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marissa [1.9K]
3 years ago
9

Write the standard equation of a circle with a center (2,-8) and radius 9

Mathematics
1 answer:
Anna11 [10]3 years ago
6 0

The standard equation of a circle:

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

(h, k) - center

r - radius

We have:

(2, -8) → h = 2, k = -8

r = 9

Substitute:

(x-2)^2+(y-(-8))^2=9^2\\\\(x-2)^2+(y+8)^2=81

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Answer:

The pattern is that they are multiplying by -3 every time. 81*-3 = -243

4 0
2 years ago
In ΔLMN, \overline{LN}
Karolina [17]

Answer:

\bold{\angle NLM = 10^\circ}

Step-by-step explanation:

Given a ΔLMN.

Line LN is extended to point O.

such that:

\text{m}\angle MNO = (5x-13)^{\circ}

\text{m}\angle NLM = (x-4)^{\circ} and

\text{m}\angle LMN = (2x+19)^{\circ}

To find:

\text{m}\angle NLM=?

Solution:

Kindly refer to the attached image for the given triangle and dimensions of angles.

Let us recall the external angle property of a triangle:

The external angle of a triangle is equal to the sum of two opposite internal angles.

i.e.

\angle MNO = \angle NLM + \angle LMN\\\Rightarrow 5x-13 = x-4+2x+19\\\Rightarrow 5x-13 = 3x+15\\\Rightarrow 5x-3x = 13+15\\\Rightarrow 2x=28\\\Rightarrow x =14

Putting the value of x in \angle NLM.

\angle NLM=14-4 \\\Rightarrow \bold{\angle NLM = 10^\circ}

5 0
3 years ago
William buys a book for $14.85. If he pays with a $20 bill, what will his change c be? Write an equation.
butalik [34]
<h3>Answer:  14.85 + c = 20</h3>

============================================================

Reason:

To compute the change, we subtract the amount William gives the cashier (the $20) and the price of the book ($14.85)

The change c is

c = 20-14.85

To rearrange this equation, we can add 14.85 to both sides to end up with 14.85 + c = 20

In other words, solving that equation in bold leads to c = 20-14.85 = 5.15 which is the change William is given.

----------------

Extra info (optional section)

If the cashier wanted to mentally figure out the change in his/her head, then notice the jump from 85 cents to 100 cents is 15 cents. That means we go from 14.85 to 15.00

Then the jump from $15 to $20 is an extra 5 dollars. Overall, the total change given back to William is 0.15+5 = 5.15 dollars.

4 0
3 years ago
Let [n] represent the greatest even integer less than n that divides n, for any positive integer n. For example, [24] = 12. What
ipn [44]
First you write down all even integers that divide 20.

Those are: 2,4,10,20

Since the request is that integer is less than n, 20 cannot be the answer.
This means that greatest even integer is 10

Answer is 10.
7 0
3 years ago
In two-equation what is the answer to 2p+14=0, i need it ASAP class is about to end PLS
Oduvanchick [21]

Answer:

p= −7

Step-by-step explanation:

7 0
3 years ago
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