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3 years ago

In Pensacola, Florida, the average rainfall

Mathematics

1 answer:

Lerok [7]3 years ago

5 0

the average rainfall, in inches, in December is 4.15 inch . Correct option C. 4.15 .

<u>Step-by-step explanation:</u>

Here we have , In Pensacola, Florida, the average rainfall in the month of July is 7.40 inches. By October, the average rainfall decreases by 35%. By December, the average rainfall drops another 0.66 inches. We need to find the average rainfall, in inches, in December .Let's find out:

In July , rainfall was 7.40 inches . By October, the average rainfall decreases by 35% i.e.

⇒ $7.4 - \frac{7.4(35)}{100}$

⇒ $7.4 - 0.074(35)$

⇒ $7.4 - 2.59$

⇒ $4.81$

By December, the average rainfall drops another 0.66 inches i.e.

⇒ $4.81-0.66$

⇒ $4.15$

Therefore, the average rainfall, in inches, in December is 4.15 inch . Correct option C. 4.15 .

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Suppose a parabola has vertex (6,5) and also passes through the point (7,7). Write the equation of the parabola in vertex form.

jek_recluse [69]

Answer:

Choice B: $y = 2\, (x - 6)^{2} + 5$ .

Step-by-step explanation:

For a parabola with vertex $(h,\, k)$ , the vertex form equation of that parabola in would be:

$\text{$y = a\, (x - h)^{2} + k$ for some constant $a$}$ .

In this question, the vertex is $(6,\, 5)$ , such that $h = 6$ and $k = 5$ . There would exist a constant $a$ such that the equation of this parabola would be:

$y = a\, (x - 6)^{2} + 5$ .

The next step is to find the value of the constant $a$ .

Given that this parabola includes the point $(7,\, 7)$ , $x = 7$ and $y = 7$ would need to satisfy the equation of this parabola, $y = a\, (x - 6)^{2} + 5$ .

Substitute these two values into the equation for this parabola:

$7 = (7 - 6)^{2}\, a + 5$ .

Solve this equation for $a$ :

$7 = a + 5$ .

$a = 2$ .

Hence, the equation of this parabola would be:

$y = 2\, (x - 6)^{2} + 5$ .

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3 years ago

Posting a screenshot.

Anna71 [15]

Since 6 is positive, it's (x+blank)^2

6/2=3, and (x+3)^2 = x^2+6x+9. We have x^2+6x-2, so we have to add 9 to both sides to get (x+3)^2-2=9, then subtract 9 from both sides to get
(x+3)^2-11=0, or (x+3)^2=11. Square root both sides to get x+3=sqrt(11), and x=sqrt(11)-3, which is approximately 0.32

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3 years ago