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3 years ago

What is the equation of the line that passes through (0, 2) and (-3, 14) in slope-intercept

1 answer:

6 0

Answer: y=-4x+2

Why: Find slope— 2-14/0+3 = -12/3 = -4

First put it in slope point form
y-2=-4(x-0)

Simplify
y-2=-4x

So...
y=-4x+2

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A car, initially at rest, accelerates at 2 meters/s/s. assuming the car starts from rest, how far will it travel in 10 s?

MrRa [10]

We shall use the formula for distance traveled:
s = ut + (1/2)at^2
where
u = initial velocity
t = time
a = acceleration.

Because
u = 0 (car starts from rest),
t = 10 s (travel tme),
a = 2 m/s^2 (acceleration), m
the di mstance traveled is
s = (1/2)*(2 m/s^2)*(10 s)^2 = (1/2)*2*100 = 100

Answer: 100 m

8 0

3 years ago

Please hurry Solve: -23 = x - 23 *

Monica [59]

Answer:

x = 0

Step-by-step explanation:

add 23 on both side and x equals zero

substitute x for 0, and the equation is still correct

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3 years ago

Read 2 more answers

The first term of an arithmetic sequence is 23 and the 37th term of the sequence is -49. What is the common difference of the se

Leona [35]

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3 years ago

Tacoma's population in 2000 was about 200 thousand, and had been growing by about 9% each year. a. Write a recursive formula for

KIM [24]

Answer:

a) The recurrence formula is $P_n = \frac{109}{100}P_{n-1}$ .

b) The general formula for the population of Tacoma is

$P_n = \left(\frac{109}{100}\right)^nP_{0}$ .

c) In 2016 the approximate population of Tacoma will be 794062 people.

d) The population of Tacoma should exceed the 400000 people by the year 2009.

Step-by-step explanation:

a) We have the population in the year 2000, which is 200 000 people. Let us write $P_0 = 200 000$ . For the population in 2001 we will use $P_1$ , for the population in 2002 we will use $P_2$ , and so on.

In the following year, 2001, the population grow 9% with respect to the previous year. This means that $P_0$ is equal to $P_1$ plus 9% of the population of 2000. Notice that this can be written as

$P_1 = P_0 + (9/100)*P_0 = \left(1-\frac{9}{100}\right)P_0 = \frac{109}{100}P_0$ .

In 2002, we will have the population of 2001, $P_1$ , plus the 9% of $P_1$ . This is

$P_2 = P_1 + (9/100)*P_1 = \left(1-\frac{9}{100}\right)P_1 = \frac{109}{100}P_1$ .

So, it is not difficult to notice that the general recurrence is

$P_n = \frac{109}{100}P_{n-1}$ .

b) In the previous formula we only need to substitute the expression for $P_{n-1}$ :

$P_{n-1} = \frac{109}{100}P_{n-2}$ .

Then,

$P_n = \left(\frac{109}{100}\right)^2P_{n-2}$ .

Repeating the procedure for $P_{n-3}$ we get

$P_n = \left(\frac{109}{100}\right)^3P_{n-3}$ .

But we can do the same operation n times, so

$P_n = \left(\frac{109}{100}\right)^nP_{0}$ .

c) Recall the notation we have used:

$P_{0}$ for 2000, $P_{1}$ for 2001, $P_{2}$ for 2002, and so on. Then, 2016 is $P_{16}$ . So, in order to obtain the approximate population of Tacoma in 2016 is