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4 years ago

13

A 10 2/3 inch long pipe is cut into 8 equal length pieces, how long is each piece

1 answer:

storchak [24]4 years ago

6 0

Answer:

$\frac{4}{3}$ inches

Step-by-step explanation:

The total length of pipe is 10 2/3rd inches

It is cut into 8 equal pieces

We need to divide total length by 8 to get length of each piece. First, we have to convert mixed number (total length) to improper fraction by using formula shown below:

$a\frac{b}{c}=\frac{(a*c)+b}{c}$

So,

$10\frac{2}{3}=\frac{32}{3}$

Each piece length is:

$\frac{\frac{32}{3}}{8}\\=\frac{32}{3}*\frac{1}{8}\\=\frac{32}{24}\\=\frac{4}{3}$

So, each piece is $\frac{4}{3}$ inches

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Perform the indicated operation to write given polynomial in standard form: (x^3+2x^2 − 3x − 1) +(4 − x − x^3)

Rzqust [24]

Answer:

$\left(x^3+2x^2-3x-1\right)+\left(4-x-x^3\right)=2x^2-4x+3$

Step-by-step explanation:

To write any polynomial in standard form, you look at the degree of each term. You then write each term in order of degree, from highest to lowest, left to write.

To add the polynomials you need to:

Remove parentheses

$\left(x^3+2x^2-3x-1\right)+\left(4-x-x^3\right)=x^3+2x^2-3x-1+4-x-x^3$

Group like terms

$\left(x^3+2x^2-3x-1\right)+\left(4-x-x^3\right)=x^3-x^3+2x^2-3x-x-1+4$

Add similar elements

$\left(x^3+2x^2-3x-1\right)+\left(4-x-x^3\right)=2x^2-3x-x-1+4\\\left(x^3+2x^2-3x-1\right)+\left(4-x-x^3\right)=2x^2-4x-1+4\\\left(x^3+2x^2-3x-1\right)+\left(4-x-x^3\right)=2x^2-4x+3$

5 0

4 years ago

Help me i'll give brainlist

Levart [38]

Answer:

$x=\frac{1}{2}$

Step-by-step explanation:

equation of a circle: $(x - h)^2+(y-k)^2=r^2$

where (h, k) = center and r = radius

From inspection, we can see that the center of the circle = (0, 0)

and the radius = 1

$\implies (x - 0)^2+(y-0)^2=1^2$

$\implies x^2+y^2=1$

Substitute $y=\frac{\sqrt{3}}{2}$ into $x^2+y^2=1$ and solve for $x$ :

$\implies x^2+(\frac{\sqrt{3}}{2})^2=1$

$\implies x^2+\frac{3}{4}=1$

$\implies x^2=\frac{1}{4}$

$\implies x=\pm \sqrt{\frac{1}{4}}$

$\implies x=\pm\frac{1}{2}$

As point P is in quadrant 1, $x$ is positive, so $x=\frac{1}{2}$

7 0

2 years ago

Write (8a^-3)^-4/3 in simplest form. <br><br> Please show your work!

german

Answer:

(a/2) ^4 or a^4/16

Step-by-step explanation:

(8a^-3)^-4/3

split into two parts

8^ -4/3 * (a^-3)^-4/3

using the power to the power rule we can multiply the exponents

8^(-4/3) *a^(-3*-4/3)

8^ (-4/3) * a^(4)

replace 8 with 2^3

(2^3)^(-4/3) * a^(4)

using the power to the power rule we can multiply the exponents

2^(3*-4/3) * a^(4)

2 ^ (-4) * a^4

the negative exponent means it goes in the denominator if it is in the numerator

a^4/2^4

make a fraction

(a/2) ^4

or a^2/16

8 0

3 years ago

Read 2 more answers

If a polynomial function f(x) has roots 4 – 13i and 5, what must be a factor of f(x)?

Morgarella [4.7K]

The factor of f(x) is (x-(4-13i))

If a polynomial function f(x) has roots 4 – 13i and 5

One of the complex roots is 4-13i

If we have one complex root then there should be one more complex root.

<h3>What is the complex root?</h3>

complex roots come in pairs like (a+ib) and (a-ib)

so another complex root for 4-13i is 4+13i

If 'a' is a root then the factor is (x-a)

4+13i is a root

So the factor is (x-(4-13i))

Read more on Brainly.com -

brainly.com/question/1459677

#SPJ1

7 0

2 years ago

Find the distance between the points given<br><br>(0, -6) and (9, 6)

Valentin [98]

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[9-0]^2+[6-(-6)]^2}\implies d=\sqrt{(9-0)^2+(6+6)^2} \\\\\\ d=\sqrt{9^2+12^2}\implies d=\sqrt{225}\implies d=15$

3 0

4 years ago