Which complex number lies in the shaded triangle in this graph?

Suppose that the functions f and g are defined for all real numbers x as follows. f(x) = 4x-1 g(x) = 3x write the expressions fo

denis-greek [22]

The result of the operations between the two functions are listed below:

(f - g) (x) = x - 1
(f + g) (x) = 7 · x - 1
(f · g) (- 1) = 15

<h3>How to perform operations between real functions</h3>

In this question we find two functions defined as two linear equations, with which we must make three kinds of operations and evaluate the resulting expression in the third case. The addition, subtraction and multiplication of two functions are defined below:

Addition

(f + g) (x) = f(x) + g(x)

Subtraction

(f - g) (x) = f(x) - g(x)

Multiplication

(f · g) (x) = f(x) · g(x)

Now we proceed to find the result for each case:

(f - g) (x) = (4 · x - 1) - (3 · x)

(f - g) (x) = 4 · x - 1 - 3 · x

(f - g) (x) = x - 1

(f + g) (x) = (4 · x - 1) + 3 · x

(f + g) (x) = 7 · x - 1

(f · g) (x) = (4 · x - 1) · (3 · x)

(f · g) (x) = 12 · x² - 3 · x

(f · g) (- 1) = 12 · (- 1)² - 3 · (- 1)

(f · g) (- 1) = 12 + 3

(f · g) (- 1) = 15

To learn more on operations for functions: brainly.com/question/14996787

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6 0

1 year ago

The multiplicative inverse of -3<br> The additive inverse of -3

TEA [102]

Answer:

multiplicative inverse: -1/3

additive inverse: 3

Step-by-step explanation:

The "multiplicative inverse" is the fancy way to say "reciprocal". It's the number you multiply by to get a result of 1.

The "additive inverse" is the fancy way to say "opposite". It's the number you add to get a result of 0.

5 0

3 years ago

rosa and brett are the only two people in a school election. rosa got 314 votes in the election. she got 18 more votes then bret

elena-s [515]

Answer:

See explantion

Step-by-step explanation:

Given

$Rosa = 314$

$Brett = 18\ more$

The question is incomplete as what is required is missing from the question. I'll solve on a general term

A possible question is: Determine the total number of votes by Brett

We have that:

$Brett = 18\ more$

So:

$Brett = 18 + Rosa$

Substitute 314 for Rosa

$Brett = 18 + 314$

$Brett = 332$

Another possible question is: Determine the total number of voters.

This is done by:

$Total = Brett + Rosa$

$Total = 332 + 314$

$Total = 646$

4 0

3 years ago

PLEASE HELP! Solve equations below.

wel

Solve them all? Or are these options

6 0

3 years ago

On May 3, 1999, 59 tornadoes hit a certain state in the largest tornado outbreak ever recorded for that state. Sixteen of these

pishuonlain [190]

The question is incomplete, here is the complete question:

On May 3, 1999, 59 tornadoes hit a certain state in the largest tornado outbreak ever recorded for that state. Sixteen of these were classified as strong (F2 or F3) or violent (F4 or F5). Length of Path (miles) Intensity:

a. 7 F.

b. 9 F2.

c. 16 F3.

d. 11 F3.

e. 8 F2.

f. 9 F2.

g. 5 F2.

h. 16 F4.

i. 15 F3.

j. 38 F5.

k. 42 F4.

l. 3 F2.

m. 8 F2.

n. 1 F2.

o. 14 F3.

p. 23 F3.

Part (a) Make a box and whisker plot

Part (b) Identify outliners. Remove them and redraw the box and whisker diagram

Part (c) How does the removal of outliners effect box and whisker plot? How does is effect the median of the set?

Answer:

Given below with explanations

Step-by-step explanation:

(a)

The data is first arranged in ascending order:

1, 3, 5, 7, 8, 8, 9, 9, 11, 14, 15, 16, 16, 23, 38, 42

Total values = 16

Minimum value = 1

Maximum value = 42

Lower Quartile = 1/4 x 16 = 4th value = 7 (1, 3, 5, 7, 8, 8, 9, 9, 11, 14, 15, 16, 16, 23, 38, 42)

Upper Quartile = 3/4 x 16 = 12th value = 16 (1, 3, 5, 7, 8, 8, 9, 9, 11, 14, 15, 16, 16, 23, 38, 42)

Median = 1/2 x 16 = 8th value = 9 (1, 3, 5, 7, 8, 8, 9, 9, 11, 14, 15, 16, 16, 23, 38, 42)

The Box and whisker plot is attached in the picture below:

(b)

Outliners are 38 and 42

1, 3, 5, 7, 8, 8, 9, 9, 11, 14, 15, 16, 16, 23

Total values = 14

Minimum value = 1

Maximum value = 23

Lower Quartile = 1/4 x 14 = 3.5th value = 6 (1, 3, 5, 7, 8, 8, 9, 9, 11, 14, 15, 16, 16, 23)

(5+7)/2

Upper Quartile = 3/4 x 14 = 10.5th value = 14.5 (1, 3, 5, 7, 8, 8, 9, 9, 11, 14, 15, 16, 16, 23)

(14+15)/2

Median = 1/2 x 14 = 7th value = 9 (1, 3, 5, 7, 8, 8, 9, 9, 11, 14, 15, 16, 16, 23)

The Box and whisker plot is attached in the picture below:

(c)

The lower and upper quartile values have changed after removing the outliners but the median remains same in this case

7 0

3 years ago