If ABCD is a rombus with side length 15 mm and if BD=24 mm, then find the length of the other diagonal, AC. Draw a diagram and show work.

  AC = 18 mm

Step-by-step explanation:

See the attachment for a diagram.

Since length BD = 24 mm, length BO = 12 mm. Then ΔBOC is a right triangle with one leg 12 and hypotenuse 15. The other leg (OC) is given by the Pythagorean theorem:

  OC² +OB² = BC²

  OC = √(BC² -OB²) = √(225 -144) = √81

  OC = 9

Diagonal AC is twice the length of OC, so is ...

  AC = 2·9 = 18 . . . . mm

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It can save a little time if you recognize that the given sides of triangle BOC have the ratio 4:5. This suggests you're dealing with a 3:4:5 right triangle, and that side OC is (3/5)·(15 mm) = 9 mm.

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1                     1

1                     2

1                     3

1                     4

2                   1

2                   2

2                   3

2                   4   = not 1, and 4

3                   1

3                   2

3                   3

3                   4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation: