How do I completely factor 4x^2-64?

A synthetic fiber used in manufacturing carpet has tensile strength that is normally distributed with mean 75.5 psi and standard

exis [7]

Answer n=6

Step-by-step explanation:

4 0

3 years ago

A _[blank 1]_ is a number whose only factors are 1 and itself. If a number has other factors besides 1 and itself, it is called

kykrilka [37]

Numbers whose only factors are 1 and itself is known as prime numbers , numbers whose factors besides 1 and itself are composite numbers, we can use the sieve of Eratosthenes to determine whether the number is prime or composite.

Given a paragraph in which there are blanks:

A _____ is a number whose only factors are 1 and itself. If a number has factors besides 1 and itself, it is called a _____. You can use divisibility rules or _______ to help you determine whether a number is prime or composite.

We are required to fill the blank with appropriate options.

We have to fill "prime numbers" in the first blank.

We have to fill "composite numbers" in the second blank.

We have to fill "the sieve of Eratosthenes" in the third blank.

Hence numbers whose only factors are 1 and itself is known as prime numbers , numbers whose factors besides 1 and itself are composite numbers, we can use the sieve of Eratosthenes to determine whether the number is prime or composite.

Learn more about prime numbers at brainly.com/question/145452

#SPJ1

3 0

1 year ago

Determine the slope and point on the line for each equation<br> C. y+ 4 = %(% - 3)

Temka [501]

Bbbbhbjjjjioiiu and his friends were the

5 0

2 years ago

Sara has 24 sweets

Tresset [83]

<h2>Hello!</h2>

The answer is:

The expression for the number of sweets that Sara and Tim have now, are:

$Sara=(17-x)Sweets\\\\Tim=\frac{(24+x)Sweets}{2}$

To write the expressions for the number of sweets that Sara and Tim have now, we need to follow the next steps:

Sara starts with 24 sweets and Tim starts with 24 sweets

$Sara=24 Sweets\\Tim=24 Sweets$

Then, Sara gives Tim x Sweets

$Sara=(24-x)Sweets\\Tim=(24+x)Sweets$

Then. Sara eats 7 of her Sweets

$Sara=(24-x-7) Sweets\\Sara=(17-x )Sweets\\Tim=(24+x) Sweets$

Then, Tim eats half of his sweets

$Sara=(17-x)Sweets\\\\Tim=\frac{(24+x)Sweets}{2}$

So, the expression for the number of sweets that Sara and Tim have now, are:

$Sara=(17-x) Sweets\\\\Tim=\frac{(24+x)Sweets}{2}$

Have a nice day!

8 0

3 years ago

During which time period does Landon's elevation change the fastest? Explain how you know?

bogdanovich [222]

<h3>1. How many inches per minute does London's elevation change between 4 minutes and 8 minutes. </h3>

The question actually asks for the slope of the line that stands for the points $(4,3) \ and \ (8,6)$ why? because the questions tells us that London's elevation changes between 4 minutes and 8 minutes here. Hence, to find the slope of this line we have to use the following formula:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ But: \\ \\ P(x_{1},y_{1})=P(4,3) \\ P(x_{2},y_{2})=P(8,6)$

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ But: \\ \\ P(x_{1},y_{1})=P(4,3) \\ P(x_{2},y_{2})=P(8,6) \\ \\ So: \\ \\ m=\frac{6-3}{8-4}=0.75in/min$

<em>So London's elevation changes 0.75 inches per minute</em>

<h3>2. During which time period does London's elevation change the fastest?</h3>

The greater the absolute value of the slope of the line the faster London's elevation changes. Since this is a Piecewise function, we must analyze each period.

FIRST:

→ Between 0 minutes and 4 minutes the function is constant, so there is no any change here.

→ Between 10 minutes and 14 minutes the function is constant, so there is no any change here.

→ Between 18 minutes and 22 minutes the function is constant, so there is no any change here.

So the solution is not in these parts of the function.

SECOND:

→ Between 4 minutes and 10 minutes the function has a positive slope, so there is change here.

In the previous item we calculated the slope between 4 and 8 minutes that is the same slope between 4 and 8 minutes and equals 0.75.

→ Between 14 minutes and 18 minutes the function has a positive slope, so there is change here.

Let's take two points here, say, $(16,5) \ and \ (18,3)$

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ But: \\ \\ P(x_{1},y_{1})=P(16,5) \\ P(x_{2},y_{2})=P(18,3) \\ \\ So: \\ \\ m=\frac{3-5}{18-16}=-1 in/min$

As you can see, the absolute value here is 1 that is greater than 0.75.

<em>In conclusion, London's elevation changes the fastest between 14 and 18 minutes</em>

7 0

3 years ago