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hoa [83]
3 years ago
7

What number goes in the highlighted box?

Mathematics
1 answer:
pentagon [3]3 years ago
3 0
-15+7=-8
Adding numbers with different signs makes it subtraction and the answer will have the sign of the bigger number
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What is the equation of the quadratic graph with a focus of (4, −3) and a directrix of y = −6?
Artyom0805 [142]

Answer:

y=\frac{1}{6} (x-4)-\frac{9}{2}

Step-by-step explanation:

∵ The quadratic equation form is :

y = [1/2(b - k)] (x - a)² + (b + k)/2

Where (a , b) is the focus and directrix y = k

∵ The focus is (4 , -3) and directix is y = -6

∵ y=\frac{1}{2(-3-(-6))} (x-4)^{2}+\frac{(-3)+(-6)}{2}

∴ y=\frac{1}{6} (x - 4)^{2}+\frac{-9}{2}

∴ y=\frac{1}{6} (x-4)-\frac{9}{2}

another way:

Assume that (x , y) is the general point on the parabola

∵ The distance between the directrix and (x , y) = the distance between the focus and (x , y)

By using the distance rule:

∵ (y - -6)² = (x - 4)² + (y - -3)² ⇒ (y + 6)² = (x - 4)² + (y + 3)

∴ y² + 12y + 36 = (x - 4)² + y² + 6y + 9

∴ 12y - 6y = (x - 4)² + 9 - 36

∴ 6y = (x - 4)² - 27 ⇒ ÷ 6

∴ y = 1/6 (x - 4)² - 9/2

4 0
3 years ago
What is the range of the relation of centimeters as a function of inches? {5.08, 10.16, 17.78, 25.4, 33.02} all positive integer
mel-nik [20]

Answer:

y>0 Option D

Step-by-step explanation:

4 0
3 years ago
A dolphin is 9 feet below the surface of the ocean. If its position can be recorded as −9 feet, what would the position of 0 rep
bearhunter [10]

Answer:

the sea line

I am guessing

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Who gets this how do I feel this out
Vesnalui [34]

Answer:

Step-by-step explanation:

3 0
2 years ago
In New York City at the spring equinox there are 12 hours 8 minutes of daylight. The
slamgirl [31]

Answer:

  independent: day number; dependent: hours of daylight

  d(t) = 12.133 +2.883sin(2π(t-80)/365.25)

  1.79 fewer hours on Feb 10

Step-by-step explanation:

a) The independent variable is the day number of the year (t), and the dependent variable is daylight hours (d).

__

b) The average value of the sinusoidal function for daylight hours is given as 12 hours, 8 minutes, about 12.133 hours. The amplitude of the function is given as 2 hours 53 minutes, about 2.883 hours. Without too much error, we can assume the year length is 365.25 days, so that is the period of the function,

March 21 is day 80 of the year, so that will be the horizontal offset of the function. Putting these values into the form ...

  d(t) = (average value) +(amplitude)sin(2π/(period)·(t -offset days))

  d(t) = 12.133 +2.883sin(2π(t-80)/365.25)

__

c) d(41) = 10.34, so February 10 will have ...

  12.13 -10.34 = 1.79

hours less daylight.

5 0
3 years ago
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