Find the x-intercepts for y = -7x2 + 4x + 9 using the quadratic formula. Choose all

1-1 Relations and Functions Marcus drives 32 miles to work each day. He records the number of minutes it takes him to drive and

Korvikt [17]

Answer:

A. <em>[0, 65]</em>

Step-by-step explanation:

Given that

Distance that Marcus drives every day = 32 miles.

The table having average speed as input and time taken as output is shown below in the table format:

$\begin{center}\begin{tabular}{ c c}Speed(mph) & Time(minutes) \\ 60 & 32 \\ 45 & 43 \\ 55 & 35 \\ 50 & 38 \\ 62 & 31 \\\end{tabular}\end{center}$

To find:

The domain that includes all possible average speeds using interval notation = ?

Solution:

First of all, let us understand what is a domain of a function.

Domain of a function is set of valid input values that can be provided to the function so that it has a valid output.

If a function is written as:

$y=f(x)$ then values of $x$ are the input given to the function.

In the given question statement, we are given that maximum Average speed attained by Marcus is 65 miles per hour.

That means domain has a maximum value of 65.

Let us learn something about interval notation.

( or ) means the value is not inclusive.

[ or ] means the value is inclusive.

Here 65 will be inclusive.

On the left side of comma, lower value is written and on the right side of comma, larger value is written.

So, domain for the current situation will be:

0 is taken as the minimum value of domain here, because average speed value can not be negative.

This interval will contain all the possible values of input (average speed) as shown in the above table of values.

8 0

3 years ago

Given limit of f (x) = 4 as x approaches 0. what is limit of one-fourth left-bracket f (x) right-bracket superscript 4 baseline

Otrada [13]

The limit of the given function if $\lim_{x \to 0} f(x)=4$ is 64

<h3>Limit of a function</h3>

Given the following limit of a function expressed as;

$\lim_{x \to 0} f(x)=4$

We are to determine the value of the function

$\frac{1}{4} \lim_{x \to 0} [f(x)]^4$

This can also be expressed as

$\frac{1}{4} \lim_{x \to 0} [f(x)]^4\\ = \frac{1}{4}(4)^4 \\=1/4\times 256\\=64$

Hence the limit of the given function if $\lim_{x \to 0} f(x)=4$ is 64

Learn more on limit of a function here: brainly.com/question/23935467

#SPJ1

4 0

1 year ago

The given line segment has a midpoint at (3, 1).

Katena32 [7]

Answer:

$y=\frac{1}{3}x$

Step-by-step explanation:

The given line segment has a midpoint at (3, 1) and goes through (2, 4), (3, 1), and (4, -2). We can use any two of the three points to calculate the equation of the line. Let us use the points (2, 4) and (4, -2)

Therefore the line goes through (2, 4) and (4, -2). The equation of a line passing through $(x_1,y_1)\ and\ (x_2,y_2)$ is:

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$ .

Therefore the line passing through (2, 4) and (4, -2) has an equation:

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}\\\frac{y-4}{x-2}=\frac{-2-4}{4-2}\\\frac{y-4}{x-2}=\frac{-6}{2}\\y-4=x-2(-3)\\y-4=-3x+6\\y=-3x+10$

Comparing with the general equation of line: y = mx + c, the slope (m) = -3 and the intercept on the y axis (c) = 10

Two lines are said to be perpendicular if the product of their slope is -1. If the slope of line one is m1 and the slope of line 2 = m2, then the two lines are perpendicular if:

$m_1m_2=-1$ .

Therefore The slope (m2) of the perpendicular bisector of y = -3x + 10 is:

$m_1m_2=-1\\-3m_2=-1\\m_2=\frac{1}{3}$

Since it is the perpendicular bisector of the given line segment, it passes through the midpoint (3, 1). The equation of the perpendicular bisector is:

$\frac{y-y_1}{x-x_1}=m\\\frac{y-1}{x-3}=\frac{1}{3}\\ y-1= \frac{1}{3}(x-3)\\ y-1=\frac{1}{3}x-1\\y=\frac{1}{3}x$

the equation, in slope-intercept form, of the perpendicular bisector of the given line segment is $y=\frac{1}{3}x$

7 0

3 years ago

Read 2 more answers

Someone help me on question 10 please!

Crazy boy [7]

Answer:

Step-by-step explanation:

500÷9=55.56miles/h (correct to 3 decimal places)

7 0

2 years ago

A particular computer takes 14 minutes to download a 56-minute TV show. How long will it take the computer to download a 2.5-h

charle [14.2K]

Answer:

240 minutes

Step-by-step explanation:

step 1 - 1:56÷14=4

step 2 - 2:4×60=240

4 0

3 years ago