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Oksana_A [137]
3 years ago
5

1) Suppose a rhombus has 12 cm sides and a 30° angle. Find the distance between the pair of opposite sides.

Mathematics
1 answer:
Sergeeva-Olga [200]3 years ago
7 0

Answer:

1) 6 cm

2) 117°

Step-by-step explanation:

1) Draw a picture of the rhombus.  The distance between opposite sides is the height of the rhombus.  If we draw the height at the vertex, we get a right triangle.  Using trigonometry:

sin 30° = h / 12

h = 12 sin 30°

h = 6 cm

2) Draw a picture of the rectangle.

∠KML is the angle the diagonal makes with the shorter side ML.  This angle is 54°.  ∠NKM is the angle the diagonal makes with the shorter side NK.  ∠KML and ∠NKM are alternate interior angles, so m∠NKM = 54°.

The angle bisector of angle ∠NKM divides the angle into two equal parts and intersects the longer side NM at point P.  So m∠PKM = 27°.

KLMN is a rectangle, so it has right angles.  That means ∠KML and ∠KMN are complementary.  So m∠KMN = 36°.

We now know the measures of two angles of triangle KPM.  Since angles of a triangle add up to 180°, we can find the measure of the third angle:

m∠KPM + 36° + 27° = 180°

m∠KPM = 117°

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Find the area of a circle with a diameter of 8cm.
Elza [17]

Answer:

50.24

Step-by-step explanation:

Area = r^2 x 3.14 (pi)

Radius = 8 ÷ 2 = 4

4² = 16

16 x 3.14 = 50.24

Area = 50.24 cm ²

6 0
2 years ago
I really need help!!!!
Brilliant_brown [7]
Check out the attached image for the answers. 

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

Statement 2 is blank, but it has the reasoning "Corresponding angles postulate"
Because BD || AE, we know that the corresponding angles are congruent. 
One pair of corresponding angles is angle 1 and angle 4. This is because they are on the same side of the transversal AC and they are both above their parallel line counter-part. Similarly, angle 2 and angle 3 are another corresponding pair.
So you'll have "angle1=angle4, angle3=angle2" in the first blank slot

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

Reason 3 is blank. The statement is that triangle ACE is similar to triangle BCD. The reason why the are similar is the AA (angle angle) similarity postulate. This says that if you know two pairs of angles are congruent, then the triangles are similar. The two pairs of angles were mentioned back on the previous line (line 2)
So you'll put "Angle-Angle Similarity Postulate" in the second blank.

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

Look at the line just above the last line. Here we have
1 + (BA/CB) = 1 + (DE/CD)
If we subtract 1 from both sides, we end up with,
BA/CB = DE/CD
which is what will go in the last blank space

Side Note: The last statement will always be what you want to prove. So you can just look at the very top of the problem where it says "Prove:" under the "Given" part. Then just copy/paste the statement you want to prove, which in this case is BA/CB = DE/CD

4 0
3 years ago
How many adult tickets were sold if each adult ticket sold was $6 and each student ticket was $4.50 and 260 tickets were sold fo
erik [133]

Answer:

   Adult tickets sold:   156

Step-by-step explanation:

   Adult ticket:   x

Student ticket:  y

x + y = 260                  ===>   -6(x + y = 260)     ===>  -6x -6y = -1560

6x + 4.5y = 1404         ===>                                           6x + 4.5y = 1404

                                                                                  ________________

add the two equations to eliminate a variable:                  -1.5y = -156

divide by -1.5:                                                                              y = 104

substitution to find x:

      x + y = 260

  x + 104 = 260

            x = 156

5 0
3 years ago
What i the product ? (2x-1)(x+4)​
kogti [31]

Answer:

2x^2+7x-4

3 0
3 years ago
Read 2 more answers
Help me and u will get 100 points at the end
Lera25 [3.4K]

Answer:

x > 0 and y < 2

Step-by-step explanation:

By definition the inverse of a function is simply, when the domain and range are swapped. So if the domain of g(x) is x < 2 and y > 0, then the inverse will have these swapped. So x > 0 and y < 2

3 0
1 year ago
Read 2 more answers
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