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klemol [59]
3 years ago
13

At what points are the equations y=x2 and y=1/x+2 equal?

Mathematics
2 answers:
Novay_Z [31]3 years ago
8 0
Try this:
1) If y=x² and y=(2x+1)/x, then 
x^2= \frac{2x+1}{x}; \ \ \textless \ =\ \textgreater \  \ x^3-2x-1=0; \ (x \neq 0) <=>   (x+1)(x^2-x-1)=0; \ (x \neq 0)\ \ \textless \ =\ \textgreater \    \left[\begin{array}{ccc}x=-1\\x= \frac{1+ \sqrt{5} }{2} \\x= \frac{1- \sqrt{5}}{2} \end{array}\right
2) after 'x' are found it need to calculate 'y':
Answer: (-1;1), (-0.618;0.382), (1.618;2.618)
Marta_Voda [28]3 years ago
5 0

Answer:

(-1,1),(-0.618,0.382), (1.618,2.618)

Step-by-step explanation:

we have

y=x^{2} ----> equation A

y=\frac{1}{x} +2 -----> equation B

we know that

The intersection points both graphs are the points where both equations have the same value

so

Using a graphing tool

The intersection points are (-1,1),(-0.618,0.382), (1.618,2.618)

see the attached figure


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Helppppppppppppppppp​
Darina [25.2K]

Answer:

3)

Step-by-step explanation:

An equation is linear if equal changes in x produce equal changes in y.

Let's look at each choice.

1)

A decrease of 10% per year. That means each year, the value of the car is 0.9 times the value of the previous year.

For example, if the original value was $10,000, after 1 year, it is worth 0.9 * $10,000 = $9,000. In 1 year it lost $1,000. In the next year, its value is now 0.9 * $9,000. The value at the end of the 2nd year is $8,100. In the second year, it lost $900 in value. In one period of 1 year it lost $1000 in value. In another equal period of 1 year, it lost $900 in value. A change of 1 year in time produces different changes in loss of value, so it is not linear.

2)

Here, the number doubles every year. Let's say it starts with 100 fish. After 5 years, it has 200 fish. In a change of 5 years in x, the change in y is 100. In the next 5 years, it goes from 200 fish to 400 fish. The change in the second period of 5 years is 200. We see that a change of 5 years can produce a change of 100 fish, but another change of 5 years can produce a change is 100 fish. Since for equal changes in x, the changes in y are not all equal, this is not linear.

3)

Here for every change of 1 day in x, the change in y is 2 liters. Each change of 1 in x always produces a change of 2 in y. This is linear.

4)

Each 2 hours, the amount of caffeine is 2/3 of what it was before. This is similar to the choice 1), and it is not linear.

Answer: 3)

7 0
3 years ago
Malik buys and sells car parts. He bought two tires for $45.00 each and later sold them for $65.00 each. He bought three rims fo
tatiyna

Answer: $75

Step-by-step explanation: First he bought tires for 45.00 dollars - later sold it as 65.0 dollars.

=> 65 - 45 = 20 dollars is his profit

he brought 3 rims for 85 dollar - then later sold it as 126 dollars

=> 126 - 85 = 41 dollars

He bought headlight for 5.00 dollars then sold it later for 15 dollars.

=> 15 - 5 = 10 dollars

Total expenses

=> 134

Total amount sold

=> 209

Profit => 209 - 134 = 75 dollars

6 0
2 years ago
2. John and Jen went to the farmers market to buy fruit. John bought 3 boxes of oranges and 9 boxes of cherries for $78. Jen bou
jenyasd209 [6]

Answer:

Let the cost of orange be X and cost of cherry be y

3x + 9y = 78

8x + 4y = 58

Solving equation using elimination method

multiplying eq 1 with 8 and eq 2 with 3

8(3x + 9y ) = 78(8)

3( 8x + 4y) = 3(58)

24x + 72 y = 624

24x + 12y = 174

subtracting,

60 y = 450

y = 7.5

3x + 9(7.5) = 78

3x + 67.5 = 78

3x = 78 - 67.5

3x = 10.5

x = 3.5

<h2>Box of orange = $3.5 </h2><h2>Box of cherry = $7.5</h2>
7 0
1 year ago
The linear regression line for Tampa Tribune Database is y=8x+367. In approximately what year is the Tampa Tribune expecting to
lakkis [162]

The Tampa Tribune expecting to add 700 new pictures per year to their database in 2041

<h3>The linear equation of the graph</h3>

The equation of the line of best fit is given as:

y = 8x + 367

When the number of pictures added is 700, we have:

y = 700

Substitute 700 for y in y = 8x + 367

700 = 8x + 367

Subtract 367 from both sides of the equation

333= 8x

Rewrite the above equation as:

8x = 333

Divide both sides by 8

x = 41.625

Remove decimal (do not approximate)

x = 41

This means that:

Year = 2000 +41

Year = 2041

Hence, the Tampa Tribune expecting to add 700 new pictures per year to their database in 2041

Read more about linear regression at:

brainly.com/question/26137159

8 0
2 years ago
If MP=6x-5,QR=3x+1, and RN=6, what is QN
stepan [7]

Answer:

12

Step-by-step explanation:

12

7 0
2 years ago
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