Which property was used to simplify the expression?

The average annual salary of the employees of a company in the Year 2005 was $70,000. It increased by the same factor each year

Novosadov [1.4K]

Answer:

$f(x)=70(1.17)^x$

Step-by-step explanation:

x is time in years

f(x) represent the average annual salary in thousand dollars

We are given

The average annual salary of the employees of a company in the Year 2005 was $70,000

We can use exponential formula

$f(x)=a(b)^x$

Since, time starts from 2005

So, at x=0 , f(x)=70

we can use it

$70=a(b)^0$

$a=70$

in 2006 the average annual salary was $82,000

So, in x=2006-2005=1

f(x)=82

we can plug it and find b

$82=70(b)^1$

$b=\frac{41}{35}$

$b=1.17$

now, we can plug it back

and we get

$f(x)=70(1.17)^x$

6 0

4 years ago

Read 2 more answers

An inspector found 40 defective batteries during an inspections. If this is 2.5% of the total number of batteries inspected, how

Gemiola [76]

Answer: 1600batteries

Step-by-step explanation:

Let the number of inspected battery be y

2.5% of y = 40

5/2% of y = 40

Change 5/2% to fraction

5/200 × y = 40

5y/200=40

Cross multiply

5y= 40×200

5y=8000

y=8000÷5

y=1600

The total number of battery inspected is 1600.

7 0

3 years ago

Which of the following equations is equivalent to x^2 - 8x = 16?

Minchanka [31]

The equation x² - 8x = 16 will equal to (x - 4)² = 32 so option (C) will be correct.

<h3> What is an expression?</h3>

An expression is a mathematical proof of the equality of two mathematical expressions.

Expressions are collections of variables, numbers, addition, subtraction, multiplication, and division.

A statement expressing the equality of two mathematical expressions is known as an equation.

Given,

x² - 8x = 16

x² - 8x - 16 = 0

Add and subtract 16 to the left-hand side

(x² - 8x +16) - 16 - 16 = 0

(x - 4)² - 32 = 0

(x - 4)² = 32

Hence the expression (x - 4)² = 32 will equal to x² - 8x = 16 .

To learn more about expression

brainly.com/question/14083225

#SPJ1

3 0

2 years ago

catering service offers 8 appetizers, 11 main courses, and 7 desserts. A banquet committee is to select 7 appetizers, 8 main

guapka [62]

Answer: The required number of ways is 46200.

Step-by-step explanation: Given that a catering service offers 8 appetizers, 11 main courses, and 7 desserts.

A banquet committee is to select 7 appetizers, 8 main courses, and 4 desserts.

We are to find the number of ways in which this can be done.

We know that

From n different things, we can choose r things at a time in $^nC_r$ ways.

So,

the number of ways in which 7 appetizers can be chosen from 8 appetizers is

$n_1=^8C_7=\dfrac{8!}{7!(8-7)!}=\dfrac{8\times7!}{7!\times1}=8,$

the number of ways in which 8 main courses can be chosen from 11 main courses is

$n_2=^{11}C_8=\dfrac{11!}{8!(11-8)!}=\dfrac{11\times10\times9\times8!}{8!\times3\times2\times1}=165$

and the number of ways in which 4 desserts can be chosen from 7 desserts is

$n_3=^7C_4=\dfrac{7!}{4!(7-4)!}=\dfrac{7\times6\times5\times4!}{4!\times3\times2\times1}=35.$

Therefore, the number of ways in which the banquet committee is to select 7 appetizers, 8 main courses, and 4 desserts is given by

$n=n_1\times n_2\times n_3=8\times165\times35=46200.$

Thus, the required number of ways is 46200.

7 0

4 years ago

Please answer asap if u know the answer!!!! completing a square. thank you!!!!

Tema [17]

Answer:

D

Step-by-step explanation:

The equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form using the method of completing the square.

Given

f(x) = 3x² - 24x + 10

We require the coefficient of the x² term to be 1 , thus factor out 3

3(x² - 8x) + 10

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² - 8x

= 3(x² + 2(- 4)x + 16 - 16) + 10

= 3(x - 4)² + (3 × - 16) + 10

= 3(x - 4)² - 48 + 10

= 3(x - 4)² - 38, thus

f(x) = 3(x - 4)² - 38 ← in vertex form

3 0

4 years ago