Answer:
The answer is B.
Step-by-step explanation:
Given that the total angles in a triangle is 180° so in order to find the value of x, you have to substract 60° and 80° from 180° :
The general form of a parabola when using the focus and directrix is:
(x - h)² = 4p(y - k) where (h, k) is the vertex of the parabola and 'p' is distance between vertex and the focus. We use this form due to the fact we can see the parabola will open up based on the directrix being below the focus. Remember that the parabola will hug the focus and run away from the directrix. The formula would be slightly different if the parabola was opening either left or right.
Given a focus of (-2,4) and a directrix of y = 0, we can assume the vertex of the parabola is exactly half way in between the focus and the directrix. The focus and vertex with be stacked one above the other, therefore the vertex will be (-2, 2) and the value of 'p' will be 2. We can now write the equation of the parabola:
(x + 2)² = 4(2)(y - 2)
(x + 2)² = 8(y - 2) Now you can solve this equation for y if you prefer solving for 'y' in terms of 'x'
Answer:
(x +9)(x +8)
Step-by-step explanation:
In a quadratic with leading coefficient 1, the coefficient of the linear term (17) is the sum of factors of the constant term (72). If you know your times tables, you know that 8×9 = 72, and you also know that 8+9 = 17.
With these facts, you can write the factorization as ...
(x +8)(x +9)
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If you need to see the working out, rather than jumping to the end, you can use the sum information to rewrite the linear term:
x^2 +(8x +9x) +72
Now factor pairs of terms:
(x^2 +8x) + (9x +72) = x(x +8) +9(x +8) = (x +9)(x +8)
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It also helps to be familiar with the product of binomials:
(x +a)(x +b) = x^2 +(a+b)x +ab
Answer:
k = 10
Step-by-step explanation:
f(x) has been moved up 10 units to get g(x). So, k = 10
