All categories

3 years ago

Identify the horizontal asymptote of f(x) = quantity x squared plus 5 x minus 3 over quantity 4 x minus 1

1 answer:

6 0

We are given with the equation <span>f(x) = (x^2 + 5x - 3) / (4x -1). The horizontal asymptote tells the value of the function when x approaches a very big number. Substituting, 1 x 10^30, we get the value of 5.541. Likewise, when we substitute -1x10^-30, the value is -5.541. Hence the horizontal asymptote is y = 5.541.</span>

You might be interested in

Which number has the least absolute value? A) −5 B) −10 C) −20 D) −30

blsea [12.9K]

The correct answer is D because -30 is far away from 0

8 0

3 years ago

Read 2 more answers

Ana can finish a certain job in 10 hours. Together, Ana and Nina can finish the same job in 3 hours. How many hours can Nina fin

Over [174]

Answer: 4.5 hours

<u>Step-by-step explanation:</u>

$Ana: \dfrac{1}{10}\ \text{job per hour}\\\\Nina: \dfrac{1}{x}\ \text{job per hour}\\\\Together: \dfrac{1}{3}\ \text{job per hour}\\\\\\Ana + Nina = Together\\\dfrac{1}{10}\quad +\dfrac{1}{x}\quad =\quad \dfrac{1}{3}\\\\\\\dfrac{1}{10}(30x)+\dfrac{1}{x}(30x) =\dfrac{1}{3}(30x)\\\\\\\rightarrow\quad 3x+30=10x\\\\.\quad 3x+30=10x\\\underline{-3x\qquad \quad -3x\quad}\\.\qquad \quad 30=7x\\\\.\qquad \quad \dfrac{30}{7}=\dfrac{7x}{7}\\\\\\.\qquad \quad \dfrac{30}{7}=x$

$.\qquad \quad 4.5=x$

5 0

2 years ago

a bag contains 6 black marbles and 6 white marbles. What is the least number of marbles that you must choose, without looking, t

o-na [289]

Given:

Number of black marbles = 6

Number of white marbles = 6

Let's determine the least number of marbles that can be chosen to be certain that you have chosen two marble of the same color.

To find the least number of marble to be chosen to be cartain you have chosen two marbles of the same color, we have:

Total number of marbles = 6 + 6 = 12

Number of marbles to ensure at least one black marble is chosen = 6 + 1 = 7

Number of marbles to ensure at least one white marble is chosen = 1 + 6 = 7

Therefore, the least number of marbles that you must choose, without looking , to be certain that you have chosen two marbles of the same color is 7.

ANSWER:

6 0

1 year ago

Consider h(x)=x^2+8+15. identify its vertex and y-intercept.

OleMash [197]

Answer:

Vertex: (-4, -1)

Y-intercept: (0, 15)

Step-by-step explanation:

Given the quaratic function, h(x) = x² + 8x + 15:

In order to determine the vertex of the given function, we can use the formula, $[x = \frac{-b}{2a}, h(\frac{-b}{2a})]$ .

<h3>Use the equation: $[x = \frac{-b}{2a}, h(\frac{-b}{2a})]$ </h3>

In the quadratic function, h(x) = x² + 8x + 15, where:

a = 1, b = 8, and c = 15:

Substitute the given values for <em>a</em> and <em>b</em> into the equation to solve for the x-coordinate of the vertex.

$x = \frac{-b}{2a}$

$x = \frac{-8}{2(1)}$

x = -4

Subsitute the value of the x-coordinate into the given function to solve for the <u>y-coordinate of the vertex</u>:

h(x) = x² + 8x + 15

h(-4) = (-4)² + 8(-4) + 15

h(-4) = 16 - 32 + 15

h(-4) = -1

Therefore, the vertex of the given function is (-4, -1).

<h3>Solve for the Y-intercept:</h3>

The <u>y-intercept</u> is the point on the graph where it crosse the y-axis. In order to find the y-intercept of the function, set x = 0, and solve for the y-intercept:

h(x) = x² + 8x + 15

h(0) = (0)² + 8(0) + 15

h(0) = 0 + 0 + 15

h(0) = 15

Therefore, the y-intercept of the quadratic function is (0, 15).

5 0

2 years ago

A large city has a population of 8,000,000 and an area of 20.5 square miles. what is the city's approximate population density?

gayaneshka [121]

Answer: Approximately 390,244 people per square mile

Work Shown:

Density = population/area

Density = (8 million people)/(20.5 square miles)

Density = 390,243.9024 approximately

This rounds to 390,244 since we're talking about the number of people.

3 0

2 years ago