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3 years ago

A circle is centered at K(0, 0). The point U(6, -4) is on the circle. Where does the point V(square root 2, -7) lie

Mathematics

1 answer:

Dominik [7]3 years ago

5 0

Answer:

V is inside the circle.

Step-by-step explanation:

We work out the radius of the circle which is the distance between K (0,0) and (6, -4).

Radius = √[(6 - 0)^2 + (-4 - 0)^2]

= √(16 + 36)

= √52.

Now find the distance of point V from K(0,0):

= √((√2-0)^2 + (-7-0)^2]

= √(2 + 49)

= √51.

This is less than the radius of the circle, so V lies inside it.

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6. Find the sum or difference<br> 1/3(9 - 6m) + 1/4 (12m-8)

romanna [79]

Answer:

m+1

Step-by-step explanation:

1/3(9 - 6m) + 1/4 (12m-8)

Distribute

1/3 *9 - 1/3 *6m + 1/4 * 12m - 1/4 *8

3 -2m + 3m -2

Combine like terms

-2m+3m +3-2

m+1

6 0

3 years ago

What are the zeros of this graph

kotegsom [21]

The zeroes ( where the graph cuts the x axis) ar (-2,0) AND (2,0)

tHE FACTOrIAL FORM IS (x - 2)(x + 2)

Its B

3 0

3 years ago

This for composite figures

Vinil7 [7]

Answer:

114 square meters

Step-by-step explanation:

The figure decomposes into two congruent trapezoids, each with bases 15 m and 4 m, and height 6 m. The area formula for a trapezoid is ...

A = 1/2(b1 +b2)h

Each trapezoid will have an area of ...

A = 1/2(15 +4)(6) = 57 . . . . square meters

The figure's area is twice that, so is ...

figure area = 2 × 57 m² = 114 m²

7 0

2 years ago

Algebra

vladimir2022 [97]

(2x + 3y = 12) x (-2)
(4x - 3y = 6) x 1

-4x - 6y = -24
4x - 3y = 6

You can cancel out the x values by adding the two equations together.
(-4x + 4x) + (-6y - 3y) = (-24 + 6)
-9y = -18
y = 2

Solve for x now...
4x - 3(2) = 6
4x - 6 = 6
4x = 12
x = 3

Check... (x = 3, y = 2)
2(3) + 3(2) = 12
6 + 6 = 12
12 = 12 <- this works!

4(3) - 3(2) = 6
12 - 6 = 6
6 = 6 <- this works!

5 0

3 years ago

Read 2 more answers

The Slow Ball Challenge or The Fast Ball Challenge.

cupoosta [38]

Answer:

Fast ball challenge

Step-by-step explanation:

Given

Slow Ball Challenge

$Pitches = 7$

$P(Hit) = 80\%$

$Win = \$60$

$Lost = \$10$

Fast Ball Challenge

$Pitches = 3$

$P(Hit) = 70\%$

$Win = \$60$

$Lost = \$10$

Required

Which should he choose?

To do this, we simply calculate the expected earnings of both.

Considering the slow ball challenge

First, we calculate the binomial probability that he hits all 7 pitches

$P(x) =^nC_x * p^x * (1 - p)^{n - x}$

Where

$n = 7$ --- pitches

$x = 7$ --- all hits

$p = 80\% = 0.80$ --- probability of hit

So, we have:

$P(x) =^nC_x * p^x * (1 - p)^{n - x}$

$P(7) =^7C_7 * 0.80^7 * (1 - 0.80)^{7 - 7}$

$P(7) =1 * 0.80^7 * (1 - 0.80)^0$

$P(7) =1 * 0.80^7 * 0.20^0$

Using a calculator:

$P(7) =0.2097152$ --- This is the probability that he wins

i.e.

$P(Win) =0.2097152$

The probability that he lose is:

$P(Lose) = 1 - P(Win)$ ---- Complement rule

$P(Lose) = 1 -0.2097152$

$P(Lose) = 0.7902848$

The expected value is then calculated as:

$Expected = P(Win) * Win + P(Lose) * Lose$

$Expected = 0.2097152 * \$60 + 0.7902848 * \$10$

Using a calculator, we have:

$Expected = \$20.48576$

Considering the fast ball challenge

First, we calculate the binomial probability that he hits all 3 pitches

$P(x) =^nC_x * p^x * (1 - p)^{n - x}$

Where

$n = 3$ --- pitches

$x = 3$ --- all hits

$p = 70\% = 0.70$ --- probability of hit

So, we have:

$P(3) =^3C_3 * 0.70^3 * (1 - 0.70)^{3 - 3}$

$P(3) =1 * 0.70^3 * (1 - 0.70)^0$

$P(3) =1 * 0.70^3 * 0.30^0$

Using a calculator:

$P(3) =0.343$ --- This is the probability that he wins

i.e.

$P(Win) =0.343$

The probability that he lose is:

$P(Lose) = 1 - P(Win)$ ---- Complement rule

$P(Lose) = 1 - 0.343$

$P(Lose) = 0.657$

The expected value is then calculated as:

$Expected = P(Win) * Win + P(Lose) * Lose$

$Expected = 0.343 * \$60 + 0.657 * \$10$

Using a calculator, we have:

$Expected = \$27.15$

So, we have:

$Expected = \$20.48576$ -- Slow ball

$Expected = \$27.15$ --- Fast ball

<em>The expected earnings of the fast ball challenge is greater than that of the slow ball. Hence, he should choose the fast ball challenge.</em>

5 0

3 years ago