1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Leya [2.2K]
3 years ago
6

△ABC△ABC is similar to △QRS△QRS. Also, sideABsideAB measures 50 cm, sideACsideAC measures 60 cm, and sideQSsideQS measures 6 cm.

What is the measure of sideQRsideQR ? Show all your calculations!
Mathematics
1 answer:
Liono4ka [1.6K]3 years ago
4 0
Assuming the triangle ABC is equal to the triangle QRS means that their sides will have the same size.
So the side AB is the same as QR. As well as  BC is the same size as RS; AC is the same as QS.
So, if AB = QR that means that both have 50 cm.
Answer: 50 cm

You might be interested in
INFO: The chairs are evenly spaced around
lana66690 [7]

Answer: About 72 feet

The more accurate value is roughly 71.7260397 feet (however, this value isn't fully exact either).

======================================================

Explanation:

Check out the diagram below. It's effectively the same diagram your teacher provided, but I've added points M and N. I've left out any unnecessary lines.

  • M = center of the circle
  • N = location where the cable is anchored to the ground

We're told that "(the length of cable from) E to the ground is 35 feet", so this is the red portion of cable that I've marked this as NE = 35, ie segment NE is 35 feet long. We're also told that NF = 40 feet, which is also shown in red.

The blue portions are chords of the circle. We're given one chord as LE = 80 ft, while the other chord JF is what we want to find out.

-----------------

What we need to find is the radius of this circle. Right away, it's not clear what the radius is; however, we can use the chord LE = 80 to help find it.

It turns out that the chord length c is connected to the radius r and central angle theta like so:

c = 2*r*sin(0.5*theta)

where theta must be in radian mode. The central angle subtends the arc that forms the chord in question.

If we started at point L, and counted the number of spaces to get to E while going clockwise, then we can see that there are 5 spaces

Those five spaces could be written as

  1. The jump from L to A
  2. The jump from A to B
  3. The jump from B to C
  4. The jump from C to D
  5. The jump from D to E

Or you could mark it as such on the diagram for a visual reference. Overall, the circle has been cut into 12 equal slices. So going from L to E, going clockwise, will have us take up 5/12 of the full circle.

There are 2pi radians in a full circle, meaning the central angle LME is (5/12)*2pi = 5pi/6 radians.

-----------------

Plug theta = 5pi/6 and c = 80 into the formula mentioned. Isolate the radius.

c = 2*r*sin(0.5*theta)

80 = 2*r*sin(0.5*5pi/6)

80 = 2*r*sin(5pi/12)

80 = 2*r*0.9659258

80 = 2*0.9659258*r

80 = 1.9318516r

1.9318516r = 80

r = 80/1.931 8516

r = 41.4110483

The radius is approximate. The radius is in feet. Make sure your calculator is in radian mode.

-----------------

Now that we know the radius, we can determine how long chord JF is.

The central angle for chord JF is angle JMF

If we start at J and go to F, along the shorter path, then we've gone 4 spaces. This is 4/12 = 1/3 of the full circle. So the radian measure of angle JMF is (1/3)*2pi = 2pi/3 radians.

So,

c = 2*r*sin(0.5*theta)

c = 2*41.4110483*sin(0.5*2pi/3)

c = 71.7260397

Chord JF is roughly 71.7260397 feet long.

When rounding to the nearest foot, that's about 72 feet.

6 0
3 years ago
John made a rectangle pen for his dog using 28 feet of fencing. If the width of the pen is 2 feet more than one-half the length,
kati45 [8]
Okay, so you know that the perimeter of the pen is 28 feet. Now we need the separate side lengths.

P = 28 ft.
Length = x
Width = (1/2)x + 2

So now we can plug in the little equations of length and width into a perimeter formula:
 2(x) + 2((1/2)x + 2) = 28
Distribute the 2's and solve as needed.
2x + x + 4 = 28
3x + 4 = 28
3x = 24
x = 8

To find the width, just plug in 8 for x in our little equation:
(1/2)(8) + 2
= 6

So, the length is 8 feet and the width is 6 feet.
5 0
3 years ago
Read 2 more answers
Consider the function graphed below.
aivan3 [116]

Answer:

B. (see attached)

Step-by-step explanation:

All the answers agree that the function is x² for x < 1. Where they disagree is in the slope and y-intercept of the linear portion for x > 1.

The line has a slope that is less than 1 unit of rise for 1 unit of run, so will not be selections A or C, which have slopes of 3.

The y-intercept is clearly positive if we extend the line to the left until it reaches the y-axis. This eliminates selection D from consideration, leaving only selection B.

8 0
3 years ago
Add and simplify 1/8 5/8
skelet666 [1.2K]
1+5=6 so 6/8 

Simplifying 6/8 is 3/4
8 0
3 years ago
Read 2 more answers
What is the value of 8/9 divided by 5/12?
bulgar [2K]

Answer: 96/45

Step-by-step explanation: The answer is 96/12 because to divide fractions you reciprocate the second fraction and turn it into a multiplication problem.  

8 times 12 = 96

9 times 5 = 45

96/45

7 0
3 years ago
Read 2 more answers
Other questions:
  • Solve for c. -3b+ac=c-4. Please show all work.
    7·2 answers
  • the marked price of a mobile is 40% above the cost price. when it is sold allowing 30% discount on the marked price, there is a
    6·1 answer
  • What is 2/3 simplified
    14·2 answers
  • Which fraction is equal a whole number ? <br><br> A. 3/6 B.7/8 C.10/4 D.8/4
    5·2 answers
  • Explain the step(s) needed to solve 4+ p = 1 and then solve for p
    10·1 answer
  • Gaurav takes 15 rounds of a rectangular park whose length is twice its breadth. If the total distance covered by Gaurav is 900m
    9·1 answer
  • A family of 8 goes to the amusement park. Each ride at the park costs 1 ticket per person. If they all go on every ride together
    13·2 answers
  • How can 86 books to 150 books
    11·1 answer
  • Solve the proportion for x. 2/9=3/(x+2)
    11·2 answers
  • Interpret two-step equation word problems (7th grade math)
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!