Yes, the women won a larger fraction of their matches played, but not a larger number.)
20x20x2 please I really need to answer this question
Answers
Answer:
800
Step-by-step explanation:
20*20=400
400*2=800
Help? im confused plss!
Find the area of the regular polygon with the given radius or apothem.
Answers
Answer:
okay so think of the polygon as like a rectangle in a way now use the method of finding a area with a triangle
Step-by-step explanation:
A= bxh divide by 2 then A= bxh x 2
it worked for me
How many times larger is 8 x 106 than 2 x 103?
Х
Answers
Answer: ~4.12 times larger
Step-by-step explanation:
1. find the values for both equation, (8*106=848) and (2*103=206).
2. divide the larger number by the smaller one. 848/206
which gives us 4.11650485, or 4.12 rounded.
hope this helped! ♡
Plss help asap!
what fraction represents numbers between 21 - 27?
Answers
Answer:
0.7778
Step-by-step explanation:
step 1
Address the input parameters and observe what to be found:
Input values:
The fraction = 21/27
What to be found:
Find the decimal expansion of fraction 21/27.
step 2
The numerator is smaller than the denominator of the fraction 21/27, so find how many 10s should be multiplied with both numerator and denominator. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 21/27.
=21
27
x10
10
step 3
Rearrange the fraction as like the below:
=10 x 21
27
x1
10
=210
27
x1
10
step 4
Simplify the above expression further:
=210
27
x1
10
=189 + 21
27
x1
10
= (189
27
+21
27
) x1
10
= (7 + 21
27
) x 1
10
step 5
Repeat the step 2 to find the decimal equivalent for the fraction 21/27 in the above expression:
= (7 + 21
27
) x 1
10
= (7 + 0.778) x1
10
step 6
Simplify the above expression further:
= (7 + 0.778) x1
10
= 7.778 x1
10
=7.778
10
21
27
= 0.7778
Hence,
21/27 as a decimal is 0.7778
FOR THE INVERSE VARIATION P- , FIND V>
WHEN P= 1/2
Answers
A and B are two companies.
The table shows some information about the sales of each company and the number of workers for each
company in 2004 and in 2014
Work out the percentage increase in sales from 2004 to 2014 for company A
Answers
Answer:
Step-by-step explanation:
How many different three digit numbers can be made with 123456789
Answers
Answer:
84
Step-by-step explanation:
Since, the digit should be in ascending order, therefore we have to group 123456789 into 3–3 groups with its digits being in ascending order.
Step 1:
Select 1 as one digit
Step 2:
Select 2 as a 2nd digit.
Step 3:
We have 7 numbers (3,4,5,6,7,8,9) as a 3rd digit of a 3-digit number. Therefore, We have 7 numbers in the form of 12_.
Go back to Step 2 and Select 3 as a 2nd digit. Then, we have 6 numbers (4,5,6,7,8,9) as a 3rd digit of the form 13_.
Continue these steps till you get the number of 3-digit numbers in the form of 1__ to 189 which will be 28 numbers.
Go back to Step 1 now and select 2 as a 1st digit and in Step 2, start with 3 as a 2nd digit.
In step 3, you’ll have 6 numbers (4,5,6,7,8,9) as a 3rd digit of the form 23_.
Continue these steps till you find the number of the 3 digit number of the form 2__ to 289 which will be 21
Repeat the steps again to find the number of 3digit number of the form 3__ to 389 which will be 15.
Then find 4__ to 489, 5__ to 589, ……till 789
the answers will be like this
1__=28
2__=21
3__=15
4__=10
5__=6
6__=3
789 which is 1
Adding all these, you’ll get 84.
The total number of different three digit numbers that can be made using any of the digits 1,2,3,4,5,6,7,8,9 is 729 digits.
What is the rule of product in combinatorics?If a work A can be done in p ways, and another work B can be done in q ways, then both A and B can be done in [tex]p \times q[/tex] distinct ways.
Remember that this count doesn't differentiate between order of doing A first or B first then doing other work after the first work.
Thus, doing A then B is considered same as doing B then A
We can use the rule of product as:
we can use the analogy of filling each of the 3 places of the three digit number, and this filling doesn't require any ordering like fill the first place and then second etc. We can take those 3 place fillings as 3 different works to be done,e each one doable in 9 different ways.For this case, the three digit number consider is going to have 3 places in it such that each place can have any of those 9 digits in them.
So each place can be filled in 9 ways.
