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n200080 [17]
3 years ago
9

The point (2, 3) is on the line given by which equation below?

Mathematics
2 answers:
love history [14]3 years ago
5 0
Plug in the points and see if y and x are equal to each other.

(2,3)
y= x-1
3= 2-1 
3= 1 (not the solution)

y=3x
3=3*3
3=9 (not the solution)

y=x+1
3=2+1
3=3 (solution) We can check to make sure.

y=-3x
3=-3*3
3=-9 (not the solution)

y=x+1 <em>is the answer.
</em>

I hope this helps!
~kaikers


alekssr [168]3 years ago
5 0
The point (2, 3) is on the graph y=x+1
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HELPPPP!!!
Hatshy [7]

Answer:

(x - 1)²/4² - (y - 2)²/2² = 1 ⇒ The bold labels are the choices

Step-by-step explanation:

* Lets explain how to solve this problem

- The equation of the hyperbola is x² - 4y² - 2x + 16y - 31 = 0

- The standard form of the equation of hyperbola is

  (x - h)²/a² - (y - k)²/b² = 1 where a > b

- So lets collect x in a bracket and make it a completing square and

  also collect y in a bracket and make it a completing square

∵ x² - 4y² - 2x + 16y - 31 = 0

∴ (x² - 2x) + (-4y² + 16y) - 31 = 0

- Take from the second bracket -4 as a common factor

∴ (x² - 2x) + -4(y² - 4y) - 31 = 0

∴ (x² - 2x) - 4(y² - 4y) - 31 = 0

- Lets make (x² - 2x) completing square

∵ √x² = x

∴ The 1st term in the bracket is x

∵ 2x ÷ 2 = x

∴ The product of the 1st term and the 2nd term is x

∵ The 1st term is x

∴ the second term = x ÷ x = 1

∴ The bracket is (x - 1)²

∵  (x - 1)² = (x² - 2x + 1)

∴ To complete the square add 1 to the bracket and subtract 1 out

   the bracket to keep the equation as it

∴ (x² - 2x + 1) - 1

- We will do the same withe bracket of y

- Lets make 4(y² - 4y) completing square

∵ √y² = y

∴ The 1st term in the bracket is x

∵ 4y ÷ 2 = 2y

∴ The product of the 1st term and the 2nd term is 2y

∵ The 1st term is y

∴ the second term = 2y ÷ y = 2

∴ The bracket is 4(y - 2)²

∵ 4(y - 2)² = 4(y² - 4y + 4)

∴ To complete the square add 4 to the bracket and subtract 4 out

   the bracket to keep the equation as it

∴ 4[y² - 4y + 4) - 4]

- Lets put the equation after making the completing square

∴ (x - 1)² - 1 - 4[(y - 2)² - 4] - 31 = 0 ⇒ simplify

∴ (x - 1)² - 1 - 4(y - 2)² + 16 - 31 = 0 ⇒ add the numerical terms

∴ (x - 1)² - 4(y - 2)² - 16 = 0 ⇒ add 14 to both sides

∴ (x - 1)² - 4(y - 2)² = 16 ⇒ divide both sides by 16

∴ (x - 1)²/16 - (y - 2)²/4 = 1

∵ 16 = (4)² and 4 = (2)²

∴ The standard form of the equation of the hyperbola is

   (x - 1)²/4² - (y - 2)²/2² = 1

4 0
3 years ago
What number needs to be added to both sides of the equation to complete the square?
Doss [256]

Answer:

9/4

Step-by-step explanation:

(-3/2)^2=9/4

6 0
3 years ago
If X is to 9 as eight is to 12 then x is equal to what'
Tems11 [23]

Answer:

X is 6.

Step-by-step explanation:

What we know:

There's a ratio between 8 and 12, which simplifies to 2/3.

So, to find what x is, just multiply 2/3 times 9, to get 6 as x.

4 0
3 years ago
Pls help will give brainliest and 5star plss
guajiro [1.7K]
For 3. It is the fourth choice. This is because angle DGF is vertical angle and thus equal to angle EGB. Then angle BGF is supplementary to this angle.
So your answer is EGB+BGF=180

For 4. It is the first choice of 62 ft. It is the midpoint so is half the total line segment.
6 0
3 years ago
The square of a number decreased by 15 is twice the number. find the number
jonny [76]

Answer:

x = 5, -3

Step-by-step explanation:

x² - 15 = 2x

x² - 2x - 15 = 0

(x - 5)(x + 3) = 0

6 0
3 years ago
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