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3 years ago

Find the distance between (3,-2) and (2,-4)

Mathematics

1 answer:

Sphinxa [80]3 years ago

4 0

Answer:

i believe it is (2,1)

Step-by-step explanation:

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Could someone help me rnnn?

GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola: $y=3x^2-4$

Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

(where (h, k) is the vertex and $a$ is some constant)

Substitute point (0, -4) into the equation:

$\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}$

Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$

Substitute point (1, -1) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}$

Equate to find h:

$\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}$

Substitute found value of h into one of the equations to find a:

$\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}$

Substitute found values of h and a to find k:

$\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}$

Therefore, the equation of the parabola in vertex form is:

$\implies y=3(x-0)^2-4=3x^2-4$

So the vertex of the parabola is (0, -4)

5 0

2 years ago

Read 2 more answers

I need help on 18,19 and 20 please help do tomorrow

Verdich [7]

You still need help?

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3 years ago

Five adult tickets and three child tickets for a movie costs £55. The cost of buying two adult tickets and three child tickets i

Allisa [31]

Answer:

adult £8
child £5

Step-by-step explanation:

If you look at the numbers you are given, you see that the first purchase has 3 more adult tickets than the second purchase, and its cost is £24 more. This means an adult ticket costs £24/3 = £8.

Two adult tickets will cost 2×£8 = £16, so three child tickets cost ...

£31 -16 = £15

Each child ticket is then £15/3 = £5.

An adult ticket costs £8; a child ticket costs £5.

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3 years ago

Hope's watch gains 8 minutes every 2 hours. How much time will it gains in ; a) 12 hours b) 13 hours

prisoha [69]

Answer:

A = 48, and B = 52

Step-by-step explanation:

Simplify 8 = 2 hours to 4 = 1 hour, then multiply 4 times 12 to get the answer to a. The answer to b would be multiplying 4 times 13.

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3 years ago

How much time will Alex need to walk to his school, which is 2 1/4 miles away from his house, if he would walk with the speed of

mojhsa [17]

It would take him 30 mins

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3 years ago