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Setler79 [48]
1 year ago
14

A parabola can be drawn given a focus of (-5, -4)(−5,−4) and a directrix of y=-6y=−6. Write the equation of the parabola in any

form.
screenshot below-

Mathematics
1 answer:
lord [1]1 year ago
4 0

Answer:

\displaystyle \large{y=\dfrac{x^2}{4} + \dfrac{5x}{2} + \dfrac{5}{4}}

Step-by-step explanation:

Given:

  • Focus = (-5,-4)
  • Directrix = -6

To find:

  • Parabola Equation

Locus of Parabola (Upward/Downward)

\displaystyle \large{\sqrt{(x-a)^2+(y-b)^2} = |y-c|}

Where:

  • (a,b) = focus
  • c = directrix

Hence:

\displaystyle \large{\sqrt{(x+5)^2+(y+4)^2}=|y+6|}

Cancel square root by squaring both sides as we get:

\displaystyle \large{(x+5)^2+(y+4)^2=(y+6)^2}

Solve for y-term:

\displaystyle \large{(x+5)^2=(y+6)^2-(y+4)^2}\\\displaystyle \large{x^2+10x+25=y^2+12y+36-y^2-8y-16}\\\displaystyle \large{x^2+10x+25=4y+20}\\\displaystyle \large{x^2+10x+5=4y}\\\displaystyle \large{y=\dfrac{x^2}{4} + \dfrac{5x}{2} + \dfrac{5}{4}}

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riadik2000 [5.3K]

Answer:

$0.50 for a pack of juice.

Step-by-step explanation:

You are finding the unit rate of the cost of each unit, or one box of juice. In this case, there is 8 juice boxes in the pack, which costs you $4. Divide 4 with 8:

4/8 = 1/2 = 0.5

$0.50 is the cost per pack of juice.

~

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2 years ago
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Identify the monomial function described as odd or even, and indicate whether a is positive or negative.
Igoryamba

Answer:

Case 1: As x > 0 increases, f(x) increases.  As x < 0 decreases, f(x) decreases.

It is an 'odd' function with 'positive' a.

Case 2: As x > 0 increases, f(x) decreases.  As x < 0 decreases, f(x) decreases.

It is an 'even' function with 'negative' a.

Case 3: As x > 0 increases, f(x) increases.  As x < 0 decreases, f(x) increases.

It is an 'even' function with 'positive' a.

Case 4: As x > 0 increases, f(x) decreases.  As x < 0 decreases, f(x) increases.

It is an 'odd' function with 'negative' a.

Step-by-step explanation:

Let us consider a monomial function:

             f(x) = axⁿ

Case 1:

As x > 0 increases, f(x) increases.  As x < 0 decreases, f(x) decreases.

This happens only if a is 'positive' and n is 'odd'.  So, it is an 'odd' function with 'positive' a.

Case 2:

As x > 0 increases, f(x) decreases.  As x < 0 decreases, f(x) decreases.

This happens only if a is 'negative' and n is 'even'. So, it is an 'even' function with 'negative' a.

Case 3:

As x > 0 increases, f(x) increases.  As x < 0 decreases, f(x) increases.

This happens only if a is 'positive' and n is 'even'. So, it is an 'even' function with 'positive' a.

Case 4:

As x > 0 increases, f(x) decreases.  As x < 0 decreases, f(x) increases.

This happens only if a is 'negative' and n is 'odd'. So, it is an 'odd' function with 'negative' a.

Keywords: monomial function, odd function, even function

Learn more about monomial function from brainly.com/question/8973176

#learnwithBrainly

3 0
3 years ago
Read 2 more answers
Ray delivered 3/8 of the newspapers on his route in the first hour and 4/5 of the rest in the second hour what fraction of the n
Temka [501]

Answer:

\frac{1}{2}

Step-by-step explanation:

Let the total number of Newspapers be x

Number of newspapers delivered in first hour of his route= \frac{3}{8} of x

Total number of newspapers delivered in first hour= \frac{3}{8}x

Number of newspapers left= x-\frac{3x}{8}

Number of newspapers left=\frac{8x-3x}{8}

Number of newspapers left=\frac{5x}{8}

Number of newspapers delivered in second hour=4/5 of\frac{5x}{8}

Number of newspapers delivered in second hour=\frac{x}{2}

Fraction of newspapers delivered in second hour is=\frac{1}{2}

Hence, the correct answer is \frac{1}{2}

8 0
3 years ago
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Vaselesa [24]

Answer:

x > −3

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

Step 2: Subtract 3 from both sides.

Step 3: Divide both sides by -3.

6 0
3 years ago
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