In this question , it is given that p represents cost of 1 container of popcorn . Therefore cost of 5 containers of popcorn = 5p and cost of 3 containers of popcorn = 3p .
And g represents cost of 1 container of granola bars. THerefore cost of 4 containers of granola bars = 4g and cost of 6 containers of granola bars = 6g .
According to the given question, the required linear equations are
5p+4g=42.50 , 3p+6g =34.50 .
And these are the the required system of linear equation .
Answer: Both the expressions are exactly same . Both are representing the number of tokens she has now.
Step-by-step explanation:
Given: The total number of tokens Angelique has= 20
Since, she lost some of them, let the number of lost tokens be t.
Then, The remaining tokens she has = 20-t
Then her father triples the tokens she has.
now, the number of token she has=
....>Angelique's expression
By using distributive property,
The number of token she has=
⇒The number of token she has=
...> Dante's expressions
Hence, both are the same expressions. Both are representing the number of tokens she has now.
The number of bacteria grown in 32 hours is 15771
<u>Step-by-step explanation:</u>
It is given that,
Researchers recorded that a group of bacteria grew from 100 to 7,000 in 14 hours.
Therefore, the bacteria has grown from 100 to 7000 in 14 hours.
<u>
To calculate number of bacteria grown in 14 hours :</u>
⇒ 7000 - 100 = 6900
6900 bacteria grows in 14 hours. We need to find out the growth of bacteria in 1 hour in order to calculate its growth in 32 hours.
<u>To calculate number of bacteria grown in 1 hour :</u>
⇒ Total bacteria growth in 14 hours / 14
⇒ 6900 / 14
⇒ 492.85
<u>To calculate number of bacteria grown in 32 hours :</u>
⇒ 492.85 × 32
⇒ 15771.2
⇒ 15771 (rounded to nearest whole number)
∴ The number of bacteria grown in 32 hours is 15771
65-9=56
56 divided by 8 is 7
So they will need 7 tents
Given : tan 235 = 2 tan 20 + tan 215
To Find : prove that
Solution:
tan 235 = 2 tan 20 + tan 215
Tan x = Tan (180 + x)
tan 235 = tan ( 180 + 55) = tan55
tan 215 = tan (180 + 35) = tan 35
=> tan 55 = 2tan 20 + tan 35
55 = 20 + 35
=> 20 = 55 - 35
taking Tan both sides
=> Tan 20 = Tan ( 55 - 35)
=> Tan 20 = (Tan55 - Tan35) /(1 + Tan55 . Tan35)
Tan35 = Cot55 = 1/tan55 => Tan55 . Tan35 =1
=> Tan 20 = (Tan 55 - Tan 35) /(1 + 1)
=> Tan 20 = (Tan 55 - Tan 35) /2
=> 2 Tan 20 = Tan 55 - Tan 35
=> 2 Tan 20 + Tan 35 = Tan 55
=> tan 55 = 2tan 20 + tan 35
=> tan 235 = 2tan 20 + tan 215
QED
Hence Proved
