Answer:
1a. 58/99
1b. 53/90
1c. 29/50
Step-by-step explanation:
let's start with the easiest one
1.(c)
0.58 = 58/100 = 29/50
that is the simplest possible form, as 29 is a prime number and not a factor of 50.
1.(a)
0.585858585858... = 58×0.0101010101010101...
now, we know that 1/"double digit" (like 1/22) mostly produces a repeating pattern with a period length of 2 after the decimal point.
and we find
1/99 = 0.01010101010101...
so, our solution is
58 × 1/99 = 58/99
that is the simplest possible form, as 58 and 99 do not share any factors.
1.(b)
0.5888888888888... = 0.5 + 0.0888888888888... =
= 0.5 + 8×0.01111111111111... = 0.5 + 8×1/10 × 0.1111111111...
we know how to create 0.11111111111... :
1/9 = 0.111111111111111...
so, our solution is
0.5 + 8 × 1/10 × 1/9 = 0.5 + 8/90 = 5/10 + 8/90 =
= 45/90 + 8/90 = 53/90
this is the simplest possible form, as 53 is already a prime number and not a factor of 90.
Answer:
B
Step-by-step explanation:
The volume (V) of the prism is calculate as
V = lbh ( l is the length, b the width and h the height )
l = h = 4 ×
= 
b = 3 ×
= 1, thus
V =
× 1 ×
=
ft³
Answer: 60/13
Step-by-step explanation:
Answer:
5√2
Step-by-step explanation:
<u>Finding</u><u> </u><u>distance</u><u> </u><u>:</u><u>-</u><u> </u>
- d = √{ ( 1 -6)² + (4+1)²}
- d = √{ -5² + 5² }
- d = √{ 25 + 25}
- d = √50
- d = 5√2
ANSWER
None of the above
EXPLANATION
Recall the mnemonic CAH, from trigonometric ratios.
CAH means the cosine ratio is the ratio of the length of the adjacent side to the length of the hypotenuse.
This implies that,

The side adjacent to the 23° angle is 12 units and the hypotenuse is 13 units.
This implies that,

None of the provided options is correct