if a function f is defined such that f(x+3) = f (x) + f(3) show that f(-3) = -f(3)

Answers

Answer 1

Answer:

[tex]Solution,\\f(x+3)=f(x)+f(3).......(1)\\Put~x=0~in~eq^n~(1),\\f(0+3)=f(0)+f(3)\\or, f(3)=f(0)+f(3)\\or, f(0)=0.........(2)\\Now,\\Put~x=-3~in~eq^n(1),\\f(-3+3)=f(-3)+f(3)\\or, f(0)=f(-3)+f(3)\\From~eq^n(2),\\0 = f(-3)+f(3)\\or, f(-3)=-f(3)~proved[/tex]


Related Questions

Solve the equation 2(x-3) = 14

Answers

The answer is X=10.

Help me from 3 through 8

Answers

Answer:

3)x=−9  and x=4

4)x=−12  and x=−5

5)x=8  and x=14

6)x=−7  and x=3

7)x=-1 2/3 and x = 1/4

8)x=2/5

Step-by-step explanation:

Hope this helps

subtract 10x^2-10x+2 from -8x^2+7x-7

Answers

Answer:

-18x^2+17x-9

Step-by-step explanation:

it cost 0.60 cents to run a fan for 4 hours how much does it cost to run the fan for 6 hours I need an answer asap

Answers

Answer:

$0.90

Step-by-step explanation:

So first you need to find the rate (showing how much money it costs to run for 1 hour) so you get 0.60 and divide it by 4 and its 0.15, then multiply 0.15 by 6 and get 0.90

Calculate the sample mean and sample variance for the following frequency distribution of heart rates for a sample of American adults. If necessary, round to one more decimal place than the largest number of decimal places given in the data. Heart Rates in Beats per Minute Class Frequency 51 - 58 6 59 - 66 3 67 - 74 11 75 - 82 13 83 - 90 4

Answers

Answer:

[tex]Mean = 68.9[/tex]

[tex]s^2 =18.1[/tex] --- Variance

Step-by-step explanation:

Given

[tex]\begin{array}{cccccc}{Class} & {51-58} & {59-66} & {67-74} & {75-82} & {83-90} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}[/tex]

Solving (a): Calculate the mean.

The given data is a grouped data. So, first we calculate the class midpoint (x)

For 51 - 58.

[tex]x = \frac{1}{2}(51+58) = \frac{1}{2}(109) = 54.5[/tex]

For 59 - 66

[tex]x = \frac{1}{2}(59+66) = \frac{1}{2}(125) = 62.5[/tex]

For 67 - 74

[tex]x = \frac{1}{2}(67+74) = \frac{1}{2}(141) = 70.5[/tex]

For 75 - 82

[tex]x = \frac{1}{2}(75+82) = \frac{1}{2}(157) = 78.5[/tex]

For 83 - 90

[tex]x = \frac{1}{2}(83+90) = \frac{1}{2}(173) = 86.5[/tex]

So, the table becomes:

[tex]\begin{array}{cccccc}{x} & {54.5} & {62.5} & {70.5} & {78.5} & {86.5} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}[/tex]

The mean is then calculated as:

[tex]Mean = \frac{\sum fx}{\sum f}[/tex]

[tex]Mean = \frac{54.5*4+62.5*3+70.5*11+78.5*13+86.5*4}{6+3+11+13+4}[/tex]

[tex]Mean = \frac{2547.5}{37}[/tex]

[tex]Mean = 68.9[/tex] -- approximated

Solving (b): The sample variance:

This is calculated as:

[tex]s^2 =\frac{\sum (x - \overline x)^2}{\sum f - 1}[/tex]

So, we have:

[tex]s^2 =\frac{(54.5-68.9)^2+(62.5-68.9)^2+(70.5-68.9)^2+(78.5-68.9)^2+(86.5-68.9)^2}{37 - 1}[/tex]

[tex]s^2 =\frac{652.8}{36}[/tex]

[tex]s^2 =18.1[/tex] -- approximated

What is the value of the expression? 21.18
÷
6 =

ASAP PLEASE

Answers

Answer:

3.53

Step-by-step explanation:

I checked it using a calculator. :)


So far, Monica has read ã of a book. She
has read the same number of pages each
day for 5 days. What fraction of the book
does Monica read each day?

Answers

How many pages are their?

A coffee pot had 1
1/2 pints of coffee.
After a mug was
filled, there were 1
pint left in the pot.
How many ounces of
coffee were in the
mug?

Answers

Answer:

8 ounces

Step-by-step explanation:

Since there was 1 pint left, that means the mug had 1/2 pints of coffee.

Now, convert this to ounces. There are 16 ounces in a pint, so we can find how many ounces there were by multiplying 16 by 1/2

16(1/2)

= 8

So, there were 8 ounces of coffee in the mug

-7(y – 5) + 8 = -27
help?

Answers

Answer:

10

Step-by-step explanation:

-7y + 35 + 8 = -27

collect like terms

-7y = -27 - 35 - 8

-7y = -70

y= -70/-7

y= 10

10 is the answer because u are combining like terms

What type of jobs offer commissions?

Answers

Answer:

Sales Engineers. ...

Wholesale and Manufacturing Sales Representatives. ...

Securities, Commodities, and Financial Services Sales Agents. ...

Advertising Sales Agent. ...

Insurance Sales Agent. ...

Real Estate Brokers and Sales Agents. ...

Travel Agents.

Step-by-step explanation:

What type of jobs offer commissions?

-Sales Engineers

-Wholesale and Manufacturing Sales Representatives

-Securities, Commodities, and Financial Services Sales Agents

-Advertising Sales Agent

-Insurance Sales Agent

-Real Estate Brokers and Sales Agents

-Travel Agents

Change x+2y=-6 into y=mx+b form

Answers

The answer would be Y= -1/2x-3

Answer:

y = -3 - x/2

Step-by-step explanation:

x + 2y = -6  

You have to isolate y by minusing x on both sides

2y = -6 - x    

Then you will isolate y by dividing both sides by 2

y = -3 - x/2

12 children in art class have to share 8 packages of clay so that everyone gets the same amount. How much clay can each child have?

Answers

Answer:8 y sobran 4

Step-by-step explanation:

8entre  4

Answer:

1.5

Step-by-step explanation:

Solve this system by substitution. y = 3x - 12 6x + y = 6 *Remember to write your answer as a coordinate voint (x, y).​

Answers

6x+1(3x-12)=6
6x+3x-12=6
9x-12=6
+12= 18/9 x=2

Y=6-12
Y=-6 (2,-6

Which is the slowest reading rate?
A. 3 pages in 9 minutes
B. 4 pages in 10 minutes
C. 5 pages in 13 minutes
D. 7 pages in 20 minutes

Answers

Answer:

A. 3 pages in 9 minutes

Step-by-step explanation:

3 & 9 are all the lowest out of those options.

If 3/4 pounds of Fudge coast $6. 75, how much does 1 pound cost. Write as an equation.

Answers

Divide 6.75 by 4 then you know the unit rate then multiply that by 4

What is the distance between the points (2, 1) and (14, 6) on a coordinate
plane?

Answers

Answer:

the answer is 13 units

Step-by-step explanation:

60÷(63÷7)=
I don't understand plz help​

Answers

Answer:

answer is simple

first we will solve the bracket

(63÷7)

it is 9

and then 60÷ 9

which gives 6.67

Help me pls pls pls

Answers

Answer:

1.61

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.61

The value of a boat is depreciating at a rate of 7% per year. In 2006, the boat was worth $17,300. Find the value of the boat in 2011. Enter the exponential decay function for this situation.
The exponential decay function is y = .

In 2011 the boat will be worth $ .

Answers

Answer:

Step-by-step explanation:

[tex]V=Ar^t\\ \\ V=17300((100-7)/100)^t\\ V=17300(0.93)^{(y-2006)}\\ V(2011)=17300(0.93)^{(2012-2006)}=\$ 11192.29[/tex]

Pls help!!! Will mark Brainiest!

Factor each expression using the GCF. Check your work using the Distributive Property.
9. 3x + 12
10. 6x - 30
11. 20x - 16
12.-50x + 80
13. 77 + 22x
14. 21x - 14

Answers

Answer:

9.3(x+4)

10.6(x-5)

11.4(5x-4)

12.-10(5x-8)

13.11(7+2x)

14.7(3x-2)

Step-by-step explanation:

Brainliest to best answer :D
The difference of two numbers is 63. The sum of two numbers is 111. What are the two numbers?

Answers

Answer:

Step-by-step explanation:

Let b>a

b-a=63

b=63+a

a+b=111, substituting 63+a from above in this equation gives you

a+63+a=111

2a+63=111

2a=48

a=24, since b=63+a

b=63+24

b=87 so the two numbers are

24 and 87

Please help I don't get this question

Answers

The first one: 10x+30

Answer:

10x+30

Step-by-step explanation:

Distributive property is distributing what is in the parentheses.

To do that on this problem you have multiply each of these numbers by 10!

10 times x is 10x

10 times 3 is 30

Put them back together and you get 10x+30!

I hope this helps, and have a great day! :)

P.S. If you need a better explanation I can help. I just didn't want to make this to long.  :D

Which amount is greater, 5 feet or 2 yards?

Answers

Answer:

2 yards is greater then 5 feet

Step-by-step explanation:

A yard is 3 feet, 3+3=6     I hope this helps!

A shoe store uses a 60​% markup for all of the shoes it sells. What would be the selling price of a pair of shoes that has a wholesale cost of ​$55​?

Answers

The selling price should be $88

Given that,

The markup percentage is 60% and the wholesale cost is $55.

calculation:

= $55 + (60% of $55)

= $55 + $33

= $88

Learn more about the price here: https://brainly.com/question/25300841?referrer=searchResults

Answer:

88

Step-by-step explanation:

work out yhe value of 6.105×10^8/3.7×10^3 give your answer in standard form​

Answers

1.65 x 10^11

Hope this helps

Which expression shows another way to write 36+16?
4(9)+4
4(9+4)
6(6+8)
(6+4)(6+4)

Answers

Answer:

36+16= 52

4(9)+4= 40, which does not equal 52.

4(9+4) = 52.

6(6+8) = 84, which does not equal 52.

(6+4)(6+4) = 100, which does not equal 52.

So, 4(9+4) is correct.

Let me know if this helps!

What is the product of 3.6 x 4.2

Answers

Answer:

15. 12

Step-by-step explanation:

just multiply them

21< -4+5x Hurry I need it ​

Answers

x=5
uhhhhh because yea

You are given the following equation: (x+3)^2 + (y+9)^2 = 144 What is the
(h,k)

Answers

Answer:

Step-by-step explanation:

Equation of circle: (x - h)² + (y -k)² = r²

(x+ 3)² + (y + 9)² = 144

(x+ 3)² + (y + 9)² = 12²

h = -3 ; k = -9

it takes 15 cups of water to fill 1/3 bucket. How much water is needed to fill 1 bucket?

Answers

Answer: 15/(1/3) = X/ 1
15 ÷1\3 = 15 x 3 =45 cups

Hope this helps (:

Answer:

45 cups

Step-by-step explanation:

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