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3 years ago

. Center at (-4,-1), radius = 2

Mathematics

1 answer:

valkas [14]3 years ago

6 0

Consider we need to find the equation of the circle.

Given:

The Center at (-4,-1), radius = 2.

To find:

The equation of the circle.

Solution:

The standard form of a circle is

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

Where, (h,k) is the center of the circle and r is the radius of the circle.

Putting h=-4, k=-1 and r=2, we get

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

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

Therefore, the equation of the circle is $(x+4)^2+(y+1)^2=4$ .

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nataly862011 [7]

So what you do is go 5(3y+5)-4y=14 which equals 15y+25-4y=14 which turns into 11y+25=14 than you move the 25 over which equals 11y=-11 so y=-1 then you enter -1 in for y which looks like 5x-4(-1)=14 than you solve that which is 5x+4=14 than you move the 4 over and you get 5x=10 than x=2

x=2
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3 years ago

How are determinants used to find areas of polygons?

ANTONII [103]

When you arrange the N points in sequence around the polygon (clockwise or counterclockwise), the area is half the magnitude of the sum of the determinants of the points taken pairwise. The N determinants will also include the one involving the last point and the first one.

For example, consider the vertices of a triangle: (1,1), (2,3), (3,-1). Its area can be computed as
(1/2)*|(1*3-1*2) +(2*-1-3*3) +(3*1-(-1)*1)|
= (1/2)*|1 -11 +4| = 3

4 0

3 years ago

You borrow money for 4 years. The total amount that you repay is $7,840, which includes $840 in simple interest. How much was th

Lina20 [59]

Answer:

principal: $7000
interest rate: 3%

Step-by-step explanation:

amount repaid = principal + interest

$7840 = principal + $840

$7000 = principal . . . . . . . . subtract $840 from both sides of the equation

___

I = Prt

840 = 7000·r·4

840/(4·7000) = r = 0.03 = 3%

The principal was $7000; the interest rate was 3%.

6 0

3 years ago

Simplify the expression.<br><br> [(11 - 4)^3]^2 ÷ (4 + 3)^5

MAXImum [283]

Answer:

Step-by-step explanation:

$\left[\left(11\:-\:4\right)^3\right]^2\:\div \left(4\:+\:3\right)^5\\\\\frac{\left(\left(11-4\right)^3\right)^2}{\left(4+3\right)^5}\\\\\mathrm{Subtract\:the\:numbers:}\:11-4=7\\\\=\frac{\left(7^3\right)^2}{\left(4+3\right)^5}\\\\\mathrm{Add\:the\:numbers:}\:4+3=7\\\\=\frac{\left(7^3\right)^2}{7^5}\\\\\left(7^3\right)^2=7^6\\\\=\frac{7^6}{7^5}\\\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\\\\\frac{7^6}{7^5}=7^{6-5}\\\\\mathrm{Subtract\:the\:numbers:}\:6-5=1\\\\=7$

5 0

3 years ago

Company has 189 employees that share an office that has 32 floors. If they built another building for 50 employees, how high sho

iris [78.8K]

Answer:

8 floors

Step-by-step explanation:

The number of employees is directly proportional to the number of floors that each building has.

The first building has 32 floors and it occupies 189 employees. Therefore:

189 α 32

=> 189 = k * 32 = 32k

where k = constant of proportionality

=> k = 189/32

The new building has 50 employees, therefore:

50 = kN

where N = number of floors

=> 50 = 189/32 * N

N = (50 * 32) / 189 ≅ 8 floors

The new building should have 8 floors

5 0

3 years ago

. Center at (-4,-1), radius = 2​

. Center at (-4,-1), radius = 2