X=quarters, y=dimes
7+2x=y
0.25x+0.1y=10.15
we substitute the first equation into the second equation
0.25x+0.1(7+2x)=10.15
0.25x+0.7+0.2x=10.15
0.45x+0.7-0.7=10.15-0.7
0.45x=9.45
0.45x/0.45=9.45/0.45
x=21 quarters
7+2x=y, x=21
7+2(21)=y
7+42=y
y=49 dimes
check: 0.25x+0.1y=10.15 when x=21, y=49
21(0.25)=5.25 in quarters
49(0.1)=4.90 in dimes
5.25+4.90=10.15
Answer:
Part a) The approximate years were 1998 and 2008
Part b) The graph in the attached figure
Step-by-step explanation:
Part a) we have

For
Solve the quadratic equation


we know that
The formula to solve a quadratic equation of the form
is equal to
in this problem we have

so
substitute in the formula
therefore
The approximate years are
1997+11=2008
1997+1=1998
Part b)
Using a graphing tool
we have


The solution of the system of equations is the intersection point both graphs
The intersection point are (0.99,80) and (11.23,80)
see the attached figure
therefore
The solution part a) is correct
Answer: The ratio value of oil to popcorn kernels for theatre C is 6 / 32 = 3 / 16.
Step-by-step explanation: Given that the manager of Theatre A says that they usually go through about 15 cups of popcorn kernels and about 5 cups of oil each weeknight.
Then, the ratio value of oil to popcorn kernels for theatre A is 5 / 15 = 1 / 5.
Given that the manager of Theatre B says that they order 18 cups of oil and 72 cups of popcorn kernels each week.
Then, the ratio value of oil to popcorn kernels for theatre B is 18 / 72 = 1 / 4.
Given that the manager of Theatre C says that their concessions use 6 cups of oil and 32 cups of popcorn kernels on a busy Saturday.
Then, the ratio value of oil to popcorn kernels for theatre C is 6 / 32 = 3 / 16.
This is just simple Pythagorean’s theorem. a^2 + b^2 = c^2
Number 2:
5^2 + x^2 = 10^2
25 + x^2 = 100
x^2 = 75
x = sqrt 75 = 5*sqrt(3)
Number 3:
4^2 + x^2 = 7^2
16 + x^2 = 49
x^2 = 33
x = sqrt 33
Answer:
-29
Step-by-step explanation:
(-4 + -3) x 2^2 - 1
follow order of operations PEMDAS
Parentheses:
(-4 + -3) x 2^2 - 1
(-7) x 2^2 -1
exponents:
(-7) x 4 - 1
multiplication
-28 - 1
subtraction
-29