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3 years ago

Find radius and center

Mathematics

1 answer:

Sliva [168]3 years ago

5 0

Answer:

(0,0) and r=3

Step-by-step explanation:

To find the radius and center rewrite the equation in vertex form $(x-h)^2+(y-k)^2 = r^2$ .

First move x and y to the other side so they have positive signs. Then move 9 across to the other side too.

$-9 = -y^2 -x^2\\x^2 + y^2 -9 = 0\\x^2 + y^2 = 9$

Here you can see there is no h or k meaning h=0 and k=0. The radius is the square root of 9 which is 3.

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Multiply: (-4 + i)(-1 + 5i)

Olegator [25]

Answer:

$( - 4 + i) ( - 1 + 5i) \\ = 4 - 20i - 1i + 5 {i}^{2} \\ = 4 - ( -21i )+ 5i {}^{2}$

3 0

3 years ago

The graph of an absolute value function has a vertex of (2,3) and crosses the x-axis at (−1,0) and (5,0). What is the equation f

frez [133]

Answer:

Option D.

Step-by-step explanation:

The vertex form of an absolute function is

$y=a|x-h|+k$

where, a is a constant, (h,k) is vertex.

It is given that, vertex of an absolute function is (2,3). So, h=2 and k=3.

$y=a|x-2|+3$ ...(1)

It crosses the x-axis at (5,0). So put x=5 and y=0 to find the value of a.

$0=a|5-2|+3$

$-3=3a$

$-1=a$

Put a=-1 in (1).

$y=(-1)|x-2|+3$

$y=-|x-2|+3$

Now, put y=0, to find the equation for this absolute value function when y=0.

$0=-|x-2|+3$

Therefore, the correct option is D.

4 0

3 years ago

Read 2 more answers

What is the equation of a parabola with a directrix of y=2 and a focus point of 0,-2

KiRa [710]

Hope this helped. :)

Any point, (x0,y0)(x0,y0) on the parabola satisfies the definition of parabola, so there are two distances to calculate:

Distance between the point on the parabola to the focusDistance between the point on the parabola to the directrix

To find the equation of the parabola, equate these two expressions and solve for y0y0 .

Find the equation of the parabola in the example above.

Distance between the point (x0,y0)(x0,y0) and (a,b)(a,b) :

(x0−a)2+(y0−b)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√(x0−a)2+(y0−b)2

Distance between point (x0,y0)(x0,y0) and the line y=cy=c :

∣∣y0−c∣∣| y0−c |

(Here, the distance between the point and horizontal line is difference of their yy -coordinates.)

Equate the two expressions.

(x0−a)2+(y0−b)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√=∣∣y0−c∣∣(x0−a)2+(y0−b)2=| y0−c |

Square both sides.

(x0−a)2+(y0−b)2=(y0−c)2(x0−a)2+(y0−b)2=(y0−c)2

Expand the expression in y0y0 on both sides and simplify.

(x0−a)2+b2−c2=2(b−c)y0(x0−a)2+b2−c2=2(b−c)y0

This equation in (x0,y0)(x0,y0) is true for all other values on the parabola and hence we can rewrite with (x,y)(x,y) .

Therefore, the equation of the parabola with focus (a,b)(a,b) and directrix y=cy=c is

(x−a)2+b2−c2=2(b−c)y

3 0

3 years ago

A number cube is tossed 8 times. What is the probability that the cube never lands on 3?.

tino4ka555 [31]

The probability that the cube never lands on 3 is (D) 23.3%.

<h3>What is probability?</h3>

A probability formula can be used to calculate the likelihood of an occurrence by simply dividing the favorable number of possibilities by the entire number of possible outcomes.

To find the probability that the cube never lands on 3:

Given -

Number cube toss = 8

Required

Probability of not landing on 3.

First, we need to get the probability of landing on 3 in a single toss.

For a number cube,

n(3) = 1 and n(total) = 6

So, the probability is P(3) = 1/6

First, we need to get the probability of not landing on 3 in a single toss.

Opposite probability = 1.

So, P(3) = P(3') = 1.

Make P(3') the subject of the formula.

P(3') = 1 - P(3)
P(3') = 1 - 1/6
P(3') = 5/6

In 8 toss, the required probability is (P(3'))⁸

This gives:

P = (5/6)⁸
P = 390625/1679616
P = 0.23256803936

Approximate to 1 decimal place, P = 23.3%.

Therefore, the probability that the cube never lands on 3 is (D) 23.3%.

Know more about probability here:

brainly.com/question/25870256

#SPJ4

The correct question is given below:
A number cube is tossed 8 times. What is the probability that the cube never lands on 3?

A. 6.0%

B. 10.4%

C. 16.7%

D. 23.3%

5 0

11 months ago

ally spent half of her weekly allowance at the movies. to earn more money her parents let her clean the windows in the house for

Orlov [11]

Answer: Her weekly allowance is 24 dollars

Step-by-step explanation:

If she is left with $12 spending half of her weekly allowance the we could set up the equation.

1/2 of x = 12 where x is her weekly allowance.

1/2x = 12

x = 24

3 0

3 years ago