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3 years ago

30 POINTS

Mathematics

1 answer:

Romashka [77]3 years ago

7 0

calculating each of the products

noting that i² = (√- 1 )² = - 1

(1 + 2i)(8i) ( distribute by 8i )

= 8i + 16i² = - 16 + 8i ← complex number

(1 + 2i)(2 - 5i) ( expand using FOIL )

= 2 - 5i + 4i - 10i²

= 2 - i + 10 = 12 - i ← complex number

(1 + 2i)(1 - 2i) ( expand using FOIL )

= 1 - 2i + 2i - 4i²

= 1 + 4 = 5 ← real number

(1 + 2i)(4i) ( distribute by 4i )

= 4i +8i² = - 8 + 4i ← complex number

(1 + 2i)(1 - 2i) is the only product which results in a real number

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Elle wanted to order candy online. Company A is offering 2 1/2 pounds of chocolate for $32.50, while Company B is offering 2 3/4

podryga [215]

To determine price per lb, divide dollar amount by lbs.
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4 years ago

At the school bookstore, Quinn purchased a binder for $4.75 and 4 pens for $0.79 each. What was Quinn's total cost.

gregori [183]

Answer:

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Step-by-step explanation:

4.75 + .79(4)

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7.91

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4 years ago

What are the values of a, b and c in the quadratic equation -2x^2+4x-3=0?

AlladinOne [14]

Answer:

$a=-2\\b=4\\c=-3$

Step-by-step explanation:

In a quadratic equation in the Standard form

$ax^2+bx+c=0$

You need to remember that "a", "b" and "c" are the numerical coefficients (Where "a" is the leading coefficient and it cannot be zero: $a\neq0$ ).

You can observe that the given quadratic equation is written in the Standard form mentioned before. This is:

$-2x^2+4x-3=0$

Therefore, you can identify that the values of "a", "b" and "c" are the following:

$a=-2\\b=4\\c=-3$

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4 years ago

Read 2 more answers

Tickets at a particular movie theater have different rates for adults and children. On Friday, the theater sold 4 adult tickets

Thepotemich [5.8K]

Answer: The price for the adult tickets is $12 and the price for the child ticket is $5.

Step-by-step explanation:

Let the price for the adult ticket be x

Let the price for the child ticket be y

According to question, On Friday ,

$4x+7y=83$

and on next day,

$5x+6y=90$

Now, we will use "Substitution Method" to solve the system of equations :

$5x+6y=90\\\\5x=90-6y\\\\x=\frac{90-6y}{5}$

so, we will put the value of x in the first equation i.e.

$4x+7y=83\\\\4(\frac{90-6y}{5})+7y=83\\\\360-24y+35y=83\times 5\\\\35y-24y=415-360\\\\11y=55\\\\y=\frac{55}{11}\\\\y=5$

Now, put the value of y in the equation that is given by

$x=\frac{90-6y}{5}\\\\x=\frac{90-6\times 5}{5}\\\\x=\frac{90-30}{5}\\\\x=\frac{60}{5}\\\\x=\$12$

Hence, the price for the adult tickets is $12 and the price for the child ticket is $5.

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3 years ago

Answer with the explanation step by step

andrey2020 [161]

Answer:

The answer is A. $\frac{3(x-21)}{(x+7)(x-7)}$ .

Step-by-step explanation:

To find the difference of this problem, start by simplifying the denominator, which will look like $\frac{3}{x+7}-\frac{42}{(x+7)(x-7)}$ . Next, multiply $\frac{3}{x+7}$ by $\frac{x-7}{x-7}$ to create a fraction with a common denominator in order to subtract from $\frac{42}{(x+7)(x-7)}$ . The problem will now look like $\frac{3}{x+7}*\frac{x-7}{x-7}-\frac{42}{(x+7)(x-7)}$ .

Then, simplify the terms in the problem by first multiplying $\frac{3}{x+7}$ and $\frac{x-7}{x-7}$ , which will look like $\frac{3(x-7)}{(x+7)(x-7)}-\frac{42}{(x+7)(x-7)}$ . The next step is to combine the numerators over the common denominator, which will look like $\frac{3(x-7)-42}{(x+7)(x-7)}$ .

Next, simplify the numerator, and to simplify the numerator start by factoring 3 out of $3(x-7)-42$ , which will look like $\frac{3(x-7-14)}{(x+7)(x-7)}$ . Then, subtract 14 from -7, which will look like $\frac{3(x-21)}{(x+7)(x-7)}$ . The final answer will be $\frac{3(x-21)}{(x+7)(x-7)}$ .

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3 years ago