Doris made a list of all the whole number from 1 to 100 how many times did she write the digit 2

Laticia randomly selected 25% of the seventh grade students in her school and asked them their favorite season. Of the students

Marysya12 [62]

I would say 75 or 150
Do u know how many students are in her school?

4 0

2 years ago

Rationalize the denominator of sqrt -49 over (7 - 2i) - (4 + 9i)

zubka84 [21]

$\sqrt{ \frac{-49}{(7-2i)-(4+9i) } } 
$

This one is quite the deal, but we can begin by distributing the negative on the denominator and getting rid of the parenthesis:

$\frac{ \sqrt{-49}}{7-2i-4-9i}$

See how the denominator now is more a simplification of like terms, with this I mean that you operate the numbers with an "i" together and the ones that do not have an "i" together as well. Namely, the 7 and the -4, the -2i with the -9i.
Therefore having the result:

$\frac{ \sqrt{-49} }{3-11i}$

Now, the $\sqrt{-49}$ must be respresented as an imaginary number, and using the multiplication of radicals, we can simplify it to $\sqrt{49} \sqrt{-1}$
This means that we get the result 7i for the numerator.

$\frac{7i}{3-11i}$

In order to rationalize this fraction even further, we have to remember an identity from the previous algebra classes, namely: $x^2 - y^2 =(x+y)(x-y)$
The difference of squares allows us to remove the imaginary part of this fraction, leaving us with a real number, hopefully, on the denominator.

$\frac{7i (3+11i)}{(3-11i)(3+11i)}$

See, all I did there was multiply both numerator and denominator with (3+11i) so I could complete the difference of squares.
See how $(3-11i)(3+11i)= 3^2 -(11i)^2$ therefore, we can finally write:

$\frac{7i(3+11i)}{3^2 - (11i)^2 }$

I'll let you take it from here, all you have to do is simplify it further.
The simplification is quite straightforward, the numerator distributed the 7i. Namely the product $7i(3+11i) = 21i+77i^2$ .
You should know from your classes that i^2 = -1, thefore the numerator simplifies to $-77+21i$
You can do it as a curious thing, but simplifying yields the result:
$\frac{-77+21i}{130}$

7 0

3 years ago

Brainliest! Will give!Felicia had $80 when she went to a music store that charges $18 for each CD. She needs to have no less tha

Tju [1.3M]

3

dfihmuitwkgnuvjneoimndgfmh

3 0

3 years ago

Read 2 more answers

Mr. Nichols put $1,200 in a savings account at a local bank. The simple annual interest rate was 5%. How much interest did his a

satela [25.4K]

$\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\to& \$1200\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ t=years\to &3 \end{cases} \\\\\\ I=(1200)(0.05)(3)\implies I=180$

8 0

3 years ago

determine whether the triangles are similar if so what is the similarity statement and the postulate or theorem used.

zmey [24]

The triangles are similar because of the SAS postulate. The sides are proportional and angle T is equal in both.

6 0

3 years ago