The populations of two towns, town A and town B, are being compared. The population of town A is 4×104 and the population of B is 2×105. How many times greater is the population of town B than town A? The masses of two objects are compared during a physics experiment. It is determined that object A has a mass of 4×10−3 grams and object B has a mass of 4×10−4 grams. How many times larger is the mass of object A than the mass of object B?

1. 5 times

2. 10 times

Step-by-step explanation:

1. Here, we want to know the number of times the population of town B is greater than the population of town A

The simple thing to do here is to divide the population of town B by the population of town A

From the question; population of town B is 2 * 10^5 while the population of town A is 4 * 10^4

So the number of times greater will be;

(2 * 10^5) / (4 * 10^4) = 5

So population of town B is 5 times greater

2. Just like the first question, to know the number of times, we simply divide the mass of object A by the mass of object B

That will be;

(4 * 10^-3) / (4 * 10^-4) = 10 times

So therefore object A is 10 times larger than object B

see below

Step-by-step explanation:

A.  f(x) = 4x^2 - 7x - 15

We need the numbers to multiply to- 15

1*15  and 3*5  

One of the terms multiplies by 4 (or 2)

Try 4 first

4*-3 +5 = -7   That works

-3+5 = -15

f(x) = (4x+5)(x-3)

B.  We want the x intercepts so set equal to 0

0 = (4x+5)(x-3)

Using  the zero product  property

0 = 4x+5    x-3 =0

-5 = 4x           x=3

-5/4 =x            x=3

C  End behavior

Let x be negative infinity

The function is dominate by 4x^2

f(-∞) = 4 ( -∞) ^2 = 4 (∞) = ∞  

At negative infinity the functions goes to infinity

Let x be  infinity

The function is dominate by 4x^2

f(∞) = 4 ( ∞) ^2 = 4 (∞) = ∞  

At  infinity the functions goes to infinity

Part D:

We know the zeros at 3 and -5/4

We know the vertex is at  halfway between the zeros

(3 -5/4) /2 =  7/4 /2 = 7/8

Since the parabola opens up (The coefficient of the x^2 term is positive), we know we have a minimum.

f(7/8) = 4 (7/8)^2 -7(7/8) -15 = 4(49/64) -1/8 -15 =-289/16

We know the minimum the zeros and the end behavior, we can graph the functions