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3 years ago

Find the distance between the pair points (-2, -3) and (-12,-19)

1 answer:

7 0

D = √(y2-y1)² + (x2-x1)²

d = √(-3+19)² + (-2+12)²

d = √16² + 10²

d = √256 + 100
d = √356
d = 18.87 units

In short, Your Answer would be: 18.87 units

Hope this helps!

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1 , 3 , 6 , 10 , 15

Bas_tet [7]

First difference,

$\Delta_{1} = a_{2} - a_{1} = 3 - 1 = 2 = 1 + 1$

Second difference,

$\Delta_{2} = a_{3} - a_{2} = 6 - 3 = 3 = 2 + 1$

Third difference,

$\Delta_{3} = a_{4} - a_{3} = 10 - 6 = 4 = 3 + 1$

And so on.

Assuming the pattern holds on, we see that

i-th difference,

$\Delta_{i} = a_{i + 1} - a_{i} = i + 1$

$\implies a_{i + 1} = a_{i} + i + 1$

Then, nth term is,

$\implies a_{n} = a_{n - 1} + n$

$= a_{n - 2}+ (n + (n - 1))$

$= a_{n - 3} + (n + (n - 1) +(n - 2))$

$= a_{n - (n - 1)} + \sum \limits^{n - 2}_{k = 0}(n - k)$

$= a_1 + \sum \limits^{n - 2}_{k = 0}n- \sum \limits^{n - 2}_{k = 0}k$

$= a_1 +n(n -2 + 1 )- \frac{1}{2} (n - 2)(n - 1)$

$= a_1 +n(n -1 )- \frac{1}{2} (n - 2)(n - 1)$

$= a_1 +(n -1 )(n- \frac{1}{2} (n - 2))$

$= a_1 + \frac{1}{2} (n -1 )(2n- n + 2)$

$= a_1 + \frac{1}{2} (n -1 )(n + 2)$

$\implies a_{n} = 1 + \frac{1}{2} (n -1 )(n + 2)$

Now, the 21st term in the sequence is,

$\implies a_{21} = 1 + \frac{1}{2} (21 -1 )(21 + 2)$

$= 1 + \frac{1}{2} \times 20 \times 23$

$= 231$

4 0

3 years ago

10 30 (2.-4) 10 A. 5 B. 1 C. -1 D. -5

mr Goodwill [35]

Answer:

Step-by-step explanation:

correct me if I'm wrong

4 0

3 years ago

Find the value of x if GH and JH are both 13 units long. Justify your answer.

const2013 [10]

Answer:

$x=7$

Step-by-step explanation:

we have the triangle GHJ

If the segment side GH is equal to the segment JH

then

The triangle GHJ is an isosceles triangle

Remember that

An isosceles triangle has two equal interior angles and two equal sides

m∠G=m∠J

we have

m∠G=(7x+5)°

m∠J=(x+47)°

equate the equations

(7x+5)°=(x+47)°

Solve for x

$7x-x=47-5\\6x=42\\x=7$

4 0

3 years ago

40 percent of what number equals 19.2

worty [1.4K]

You can get the number by dividing 19.2 by 0.40

The number is 19.2/0.40 = 48

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4 years ago

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Find the unit price if a dozen apples cost $4.80

mixas84 [53]

Answer:

0.40 cens

Step-by-step explanation:

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3 years ago