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3 years ago

Simplify the expression -5d+3c-4d

Mathematics

2 answers:

Tasya [4]3 years ago

8 0

Subtract 4d From -5d

Answer:3c-9d

Sever21 [200]3 years ago

5 0

Answer:

4d i think im not sure???hoped it helped?

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The focus of a parabola is (0, -3) and the directrix is y = 3. What is the equation of the parabola?

OleMash [197]

Answer:

The equation of the parabola is $y = -12\cdot x^{2}$ .

Step-by-step explanation:

Since the directrix is of the form $y = a$ , the parabola is vertical. The vertex of the parabola ( $V(x,y)$ ) is the midpoint between the focus ( $F(x,y)$ ) and a point of the directrix ( $P(x,y)$ ), that is to say:

$V(x,y) = \frac{1}{2}\cdot F(x,y) + \frac{1}{2}\cdot P(x,y)$ (1)

If we know that $F(x,y) = (0, -3)$ and $P(x,y) = (0, 3)$ , then the coordinates of the vertex of the parabola:

$V(x,y) = \frac{1}{2}\cdot (0, -3) + \frac{1}{2}\cdot (0, 3)$

$V(x,y) = (0, 0)$

The vertex factor ( $p$ ) is the distance of the focus with respect to the vertex:

$p = \sqrt{[F(x,y)-V(x,y)]\,\bullet \,[F(x,y)-V(x,y)]}$ (2)

If we know that $F(x,y) = (0, -3)$ and $V(x,y) = (0, 0)$ , then the vertex factor is:

$p = \sqrt{0^{2}+(-3)^{2}}$

$p = -3$

The equation of the parabola in the vertex form is described below:

$y - k = 4\cdot p \cdot (x-h)^{2}$ (3)

Where:

$x$ - Independent variable.

$y$ - Dependent variable.

$h, k$ - Coordinates of the vertex.

If we know that $(h,k) = (0, 0)$ and $p = -3$ , then the equation of the parabola is $y = -12\cdot x^{2}$ .

6 0

3 years ago

A house on the market was valued at $245,000. After several years, the value increased by 9%. By how much did the house's value

aniked [119]

We are given that a house had a value of $245000 and its value was increased by 9%. To determine how much is this value increase in dollars we need to multiply the value of the house by 9/100. We get this: