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nydimaria [60]
2 years ago
9

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

Mathematics
1 answer:
Arisa [49]2 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. 1/0 is undefined
  2. 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/(1/5) > 1/5
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Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.
LuckyWell [14K]

Step-by-step explanation:

Quadrilateral ABCD is inscribed in a circle.

Opposite angles of a Quadrilateral are Supplementary.

\therefore \: \angle A + \angle C = 180° \\  \therefore \:(2x + 3) \degree+ (2x + 1) \degree = 180° \\  \therefore \: (4x + 4) \degree = 180° \\ \therefore \: (4x + 4) = 180 \\ \therefore \: 4x = 180 - 4 \\ \therefore \: 4x = 176 \\ \therefore \: x =  \frac{176}{4}  \\ \therefore \: x =  44 \\  \\  m\angle A  = (2x + 3) \degree \\  = (2 \times 44 + 3) \degree \\ = (88 + 3) \degree \\  \huge \red{ \boxed{ \therefore \: m\angle A  =91 \degree}} \\  \\ m\angle  C = (2x + 1) \degree \\  = (2 \times 44 + 1) \degree \\ = (88 + 1) \degree \\  \huge \red{ \boxed{ \therefore \: m\angle   C=89\degree}}  \\  \\ m\angle  D= (x - 10) \degree \\  = (44 - 10) \degree \\  \huge \red{ \boxed{ \therefore \: m\angle  D =34\degree}}  \\  \\ similarly \\  \\  \huge \red{ \boxed{ \therefore \: m\angle  B  = 146\degree}}   \\  \\

6 0
3 years ago
Kaylee and Olivia go to the movie theater and purchase refreshments for their friends.
KatRina [158]

The price of one bag of popcorn is $3.75

Step-by-step explanation:

Let,

x represent the cost of a bag of popcorn

y represent the cost of a drink.

According to given statement;

4x+12y=30      Eqn 1

x+6y=11.25      Eqn 2

Multplying Eqn 2 by 2

2(x+6y=11.25)\\2x+12y=22.50\ \ \ Eqn\ 3

Subtracting Eqn 3 from Eqn 1

(4x+12y)-(2x+12y)=30-22.50\\4x+12y-2x-12y=7.50\\2x=7.50

Dividing both sides by 2

\frac{2x}{2}=\frac{7.50}{2}\\x=3.75

4x+12y=30 and x+6y=11.25 can be used to find the price of one bag of popcorn and the price of one drink.

The price of one bag of popcorn is $3.75

Keywords: linear equation, elimination method

Learn more about elimination method at:

  • brainly.com/question/11821063
  • brainly.com/question/11871074

#LearnwithBrainly

3 0
3 years ago
Solve the Fahrenheit equation for Celsius
horrorfan [7]
The first step you should do is subtract 32 from both sides so your answer will turn out like this -

F = (9/5) C + 32
- 
F - 32 = (9/5)

Then we will multiply both sides by 5. 

5 ( F - 32 ) = 9 C

Divide both sides by 9 to isolate C.

(5/9)  ( F - 32 ) = C

So the answer is :

C = (5/9) ( F - 32 )

Hope this helps :)

7 0
3 years ago
Read 2 more answers
You are on the high school basketball team. The ball you use has a diameter of 9 inches. What is the volume of the ball? Use 3.1
nlexa [21]

Answer:

63.6

Step-by-step explanation:

5 0
2 years ago
Luke runs a farm stand that sells strawberries and blueberries. Each pound of
koban [17]
Answer:
He would make $36 for 12 pounds of strawberries
He would make $196 for 49 pounds of blueberries

He would make 3S if he sold S pounds of strawberries
He would make 4B if he sold B pounds of blueberries

Working:
We know that strawberries are $3/pound so $3 x 12pounds = $36
We know that blueberries are $4/pound so $4 x 49pounds = $196

The letters represent the amount of pounds of fruit being bought so the calculation for that is ($ x pounds) so you would write this but without assigning a numerical value to the amount. So if the strawberries are $3/pound and Luke sold ‘s’ pounds then it would be 3S (or 3xS but that is already assumed). The same goes for the blueberries. We know that they are $4/pound so it would be 4B.

Sorry if this doesn’t make any sense but I hope this helped

4 0
3 years ago
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