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luda_lava [24]
3 years ago
15

About 150,000 people live in a circular region with a population density of about

Mathematics
1 answer:
morpeh [17]3 years ago
8 0

Area of a circle = pi x r^2

Area of circle = 150,000/ 1578 = 95.06 square miles

95.06 = 3.14 x r ^2

Divide both sides by 3.14

R^2 = 30.27

Find the square root:

R = sqrt(30.27)

R = 5.5

The radius is c) 5.5 miles

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2. Solve the following system. Show all your work. {3x - 2y + 2z = 30 {-x + 3y - 4z = -33 {2x - 4y + 3z = 42
Semmy [17]
From the system of equations, we have 3 unknowns and 3 equations. Therefore, it can be solved. 

<span>3x - 2y + 2z = 30  (1)
</span><span>-x + 3y - 4z = -33  (2)
</span><span>2x - 4y + 3z = 42   (3)

We can write equation 2 x as a function of y and z and substitute the new equation to the other equations.
</span>x =3y - 4z + 33  (2)

3 (3y - 4z + 3)<span> - 2y + 2z = 30  (1)
</span>2 (3y - 4z + <span>3)</span> - 4y + 3z = 42   (3)

We simplify and solve the equations and we get values,

x = 4
y = -7
z = 2
6 0
3 years ago
Nth term sequences, please may I get some help. 15 p.
Dovator [93]

Answer:

(n+2)^2+6

Step-by-step explanation:

Pattern 1 consists of

3+3\times 3+3 small squares (here n = 1 and 3\times 3=(1+2)\times (1+2)).

Pattern 2 consists of

3+4\times 4+3 small squares (here n = 2 and 4\times 4=(2+2)\times (2+2)).

Pattern 3 consists of

3+5\times 5+3 small squares (here n = 3 and 5\times 5=(3+2)\times (3+2)).

Thus, pattern n consists of

3+(n+2)\times (n+2)+3=6+(n+2)^2 small squares.

3 0
3 years ago
The sum of w and 5 into algebraic expression
Alina [70]

Answer: w + 5

Step-by-step explanation: The sum of w and 5 translates into an algebraic expression form to w + 5.

7 0
3 years ago
What is the maximum volume in cubic inches of an open box to be made from a 12-inch by 16-inch piece of cardboard by cutting out
Romashka-Z-Leto [24]

If you start with a 12x16 rectangle and cut square with side length x, when you bend the sides you'll have an inner rectangle with sides 12-2x and 16-2x, and a height of x.

So, the volume will be given by the product of the dimensions, i.e.

(12-2x)(16-2x)x = 4x^3-56x^2+192x

The derivative of this function is

12x^2-112x+192

and it equals zero if and only if

12x^2-112x+192=0 \iff x = \dfrac{14\pm 2\sqrt{13}}{3}

If we evaluate the volume function at these points, we have

f\left(\dfrac{14-2\sqrt{13}}{3}\right) = \dfrac{64}{27}(35+13\sqrt{13})> f\left(\dfrac{14-2\sqrt{13}}{3}\right) = -\dfrac{64}{27}(13\sqrt{13}-35)

So, the maximum volume is given if you cut a square with side length

x=\dfrac{14-2\sqrt{13}}{3}\approx 2.7

5 0
3 years ago
Help find out what the x is please
miss Akunina [59]

Answer:

x=4

Step-by-step explanation:

First you want to add 8.8 to 7.2 and get 16 because you want to get x alone

Next divide divide 4x on both sides so 4x/4x cross out and left with just x. 16/4 =4

x=4

Hope this helps!


6 0
3 years ago
Read 2 more answers
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