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IRINA_888 [86]
3 years ago
12

To vertoes of a rectangle gre

Mathematics
1 answer:
Mariana [72]3 years ago
3 0

Answer:

we have standard deviation of 12 so 298-322 would be 34.1% times 2 which is 68.2%.  We also have 12 more in a lower region and we can use normal distribution to find that it would be 13.6% + 68.2%

Answer is 81.8%

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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
Which algebraic expression could NOT represent the phrase below?
skad [1K]

Answer:

B

Step-by-step explanation:

because 4 and 3 are grouped together you would add them first. this would change the outcome of the problem.

6 0
3 years ago
Read 2 more answers
Which of the following is a proportion?
poizon [28]

Answer:

Option C, 14/21=9/21 is the proportion.

Step-by-step explanation:

Given:

a.5/7 = 10/12

b.9/15 = 12/18

c.4/6 = 8/12

d.14/21 = 9/12

We have to find the proportions.

In proportion two ratios are equal, as it has an equality sign in between so both side must be of same ratio in its simplest form.

Let's work with option C

⇒ \frac{4}{6}=\frac{8}{12}

To find the simplest form we have to divide the numerator and denominator with same digit (or its factor).

Simplest form of  \frac{8/2}{12/2} = \frac{4}{6} , \frac{4/2}{6/2}= \frac{2}{3}

Simplest form of \frac{4}{6} = \frac{2}{3}

Both sides in option C have equal ratios of 2/3.

So 4/6=8/12 is in proportion.

6 0
3 years ago
Which scenario shows the best example of intrinsic motivation? O Zareem takes good notes in class to know the lesson better. O Y
dedylja [7]

Answer:

The first one. Zareem takes good notes in class to know the lesson better

5 0
3 years ago
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How many 6 ounce cups can you completely fill using a package of Kool-aid that makes two quarts Remember that there are 32fl oz
aliya0001 [1]
You can completely fill 10 cups
4 0
3 years ago
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