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3 years ago

Multiply (9 − 4i)(2 + 5i).

Mathematics

2 answers:

Verdich [7]3 years ago

7 0

Answer:

38+37i

Step-by-step explanation:

(9 − 4i)(2 + 5i)= 18+45i-8i-20i²= 18+20+37i= 38+37i

lara [203]3 years ago

5 0

Answer:

38 + 37i

Step-by-step explanation:

(9 − 4i)(2 + 5i)

FOIL

first: 9*2 = 18

Outer: 9*5i = 45i

inner: -4i * 2 = -8i

last : -4i * 5i = -20i^2 = -20(-1) = 20

Combine together

18+45i-8i +20

38 + 37i

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Determine whether the three points are collinear.<br> (0, - 10). (-3,- 13), (2,-8)

LUCKY_DIMON [66]

Answer:

<h2>YES. These points are collinear.</h2>

Step-by-step explanation:

If three points are collinear, then the slopes are the same.

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

For (0, -10) and (-3, -13):

$m=\dfrac{-13-(-10)}{-3-0}=\dfrac{-13+10}{-3}=\dfrac{-3}{-3}=1$

For (-3, -13) and (2, -8):

$m=\dfrac{-8-(-13)}{2-(-3)}=\dfrac{-8+13}{2+3}=\dfrac{5}{5}=1$

We can check the last pair (0, -10) and (2, -8):

$m=\dfrac{-8-(-10)}{2-0}=\dfrac{-8+10}{2}=\dfrac{2}{2}=1$

5 0

3 years ago

A hiker climbs a 5-mile trail up a mountain in 2 hours. On the return trip downhill, she walks the same trail and returns to her

Ivahew [28]

Answer:

3.33 miles per hour

Step-by-step explanation:

The total distance traveled by the hiker is 5 * 2 = 10 miles, and the total time travelled is 2 + 1 = 3 hours.

So, to find the average speed of the entire trip, we can use the formula:

distance = speed * time

With distance = 10 and time = 3, we have:

10 = speed * 3

speed = 10/3 = 3.33 miles per hour.

7 0

3 years ago

Which statements about the graph of the function f(x) = 2x2 – x – 6 are true? Select two options.

natka813 [3]

Answer:

D and C

Step-by-step explanation:

Took the quiz

5 0

3 years ago

Read 2 more answers

Find the value of x

ad-work [718]

Answer:
18

It’s literally 72 divided by 4 which equals 18

7 0

4 years ago

phyllis invested 66000 dollars, a portion earning simple interest rate of 5% per year and the rest earning a rate of 7% per year

Lelechka [254]

<u>Answer: </u>

Physliis invested 32000 dollar at 5% interest rate and 34000 dollar at 7% interest rate.

<u>Solution:</u>

Let Phyllis invest ‘x’ dollar at 5% per year and (66000-x) dollar at 7% per year.

We know,

$\text { Simple interest }=\frac{\text {Principal} \times r a t e \times T i m e}{100}$

In the question it is given that Simple interest earned from both the investments at the end of the year is $3980.

Using the given below equation, we will try to find out the investments at each rate.

$\begin{array}{l}{\frac{x \times 5 \times 1}{100}+\frac{(66000-x) \times 7 \times 1}{100}=3980} \\\\ {\frac{5 x}{100}+\frac{462000-7 x}{100}=3980} \\\\ {\frac{5 x+462000-7 x}{100}=3980} \\\\ {-2 \mathrm{x}+462000=3980 \times 100} \\\\ {-2 \mathrm{x}=398000-462000} \\\\ {-2 \mathrm{x}=-64000} \\\\ {\mathrm{x}=\frac{-64000}{-2}}\end{array}$

x = 32000

We can calculate amount for 7% interest rate by,

(66000-32000) =34000

Thus Phyllis invested 32000 dollar at 5% interest rate and 34000 dollar at 7% interest rate.

8 0

3 years ago