Answer:
a. LK = 4√3, JL= 4√6
b. PQ = 10√3, RP = 5√3
Step-by-step explanation:
a. LK =4√3,
LK=KJ= 4√3
sin(45°) = opposite/hypotenuse
hypotenuse (JL)= opposite/sin 45° = 4√3/√2/2 = 8√3/√2 = 8√3√2/2 = 4√6
b.
cos 30° = adjacent/hypotenuse = QR/PQ = 15/PQ
cos 30° = 15/PQ
PQ = 15/cos 30° = 15/√3/2)= 30/√3 = 30√3/3 = 10√3
tan 30° = opposite/adjacent = RP/QR
√3/3 = RP/QR
√3/3 = RP/15
RP = √3*15/3 = 5√3
Answer:
20,365.7 seconds
Step-by-step explanation:
First, we need to know how to convert yards to miles, as the question is in miles. We know that 1 mile is equivalent to 1760 yards. So we have:
1 mi = 1760 yards
If we multiply both sides by 81:
81 mi = 142,560 yards
And we know that the sprinter needs 8 second to run 56 yards:
8 s = 56 yards
If we divide both sides by 56 we get the time he needs for 1 yard:
8/56 s = 56/56 yards
1/7 s = 1 yard
So, takes him 1/7 seconds to run one yard. At this rate he runs 142,560 yards in:
(1/7) * 142,560 = 20,365.7
So, he needs 20,365.7 seconds to run 81 miles (142,560 yards)
Answer: option iii
The perimeter of an isosceles triangle with congruent sides of 16.2 cm and a third side half that length is 16.2+16.2+8.1 = 40.5 cm
Explanation:
The perimeter of an isosceles triangle with congruent sides of 16.2 cm and a third side half that length is 16.2+16.2+8.1 = 40.5 cm
First side is = 16.2 cm
Second side is = 16.2 cm
Third side = half of 16.2 = 8.1 cm
The perimeter of an isosceles triangle with congruent sides of 16.2 cm and a third side half that length is 16.2+16.2+8.1 = 40.5 cm
Answer:
y=3x+3.
Step-by-step explanation:
the given graph intersect the X-axis in (-1;0), the Y-axis in (0;3). Then the slope of the required line is (3-0)/(0+1)=3 and the interception is 3 (point (0;3)).
Finally, the required equation in slope-interception form is y=3x+3.
