First, let x or any variable represent the number of paintings Kate initially has. After selling 12 of it, her paintings now becomes only x - 12. Then, she purchased 7 more making the number of her paintings become x - 12 + 7 = x - 5. This number tantamount to 21.
x - 5 = 21 ; x = 26
Thus, Kate initially had 26 paintings.
Cylinder:
V = pi * r^2 * h
V = 3.14 * 9^2 * 11
Simplify exponent:
V = 3.14 * 81 * 11
Multiply:
V = 2797.74
Sphere:
V = 4/3 * pi * r^3
V = 4/3 * 3.14 * 9^3
Simplify exponent:
V = 4/3 * 3.14 * 729
Multiply:
V = 3052.08
Cone:
V = 1/3 * pi * r^2 * h
V = 1/3 * 3.14 * 12^2 * 20
Simplify exponent:
V = 1/3 * 3.14 * 144 * 20
Multiply:
V = 3014.4
So the Sphere holds the most.
Jax gets 4 packs per month...each pack contains 4 cards...so he gets 16 cards per month.
Sofia gets 3 packs per month..each pack contains 4 cards...so she gets 12 cards per month..
56 + 16m = 68 + 12m
16m - 12m = 68 - 56
4m = 12
m = 12/4
m = 3.....they will have the same number of cards in 3 months
Jax : 56 + 16(3) = 104 cards
Sofia : 68 + 12(3) = 104 cards
and they will both have 104 cards
Answer:
The system if equation that can be used to derive this are
6x + 4y = 69 AND
12x + y = 96
The price of a drink is $7.5
Step-by-step explanation:
The question here says that Taylor and Nora went to the movie theater and purchase refreshments for their friends. Taylor spends a total of $69.00 on 6 drinks and 4 bags of popcorn Nora spends a total of $96.00 on 12 drinks and bag of popcorn.And we are now told to write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations,we should determine and state the price of a drink, to the nearest cent .
Now, Let's assume that the price of a drink is "X" and that of a bag of popcorn to be Y
The first person made a purchase which led to the equation
6x + 4y = 69______ equation 1
And the second person also made a purchase that lead to the equation
12x + y = 96_____ equation 2
We make y the subject of the formula in equation 2 and apply it in 1
Y = 96 - 12x
Now apply the above in equation 1
6x + 4y = 69
6x + 4(96 - 12x)= 69
6x + 384 - 48x = 69
42x = 384 - 69
X = 315/42
X = 7.5
Substitute x= 7.5 in equation 2
12x + y = 96
12(7.5) + y = 96
90 + y = 96
Y = 6
Therefore, the price of a drink is $7.5