There are 3 such places, so, using the rule of product, the filling of those places can be done in:
[tex]9 \times 9 \times 9 = 9^3 = 729 \: \rm ways[/tex]
Thus, the total number of different three digit numbers that can be made using any of the digits 1,2,3,4,5,6,7,8,9 is 729 digits.
Learn more about rule of product combinations here:
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Which expression is equivalent to cosine (startfraction pi over 2 endfraction r) for all values of r?
Answers
The trigonometric expression cos (π/2 + r) is equivalent to the negative of sin r. Then the correct option is C.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
The trigonometric expression is given below.
[tex]\cos (\dfrac{\pi}{2} + r)[/tex]
We know that the formula
[tex]\cos (\dfrac{\pi}{2} + r) = -\sin r[/tex]
Thus, the cos (π/2 + r) is equivalent to the negative of sin r.
More about the trigonometry link is given below.
https://brainly.com/question/22698523
Answer:
C?
Step-by-step explanation:
, someone confirm
What is the area of this figure?
3 mi
7 mi
4 mi
2 mi
5 mi
12 mi
3 mi
2 mi
Write your answer using decimals, if
necessary.
square miles
Answers
Answer:
38.5
Step-by-step explanation:
I would give explanation but it's kind of hard
What is the number with the mark
Answers
[tex]\huge\mathsf\blue{♧ANSWER♧}[/tex]
[tex]\huge \mathfrak \blue{\frac{ - 7}{8} }[/tex]
A company just paid a dividend of $1.20 per share at the end of the year. It is expected to grow at 12% per year for three years, after that it grows constantly at 6%. The cost of equity is 9.5%. What is the current price of stock?
Answers
The current price of the stock given the dividend, cost of equity and growth rates is $46.90.
What is the current stock price?Thw two-stage dividend growth model would be used to determine the value of the stock.
First stage:
dividend in Y1 = 1.20x 1.12 = 1.344dividend in Y2 = 1.20 x 1.12^2 = 1.505dividend in Y3 = 1.20 x 1.12^3 = 1.69Second stage:
Y3 = (1.69 X 1.06) / (0.095 - 0.06) = 51.059
Find the present value of these cash flows
(1.344 / 1.095) + (1.505 / 1.095²) + (1.69 / 1.095³) + (51.059/1.095³) = $46.90
To learn more about the two stage dividend model, please check: https://brainly.com/question/26564273
Solve for h.
2 < -19 - 7h
Answers
Answer:
h < -3
Step-by-step explanation:
2 < -19 - 7h
2 + 19 < -7h
21 < - 7h
21/7 < -h
bringing -h to the left
-h > 3
changing the sign to positive h
h < -3
solution set : {h < -3}
Hope that helps...
Which agency is responsible for promoting the welfare and opportunities of wage earners? a. fda b. hud c. dol d. cpsc
Answers
Answer:
DOL, also known as the Department of Labor, is the agency responsible for promoting the welfare and opportunities of wage earners.
Their main goal is to fight for equal rights among workers and to make their wishes and needs at the workplace come true.
Answer:
c
Step-by-step explanation:
So far, 907907907 of the 122312231223 voters have agreed to the new amendment.
Based on this data, what is a reasonable estimate of the probability that the next voter does not agree to the new amendment?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
\dfrac{316}{907}
907
316
start fraction, 316, divided by, 907, end fraction
(Choice B)
B
\dfrac{907}{1223}
1223
907
start fraction, 907, divided by, 1223, end fraction
(Choice C)
C
\dfrac{1223}{2130}
2130
1223
start fraction, 1223, divided by, 2130, end fraction
(Choice D)
D
\dfrac{316}{1223}
1223
316
Answers
Answer:
I do not know the answer but I need to answer a question to finish logging into brainly
Answer: 316/1223
Step-by-step explanation: I checked on khan
The swimming pool shown below has a 6 foot wide concrete deck around it.
What is the area, in square feet, of the deck around the pool?
O512
O720
O864
O1232
Answers
Area of the rectangle inside:-
32(16)=512ft^2Area of the rectangle outside
28(44)=1232ft^2Area of the deck:-
Area of rectangle outside-inside1232-512720ft^2Answer:
pretty sure it's D for this question
Select the action you would use to solve 3x = 12. Then select the property
that justifies that action.
Select all that apply.
I A. Action: Add 3 to both sides.
OB. Action: Multiply both sides by 3.
O C. Action: Divide both sides by 3.
