Answer:
QR = 17 cm
Step-by-step explanation:
Δ RST is a 5- 12- 13 triangle with hypotenuse RT = 13 cm , then
TS = 5 cm and PT = 2 × 5 = 10 cm
So PS = 10 + 5 = 15 cm
PS is parallel to the vertical line from vertex Q and intersects the horizontal line projected from SR of length 20 - 12 = 8 cm
Using the right triangle formed calculate QR using Pythagoras' identity
QR² = 15² + 8² = 225 + 64 = 289 ( take square root of both sides )
QR = 
= 17
We have the formula (sin x)^2 + (cos x)^2 = 1;
Then, sin α =
cos β =
We apply the formula sin ( α + β ) = sin α x cos β + sin β x cos α = (3/5)x(4/5) + (4/5)x(3/5) = 12/25 + 12/25 = 24/25;
Answer:
x = 8.75, y = 8.125
Step-by-step explanation:
The triangles are similar thus the ratios of corresponding sides are equal, that is
= 
( cross- multiply )
8x = 70 ( divide both sides by 8 )
x = 8.75
And
= 
( cross- multiply )
8y = 65 ( divide both sides by 8 )
y = 8.125
In 52-card deck there are 36 numbered card and 52/4=13 spade card
so probability that you are dealt a numbered card is 36/52 =9/13 a spade card is 13/52=1/4
Answer:
4 hours at 8 miles an hour: 8(4) = 32 miles in total
8 hours at 2 miles an hour: 2(8) = 16 miles in total
Miles in total: 32 + 16 = 48
The answer is A. 48 miles
