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3 years ago

Henry is dividing a length of rope into pieces that are each foot long. How many pieces will he get from 8 feet of rope?

Mathematics

2 answers:

ASHA 777 [7]3 years ago

6 0

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Hello!

✧･ﾟ: *✧･ﾟ:* *:･ﾟ✧*:･ﾟ✧

❖ Henry will get 8 pieces from 8 ft of rope.

If 1 ft of rope is equal to one piece, that means that 8 ft is equal to 8 pieces.

~ ʜᴏᴘᴇ ᴛʜɪꜱ ʜᴇʟᴘꜱ! :) ♡

~ ᴄʟᴏᴜᴛᴀɴꜱᴡᴇʀꜱ

sammy [17]3 years ago

4 0

Answer:

8 pieces of rope.

Step-by-step explanation:

8/1=8, so he has 8 pieces in an 8 feet long rope.

Hope this helps!

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Write the ratio 2/11 to 7/11 as a fraction in the lowest terms.

Svetradugi [14.3K]

The lowest term for 2/11 is 2/11 because it can not be reduced. The lowest term for 7/11 is 7/11 to because it can not be reduced

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3 years ago

Given f(x) =

inysia [295]

The end behavior of the given function (range) is x< 4 or x > 4. So, f(x) < 4 or f(x) > 4. The solution in interval notation is $\mathbf{(-\infty, 4) \cup (4, \infty)}$ .

The last option is correct.

<h3>What is the range of the function?</h3>

The end behavior of the given function f(x) = (8x+1)/2x-9 wants us to identify the range of the given function.

The range is the set of values of the dependent variable for which a function is defined. The function range is the combined domain of the inverse function.

From the information given:

$\mathbf{f(x) = \dfrac{8x +1}{2x -9 }}$

Inverse of $\mathbf{\dfrac{8x +1}{2x -9 }}$ becomes $\mathbf{f(x) = \dfrac{1+9x}{2(-4+x) }}$

The domain of the inverse is x< 4 or x > 4. So, f(x) < 4 or f(x) > 4. Now, representing the solution in interval notation, we have:

$\mathbf{(-\infty, 4) \cup (4, \infty)}$

Learn more about the range of a given function here:

brainly.com/question/1466393

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6 0

2 years ago

Find the answer to the question please 16t^4/8t

sammy [17]

Answer:

STEP

Equation at the end of step 1

((16 • (t4)) - 23t2) + 1

STEP

Equation at the end of step

(24t4 - 23t2) + 1

STEP

Trying to factor by splitting the middle term

3.1 Factoring 16t4-8t2+1

The first term is, 16t4 its coefficient is 16 .

The middle term is, -8t2 its coefficient is -8 .

The last term, "the constant", is +1

Step-1 : Multiply the coefficient of the first term by the constant 16 • 1 = 16

Step-2 : Find two factors of 16 whose sum equals the coefficient of the middle term, which is -8 .

-16 + -1 = -17

-8 + -2 = -10

-4 + -4 = -8 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and -4

16t4 - 4t2 - 4t2 - 1

Step-4 : Add up the first 2 terms, pulling out like factors :

4t2 • (4t2-1)

Add up the last 2 terms, pulling out common factors :

1 • (4t2-1)

Step-5 : Add up the four terms of step 4 :

(4t2-1) • (4t2-1)

Which is the desired factorization

Trying to factor as a Difference of Squares:

3.2 Factoring: 4t2-1

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 4 is the square of 2

Check : 1 is the square of 1

Check : t2 is the square of t1

Factorization is : (2t + 1) • (2t - 1)

Trying to factor as a Difference of Squares:

3.3 Factoring: 4t2 - 1

Check : 4 is the square of 2

Check : 1 is the square of 1

Check : t2 is the square of t1

Factorization is : (2t + 1) • (2t - 1)

Multiplying Exponential Expressions:

3.4 Multiply (2t + 1) by (2t + 1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (2t+1) and the exponents are :

1 , as (2t+1) is the same number as (2t+1)1

and 1 , as (2t+1) is the same number as (2t+1)1

The product is therefore, (2t+1)(1+1) = (2t+1)2

Multiplying Exponential Expressions:

3.5 Multiply (2t-1) by (2t-1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (2t-1) and the exponents are :

1 , as (2t-1) is the same number as (2t-1)1

and 1 , as (2t-1) is the same number as (2t-1)1

The product is therefore, (2t-1)(1+1) = (2t-1)2

Final result :

(2t + 1)2 • (2t - 1)2

Step-by-step explanation:

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3 years ago

Still waiting for the server? How does your web browser get a file from the

disa [49]

Answer:

Your computer sends a request for the file to a Web server, and the Web server sends back a response.

Step-by-step explanation:

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3 years ago

The polynomial p(x)=7^3-7x-6 has a known factor of (x+1) rewrite p(x) as a product of linear functions

san4es73 [151]

Answer:

$p(x)=(x+1)(x+2)(x-3)$ .

Step-by-step explanation:

Note: The given function is not correct.

Consider the given polynomial is

$p(x)=x^3-7x-6$

It is given that (x+1) is a factor of given function.

Using synthetic division, divide P(x) by (x+1) as shown below.

-1 | 1 0 -7 -6

| -1 1 6

--------------------------------------

1 -1 -6 0

--------------------------------------

Bottom line represents the coefficients of quotient except the last element because it is remainder. So, the given function can be written as

$p(x)=(x+1)(x^2-x-6)$

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

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

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

Therefore, the function as a product of linear functions is $p(x)=(x+1)(x+2)(x-3)$ .

7 0

3 years ago