All categories

3 years ago

Determine if the conjecture is true or false. If true, explain your reasoning briefly. If false provide a counterexample.

Mathematics

1 answer:

Arisa [49]3 years ago

7 0

9514 1404 393

Answer:

false

Step-by-step explanation:

The conjecture shown in this problem statement does not follow from the examples offered. They support the notion that ...

1/x ≤ x . . . . for x ≥ 0 (<u>not x ≤ 0</u>)

There are several possible counterexamples showing the conjecture is FALSE.

1/0 is undefined
1/(-5) > -5 . . . . . . . . a case for x < 0

If the intended domain is x ≥ 0, then the conjecture can also be demonstrated to be false for 0 < x < 1:

1/(1/5) > 1/5

You might be interested in

A pigeon can fly 84 kilometers per hour. how long does the pigeon take to fly 7 kilometers?

Leviafan [203]

84 kilometers ... 1 hour
7 kilometers ... x hours = ?

If you would like to know how long does the pigeon take to fly 7 kilometers, you can calculate this using the following steps:

84 * x = 1 * 7
84 * x = 7 /84
x = 7/84
x = 1/12 hour

Result: A pigeon can fly 7 kilometers in 1/12 hour.

6 0

3 years ago

Read 2 more answers

I need help for Brainliest

Olegator [25]

Answer: 1/8

Step-by-step explanation:

If you look at the circle, there are 4 R, 1B, 2G, and 1Y which then equals 8. Therefor there is a 1/8 chance of the spinner landing on B.

Hope this helps...

Have a great day.

6 0

3 years ago

Read 2 more answers

What is the average rate of change for the function f(x)=3x^2 -5 on the interval −3 ≤ x ≤ −1 ?

Anestetic [448]

Answer:

-12

Step-by-step explanation:

Let b = -1 and a = -3

The average rate of change = $\frac{f(b) - f(a)}{b - a}$

f(b) = f(-1) = 3(-1)^2 - 5 = 3 - 5 = -2

f(a) = f(-3) = 3(-3)^2 - 5 =27 - 5 = 22

f(b) - f(a) = -2 - 22 = -24

b - a = -1 + 3 = 2

$\frac{f(b) - f(a)}{b - a}$ = -24/2 = -12

4 0

3 years ago

Given the function f(x) = 2|x + 6| – 4, for what values of x is f(x) = 6?

lara [203]

Answer:

x = -1 , - 11,

Step-by-step explanation:

| x | = x

|- x | = x

f(x) = 2 | x + 6 | - 4

x = - 1 , f( - 1) = 2 | - 1 + 6 | - 4 = 2 | 5 | - 4 = 10 - 4 = 6 , True

x = 1 , f( 1 ) = 2 | 1 + 6 | - 4 = 2 | 7 | - 4 = 14 - 4 = 10 , False

x = 11, f( 11 ) = 2 | 11 + 6 | - 4 = 2 | 17 | - 4 = 34 - 4 = 30 , False

x = - 11, f( - 11) = 2 | -11 + 6 | - 4 = 2 | - 5 | - 4 = 10 - 4 = 6 , True

x = 14 , f( 14 ) = 2 | 14 + 6 | - 4 = 2 | 20 | - 4 = 40 - 4 = 36 , False

x = -14 , f( - 14 ) = 2 | - 14 + 6 | - 4 = 2 | - 8 | - 4 = 16 - 4 = 12 , False

x = - 26 , f( - 26) = 2 | -26 + 6 | - 4 = 2 | -20 | - 4 = 40 - 4 = 36 , False

x = 26, f( 26 ) = 2 | 26 + 6 | - 4 = 2 | 32 | - 4 = 64 - 4 = 60 , False

Given f ( x ) = 6

f( x ) = 2 | x + 6 | - 4

6 = 2 | x + 6 | - 4

6 + 4 = 2 | x + 6| - 4 + 4 [ adding 4 to both sides ]

10 = 2 | x + 6 | + 0

5 = | x + 6 | [ dividing both sides by 2 ]

$- 5 =\ ( x+ 6) \ = 5\\\\$ $[ \ | x | = a\ => \ -a \ = x \ = a \ ]$

$- 5 - 6 = \ x + 6 - 6 \ = \ 5 - 6\\$ $[ \ subtracting \ by \ 6 \ ]$

$-11 = \ x \ = - 1$

3 0

3 years ago

14+3x≤23<br> please help me

nignag [31]

Answer:

x≤3

Step-by-step explanation:

<em>Step one- This equation has 23 greater than or equal to sign. Which means It can be at most 23</em>

<em>Step two- Find out what times 3x+14=23 In this case the answer is 3.3 Is the biggest number that can be multiplied by 3, +14 to get to 23.</em>

<em>Step three- Rewrite the Answer. Since we know that 3 is the highest numebr possible, we rewrite it to this equation</em>

<h3>x≤3</h3><h3>HOPE THIS HELPS :)</h3>

5 0

3 years ago