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3 years ago

Which equation represents a linear function?

Mathematics

1 answer:

Anna007 [38]3 years ago

5 0

Answer:

$y-2=-5(x - 2)$

Step-by-step explanation:

Given:

The equations given are:

$y-2=-5(x - 2)\\X+ 7 = -4(X + 8)\\y - 3 = y(x + 4)\\y + 9 = x(x - 1)$

Now, a linear function is of the form:

$y=mx+b$

Where, 'm' and 'b' are real numbers and $m\ne0$

Equation 1: $y-2=-5(x - 2)$

Simplifying using distributive property, we get:

$y-2=-5x+10\\y=-5x+10+2\\y=-5x+12$

The above equation is of the form $y=mx+b$ . So, it represents a linear function.

Equation 2: $X+ 7 = -4(X + 8)$

Here, both sides of the equation has same variable 'X'. So, it will form an equation of 1 variable. So, it's not a linear function.

Equation 3: $y - 3 = y(x + 4)$

Simplifying the above equation. This gives,

$y-3=yx+4y\\y-4y-yx=3\\y(1-4-x)=3\\y(-3-x)=3\\y=\frac{3}{(-3-x)}$

This is not of the form of the linear function. So, it is also not a linear function.

Equation 4: $y + 9 = x(x - 1)$

Simplifying the above equation. This gives,

$y+9=x^2-x\\y=x^2-x-9$

This is not of the form of the linear function. So, it is also not a linear function.

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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

A 13 meter long cylinder with a diameter of 8 meters has a square prism with a base length of 3 meters hole going all the way th

BartSMP [9]

The volume of the solid is 626.12m³

<h3>Volume of composite solids.</h3>

The volume of the given composite solid = volume of cylinder - volume of cube

The volume of cylinder Vc = πr²h

Vc = 3.14(8/2)²(13)

Vc = 3.14(16)(13)

Vc = 653.12 m³

Similarly the volume of the cube:

Volume of cube = 3³

Volume of cube = 27 m³

Volume of the solid = 626.12m³

Hence the volume of the solid is 626.12m³

Learn more on volume of composite solid here; brainly.com/question/9076728

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2 years ago

What is 7p-(-5)+(-1)

nika2105 [10]

7p-(-5)+(-1)
7p+5-1
7p+4

7 0

3 years ago

Read 2 more answers

Ayuda con mates por favor

QveST [7]

Answer:

a) $x = -1$ and $y = 5$ , b) $x = 2$ and $y = -1$ , c) $x = -2$ and $y = 1$ , d) $x = 2$ and $y = -9$ , e) $x = 2$ and $y = -2$ , f) $x = 2$ and $y = -1$ , g) $x = 2$ and $y = -1$ , h) $x = 1$ and $y = 2$ .

Step-by-step explanation:

Each system is solved as follows (Cada sistema es resuelto como sigue):

a) $2\cdot x + y = 3$ and $3\cdot x - y = -8$

$y = 3 - 2\cdot x$

$3\cdot x - 3 + 2\cdot x = -8$

$5\cdot x = -5$

$x = -1$

$y = 5$

b) $x - 2\cdot y = 4$ and $-x+3\cdot y = -5$

$x = 4 + 2\cdot y$

$-4-2\cdot y+3\cdot y = - 5$

$-4+y = -5$

$y = -1$

$x = 2$

c) $-2\cdot x + 5\cdot y = 9$ and $x - y = -3$

$x = y-3$

$-2\cdot y +6 +5\cdot y = 9$

$3\cdot y = 3$

$y = 1$

$x = -2$

d) $5\cdot x - 4\cdot y = 2$ and $3\cdot x + 2\cdot y = -12$

$3\cdot x + 2\cdot y = -12$

$6\cdot x + 4\cdot y = -24$

$4\cdot y = -6\cdot x -24$

$5\cdot x +6\cdot x +24 = 2$

$11\cdot x = -22$

$x = 2$

$y = -9$

e) $x + y = 0$ and $2\cdot x +3\cdot y = -2$

$y = -x$

$2\cdot x -3\cdot x = -2$

$-x = -2$

$x = 2$

$y = -2$

f) $3\cdot x + 5\cdot y = 1$ and $x + y = 1$

$y = 1 - x$

$3\cdot x + 5 - 5\cdot x = 1$

$-2\cdot x = -4$

$x = 2$

$y = -1$

g) $5\cdot x - 2\cdot y = 12$ and $4\cdot x + 3\cdot y = 5$

$x = \frac{12+2\cdot y}{5}$

$x = \frac{5-3\cdot y}{4}$

$\frac{12+2\cdot y}{5} = \frac{5-3\cdot y}{4}$

$4\cdot (12+2\cdot y) = 5\cdot (5-3\cdot y)$

$48 + 8\cdot y = 25 - 15\cdot y$

$23\cdot y = -23$

$y = -1$

$x = 2$

h) $7\cdot x + 8\cdot y = 23$ and $3\cdot x + 2\cdot y = 7$

$3\cdot x + 2\cdot y = 7$

$12\cdot x + 8\cdot y = 28$

$8\cdot y = 28 - 12\cdot x$

$7\cdot x +28-12\cdot x = 23$

$-5\cdot x = -5$

$x = 1$

$y = 2$

8 0

3 years ago

Jeanine is twice as old as her brother Marc. If the sum of their ages is 24. How old is Jeanine?

Tanya [424]

Let Marc's age be x. If Jeanine is twice as old as Marc, then her age will be 2x. If their ages added together are 24, then you can create the following equation:

2x + x = 24
3x = 24
x = 8

Remember that x is Marc's age. So if Marc is 8, and Jeanine is twice as old, she will be 16.

4 0

3 years ago