(-1/2)^3 divided by (1/4)^5

A movie theater has increased their ticket prices. They are shown below

hram777 [196]

Answer:

k = 12

Step-by-step explanation:

Given in the question,

Cost of the the movie tickets is proportional to the number of tickets sold.

Cost of movie tickets (C) ∝ number of tickets sold (T)

C ∝ T

C = kT

Here 'k' is a proportionality constant.

Since, line given in the graph passes through a point (5, 60)

60 = k(5)

k = $\frac{60}{5}$

k = 12

Therefore, value of proportionality constant is 12.

6 0

3 years ago

The population of a rabbit colony triples every 3 days. The population starts at 10 rabbits. Write an exponential function that

qaws [65]

Answer:

Step-by-step explanation:

The population at various days is as follows since population triples every 3 days

Day Population

0 10

3 30

6 90

9 270

.... ......

This can be modeled by the general equation

$n_{t} = n_{0}(r)^{t/k}$

where

$n_{t}$ is the population after t days

$n_{0}$ is the population at start (10)

$r$ is the rate at which population changes ie 3

$t$ is the number days from start

$k$ is the number of days at which the population triples(here k =3 days)

We can check this by plugging in values for each of the variables

At day 0, population = 10(3)⁰ = 10. 1 = 10

Similarly populations for days 3, 6, 9 are:

$\\\\10.3^{3/3} = 10. 3^1 = 10.3 = 30\\10.3^{6/3} = 10. 3^2 = 10.9 = 90\\\\10.3^{9/3} = 10. 3^3 = 10.27 = 270$

8 0

1 year ago

Read 2 more answers

8(x-4) simplify this equation

creativ13 [48]

Answer: 8x - 32

Work:

Simplify using the distributive property of multiplication.

8(x) = 8x
8(-4) = -32

Simplified expression: 8x - 32

3 0

3 years ago

Solve using the quadratic formula 2x^2+x+67=0

telo118 [61]

Answer:

$\displaystyle x=\frac{-1 \pm i\sqrt{535}}{2}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Multiple Roots
Standard Form: ax² + bx + c = 0
Quadratic Formula: $\displaystyle x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

Algebra II

Imaginary Root i = √-1

Step-by-step explanation:

Step 1: Define

Identify

2x² + x + 67 = 0

a = 2

b = 1

c = 67

Step 2: Solve for x

Substitute in variables [Quadratic Formula]: $\displaystyle x=\frac{-1 \pm \sqrt{1^2-4(2)(67)}}{2(1)}$
Multiply: $\displaystyle x=\frac{-1 \pm \sqrt{1^2-4(2)(67)}}{2}$
[√Radical] Evaluate exponents: $\displaystyle x=\frac{-1 \pm \sqrt{1-4(2)(67)}}{2}$
[√Radical] Multiply: $\displaystyle x=\frac{-1 \pm \sqrt{1-536}}{2}$
[√Radical] Subtract: $\displaystyle x=\frac{-1 \pm \sqrt{-535}}{2}$
[√Radical] Simplify: $\displaystyle x=\frac{-1 \pm i\sqrt{535}}{2}$