megan is going to make a drink using the instrutions below mix 2 parts of fruit juice with 5 parts if sparkling water. megan has
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Check the picture below, keeping in mind that opposides sides and interior angles in a parallelogram are congruent.
Answer:
PB = 1.8
Step-by-step explanation:
PQ = 8 cm, BC = 10 cm and AB = 9 cm
∆ABC is similar to ∆APQ.
Therefore:
Plug in the values
Cross multiply
AP × 10 = 8 × 9
AP × 10 = 72
Divide both sides by 10
AP = 7.2
PB = AB - AP
PB = 9 - 7.2
PB = 1.8
Recall that the vertex form of a quadratic function (or parabolic function) is equal to
Now, given that we have f(x) = x² + 14x + 40, to express f into its vertex form, we must first fill in the expression to form a perfect square.
One concept that we must remember when completing the square is that
(a + b)² = a² + 2ab + b²
So, to complete the square for (x² + 14x + ____), we have 2ab = 14 where a = 1. Thus, b = 14/2 = 7. Hence, the last term of the perfect square must equal to 7² = 49.
So, going back to the function, we have
Thus, we have derived the vertex form of the function.
Answer: f(x) = (x + 7)² - 9
Now, given that we have f(x) = x² + 14x + 40, to express f into its vertex form, we must first fill in the expression to form a perfect square.
One concept that we must remember when completing the square is that
(a + b)² = a² + 2ab + b²
So, to complete the square for (x² + 14x + ____), we have 2ab = 14 where a = 1. Thus, b = 14/2 = 7. Hence, the last term of the perfect square must equal to 7² = 49.
So, going back to the function, we have
Thus, we have derived the vertex form of the function.
Answer: f(x) = (x + 7)² - 9