A) Find KM∠KEM is a right angle hence ΔKEM is a right angled triangle Using Pythogoras' theorem where the square of hypotenuse is equal to the sum of the squares of the adjacent sides we can answer the
KM² = KE² + ME²KM² = 8² + (3√5)² = 64 + 9x5KM = √109KM = 10.44
b)Find LMThe ratio of LM:KN is 3:5 hence if we take the length of one unit as xlength of LM is 3xand the length of KN is 5x ∠K and ∠N are equal making it a isosceles trapezoid. A line from L that cuts KN perpendicularly at D makes KE = DN
KN = LM + 2x 2x = KE + DN2x = 8+8x = 8LM = 3x = 3*8 = 24
c)Find KN Since ∠K and ∠N are equal, when we take the 2 triangles KEM and LDN, they both have the same height ME = LD.
∠K = ∠N Hence KE = DN the distance ED = LMhence KN = KE + ED + DN since ED = LM = 24and KE + DN = 16KN = 16 + 24 = 40
d)Find area KLMNArea of trapezium can be calculated using the formula below Area = 1/2 x perpendicular height between parallel lines x (sum of the parallel sides)substituting values into the general equationArea = 1/2 * ME * (KN+ LM) = 1/2 * 3√5 * (40 + 24) = 1/2 * 3√5 * 64 = 3 x 2.23 * 32 = 214.66 units²
<u>Answer:</u>
<u><em>$2.53 left</em></u>
<u><em /></u>
<u>Explanation:</u>
Since the question is asking us how much money Daniel has left, we must subtract the amount he spent on the video game by the original amount (the amount of money his grandmother sent him).
So, based on our calculations, Daniel should have <em><u>$2.53 left.</u></em>
Answer:
11743
Step-by-step explanation:
correct on deltamath
Answer:
The possible pairs of arrangement of cookies are (12,07) (14,06) (21,04) and (42,2).
Step-by-step explanation:
Given:
Daniel makes 84 cookies and we have to find how many cookies are there in each row and how many rows are there.
Basically we have to find the possible factors of 84.
⇒ Factors:
⇒ 
The possible pairs are.
⇒ 
or 
⇒ 
or 
⇒ 
or 
⇒ 
or 
So,
there can be 12 cookies in 07 rows or 07 cookies in 12 rows.
there can be 14 cookies in 06 rows or 06 cookies in 14 rows.
there can be 21 cookies in 04 rows or 04 cookies in 21 rows.
there can be 42 cookies in 02 rows or 02 cookies in 42 rows.
The possible pairs are (12,07) (14,06) (21,04) and (42,2) in which Daniel can arrange the cookies.
We can calculate the age by using the formula: final amount=initial amount*(1/2)^(time/half-life), or t=ln(final amount/initial amount)/(-0.693)*half-life. The half life of C-14 is 5730 years, and final amount=initial amount is 71% or 0.71, so t=ln(0.71)/(-0.693)*5730=2832 years approximately.
