A.)
The first thing we must do for this case is to find the area of the complete figure.
We have then:
Triangle 1:
A1 = (1/2) * (1.5) * (1)
A1 = 0.75 feet ^ 2
Triangle 2:
A2 = (1/2) * (1.5) * (2)
A2 = 1.5 feet ^ 2
Triangle 3:
A3 = (1/2) * (0.75) * (1)
A3 = 0.375 feet ^ 2
Rectangle:
A4 = (5) * (0.75)
A4 = 3.75 feet ^ 2
Adding the areas we have:
A = A1 + A2 + A3 + A4
A = 0.75 + 1.5 + 0.375 + 3.75
A = 6.375 feet ^ 2
Answer:
there are 6,375 feet ^ 2 of plywood in the scenery
B.)
Triangles:
A = A1 + A2 + A3
A = 0.75 + 1.5 + 0.375
A = 2,625 feet ^ 2
Two layers of paint:
A = 5.25 feet ^ 2 <45 feet ^ 2
Rectangle:
A = 3.75 feet ^ 2
Two layers of paint:
A = 7.5 feet ^ 2 <45 feet ^ 2
Answer:
One quart of each color is needed.
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.
None of your options, not via complete the square nor quadratic the formula.
Solve for x over the real numbers:
x^2 + 8 x + 9 = 0
x = (-8 ± sqrt(8^2 - 4×9))/2 = (-8 ± sqrt(64 - 36))/2 = (-8 ± sqrt(28))/2:
x = (-8 + sqrt(28))/2 or x = (-8 - sqrt(28))/2
sqrt(28) = sqrt(4×7) = sqrt(2^2×7) = 2sqrt(7):
x = (2 sqrt(7) - 8)/2 or x = (-2 sqrt(7) - 8)/2
Factor 2 from -8 + 2 sqrt(7) giving 2 (sqrt(7) - 4):
x = 1/22 (sqrt(7) - 4) or x = (-2 sqrt(7) - 8)/2
(2 (sqrt(7) - 4))/2 = sqrt(7) - 4:
x = sqrt(7) - 4 or x = (-2 sqrt(7) - 8)/2
Factor 2 from -8 - 2 sqrt(7) giving 2 (-sqrt(7) - 4):
x = sqrt(7) - 4 or x = 1/22 (-sqrt(7) - 4)
(2 (-sqrt(7) - 4))/2 = -sqrt(7) - 4:
Answer: x = sqrt(7) - 4 or x = -sqrt(7) - 4_____________________________________________________
Solve for x:
x^2 + 8 x + 9 = 0
Subtract 9 from both sides:
x^2 + 8 x = -9
Add 16 to both sides:
x^2 + 8 x + 16 = 7
Write the left hand side as a square:
(x + 4)^2 = 7
Take the square root of both sides:
x + 4 = sqrt(7) or x + 4 = -sqrt(7)
Subtract 4 from both sides:
x = sqrt(7) - 4 or x + 4 = -sqrt(7)
Subtract 4 from both sides:
Answer: x = sqrt(7) - 4 or x = -4 - sqrt(7)
Here's the solution ~
Let's find the measure of hypotenuse first, by using Pythagoras theorem ;
Now, let's find the asked values ~
For Cos y :
As we can see that both sin x and Cos y have equal values, therefore The required relationships is equality.
I.e Sin x = Cos y
Hope it helps ~
The slope of a vertical line is undefined, D.
If you were to try to solve use something like the rise over run method, you would end up with a 0 in the denominator. Since dividing by 0 gives you an undefined result, the slope would be undefined.
