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valkas [14]
3 years ago
9

Which expression is equivalent to (4 + 7¡)(3 + 4¡)?

Mathematics
1 answer:
jarptica [38.1K]3 years ago
5 0

Answer:

37i-16

Step-by-step explanation:

(4+7i)(3+4i)

12+21i+16i+28i^2

12+37i+28(-1)

37i+12-28

37i-16

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3 years ago
50 POINTS WILL GIVE BRAINIEST. Which of the following numbers are irrational?
Otrada [13]

Answer:

\sf \dfrac{\pi}{3}\:\:and\:\:\sqrt[\sf 3]{\sf 25}

Step-by-step explanation:

<u>Definitions</u>

Integer: A whole number that can be positive, negative, or zero.

Rational Number: A number that can be expressed as the ratio of two integers (where the denominator does not equal zero).

Irrational Number: A real number that <u>cannot</u> be written as a rational number.

\sf -8.2183 \times 10000=-82183

\implies \sf -8.2183=-\dfrac{82183}{10000}

Therefore, -8.2183 can be expressed as a <u>rational number</u>.

π is an <u>infinite decimal</u>, so it cannot be expressed as a rational number.  

\textsf{Therefore},\:\dfrac{\pi}{3}\:\textsf{is irrational}.

\sqrt[\sf 3]{\sf 25} is an irrational number.

\sf 9+ \sqrt{4}=9+\sqrt{2^2}=9+2=11

As 11 can be expressed as ¹¹/₁ then 9 + √4 is <u>rational</u>.

<u>Conclusion</u>

Therefore, the numbers that are irrational are:

\sf \dfrac{\pi}{3}\:\:and\:\:\sqrt[\sf 3]{\sf 25}

8 0
2 years ago
Can anyone help me? Which function is graphed on the right?
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<h2>Answer:</h2>

y=2^{\left(x-2\right)}+3

<h2>Step-by-step explanation:</h2>

To solve this problem, we need to start with the parent function of the exponential function, which is f(x)=a^x, where a is the base. In our problem, a=2, so our parent function here is y=2^x. Then, we need to perform some transformations to our parent function. Thus:

1. Vertical shrink:

A vertical shrink is a nonrigid transformation because the graph of the function get a distortion in the shape, so this transformation is as follows:

g(x)=cf(x)

where c in this problem equals 0.25 because:

y=0.25(2^x) \\ \\ y=\frac{1}{4}(2^x) \\ \\ y=\frac{2^x}{2^2} \\ \\ y=2^{(x-2)}

2. Vertical shift:

The graph of the function y=2^{(x-2)} get a vertical shift given by:

y=2^{(x-2)}+3

So the graph is shifted 3 units up. So the result is the graph shown above.

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matrices can be simple added by ading the adjacent elements of the two matrices

The matrix multiplication is done by multiplying row of first matrix to columns of the other matrix.

each multiplication for each element of the resultant matrix.

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