If 2000 miles increased by 33%, how many miles did it increase?

Worth 25 points!

MrRissso [65]

Answer:

1) $\sqrt{-48}=4\sqrt{3} \ i$

2) $\sqrt{-63}=3\sqrt{7} \ i$

3) $\sqrt{-72}=6\sqrt{2} \ i$

4) $\sqrt{-24}=4\sqrt{6} \ i$

5) $\sqrt{-84}=2\sqrt{21} \ i$

6) $\sqrt{-99}=3\sqrt{11} \ i$

Step-by-step explanation:

We need to simply the following :

Note: For all questions given we know that $\sqrt{-1}=i$ using it in all the given questions.

1) $\sqrt{-48}$

Factors of 48 are: 2x2x2x2x3

$\sqrt{-48}\\=\sqrt{48}\sqrt{-1} \\=\sqrt{2\times2\times2\times2\times3}\ i\\= \sqrt{2^2\times2^2\times3}\ i\\=2\times2\sqrt{3} \ i \\=4\sqrt{3} \ i$

2) $\sqrt{-63}$

Factors of 63 are: 3x3x7

$\sqrt{-63}\\=\sqrt{63}\sqrt{-1} \\=\sqrt{3\times3\times7}\ i\\= \sqrt{3^2\times7}\ i\\=3\sqrt{7} \ i$

3) $\sqrt{-72}$

Factors of 72 are: 2x2x2x3x3

$\sqrt{-72}\\=\sqrt{72}\sqrt{-1} \\=\sqrt{2\times2\times2\times3\times3}\ i\\= \sqrt{2^2\times3^2\times2}\ i\\=2\times3\sqrt{2} \ i \\=6\sqrt{2} \ i$

4) $\sqrt{-24}$

Factors of 24 are: 2x2x2x3

$\sqrt{-24}\\=\sqrt{24}\sqrt{-1} \\=\sqrt{2\times2\times2\times3}\ i\\= \sqrt{2^2\times2\times3}\ i\\=2\sqrt{2\times3} \ i \\=2\sqrt{6} \ i$

5) $\sqrt{-84}$

Factors of 84 are: 2x2x3x7

$\sqrt{-84}\\=\sqrt{84}\sqrt{-1} \\=\sqrt{2\times2\times3\times7}\ i\\= \sqrt{2^2\times3\times7}\ i\\=2\sqrt{21} \ i$

6) $\sqrt{-99}\\$

Prime factors of 99 are: 3x3x11

$\sqrt{-99}\\=\sqrt{99}\sqrt{-1} \\=\sqrt{3\times3\times11}\ i\\= \sqrt{3^2\times11}\ i\\=3\sqrt{11} \ i \\=3\sqrt{11} \ i$

6 0

3 years ago

Ryan wants to describe the translation shown on the grid below. Ryan uses the following steps to describe the translation. Step

Dmitry_Shevchenko [17]

Answer:

Option C. Step 3

Step-by-step explanation:

step 1

Identify the pre-image and the image: The pre-image is triangle XYZ, and the image is X'Y'Z'

The step 1 is correct

step 2

Identify the number of units that each point moves horizontally: Each point moves one unit left.

The step 2 is correct

step 3

Identify the number of units that each point moves vertically: Each point moves three units down

The step 3 is not correct

Each point moves three units up

step 4

The translation is one unit left and three units down

the step 4 is not correct

The translation is one unit left and three units up

therefore

The first error is in the Step 3

6 0

3 years ago

Read 2 more answers

-2x-3y=-7 y+1=x solve for y and x

sertanlavr [38]

Answer:

x = 2 and y = 1

Step-by-step explanation:

First, solve for y by substituting the second equation as x into the first equation

-2x - 3y = -7

-2(y + 1) - 3y = -7

Simplify and solve for y

-2y - 2 - 3y = -7

-5y - 2 = -7

-5y = -5

y = 1

Solve for x by plugging in 1 into the second equation

y + 1 = x

1 + 1 = x

2 = x

So, the answer is x = 2 and y = 1

4 0

3 years ago

Please someone help me

Marysya12 [62]

Answer:

The correct answer option is D. 5.

Step-by-step explanation:

We are given the following expression where 4 is to be divided by a fraction 1/5:

$4$ ÷ $\frac{1}{5}$

This can also be written as:

$\frac{4}{\frac{1}{5} }$

Now to find the quotient of this, we will take the reciprocal of the fraction in the denominator to change it into multiplication.

$4 \times \frac{5}{1}$

Therefore, ignoring the 1 in denominator, we can simply multiply 4 by 5.

4 0

4 years ago

Read 2 more answers

If a finite set S of nonzero vectors spans a vector space V , then some subset of S is a basis for V . True or False

andreyandreev [35.5K]

<h3>Answer: True</h3>

Explanation:

This theorem doesn't have a name unfortunately. So searching it out is a bit tricky if you don't know the right way to word things. Luckily it wasn't too hard of a find, and I managed to track it down in a linear algebra textbook.

Check out the screenshot below for the snippet of the theorem and the corresponding proof. The book simply refers to it as "theorem 1.9", which again, is an unfortunate choice of naming.

3 0

3 years ago