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3 years ago

The circle below is centered at the point (4,1) and has a radius of length 2. What is it’s equation?

Mathematics

2 answers:

boyakko [2]3 years ago

8 0

Answer:

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k ) = (4, 1) and r = 2, hence

(x - 4)² + (y - 1)² = 4 → B

vekshin13 years ago

5 0

Answer:

Option B:

$(x-4)^2+(y-1)^2 = 4$

Step-by-step explanation:

Given

Centre = (h,k) = (4,1)

Radius = r = 2

The standard equation of circle is:

$(x-h)^2+(y-k)^2=r^2$

Putting the values of h,k and r

$(x-4)^2+(y-1)^2 = (2)^2\\(x-4)^2+(y-1)^2 = 4$

Hence, the correct option is option B

$(x-4)^2+(y-1)^2 = 4$

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What is the nth term?

kumpel [21]

Let $a_k$ denote the kth term of the sequence. Then

$a_k=a_1+d(k-1)$

where d is the common difference between consecutive terms in the sequence and a₁ is the first term.

The sum of the first n terms is

$S_n=\displaystyle\sum_{k=1}^na_k=a_1+a_2+\cdots+a_{n-1}+a_n$

From the formula for $a_k$ , we get

$S_n=\displaystyle\sum_{k=1}^n(a_1+d(k-1))=a_1\sum_{k=1}^n1+d\sum_{k=1}^n(k-1)$

$S_n=\displaystyle na_1+d\sum_{k=0}^{n-1}k$

$S_n=na_1+\dfrac{d(n-1)n}2$

$S_n=\dfrac n2(2a_1-d+dn)$

So we have $d=-5$ , and $2a_1-d=16$ so that $a_1=\frac{11}2$ .

Then the nth term in the sequence is

$a_n=\dfrac{11}2-5(n-1)=\boxed{\dfrac{21-10n}2}$

7 0

3 years ago

5d2-50d+125 = Fully factor each expression

Ede4ka [16]

First, let's start off by simplifying as much as possible before factoring.

5d^2 - 50d + 125

We can divide all the numbers by 5 in order to simplify it:

5(d^2 - 10d + 25)

Now all we need to do is factor.
Since -5*-5 = 25 and -5 - 5 = -10, we can use this to factor:

5(d - 5)(d - 5)
Or
5(d - 5)^2

8 0

2 years ago

The quarterback Tom Brady completes 60% of his passes. To simulate the outcome of a single pass we use the digits 0, 1, 2, 3, 4,

zaharov [31]

Answer:

A. Repeat the simulation several more times

Step-by-step explanation:

The purpose of the simulation model is to represent the effectivity of the passes.

The proportion of successful passes is 60%.

As we have 10 digits available, 6 (digits from 0 to 5) are used for the outcome "the pass is completed" and 4 (digits 6, 7, 8, and 9) to represent the outcome "the pass is not completed". This is correct, as it represents a probability of 60% of having a successful pass.

But to have a representative distribution of the possible and probable results, the simulation have to run enough times to have a stable distribution of the results.

6 0

2 years ago

Graph the ordered-pair solutions of y=lx-1 when x=-5, -3,,0,1,2.

34kurt

Y = x - 1
y = -5 - 1
y = -6
(x, y) = (-5, -6)

y = x - 1
y = -3 - 1
y = -4
(x, y) = (-3, -4)

y = x - 1
y = 0 - 1
y = -1
(x, y) = (0, -1)

y = x - 1
y = 1 - 1
y = 0
(x, y) = (1, 0)

y = x - 1
y = 2 - 1
y = 1
(x, y) = (2, 1)

4 0

2 years ago

Complete the point-slope equation

BigorU [14]

Answer:

y -3 = -1/2 x (x-1)

Step-by-step explanation:

4 0

2 years ago