Look at this info about a pair of numbers, k and n.k < n
And k(squared) > n(squared)
Give and example of what the numbers could be. k = ? And n = ?
Please answer clearly so I can understand!

Answers

Answer 1

Answer: $k=-2,n=1\nk=-8,n=5\n k=-(1)/(4),n=(1)/(7)$

Answer 2

Answer: both the numbers should be negative and k should be less than n.
any pair satisfies above condition is a solution.

Reason: Take any two +ve numbers a,b with a>b then a²>b².
inequality sign(> or < ) get reversed only if the number are -ve.

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What is the solution of the system? Use elimination.
3x - 4y = 9
-3x + 2y = 9

Answers

You add two equations together to eliminate a variable. This particular problem is nice, because it's already setup to eliminate X.

3x - 4y = 9
-3x + 2y = 9

When we add these two together, 3x - 3x cancels each other out, leaving us with 0x, or nothing.

We continue with -4y + 2y (leaves us with -2y) and 9+9 (18).

-2y = 18

18/-2 = -9.

Now we have y = -9, and we can go back into the problems to solve for x.

3x - 4(-9) = 9

3x + 36 = 9.

3x = -27

x = -9.

Confirm with the final equation:

-3(-9) + 2(-9) = 9
27 - 18 = 9
9 = 9 --- Confirmed.

Answer:

[-9, -9]

Step-by-step explanation:

Here is how the Eliminasyon Metòd is done:

{3x- 4y = 9

{-3x+ 2y = 9

--------------

-2y = 18; -9 = y [plug this back into both equations for y to get -9 = x]

If you are ever in need of assistance, do not hesitate to let me know by subscribing to my You-Tube channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

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I'm stuck on both of these questions. Any answer will be better than what I got. Please include brief explanation :)

Answers

Answer:

B. $x>-17.5$

C. $x\leq-30$

Step-by-step explanation:

B.)

$(-8)/(14)x+22>32\n-8x+308>448\n-8x>140\nx>-17.5$

C.)

$0.9x+12\leq-15\n0.9x\leq-27\nx\leq-30$

Hope this helped!! <3

Both Todd and Zack earn the same salary. Todd spent $716 and Zack spent $128. Then Zack had 4 times the amount of money Todd had left. How much is their salary? Please tell me how and what your answer is?

Answers

They both earn the same salary. Call it ' S '.

After Todd spent 716, he had (S - 716) left.

After Zack spent 128, he had (S - 128) left.

The question says that Zack has 4 times as much as Todd has, so

(S - 128) = 4 times (S - 716)

Eliminate parentheses on the right side:

S - 128 = 4S - 2,864

Subtract ' S ' from each side:

-128 = 3S - 2,864

Add 2,864 to each side:

2,736 = 3S

Divide each side by 3 :

912 = S
==========================

Check:
After Todd spends 716, he has (912 - 716) = 196 left.
After Zack spends 128, he has (912 - 128) = 784 left.
784/196 = exactly 4 times.
yay !

Given ƒ(x) = 8x + 25, find x when ƒ(x) = 9.
A) -2
B) -1
C) 0
D) 2

Answers

A)-2
9=8x+25
-16=8x
X=-2

The constants a, b, and c are positive. Solve the inequality for x.

ax-b is less than c

Answers

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$ax - b < c$

Add sides b

$ax - b + b < c + b$

Simplification

$ax < b + c$

Divide sides by a

$(a)/(a) x < (b + c)/(a) \n$

$x < (b + c)/(a) \n$

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4. You have a deck of 40 number cards: five of each number 2 to 9. You shuffle the deck, pick a card, look at it, return it to the deck, and then repeat for a second card. Determine each theoretical probability. a) sum is 12 b) difference is less than 5 c) product is odd

Answers

To determine the theoretical probabilities, we'll analyze the different possible outcomes for each case.

Total number of cards = 40 (5 cards for each number from 2 to 9)

a) Sum is 12:

There are several combinations of cards that can result in a sum of 12:

3 and 9
4 and 8
5 and 7
7 and 5
8 and 4
9 and 3

Total favorable outcomes = 6 (since there are 6 possible combinations)

Total possible outcomes (since you're drawing two cards) = 40 * 40 = 1600

Probability (sum is 12) = (Number of favorable outcomes) / (Total possible outcomes)

Probability (sum is 12) = 6 / 1600 = 0.00375

b) Difference is less than 5:

There are several combinations of cards that can result in a difference less than 5:

2 and 3
3 and 2
3 and 4
4 and 3
4 and 5
5 and 4
5 and 6
6 and 5
6 and 7
7 and 6
7 and 8
8 and 7
8 and 9
9 and 8

Total favorable outcomes = 14

Total possible outcomes = 1600

Probability (difference is less than 5) = 14 / 1600 = 0.00875

c) Product is odd:

For the product to be odd, one or both of the numbers drawn must be odd. Since there are five odd numbers (3, 5, 7, 7, 9), and each number has five cards, the total number of favorable outcomes is 5 + 5 + 5 + 5 + 5 = 25.

Total possible outcomes = 1600

Probability (product is odd) = 25 / 1600 = 0.015625

To summarize: