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1 year ago

For f(x)=4x+1 and g(x) = x^2 - 5, find (f+g)(x).

Mathematics

1 answer:

Rus_ich [418]1 year ago

3 0

Answer:

(f + g)(x) = x² + 4x - 4

Step-by-step explanation:

The statement (f + g)(x) is the same as f(x) + g(x). In other words, the question simply wants you to add the two functions together.

f(x) = 4x + 1

g(x) = x² - 5

(f + g)(x) <----- Original statement

f(x) + g(x) <----- Rewrite

(4x + 1) + (x² - 5) <----- Substitute the equations in f(x) and g(x)

4x + x² - 4 <----- Add 1 and -5

x² + 4x - 4 <----- Rearrange the terms

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There are 5 cards with a picture of a rose and 3 cards with a picture of a daisy. Alia keeps all the cards down on a table with

Furkat [3]

Answer:

P = 4/7

Step-by-step explanation:

There are 5 cards with a picture of a rose and 3 cards with a picture of a daisy.

Then we have a total of 8 cards.

Now Alia turns over one card, and this card has a picture of a rose, then she removes it.

This means that now there are 4 cards with a picture of a rose and 3 cards with a picture of a daisy, so now we have a total of 7 cards.

We want to find the probability that the next turned card has also a rose on it.

This will be equal to the quotient between the number of cards with a rose on it (4 cards) and the total number of cards (7)

Then the probability is:

P = 4/7

3 0

3 years ago

What is i^84? a) -i b) i c) -1 d) 1

mariarad [96]

Answer:

D) 1

Step-by-step explanation:

When you start raising i to certain powers, you begin to notice a pattern.

$i^1=i \\\\i^2=-1 \\\\i^3=-i \\\\i^4=1 \\\\i^5=i \\\\ i^6=-1 \\\\ i^7=-i \\\\i^8= 1$

This cycle repeats forever. Since 84 is a multiple of 4, i^84 must be 1. Hope this helps!

7 0

3 years ago

What is the value of x?

blsea [12.9K]

Since these are supplementary angles (two angles which sum to 180°) we can say:

4x+x=180 combine like terms on left side

5x=180 divide both sides by 5

x=36°

3 0

3 years ago

A store is having a sale. You can buy 14 cards for $6. What is the cost of 35 cards during this sale?

skad [1K]

Answer:

15$

Step-by-step explanation:

14=$6

35=6*35/14

5 0

3 years ago

Help me with these questions

Elena L [17]

Answer: a = 4, b = 163,422

Step-by-step explanation:

$P = P_{0} e^{kt}$ P is the new population, P₀ is the initial population, k is the growth rate, t is the time elapsed.

Part a) What do we know?

P = 7003

P₀ = unknown

k = .21 (converted 21% into a decimal)

t = 36 yrs (2006 - 1970)

$P = P_{0} e^{kt}$ need to solve for P₀

$7003 = P_{0} e^{(.21)(36)}$

$7003 = P_{0} e^{7.56}$

7003 = P₀ (1920)

$\frac{7003}{1920} = P_{0}$

3.6 = P₀

rounded to the nearest whole number = 4

Part b) What do we know?

P = unknown

P₀ = 7003

k = .21 (converted 21% into a decimal)

t = 15 yrs (2021 - 2006)

$P = P_{0} e^{kt}$ need to solve for P₀

$P = 7003 e^{(.21)(15)}$

$P = 7003 e^{3.15}$

P = 7003(23.33)

P = 163,422.46

rounded to the nearest whole number = 163,422

*************************************************************

Answer: 2, -1

Step-by-step explanation:

eˣ² = eˣ * e²

eˣ² = eˣ⁺²

x² = x + 2

x² - x - 2 = 0

(x - 2)(x + 1) = 0

x - 2 = 0 or x + 1 = 0

x = 2 or x = -1

Check both answer for validity:

eˣ² = eˣ⁺²

e⁴ = e⁴ or e¹ = e¹

TRUE TRUE

*****************************************

Answer: 0 = ln 1

Step-by-step explanation:

$e^{-10} = \frac{1}{e^{10}}$

$ln(e^{-10}) = ln(\frac{1}{e^{10}})$

-10 = ln 1 - 10 log rules say division is subtraction

0 = ln 1

5 0

3 years ago