D. Property: Addition property of equality
I E. Property: Multiplication property of equality
O F. Property: Division property of equality
Answers
Answer:
C , F
Step-by-step explanation:
you need to divide both sides by 3 in order to get x
3x = 12
x = 4.
the property is the division property of equality.
pls give brainliest
LAY
STOP
Solve using the Zero Product Property.
15. The height of a football after it has been kicked from the top of a hill can be modeled
by the equation h= 2(-2-4t) (2t - 5), where h is the height of the football in feet
and tiltihe time in seconds. How long is the football in the air?
A
A. t=2.5 seconds
B.
B. t=-0.5 seconds
с
C. t=1.5 seconds
Answers
Answer:
A
Step-by-step explanation:
how long is the ball in the air ?
that is the same as asking : after how many seconds will the ball hit the ground (= reach the height of 0) ?
so, that means we need to find the zero solution of h(t).
at what t is h(t) = 0 ?
when at least one of the factors is 0 :
2(-2 - 4t)(2t - 5)
we have 3 factors
2 : can never be 0.
(-2 -4t) : can only be 0 for negative t, which does not make sense in our scenario (we cannot go back in time, only forward).
(2t - 5) : is 0 when 2t = 5 or t = 2.5
so, A is the right answer.
FYI : the starting height (on the hill) is given by t = 0 :
2(-2 - 0)(0 - 5) = 2×-2×-5 = 20 ft
Which equation can be used to find A, the area of the parallelogram shown?
Answers
Answer A
Calculate it correctly you will get it
Answer:
c
Step-by-step explanation:
the area of a parallelogram is given by base ×height
in this case 10×5
How do I do this? Someone please help
Answers
The volume is [tex]135cm^3[/tex]
help pls wrong answers will be reported
Answers
Answer:
Functions A and B have the same y-intercept.
Step-by-step explanation:
Their functions both have a y-intercept of 2. These are what they look like when graphed.
What is the answer will rate you 5 stars
Answers
The format of the equation is in 'slope-intercept form'
--> y = mx + b
m: the slopeb: the value of the y-interceptIn this case, the line is missing its y-intercept
--> the y-intercept is where the x value of any coordinate is equal to '0'
--> in that case b = 5
Hope that helps!
Answer:5
Step-by-step explanation:
Plugging in (5) will solve all relations.
0 + (5) = 5
1+(5) = 6
2+(5) = 7
3+(5) = 8
4+(5) = 9
5+(5) = 10
6+(5) = 11
In the drawing, what must be the coordinates of D to show ABCD is a square?
Answers
can anyone help on this??
Answers
Answer:
For number 7 it was c which is the pink man
Step-by-step explanation:
Answer:
Runner A won the race, Runner C took a break for 4 seconds, it took Bob 10.5 seconds because his green line hits the top at the same line as 10.5 seconds
You are traveling by car to New York City. The map you will use for your journey is below. d) You plan to begin your journey in San Jose and make stops in Denver and Chicago on your way to New York City. Your father says that your journey will be about 3,000 miles. Is this a close estimation of the distance? Explain your reasoning.
Answers
Based on the cities you will go through and your starting and finishing points, your father's estimate is a close estimation of the distance.
How far is New York from San Jose?The map is not provided so we will use a general map.
The distance from San Jose to Denver is around 1,301 miles.
The distance from Denver to Chicago is around 1,004 miles.
The distance from Chicago to New York is around 796 miles.
Added together we get:
= 1,301 + 1,004 + 796
= 3,101 miles
This is close to the 3,000 miles your father estimated.
Find out more on distance at https://brainly.com/question/1839590.
A sandbox has a volume of 330 cubic feet of sand. If the sandbox is 3 feet tall, and 10 feet wide, what is the length of the sand box?
Answers
Answer:
We are given that the total volume of the sandbox is 330 cubic feet.
We are given the side measurements of 3 feet tall and 10 feet wide.
3 x 10 = 30 sq2
V(volume)= 330 ft3
330 ft3 divided by 30 sq2 = 11ft
In conclusion, the length of the box would be:
= 11 ft
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
please help me please
Answers
Answer:
2/3
Step-by-step explanation:
Looking at the graph, it looks like the line goes through (6,10) and (-6,-8). We can "subtract" the points like so:
(6-(-6))/(10-(-8))
=12/18
=2/3
You can remember this trick as "rise over run".
I hope this solution helped you. Happy mathing!