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3 years ago

A parabola has a focus of F (8.5,-4) and a directrix of x=9.5.

Mathematics

1 answer:

SVETLANKA909090 [29]3 years ago

7 0

B......is the answer

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a square garden has a diagonal of 12 m. What is the perimeter of the garden? Express in simplest radical form

lianna [129]

Answer:

The perimeter of the garden, in meters, is $24\sqrt{2}$

Step-by-step explanation:

Diagonal of a square:

The diagonal of a square is found applying the Pythagorean Theorem.

The diagonal of the square is the hypothenuse, while we have two sides.

Diagonal of 12m:

This means that $d = 12$ , side s. So

$s^2 + s^2 = 12^2$

$2s^2 = 144$

$s^2 = \frac{144}{2}$

$s^2 = 72$

$s = \sqrt{72}$

Factoring 72:

Factoring 72 into prime factors, we have that:

72|2

36|2

18|2

9|3

3|3

$72 = 2^{3}*3^{2}$

So, in simplest radical form:

$s = \sqrt{72} = \sqrt{2^{3}*3^{2}} = \sqrt{2^3}*\sqrt{3^2} = 2\sqrt{2}*3 = 6\sqrt{2}$

Perimeter of the garden:

The perimeter of a square with side of s units is given by:

$P = 4s$

In this question, since $s = 6\sqrt{2}$

$P = 4s = 4*6\sqrt{2} = 24\sqrt{2}$

The perimeter of the garden, in meters, is $24\sqrt{2}$

5 0

3 years ago

-32-(-27)= what is negative 32 minus negative 27?

tiny-mole [99]

It equals negative five

8 0

3 years ago

Read 2 more answers

In ΔBCD, the measure of ∠D=90°, DB = 96 feet, and CD = 14 feet. Find the measure of ∠B to the nearest tenth of a degree.

Reil [10]

Answer:

8.3

Step-by-step explanation:

8 0

3 years ago

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Write 56 as a product of primes. Use index notation when giving your answer.

mixas84 [53]

Answer:

56 as a product of primes using index notation is: $\mathbf{2^3 \times 7}$

Step-by-step explanation:

We need to write 56 as a product of primes.

Prime Numbers:

Numbers that are divisible by 1 or itself.

Now, writing 56 as product of primes

56 = 2 x 2 x 2 x 7

Now, Use index notation when giving your answer.

Index Notation:

Express elements in power form i.e. if we have 2 x 2 we can write it as 2^2

So, answer will be:

$56 = 2 \times 2 \times 2 \times 7$

$=2^3 \times 7$

So, 56 as a product of primes using index notation is: $\mathbf{2^3 \times 7}$

3 0

3 years ago

Which expression is equal to

melamori03 [73]

Answer:

D is the most acurate answer.

Step-by-step explanation:

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3 years ago