Answer:
The intermediate step are;
1) Separate the constants from the terms in x² and x
2) Divide the equation by the coefficient of x²
3) Add the constants that makes the expression in x² and x a perfect square and factorize the expression
Step-by-step explanation:
The function given in the question is 6·x² + 48·x + 207 = 15
The intermediate steps in the to express the given function in the form (x + a)² = b are found as follows;
6·x² + 48·x + 207 = 15
We get
1) Subtract 207 from both sides gives 6·x² + 48·x = 15 - 207 = -192
6·x² + 48·x = -192
2) Dividing by 6 x² + 8·x = -32
3) Add the constant that completes the square to both sides
x² + 8·x + 16 = -32 +16 = -16
x² + 8·x + 16 = -16
4) Factorize (x + 4)² = -16
5) Compare (x + 4)² = -16 which is in the form (x + a)² = b
Answer:
They sold 60 muffins and 60 cookies yesterday
It is a LCM problem
Step-by-step explanation:
6 muffins together
20 cookies together
To sell the same amount of muffins and cookies,
Find the lowest common multiple of 6 muffins and 20 cookies
6 muffins = 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78
20 cookies = 40, 60, 80
The lowest common multiple of 6 muffins and 20 cookies is 60
Therefore,
They sold 60 muffins and 60 cookies yesterday
It is a LCM problem
I'm ASSUMING this is a 45-45-90 right triangle and that DF is the hypotenuse.
With that said. Angle F = 45 means that angle = 45 and angle E = 90 degrees.
There is only one rule for 45-45-90 right triangles:
hypotenuse = √(2) * leg
Given the hyp = 16
16 = √(2) * leg
divide both sides by √(2)
16/√(2) = leg
Rationalize the denominator
16√(2)/(√(2)*√(2) =
(16√(2)) / 2 =
8√2
Answer:
Step-by-step explanation:
Total interior angles in a triangle=180 degrees
That is: 3x + 10 + 5x - 1 + x =180
9x+9=180
9x=180-9
9x=171
x=171/9
x=19
Therefore
Angle A =67 degrees
Angle B= 94 degrees
Angle C = 19 degrees
