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3 years ago

Find the distance between points (a,b) and Q -a,-b)

Mathematics

1 answer:

andriy [413]3 years ago

3 0

Answer:

d = 2* sqrt(a^2 + b^2)

Step-by-step explanation:

Interesting question. You should begin by noting that 0 is not the answer although it looks like it should be.

P = (a,b)

Q= (-a,-b)

x1 = a

x2 = - a

y1 = b

y2 = - b

d = sqrt( (x2 - x1)^2 + (y2 - y1)^2 )

d = sqrt( (-a - a)^2 + (-b - b)^2 )

d = sqrt ( -2a)^2 + - (2b)^2 )

d = sqrt(4a^2 + 4b^3)

d = 2* sqrt(a^2 + b^2)

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Point P is the center of the circle in the figure above. What is the value of x?

LenaWriter [7]

Answer:

x = 80°

Step-by-step explanation:

To find x, we need to create an equation.

Recall that the sum of all the 4 interior angles of a quadrilateral = 360°.

Therefore:

m<B + m<A + m<C + m<P = 360°

m<B = 20° (given)

m<C = 20° (given)

m<A = ½*x = x/2 (inscribed angle theorem)

m<P = (360 - x)°

Plug in the values and solve for x

$20 + \frac{x}{2} + 20 + (360 - x) = 360$

$20 + \frac{x}{2} + 20 + 360 - x = 360$

Collect like terms

$20 + 20 + 360 + \frac{x}{2} - x = 360$

$400 + \frac{x}{2} - x = 360$

Subtract 400 from each side 

$400 + \frac{x}{2} - x - 400 = 360 - 400$

$\frac{x}{2} - x = -40$

$\frac{x - 2x}{2} = -40$

$\frac{-x}{2} = -40$

Multiply both sides by 2

$\frac{-x}{2} \times 2 = -40 \times 2$

$-x = -80$

Divide both sides by -1

$\frac{-x}{-1} = \frac{-80}{-1}$

$x = 80$

3 0

3 years ago

If using the method of completing the square to solve the quadratic equation x^2 + 3x +21 =0?

goldfiish [28.3K]

Answer:

$x= \dfrac 12 \left( -3 +i5\sqrt 3\right)\\\\x= \dfrac 12 \left( -3 -i5\sqrt 3\right)$

Step-by-step explanation:

$~~~~~~x^2 +3x +21 = 0\\\\\implies x^2 +3x = -21\\\\\implies x^2 + 2\cdot \dfrac 32 \cdot x + \left( \dfrac 32 \right)^2 = -21 + \left( \dfrac 32 \right)^2\\\\\implies \left(x + \dfrac 32 \right)^2 = -21+\dfrac 94\\\\\implies \left(x + \dfrac 32 \right)^2 = -\dfrac{75}4\\\\\implies x+ \dfrac 32 = \pm\sqrt{-\dfrac{75}4 \right)\\\\\implies x + \dfrac 32 = \pm i \dfrac{5\sqrt 3}{2}\\\\\implies x = -\dfrac 32 \pm i \dfrac {5\sqrt 3}2\\\\\implies x = \dfrac 12 \left( -3 \pm i5\sqrt 3\right)$

8 0

2 years ago

Lewis paid $13.55 for a beach chair and $5.75 for a book. How much did Lewis spend?

BartSMP [9]

Answer:

$19.30

Step-by-step explanation:

Add $13.55+5.75= $19.30

7 0

3 years ago

Read 2 more answers

Hiram drove a total of 1542.75 miles in 3 days. Each day he drove 81 hours and then

Tems11 [23]

167. Lllllllllpllllllijjdjhdhdhdhd

3 0

3 years ago

Omg pls help ill give you 20 points

ElenaW [278]

Answer:

Step-by-step explanation:

Amount of water in tank 1 = amount of water in tank 2

30t +25 = -20t + 1000

Add 20t to both sides

30t + 20t + 25 = -20t + 20t + 1000

50t + 25 = 1000

Subtract 25 from both sides

50t + 25 - 25 = 1000 - 25

50t = 975

Divide both sides by 50

t = 975/50 = 39/2

$= 19 \frac{1}2}$

t = 19 minutes 30 seconds

After 19 1/2 minutes both tanks will have 610 liters of water

5 0

3 years ago

Find the distance between points (a,b) and Q -a,-b)​

Find the distance between points (a,b) and Q -a,-b)