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
SashulF [63]
3 years ago
7

James cut out four parallelograms, the dimensions of which are shown below. Parallelogram 1 length: 12 in. width: 15 in. diagona

l: 20 in. Parallelogram 2 length: 16 in. width: 30 in. diagonal: 34 in. Parallelogram 3 length: 20 in. width: 21 in. diagonal: 29 in. Parallelogram 4 length: 18 in. width: 20 in. diagonal: 26 in. James put the parallelograms together so one vertex from each paper exists on a point, as shown in the circle. 4 parallelograms are put together so that one vertex from each paper exists on a point. Which statement explains whether or not the parallelgrams can be put together so each occupies one-quarter of the area of the circle without overlapping any other pieces? Check all that apply. The quadrilaterals can be placed such that each occupies one-quarter of the circle. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 1 do not form right angles. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 2 do not form right angles. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 3 do not form right angles. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 4 do not form right angles.
Mathematics
2 answers:
MrRa [10]3 years ago
8 0

Answer: The correct options are;

*The quadrilaterals cannot be placed such that each occupies one quarter of the circle because the vertices of parallelogram 1 do not form right angles

**The quadrilaterals cannot be placed such that each occupies one quarter of the circle because the vertices of parallelogram 4 do not form right angles.

Step-by-step explanation: What James is trying to do is quite simple which is, he wants to place four quadrilaterals inside a circle and he wants the vertices to touch one another at the center of the circle without having to overlap.

This is possible and quite simple, provided all the quadrilaterals have right angles (90 degrees). This is because the center of the circle measures 360 degrees and we can only have four vertices placed there without overlapping only if they all measure 90 degrees each (that is, 90 times 4 equals 360).

We can now show whether or not all four parallelograms have right angles by applying the Pythagoras' theorem to each of them. Note that James has cut the shapes in such a way that the hypotenuse (diagonal) and the other two legs have already been given in the question. As a reminder, the  Pythagoras' theorem is given as,

AC² = AB² + BC² Where AC is the hypotenuse (diagonal) and AB and BC are the other two legs. The experiment would now be as follows;

Quadrilateral 1;

20² = 12² + 15²

400 = 144 + 225

400 ≠ 369

Therefore the vertices of parallelogram 1 do not form a right angle

Quadrilateral 2;

34² = 16² + 30²

1156 = 256 + 900

1156 = 1156

Therefore the vertices of parallelogram 2 forms a right angle

Quadrilateral 3;

29² = 20² + 21²

841 = 400 + 441

841 = 841

Therefore the vertices of parallelogram 3 forms a right angle

Quadrilateral 4;

26² = 18² + 20²

676 = 324 + 400

676 ≠ 724

Therefore the vertices of parallelogram 4 do not form a right angle

The results above shows that only two of the parallelograms cut out have right angles (like a proper square or rectangle for instance), while the other two do not have right angles.

Therefore, the correct option are as follows;

The quadrilaterals cannot be placed such that each occupies one quarter of the circle because the vertices of parallelogram 1 do not form right angles.

The quadrilaterals cannot be placed such that each occupies one quarter of the circle because the vertices of parallelogram 4 do not form right angles.

adoni [48]3 years ago
8 0

Answer:

B and E

Step-by-step explanation:

The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 1 do not form right angles.

The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 4 do not form right angles.

You might be interested in
PLEASE PLEASE PLEASE HELP I WIL GIVE BRAINLIEST<br> ALSO PLS SHOW WORK
Tasya [4]
3 5/6 I took the test
5 0
3 years ago
Read 2 more answers
A local hamburger shop sold a combined total of 445 hamburgers and cheeseburgers on Tuesday. There were 55 fewer cheeseburgers s
liberstina [14]
Let x represent the number of hamburgers sold, and (x - 55) represent the number of cheeseburgers sold.

Set up an equation:
hamburgers + cheeseburgers = total number of burgers

x + (x-55) = 445

solve for x: 
2x - 55 = 445

2x = 445 + 55

2x = 500

x = 500÷2

x = 250

This means 250 hamburgers were sold on Tuesday.

Hope this helps!

-Jabba


4 0
3 years ago
Fractions less then 1/2
Vinvika [58]

Answer:

Step-by-step explanation:

16 fractions less than one half

1/9, 2/9, 3/9, 4/9, 1/8, 2/8, 3/8, 1/7, 2/7, 3/7, 1/6, 2/6, 1/5, 2/5, 1/4, 1/3

4 0
3 years ago
Read 2 more answers
What is the slope of a line PARALLEL to the graph?
SSSSS [86.1K]
If you mean parallel to another line, you have to find the the equation of that line. Lets just say it was y= 7x-2. To find the slope of a line parallel to that, then you look at the slope of that line, which in this case would be 7. The slope of a line parallel would have to be the same. So, I can't give you a direct answer because I can't see the graph but that is how you get the answer.
8 0
3 years ago
Two angles are complementary. The measure of one angle is 6º more than five times the measure of the other angle. Find the
Salsk061 [2.6K]

Complementary means that the two angles sum to 90 degrees.

So based on the problem, let:

1st angle=5x+6

2nd angle=x

Now create an equation.

x+5x+6=90

6x=84

x=14

5x+6=76

answer: 14 degrees and 76 degrees

6 0
3 years ago
Read 2 more answers
Other questions:
  • Richard buys one tooth cleaning kit for $25 and a toothbrush for $15. He spends the rest of his money on body soap. He has $80 a
    14·2 answers
  • Jeff saved $500 from his summer job so he would have spending money during the school year. He withdraws $12 from his account ea
    12·1 answer
  • Plzz <br> Answer quick plzzzz
    14·1 answer
  • The scatter plot shows the number of years of experience x and the hourly pay rate y for each of 25 cashiers in Ohio.
    5·1 answer
  • 3t+10=16 what is the answer
    8·2 answers
  • Encuentra la forma de la ecuacion de la recta que pasa por el punto P(-1,5) y que es perpendicular a la recta 2x + 3y - 8= 0
    11·2 answers
  • A glass company is repairing a window in the shape of an equilateral triangle. If the length of one side of the triangle is 17 i
    6·1 answer
  • 1. Solve the following inequality -2(x - 4) &gt; -10.<br><br><br> I need this with Work shown pls
    14·1 answer
  • Find the sum of the arithmetic series given a1=8,a14=99,n=14.
    11·1 answer
  • Can somebody plz help?
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!