Which statement about property tax is

What is the equation of the line that goes through (-3,-1) and (3,3)?

Monica [59]

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, - 1) and (x₂, y₂ ) = (3, 3)

m = $\frac{3+1}{3+3}$ = $\frac{4}{6}$ = $\frac{2}{3}$ , thus

y = $\frac{2}{3}$ x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (3, 3), then

3 = 2 + c ⇒ c = 3 - 2 = 1

y = $\frac{2}{3}$ x + 1 ← equation of line

Multiply through by 3

3y = 2x + 3 ( subtract 3y from both sides )

0 = 2x - 3y + 3 ( subtract 3 from both sides )

- 3 = 2x - 3y, that is

2x - 3y = - 3 ← in standard form

8 0

4 years ago

Read 2 more answers

Use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of t.) −

aleksley [76]

When it comes to laplace equations, there are transformation equations to follow. Generally, when you want to transform a laplace equation, you change the equation from f(t) to F(s). If you do the reverse, it is called the reverse laplace equation.

Based on the given, the useful transformation equation is shown in the attached picture.

When the term is s^2, that must mean that the equation is 1!/s^(1+1) to yield 1/s^2. This means that n=1. Taking the reciprocal s^2 must be equal to 1/t. Thus, for the first term, -11s^2 is equal to -11/t. For the second term, n must be equal to 6 so that 6!/s^(6+1) would yield 720/s^7. Thus, 720s^7 is equal to 1/t^6.

Hence, the transformed equation is -11/t - 1/t^6

4 0

3 years ago

A hotel rents 210 rooms at a rate of $ 60 per day. For each $ 2 increase in the rate, three fewer rooms are rented. Find the roo

lidiya [134]

Answer:

r=$14,400

The hotel should charge $120

Step-by-step explanation:

Revenue (r)= p * n

where,

p = price per item

n = number of items sold

A change in price leads to a change in number sold

A variable to measure the change in p and n needs to be introduced

Let the variable=x

Such that

p + x means a one dollar price increase

p - x means a one dollar price decrease

n + x means a one item number-sold increase

n - x means a one item number-sold decrease

for each $2 price increase (p + 2x) there are 3 fewer rooms are rented (n-3x)

know that at $60 per room, the hotel rents 210 rooms

r = (60 + 2x) * (210 - 3x)

=12,600-180x+420x-6x^2

=12,600+240x-6x^2

r=2100+40x-x^2

= -x^2 +40x+2100=0

Solve the quadratic equation

x= -b +or- √b^2-4ac / 2a

a= -1

b=40

c=2100

x= -b +or- √b^2-4ac / 2a

= -40 +or- √(40)^2 - (4)(-1)(2100) / (2)(-1)

= -40 +or- √1600-(-8400) / -2

= -40 +or- √ 1600+8400 / -2

= -40 +or- √10,000 / -2

= -40 +or- 100 / -2

x= -40+100/-2 OR -40-100/-2

=60/-2 OR -140/-2

= -30 OR 70

x=70

The quadratic equation has a maximum at x=70

p+2x

=60+2(30)

=60+60

=$120

r= (60 + 2x) * (210 - 3x)

={60+2(30)}*{(210-3(30)}

r=(60+60)*(210-90)

=120*120

=$14,400

7 0

3 years ago

The table shows a proportional relationship.

Ann [662]

X + (.8 x 1/2 of x) = y

5 0

3 years ago

When her number is divided by 12, the remainder is 6, what is the remainder when the number is idvided by 9?

pentagon [3]

Remainder: 6 when divided by 12
So 12x6= 72
Original number: 72
72/9= 8
The remainder: 8

3 0

4 years ago