Answer:
PQ = 34.4
Step-by-step explanation:
First, we know that the angles in a triangle add up to 180 degrees. Therefore, angle M = 48 and angle R = 74
Next, because there is a corresponding angle in each triangle, they are similar. This means that the ratios between corresponding sides are the same. For example, the side opposite angle O (MN) over the side opposite angle R (PQ) is equal to the side opposite angle N (OM) over the side opposite angle Q (RP)
This can be written as MN/PQ = OM/RP. Note that both the numerators are on the same triangle, and MN and PQ correspond, as well as OM and RP.
We are given MN, NO, and QR. Because NO is opposite a 48 degree angle (angle M) as well as QR (angle P), we can say that NO/QR = another ratio of a pair of corresponding sides. Because we want to find PQ, and both PQ and MN are opposite 74 degree angles, we can say that
NO/QR = MN/PQ
Thus,
11/27 = 14/PQ
multiply both sides by PQ to remove a denominator
PQ * 11/27 = 14
multiply both sides by 27 to remove the other denominator
PQ * 11 = 14 * 27
divide both sides by 11 to isolate the PQ
PQ = 14 * 27 /11
PQ = 34.4
Answer: the weight in kilograms is 9.76kg
Step-by-step explanation:
1 meter of length of rope = 800 g
12.2 meters of the rope= (12.2meters x 800g)/ 1 meter=9760grams
We know that 1000 g = 1kg
9760 grams = 9760/1000=9.76 kilograms
You have the original function as 2x-5
and you are given the value of x to be -1/2
Therefore, all you have to do is substitute the value of x in the function and calculate it as follows:
f(-1/2) = 2(-1/2) - 5 = -1 -5 = -6
Answer:
18 nuts in 12 minutes, 13.5 nuts in 4 minutes and 90 nuts in one hour
Step-by-step explanation:
12 min :
12/6 = 2
2 x 9 = 18 nuts in 12 minuts
4 min:
6/4 = 1.5
1.5 x 9 = 13.5 nuts in 4 minutes
(round to 13 if whole nuts only)
1 hour:
1 hour = 60 mins
60/6 = 10
9 x 10 = 90 nuts in one hour
Answer: R x 4 - 6
Step-by-step explanation:
