Which of the following equations is an example of direct variation?

Find the product of (x + 3)(x − 3). x2 − 6x + 9 x2 + 6x + 9 x2 + 9 x2 − 9

julia-pushkina [17]

The answer would be x^2-9

3 0

3 years ago

If x and y are two nonnegative numbers and the sum of twice the first ( x ) and three times the second ( y ) is 60, find x so th

stepan [7]

2x+3y=60 solve for x...

x=(60-3y)/2

p=xy^3, using x from above:

p=y^3(60-3y)/2

p=(60y^3-3y^4)/2

dp/dy=(180y^2-12y^3)/2

dp/dy=90y^2-6y^2

dp/dy=0 when:

90y^2-6y^3=0

6y^2(15-y)=0, we know y>0 so

y=15, since x=(60-3y)/2

x=7.5

(We solved it this way because otherwise you get quartic equations and cubic derivatives, yuck :P)

4 0

3 years ago

Read 2 more answers

For each sequence shown find the growth factor or rate of change. 5, 15, 25, 35, 45

olga nikolaevna [1]

The numbers are increasing by positive 10 each time. So the rate of change is 10.

6 0

3 years ago

Express the terms of the following sequence by giving a recursive formula.

emmasim [6.3K]

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

$a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\$

Step-by-step explanation:

First of all, we have to determine if the given sequence is arithmetic sequence or geometric. For that purpose, we calculate the common difference and common ratio

Given sequence is:

11,4,-3,-10,-17...

Here

$a_1 = 11\\a_2 = 4\\a_3 = -3\\So,\\d = a_2 - a_1 = 4-11 = -7\\d = a_3-a_2 = -3-4 = -7$

As the common difference is same, given sequence is an arithmetic sequence.

A recursive formula is a formula that is used to generate the next term of the sequence using the previous term and common difference

So, the recursive formula for an arithmetic sequence is given by:

$a_n = a_{n-1} +d\\Putting\ d = -7\\a_n = a_{n-1}-7$

Hence,

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

$a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\$

Keywords: arithmetic sequence, common difference

Learn more about arithmetic sequence at:

#LearnwithBrainly

6 0

3 years ago

Please help me ASAP!!!! It is greatly appreciated!!! Will mark as Brainliest!!!!

Karo-lina-s [1.5K]

Answer: 5/4

Step-by-step explanation:

6 0

3 years ago