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patriot [66]
1 year ago
15

50 points!! help asap pls

Mathematics
2 answers:
Roman55 [17]1 year ago
8 0

Answer:

Option D

Step-by-step explanation:

Given:

  • Radius = 10 units
  • Center point = (h, k) = (-4, -9)

∴ x coordinate of center point: (h, k) ⇒ (-4, -9)

∴ y coordinate of center point: (h, k) ⇒ (-4, -9)

<u>Equation of circle formula:</u>

  • ⇒ (x - h)² + (y - k)² = r²

<u>Substitute the radius in the formula;</u>

  • ⇒ (x - h)² + (y - k)² = r²
  • ⇒ (x - h)² + (y - k)² = (10)²

<u>Substitute the x and y coordinate in the formula;</u>

  • ⇒ [x - (-4)]² + [y - (-9)]² = (10)²      [x coordinate (h): -4; y coordinate (k): -9]
  • ⇒ [x + 4]² + [y + 9]² = 100   (Option D)

Therefore, Option D is correct.

Korvikt [17]1 year ago
6 0

Answer:

(x+4)² + (y+9)² = 100

Step-by-step explanation:

We want to find the equation of a circle with a radius of length 10 and a center at (-4, -9).

general equation of circle : (x-h)² + (y-k)² = r²

where (h,k) is at center and r = radius

the center is at (-4,-9) so h = -4 and k = -9 and the circle has a radius of 10 so r = 10

so we have (x-h)² + (y-k)² = r²

h = -4 , k = -9  and r = 10

(x-(-4))² + (y-(-9))² = 10²

==> apply double negative sign rule and remove parenthesis for -(-4) and -(-9)

(x+4)² + (y+9)² = 10²

==> simplify exponent

(x+4)² + (y+9)² = 100

and we are done!

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Thepotemich [5.8K]

To solve, simply do this:

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Then you'll get the answer, -7/16

7 0
3 years ago
Estimate the solution to the system of equations. asap, please!! I will mark for brain list
Darya [45]

Answer:

(1 \frac{1}{3}, 2 \frac{1}{3} )

Step-by-step explanation:

Given the 2 equations

7x - y = 7 → (1)

x + 2y = 6 → (2)

Multiplying (1) by 2 and adding to (2) will eliminate the y- term

14x - 2y = 14 → (3)

Add (2) and (3) term by term to eliminate y

15x = 20 ( divide both sides by 15 )

x = \frac{20}{15} = \frac{4}{3} = 1 \frac{1}{3}

Substitute this value of x into either of the 2 equations and solve for y

Substituting in (2)

\frac{4}{3} + 2y = 6

2y = 6 - \frac{4}{3} = \frac{14}{3} ( divide both sides by 2 )

y = \frac{7}{3} = 2 \frac{1}{3}

7 0
3 years ago
What is the value of 7(10 - 2^3) + 8 divided by 2
Zielflug [23.3K]

7(10-2^3)+8 \div 2 \\ \\ 7(10-8)+8 \div 2 \\ \\ 7(2)+8 \div 2 \\ \\ 7(2)+4 \\ \\ 14+4 \\ \\ \boxed{18}

5 0
1 year ago
Put these in order starting with the smallest.<br>9 3/2 <br>27 1/3 <br>125 2/3​
Pepsi [2]

Answer:

second, third,first

Step-by-step explanation:

first

3/2=1.5

9^1.5=27

second

1/3=0.333

27^0.333=3

third

2/3=0.667

125^0.667=25

3 0
3 years ago
A grain silo has the shape of a right circular cylinder surmounted by a hemisphere. If the silo is to have a volume of 505π ft3,
Romashka-Z-Leto [24]

Answer:

radius   x  = 3 ft

height   h = 23,8  ft

Step-by-step explanation:

From problem statement

V(t)  = V(cylinder) + V(hemisphere)

let x be radius of base of cylinder (at the same time radius of the hemisphere)

and h the height of the cylinder, then:

V(c)  = π*x²*h       area of cylinder = area of base + lateral area

                                              A(c)  = π*x²  +   2*π*x*h

V(h) = (2/3)*π*x³   area of hemisphere   A(h)  =   (2/3)*π*x²

A(t)  =  π*x²  +   2*π*x*h +   (2/3)*π*x²

Now A as fuction of x    

total volume   505  = π*x²*h  +  (2/3)*π*x³

h = [505 - (2/3)* π*x³ ]  /2* π*x    

Now we have the expression for A as function of x

A(x) =  3π*x² + 2π*x*h     A(x) = 3π*x² + 505  - (2/3)π*x³

Taking derivatives both sides

A´(x) =  6πx -  2πx²              A´(x) =  0         6x  - 2x²  = 0

x₁  =  0  we dismiss

6 - 2x = 0

x = 3     and   h = [505 - (2/3)* π*x³]/2* π*x

h  =  (505 - 18.84) / 6.28*3

h  = 23,8  ft

7 0
3 years ago
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