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2 years ago

Write the equation of a parabola with a vertex at (0,0), a focus at (2,0), and directrix x=-2

1 answer:

8 0

The directrix is x=-2, which means the parabola opens horizontally instead of vertically. The equation is (y - k)²<span> = 4p (x - h), where the </span>focus<span> is (h + p, k) and the </span>directrix<span> is x = h - p
in this case, h+p=2, k=0, and h-p=-2
solve for h and p: h=0, p=2
plug the numbers into the equation: (y-0)</span>²=4*2(x-0)
simplify: y²=8x

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Use one or more properties to rewrite each expression as an expression that does not use parentheses.

maria [59]

Answer:

b + 9

Step-by-step explanation:

Given:

(b + 3) + 6

Required:

Rewrite expression without the parentheses.

SOLUTION:

(b + 3) + 6

Eliminate the parentheses

b + 3 + 6

Add like terms

b + 9

Thus:

(b + 3) + 6 = b + 9

4 0

2 years ago

9.12cm<br> 10.36cm<br> 11.34cm<br> 12.61cm

Vinvika [58]

Tan80 = QR / RS
QR = 5.67 (2)
QR = 11.34

answer

<span>11.34cm</span>

8 0

2 years ago

Simplify the following expression as much as you can use exponential properties. (6^-2)(3^-3)(3*6)^4

gtnhenbr [62]

Answer:

Simplifying the expression $(6^{-2})(3^{-3})(3*6)^4$ we get $\mathbf{108}$

Step-by-step explanation:

We need to simplify the expression $(6^{-2})(3^{-3})(3*6)^4$

Solving:

$(6^{-2})(3^{-3})(3*6)^4$

Applying exponent rule: $a^{-m}=\frac{1}{a^m}$

$=\frac{1}{(6^{2})}\frac{1}{(3^{3})}(18)^4\\=\frac{(18)^4}{6^{2}\:.\:3^{3}} \\$

Factors of $18=2\times 3\times 3=2\times3^2$

Factors of $6=2\times 3$

Replacing terms with factors

$=\frac{(2\times3^2)^4}{(2\times 3)^{2}\:.\:3^{3}} \\=\frac{(2)^4\times(3^2)^4}{(2)^2\times (3)^{2}\:.\:3^{3}} \\$

Using exponent rule: $(a^m)^n=a^{m\times n}$

$=\frac{(2)^4\times(3)^8}{(2)^2\times (3)^{2}\:.\:3^{3}} \\=\frac{2^4\times 3^8}{2^2\times 3^{2}\:.\:3^{3}}$

Using exponent rule: $a^m.a^n=a^{m+n}$

$=\frac{2^4\times 3^8}{2^2\times 3^{2+3}}\\=\frac{2^4\times 3^8}{2^2\times 3^{5}}$

Now using exponent rule: $\frac{a^m}{a^n}=a^{m-n}$

$=2^{4-2}\times 3^{8-5}\\=2^{2}\times 3^{3}\\=4\times 27\\=108$

So, simplifying the expression $(6^{-2})(3^{-3})(3*6)^4$ we get $\mathbf{108}$

7 0

2 years ago

I need help on this 2 problems please help

daser333 [38]

<h3>Answer:</h3>

7) 0.76 is a rational number

8) The list of favorable outcomes is {orange pop #1, orange pop #2}.

<h3>Step-by-step explanation:</h3>

7) The product 0.4 × 1.9 is 0.76. This is not an integer, whole number, or natural number. It is a decimal fraction of finite length, so is a rational number.

___

8) Often, a problem of this sort will ask for the probability of an orange pop outcome. This problem doesn't ask that. Rather it asks what the possible orange pop outcomes are. Drawing one orange pop from the box will give you one of ...

orange pop #1
orange pop #2

These are the possible outcomes.

5 0

3 years ago

A flash disk has the capacity of storing 1 megabyte of data. How many kilobytes of data can be stored in the same flash disk

Luden [163]

For this sort of problem, you need to be familiar with prefixes.

So:

megabyte = $1 *10^6$ bytes

kilobyte = $1*10^3$ bytes

and a regular byte would just be $1$

Now, you will need to do a conversion:

$1megabyte*\frac{1*10^6bytes}{1megabyte}*\frac{1*10^{-3}kilobyte}{1byte}$

I'm going to explain this just in case, but we convert megabytes to regular bytes in the first half by using the information I gave you above. (In one megabyte, there are $1*10^6$ bytes!)

In the second fraction thought, remember one kilobyte is $1*10^3$ bytes. However, you usually only see one of each thing on the bottom of fractions, so you need to add a negative sign to the 3. (technically you could just do $\frac{1kilobyte}{1*10^3bytes}$ , but I think it is more correct to do write it out how I did).

*** They do equal the same thing though! Do whichever way is easier for you!

Now, your answer should be:

$10^3$ kilobytes (1000 kilobytes)

Hope this helped!

6 0

2 years ago