Does the relationship between elapsed time x and distance traveled Y represent a proportional relationship?

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The population of a city is represented by the function p(t)=33,500(1.014)^t where t represents time in years and corresponds to the year 2000. According to this model, what is the expected population of the city 2015

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Replace t with 15 (2015-2000):

$p(15)=33,500(1.014)^(15)\n \n p(15)=33,500(3,8729)\n \n p(15) \approx 129,742 \ inhabitants$

$p(t) = 33500(1.014)^t\n \n t = (2015 - 2000) = 15\n \n i.e., p(15) = 33500(1.014)^(15) \n \n => p(15) = 33500.38729 \n \n => 1297421500$

A circle is defined by the equation x2 + y2 + 8x + 22y + 37 = 0. What are the coordinates for the center of the circle and the length of the radius?

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The center of the circle is: (-4 ; -11) and the radius of the circle is r = 10

What is equation of circle?

The general equation for a circle is (x-a)² + (y-b)² = r², where ( a, b ) is the center and r is the radius.

Given:

x² + y² + 8x + 22y + 37 = 0.

Now, to find both coordinates and radius write the given equation in standard form:

(x-a)² + (y-b)² = r²

x² + 8x + y²+ 22y= -37

( x² + 2* x*4 + 4²)+( y² + 2*y* 11 + 11²) = -37 + 16 + 121

(x + 4)² + ( y+ 11)² = 100

(x + 4)² + ( y+ 11)² = 10²

So, center of the circle is: (-4 ; -11)

and the radius of the circle is r = 10

Learn more about this concept here;

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We can say that:
8x = -2ax
8 = -2a
a = -4

22y = - 2by
22 = -2b
b = -11

37 = a² + b² - r²
37 = (-4)² + (-11)² - r²
r² = 16 + 121 - 37
r² = 100
r = 10

With all this information, we can say that:
The center of the circle is: (-4 ; -11)
and the radius of the circle is r = 10

P.S:
(a - x)² + (b-y)² = r²
a² - 2ax + x² + b² -2by + y² - r² = 0
x² + y² -2ax - 2by + a² + b² - r² = 0

A worker at a mill is loading 5 pound bags of flour into boxes to deliver to a local warehouse. Each box holds 16 bags of flour. If the warehouse orders 4 tons of flour how many boxes are needed to fulfill the order ?

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Answer:

100

Step-by-step explanation:

volume of 16 bags of flour: 16 x 5 = 80 pounds

We know that: 1 ton = 2,000 pounds -> 4 tons = 2,000 x 4 = 8,000

So we need: 8,000 : 80 = 100 boxes to fulfill the order

Mr. Ishimoto ordered x new math books and y new workbooks for his class. The total weight of the box of books cannot be more than 50 pounds. If each math book weighs 3.2 pounds and each workbook weighs 0.8 pounds, which inequality represents the maximum number of each type of book that can be shipped in a single box?

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Answer:

3.2x + 0.8y ≤ 50

Step-by-step explanation:

Mr. Ishimoto ordered math books and workbooks for his class.

Weight of each math book = 3.2 pounds

number of math books ordered = x

so, total weight of math books = 3.2x

Weight of each workbook = 0.8 pounds

number of workbooks ordered = y

so, total weight of workbooks = 0.8y

Since the total weight of the box of books cannot be more than 50 pounds, the equation would be

3.2x + 0.8y ≤ 50

Answer: B

Step-by-step explanation:

How to solve pemdas?

Answers

PEMDAS
P=Parenthesis.
E=Exponent.
MD=Multiplication/Division
AS=Addition/Subtraction

Be sure to follow the order

Answer: PEMDAS Stands for:

P- Parentheses

E- Exponents

M- Multiplication

D- Division

A- Addition

S- Subtraction

All you have to do is do the equation in this order!

when (2x - 3)^2 is subtracted from 5x^2, what is the result? And how can I show the answer? Thank you x

Answers

5x^2 - (2x - 3)^2 =
5x^2 - ((2x - 3)(2x - 3)) =
5x^2 - (4x^2 - 6x - 6x + 9) =
5x^2 - (4x^2 - 12x + 9) =
5x^2 - 4x^2 + 12x - 9 =
x^2 + 12x - 9 <===

first expand (2x-3)^2
(2x-3)(2x-3)=(2x-3)(2x)+(2x-3)(-3)=4x²-6x-6x+9=4x²-12x+9

so
5x²-(4x²-12x+9)=5x²-4x²+12x-9=x²+12x-9

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