If 1 gallon of paint covers 300 square feet, how many gallons

Without using a calculator, determine the number of real zeros of the function

kumpel [21]

The number of real zeros of the function f(x) = x3 + 4x2 + x − 6 is 3

<h3>How to determine the number of real zeros?</h3>

The equation of the function is given as:

$f(x) = x^3 + 4x^2 + x - 6$

Expand the function

$f(x) = x^3 + 5x^2 - x^2 + 6x - 5x - 6$

Reorder the terms

$f(x) = x^3 + 5x^2 + 6x - x^2 - 5x - 6$

Factor the expression

$f(x) = x(x^2 + 5x + 6) -1(x^2 + 5x + 6)$

Factor out x -1

$f(x) = (x^2 + 5x + 6)(x -1)$

Expand

$f(x) = (x^2 + 3x + 2x + 6)(x -1)$

Factorize

$f(x) = [x(x + 3) + 2(x + 3)](x - 1)$

Factor out x + 2

$f(x) = (x + 3)(x + 2)(x- 1)$

The function has been completely factored and it has 3 linear factors

Hence, the number of real zeros of the function f(x) = x3 + 4x2 + x − 6 is 3

Read more about functions at:

brainly.com/question/7784687

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3 0

2 years ago

The temperature in Greenland is -8.3°C. The temperature in Jamaica is 30°C. What is the difference between the temperatures in t

Fantom [35]

Answer:

The difference between the temperatures in the two countries is 38.3°C.

Step-by-step explanation:

Given:

Temperature in Greenland = - 8.3°C

Temperature in Jamaica = 30°C

To find :

The difference between the temperature in the two countries = ?

$\textrm{difference between the temperature in the two countries} =\textrm{temperature in Jamaica} - \textrm{temperature in Greenland}\\= 30 - (-8.3)\\= 30 +8.3\\= 38.3\°C$

Therefore,the difference between the temperatures in the two countries is 38.3°C

6 0

4 years ago

Solve pattern 66 73 13 21 52 _ 10 20

8090 [49]

The answer would be 61. First, if you are trying to figure out the pattern. You must subtract the second number with the first then fourth number with the fifth and so on, you get.

73 minus 66 equals 7.
21 minus 13 equals 8.
XX minus 52 equals x.
20 minus 10 equals 10.

Basing on the pattern of the set of numbers, x will equal 9, To get this you must do 52 and 9 which will equal 61.

4 0

4 years ago

3. In an auditorium, 1/6 of the students are fifth graders, 1/3 are fourth graders, and 1/4 of the remaining students are second

Katen [24]

12

<h3>Further explanation</h3>

Given:

In an auditorium,

$\frac{1}{6}$ of the students are fifth graders,
$\frac{1}{3}$ are fourth graders, and
$\frac{1}{4}$ of the remaining students are second graders.

There are 96 students in the auditorium.

Question:

How many second graders are there?

The Process:

The least common multiple (LCM) of 3 and 6 is 6.

Let us draw the diagram of all students.

$96 \div 6 \ units = 16 \rightarrow \boxed{16}\boxed{16}\boxed{16}\boxed{16}\boxed{16}\boxed{16} = 96 \ students$

$\frac{1}{6}$ of the students are fifth graders, or 1 of 6 units above, that is $\boxed{16} = 16 \ students$
$\frac{1}{3} = \frac{2}{6}$ are fourth graders, or 2 of 6 units above, that is $\boxed{16}\boxed{16} = 32 \ students$

The remainder is 6 units - (1 unit + 2 units) = 3 units, that is $\boxed{16}\boxed{16}\boxed{16} = 48 \ students$ . Or, 96 - 16 - 32 = 48 students.

$\frac{1}{4}$ of the remaining students are second graders.

Let us count how many second graders are there.

$\boxed{ \ \frac{1}{4} \times 48 \ students = ? \ }$

Thus, there are 12 second-graders in the auditorium.

- - - - - - - - - -

Quick Steps

$\boxed{ \ \frac{1}{4} \times \bigg(1 - \frac{1}{6} - \frac{1}{3} \bigg) \times 96 = ? \ }$

$\boxed{ \ = \frac{1}{4} \times \bigg(\frac{6}{6} - \frac{1}{6} - \frac{2}{6} \bigg) \times 96 \ }$

$\boxed{ \ = \frac{1}{4} \times \frac{3}{6} \times 96 \ }$

$\boxed{ \ = \frac{3}{24} \times 96 \ }$

We crossed out 24 and 96.

$\boxed{ \ = 3 \times 4 \ }$

$\boxed{\boxed{ \ = 12 \ students \ }}$

<h3>Learn more</h3>

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Create and solve a story problem about two friends and their weekly allowance brainly.com/question/2968321

Keywords: In an auditorium, 1/6 of the students, fifth graders, 1/3, fourth, 1/4, the remaining students, second, 96, how many, second graders

3 0

3 years ago

Read 2 more answers

What is the mean of the data set? 17, 24, 26, 13 Pls I need this fast

jek_recluse [69]

So the right answer is 20.

Look at the attached picture⤴

Hope it will help u...

5 0

3 years ago

Read 2 more answers