All categories

2 years ago

Graph each equation. 56) y = |x-31-3 I if it if it it of .

Mathematics

1 answer:

BabaBlast [244]2 years ago

3 0

Step-by-step explanation:

The slope-intercept form is y=mx+b y = m x + b , where m m is the slope and b b is the y-intercept. Find the values of m m and b b using the form y=mx+b y = m x + b .

You might be interested in

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

$P_{16} = \left(\frac{109}{100}\right)^{16}P_{0} = (1.09)^{16}P_0 = 3.97\cdot 200000 \approx 794062$

d) In this case we want to know when $P_n>400000$ , which is equivalent to

$(1.09)^{n}P_0>400000$ .

Substituting the value of $P_0$ , we get

$(1.09)^{n}200000>400000$ .

Simplifying the expression:

$(1.09)^{n}>2$ .

So, we need to find the value of $n$ such that the above inequality holds.

The easiest way to do this is take logarithm in both hands. Then,

$n\ln(1.09)>\ln 2$ .

So, $n>\frac{\ln 2}{\ln(1.09)} = 8.04323172693$ .

So, the population of Tacoma should exceed the 400 000 by the year 2009.

8 0

3 years ago

Read 2 more answers

It takes 54 minutes for 4 people to paint 6 walls. How many minutes does it take 6 people to paint 7 walls?

Nady [450]

It takes 35 mins for 6 people to paint 7 walls if you would like this answer described to you let me know please

6 0

3 years ago

Read 2 more answers

The total number of items sold by each student who participated in the fundraiser is showing in the stem and leaf plot

kenny6666 [7]

The statement that is best supported by the data in the stem and leaf plot is D. The most common number of items sold is 15.

<h3>How to illustrate the information?</h3>

It should be noted that the stem and plot diagram is important to illustrate the data given.

Based on the information given, the most common number of items sold is 15.

In conclusion, the correct option is D.

Learn more about stem plot on:

brainly.com/question/23450543

#SPJ1

The total number of items sold by each student who participated in a fund-raiser is shown in the stem and leaf plot.

Which statement is best supported by the data in the stem and leaf plot?

The number of students who sold between 10 and 20 items is greater than the number of students who sold more then 40 items.

The number of students who sold more than 30 items is greater than the number of students who sold fewer than 30 items.

The most common number of items sold is 30.

The most common number of items sold is 15.

4 0

1 year ago

A large water tank holds 210 liters of water. About how many gallons of water does the same tank hold, if there are approximatel

shusha [124]

Answer:

Step-by-step explanation:

Set up a proportion

15 Liters / 4 gallons = 210 Liters / x Cross Multiply

15x = 4 * 210 Combine the right

15x = 840 Divide by 15

x = 840 / 15

x = 56 gallons

4 0

3 years ago

Is X=3 calculate the value of X3+X btw the 3 is a small three

Naddik [55]

The only 'small number' that I know that would affect the answer is an exponent that looks like ³ so the problem would be x³+x

remember that x³=x times x times x
if x=3 then
3³+3=27+3=30

3 0

3 years ago

Read 2 more answers