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il63 [147K]
3 years ago
12

Distance between A(2,7) and B(6,4)

Mathematics
2 answers:
r-ruslan [8.4K]3 years ago
4 0

Answer:

Approx: 2.65units

Step-by-step explanation:

ANTONII [103]3 years ago
4 0

Answer:

5

Step-by-step explanation:

d=\sqrt{(6-2)^{2}+(4-7)^{2}  } \\d=\sqrt{4^{2}+(-3)^{2}  } \\d=\sqrt{16+9} \\d=\sqrt{25} \\d=5

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Part 4: Identify the vertex, focus and directrix of each. Then sketch the graph.
Nezavi [6.7K]

Answer: 1) Vertex: (6, -2)    Focus: (6, -7/4)     Directrix: y = -9/4

              2) Vertex: (-2, -1)   Focus: (-7/4, -1)     Directrix: x = -9/4

<u>Step-by-step explanation:</u>

Rewrite the equation in vertex format y = a(x - h)² + k   or   x = a(y - k)² + h by completing the square. Divide the b-value by 2 and square it - add that value to both sides of the equation.

  • (h, k) is the vertex
  • p is the distance from the vertex to the focus
  • -p is the distance from the vertex to the directrix

    \bullet\quad a=\dfrac{1}{4p}

1) y = x² - 12x + 34

y-34=x^2-12x\\\\y-34+\bigg(\dfrac{-12}{2}\bigg)^2=x^2-12x+\bigg(\dfrac{-12}{2}\bigg)^2\\\\\\y-34+36=(x-6)^2\\\\y+2=(x-6)^2\\\\y=(x-6)^2-2\qquad \rightarrow \qquad a=1\quad (h,k)=(6,-2)\\

a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=\dfrac{1}{4}\\\\\\\text{Focus = Vertex + p}\\.\qquad \quad =\dfrac{-8}{4}+\dfrac{1}{4}\\\\.\qquad \quad =-\dfrac{7}{4}\quad \rightarrow \quad\text{Focus}=\bigg(6,-\dfrac{7}{4}\bigg)\\\\\\\text{Directrix: y= Vertex - p}\\.\qquad \qquad y=\dfrac{-8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad y=-\dfrac{9}{4}

*******************************************************************************************

2) x = y² + 2y - 1

x+1=y^2+2y\\\\x+1+\bigg(\dfrac{2}{2}\bigg)^2=y^2+2y+\bigg(\dfrac{2}{2}\bigg)^2\\\\\\x+1+1=(y+1)^2\\\\x+2=(y+1)^2\\\\x=(y+1)^2-2\qquad \rightarrow \qquad a=1\quad (h,k)=(-2,-1)\\

a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=\dfrac{1}{4}\\\\\\\text{Focus = Vertex + p}\\.\qquad \quad =\dfrac{-8}{4}+\dfrac{1}{4}\\\\.\qquad \quad =-\dfrac{7}{4}\quad \rightarrow \quad\text{Focus}=\bigg(-\dfrac{7}{4},-1\bigg)\\\\\\\text{Directrix: x= Vertex - p}\\.\qquad \qquad y=\dfrac{-8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad x=-\dfrac{9}{4}

4 0
3 years ago
Solve the system of equations using elimination 2x+y=3 and 3x-y=12
Eddi Din [679]
2x + y = 3
3x - y = 12
Add both equations
5x = 15, x = 3
2(3) + y = 3
6 + y = 3, y = -3
Solution: x = 3, y = -3... or (3,-3)
3 0
3 years ago
Brainliest and points for best answer.
jeka57 [31]

Answer:

A

Step-by-step explanation:

3 0
3 years ago
Dan has the same number of nickels and dimes in his piggy bank. If the total amount of those coins is $0.90, how many of each co
Karolina [17]

Hello There!

<u><em>n - d = 0</em></u>

<u><em>5n+10d = 90</em></u>

<u><em>----------------------</em></u>

<u><em>n-d = 0</em></u>

<u><em>n+2d = 18</em></u>

<u><em>-------------------</em></u>

<u><em>Subtract and solve for "d":</em></u>

<u><em>3d = 18</em></u>

<u><em>d = 6 (# of dimes)</em></u>

<u><em>n = d = 6 (# of nickels)</em></u>

8 0
3 years ago
What is the measure of the angle of rotation for the polygon?
m_a_m_a [10]

Answer:

360 degrees divided by that order

7 0
2 years ago
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