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Vadim26 [7]
3 years ago
9

Write the following quotient in the form a+bi. -7i/2-7i

Mathematics
2 answers:
Helga [31]3 years ago
8 0

Answer:

\large\boxed{\dfrac{49}{53}-\dfrac{14}{53}i}

Step-by-step explanation:

\text{Use}\\\\i=\sqrt{-1}\to i^2=-1\\\\(a-b)(a+b)=a^2-b^2\to(a-bi)(a+bi)=a^2+b^2\\\\\text{distributive property}\ a(b+c)=ab+ac\\---------------------\\\\\dfrac{-7i}{2-7i}=\dfrac{-7i}{2-7i}\cdot\dfrac{2+7i}{2+7i}=\dfrac{-7i(2+7i)}{2^2+7^2}=\dfrac{(-7i)(2)+(-7i)(7i)}{4+49}\\\\=\dfrac{-14i-49i^2}{53}=\dfrac{-14i-49(-1)}{53}=\dfrac{-14i+49}{53}\\\\=\dfrac{49}{53}-\dfrac{14}{53}i

Illusion [34]3 years ago
3 0

Answer:

Write the following quotient in the form a+bi.

-7i/2-7i

Step-by-step explanation:


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A cake has circumference of 25 1/7 inches. What is the area of the cake? Use 22/7 to approximate π. Round to the nearest hundred
choli [55]

Answer:

50.29 in^2

Step-by-step explanation:

From the circumference we need to find the radius.

Since C = 2*pi*r, r = C / (2*pi).

Here, with C = 25  1/7 in, r = (25  1/7 in) / [ 2(22/7) ], or r = 4 in

The area of the cake is A = pi*r^2, or (here)  A = (22/7)(4 in)^2 = 50.29 in^2

5 0
3 years ago
A local company makes a candy that is supposed to weigh 1.00 ounces. A random sample of 25 pieces of candy produces a mean of 0.
AysviL [449]

Answer:

n=(\frac{2.58(0.004)}{0.001})^2 =106.50 \approx 107

So the answer for this case would be n=107 rounded up to the nearest integer

Step-by-step explanation:

Information given

\bar X= 0.996 the sample mean

s=0.004 the sample deviation

n =25 the sample size

Solution to the problem

The margin of error is given by this formula:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}    (a)

And on this case we have that ME =0.001 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

We can use as estimator of the real population deviation the sample deviation for this case \hat \sigma = s/ The critical value for 99% of confidence interval is given by z_{\alpha/2}=2.58, replacing into formula (b) we got:

n=(\frac{2.58(0.004)}{0.001})^2 =106.50 \approx 107

So the answer for this case would be n=107 rounded up to the nearest integer

6 0
3 years ago
Which of the following demonstrates the Commutative Property of Multiplication?
Karolina [17]
I think its c. The communicative property of multiplication state that you can multiply in any order <span />
8 0
3 years ago
Read 2 more answers
PLEASE HELP WILL MARK BRAINLIEST THANK U
Naddika [18.5K]

Answer:

89°

Step-By-Step Explanation:

<WYT is the angle 4

<UYW is the angle 5

since angle 4 and 5 are on the same line and

anngle 4 is 91°,

180° - 91° = 89°

This shows that <UYW is 89°

<em><u>If this helped, please consider picking this answer as the Brainliest Answer. Thank you!</u></em>

3 0
2 years ago
, what does it mean to "substitute" a value into an equation<br> or expression
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Answer: You plug in a value for one of the variables

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x=6 2(6) +2=14

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3 years ago
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