Algebra 1 pleaseeeeeeee help me

Let $a$ and $b$ be nonzero real numbers such that

algol [13]

<h3>Answer: -7/2</h3>

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Explanation:

Let's expand out (2 - 7i)(a + bi) using the FOIL rule

(2 - 7i)(a + bi) = 2a + 2bi - 7ai - 7bi^2

(2 - 7i)(a + bi) = 2a + 2bi - 7ai - 7b(-1)

(2 - 7i)(a + bi) = 2a + 2bi - 7ai + 7b

(2 - 7i)(a + bi) = (2a+7b) + (2bi-7ai)

(2 - 7i)(a + bi) = (2a+7b) + (2b-7a)i

We're told the result is purely imaginary. What this means is that the real part (2a+7b) is zero, while the imaginary part (2b-7a) is nonzero. If both are zero, then we have 0+0i = 0 which is purely real.

For example, the complex numbers 0-7i and 0+2i are purely imaginary.

Let's use the fact that 2a+7b must be zero to do the following steps:

2a+7b = 0

2a = -7b

a = -7b/2

a/b = -7/2 which is the final answer

We must check to see if 2b-7a is nonzero

2b - 7a = 2b - 7(-7b/2)

2b - 7a = 2b + 24.5b

2b - 7a = 26.5b

The result is nonzero if and only if b is nonzero. Luckily we're told b is nonzero at the top of the problem. So we don't have any worries that (2b-7a) is zero.

Therefore, (2a+7b) + (2b-7a)i will be purely imaginary with a/b = -7/2

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A concrete example:

Let a = -14 and b = 4

a/b = -14/4 = -7/2

(2-7i)(a+bi) = (2-7i)(-14+4i) = 0 + 106i which is purely imaginary.

I'll let you do the steps in expanding that out using the FOIL rule.

4 0

1 year ago

What is the probability of getting 6 as a product explanation and calculation

Mrrafil [7]

For an individual die roll, the probability of rolling 6 is \dfrac{1}{6}

6

1

.

Effectively, this problem is asking for P(\text{1st roll is 6}\cap\text{2nd roll is 6})P(1st roll is 6∩2nd roll is 6).

Using the rule of product, this is:

\dfrac{1}{6}\times\dfrac{1}{6}=\dfrac{1}{36}

6

1

×

6

1

=

36

1

.

8 0

2 years ago

A 2-column table has 4 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1. The second column is label

JulijaS [17]

The growth factor of the exponential function represented by the table is 5.

The correct option is c.

<h3>What is the growth factor of the exponential function?</h3>

The growth factor of the exponential function is the ratio of the two consecutive terms (y-values).

The growth factor of the exponential function is given by;

$\rm Growth\ factor=\dfrac{y(x_2)}{y(x_1)}\\\\$

As per given, we have a table;

x y

-2 0.004

-1 0.02

0 0.1

1 0.5

The value $\rm x_2$ is -2 and $\rm x_1$ is -1.

Therefore,

the growth factor of the exponential function represented by the table would be :

$\rm Growth\ factor=\dfrac{y(x_2)}{y(x_1)}\\\ \rm Growth\ factor=\dfrac{y(-1)}{y(-2)}\\\\\rm Growth\ factor=\dfrac{0.02}{0.004}\\\\ \rm Growth\ factor=5$

Hence, the growth factor of the exponential function represented by the table is 5.

To know more about the Growth factor click the link given below.

brainly.com/question/985668

6 0

2 years ago

By hiring 45 new employees, a department store increased its help by 18% during the Christmas season. How many employees did the

bagirrra123 [75]

Hi!

We can set up a proportion then cross multiply to solve this.

$\frac{45}{x} \frac{18}{100}$

45 x 100 = 4500
4500/18 = 250

The answer is 250

Hope this helps! :)

7 0

3 years ago

I need help with this math problem

Alex17521 [72]

your answer is (1,3) but positive

6 0

3 years ago