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Elis [28]
3 years ago
14

Rationalize the denominator of square root of negative 49 over open parentheses 7 minus 2 i close parentheses minus open parenth

eses 4 plus 9 i.
a) -49+2i/-40
b)49+21i/58
c)77+21i/-2
d)-77+21i/130

Mathematics
1 answer:
navik [9.2K]3 years ago
3 0

The answer is the option d, which is: d) \frac{-77+21i}{130}

The explanation for this problem is shown below:

1. Smplify the denominator and rewrite the numerator in this form:

\frac{7i}{7-2i-4-9i} \\\frac{7i}{3-11i}

2. Multiply the denominator and the numerator by the conjugated (3+11i) and simplify the expression, as following:

\frac{7i(3+11i)}{(3-11i)(3+11i)} \\ \frac{21i+77i^{2}}{121+9}  \\ \frac{-77+21i}{130}

3. As you can see, you obtain the expression shown in the option mentioned above.

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5 0
3 years ago
The square of a number is 12 less than 7 times the number. What is the number?
hjlf

<u><em>Answer:</em></u>

The number is either 3 or 4


<u><em>Explanation:</em></u>

Assume that the number we are looking for is x

The square of the number would be x²

7 times the number would be 7x


<u>We are given that:</u>

square of the number (x²) is 12 less than 7 times the number (7x)


<u>Translating this into an equation, we would have:</u>

x² = 7x - 12


<u>Rearranging the quadratic equation:</u>

x² - 7x + 12 = 0


<u>Now, we factor the equation:</u>

(x-4)(x-3) = 0


<u>This means that:</u>

either x-4 = 0 ..................> x = 4

or x-3 = 0 ........................> x = 3


<u>Let's check if any of the solutions is an extrovert:</u>

For x = 3 .............> (3)² = 7(3) - 12 .........> 9 = 21 - 12 .......> 9 = 9 .......> not extrovert

For x = 4 .............> (4)² = 7(4) - 12 .........> 16 = 28 - 12 .....> 16 = 16 ....> not extrovert


Since we have no restrictions on the number, therefore, both solutions would be accepted


Hope this helps :)


7 0
3 years ago
Two mathematical questions attached below.
BartSMP [9]

Answer:

See below

Step-by-step explanation:

9.( {m}^{3}  {n}^{5} )^{ \frac{1}{4} }   \\   =  m^{\frac{3}{4}}n^{\frac{5}{4}}\\  \\ 10. \sqrt[5]{ \sqrt[4]{x} }  \\  =  \sqrt[5]{ {x}^{ \frac{1}{4} } }  \\  =  {( {x}^{ \frac{1}{4} } )}^{ \frac{1}{5} }  \\   =  {x}^{ \frac{1}{4}  \times  \frac{1}{5} }  \\  =  {x}^{ \frac{1}{20} }  \\  \\ \sqrt[5]{ \sqrt[3]{ {a}^{2} } }  \\  =  \sqrt[5]{ {a}^{ \frac{2}{3} } }  \\  =  {( {a}^{ \frac{2}{3} } )}^{ \frac{1}{5} }  \\   =  {a}^{ \frac{2}{3}  \times  \frac{1}{5} }  \\  =  {a}^{ \frac{2}{15} }

4 0
3 years ago
A boy is standing next to a radio. As he moves away from the radio, which would MOST LIKELY occur?
Alexxandr [17]
The last one im pretty sure
5 0
3 years ago
Read 2 more answers
Write an exponential function in the form of y=ab^x passing through the points (0,6) and (2,96)
taurus [48]
Here you have an equation with two unknown constants, a and b, plus 2 sets of points through which the graph goes.

Second point:  96 = a(b)^2
First point:          6 = a(b)^0             Then a = 6.

With a = 6, we can now write:  96 = 6b^2.  Then b^2 = 16, and b=4.

Then y =6(4)^x (answer)

3 0
3 years ago
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