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3 years ago

Ramon has a rope that is 25 1/2 feet long.He wants to cut into 6 pieces that are equal in length. how long will each piece be?

1 answer:

6 0

If you have a rope that is 25 1/2 feet long and you want to cut it into 6 pieces that are equal in length, and you want to know how long will each piece be, you can calculate this using the following steps:

25 1/2 feet = 51/2 feet

25 1/2 / 6 = 51/2 / 6 = 51/2 * 1/6 = 51/12 = 17/4 = 4 1/4 feet

Result: Each piece will be 4 1/4 feet long.

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Explain how you know which method you should use to solve a rational equation.

notsponge [240]

<u>Methods to solve rational equation:</u>

Rational equation:

A rational equation is an equation containing at least one rational expression.

Method 1:

The method for solving rational equations is to rewrite the rational expressions in terms of a common denominator. Then, since we know the numerators are equal, we can solve for the variable.

For example,

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

This can be used for rational equations with polynomials too.

For example,

$\frac{1+x}{x-3}=\frac{4}{x-3}\Rightarrow(1+x)=4 \Rightarrow x=3$

When the terms in a rational equation have unlike denominators, solving the equation will be as follows

$\frac{x+2}{8}=\frac{3}{4}$

$\Rightarrow\frac{x+2}{1}=\frac{3\times8}{4}\Rightarrow{x+2}=2\times3$

$\Rightarrow{x+2}=6\Rightarrow x=6-2\Rightarrow x=4$

Method 2:

Another way of solving the above equation is by finding least common denominator (LCD)

$\frac{x+2}{8}=\frac{3}{4}$

Factors of 4: $1\times2\times2$

Factors of 8: $1\times2\times2\times2$

The LCD of 4 and 8 is 8. So, we have to make the right hand side denominator as 8. This is done by the following step,

$\Rightarrow\frac{x+2}{8}=\frac{3}{4}\times{2}{2}$

we get,

$\Rightarrow\frac{x+2}{8}=\frac{6}{8}$

On cancelling 8 on both sides we get,

$\Rightarrow(x+2)=6\rightarrow x=6-2\rightarrow x=4$

Hence, these are the ways to solve a rational equation.

7 0

3 years ago

Which statements are true about the residual plot and the equation for the line of best fit for the data? select two options.. t

Nataly [62]

The statements are true about the residual plot and the equation for the line of best fit include:

The equation for the line of best fit is not a good approximation for the data because the points have a curved pattern.

The residual plot has the pattern of a curve.

<h3>What is Residual plot?</h3>

This shows the residuals on the vertical axis and the independent variable on the horizontal axis.

Since the plot has a curved pattern, the equation for the line of best fit is not a good approximation for the data as the result will be inaccurate.

Read more about Residual plot here brainly.com/question/16180255

#SPJ4

8 0

2 years ago

The volume of a cone is 1/3 that of a cylinder when the radius and height are the same (v= 1/3(pi)(r)^2(h). What is the volume o

Ira Lisetskai [31]

$\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}$

Actually Welcome to the Concept of the Surface Areas and Volumes.

Since, Volume of cone = 1/3 π r^2 h,

here, r = 10 Inches and h= 12 inches, also π =3.14

so, VOC = 1/3 π (10)^2 × (20)

VOC = 1/3(3.14)(100)(20)= 2093.33 inch^3

=> so the volume of the cone is 2093.33 cubic inches.

5 0

3 years ago

Kenji is decorating papers with a total of 15 heart stickers and 12 star stickers for the child he is babysitting. If he wants t

Marina CMI [18]

Answer: The greatest number of pages Kenji can decorate = 3

Step-by-step explanation:

Given: Total heart stickers = 15

Total star stickers =12

If all the papers identical, with the same combination of heart and star stickers and no stickers left over.

Then the greatest number of pages Kenji can decorate = GCD(15,12) [GCD=greatest common divisor]

Since 15 = 3 x 5

12=2 x 2 x 3

GCD(15,12) =3

Hence, the greatest number of pages Kenji can decorate = 3

7 0

3 years ago

Complete the following sentence. The slope of the graph of y = 5 x is ___

Y_Kistochka [10]

Answer:

We conclude that the slope of the graph of y = 5 x is 5.

Step-by-step explanation:

We know the slope-intercept form of the line equation

y = mx+b

where

m is the slope

b is the y-intercept

Given the line

y = 5x

comparing with the slope-intercept form of the line equation

The slope of the line = m = 5

Therefore, we conclude that the slope of the graph of y = 5 x is 5.

4 0

3 years ago