Laura collects old foreign coins. She has 83 coins in total. She has 53 lira and drachma coins. She has 51 lira and peseta coins. How many lira coins does she have?

She has 21 lira coins.

Step-by-step explanation:

Given, Laura collects old foreign coins. She has 83 coins in total. She has 53 lira and drachma coins. She has 51 lira and peseta coins.

Let x = the number of lira coins.

y= the number of drachma coins.

z= the number of peseta coins.

Then, as per given, we have

x+y+z=83   (i)

x+y=53   (ii)

x+z=51   (iii)

From (ii) and (iii)

y=53-x

z=51-x

Put these values in (i) , we get

x+(53-x)+(51-x)=83

⇒ x+53-x+51-x=83

⇒ 104-x=83

⇒104-83=x

⇒x= 21

Hence, she has 21 lira coins.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

answer: cos [   arcsin (3/5) - arccos (1/2) ] =

step-by-step explanation: × = 3/5 = 0.6--> x = 36.87 and x = 180 - 36.87 = 143.13 deg

cos y = 1/2 --> y = +- 60 deg a. cos (x - y) = cos (143.13 - 60) = cos 83,13  

=

0.12

b. cos (36.87 - 60) = cos (-23.23) = 0.92