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3 years ago

A board 60 in. Long is cut two parts so that the longer piece is 5 times the shorter. What are the length of the two pieces?

Mathematics

1 answer:

vlada-n [284]3 years ago

7 0

Answer:

The shorter piece is 10 in. and the longer one is 50 in.

Step-by-step explanation:

First, let's set the shorter piece to be length x. Then the longer piece is 5x, or 5 times longer than the shorter piece.

Since both pieces combined equals to the length of the entire board, we can set these two lengths equal to it:

x + 5x = 60

And now solve for x:

6x = 60

x = 10 in (length of shorter piece)

Now let's find the length of the longer piece:

Longer = 5x = 5(10) = 50 in.

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3 years ago

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Step-by-step explanation:

The equation of a line can be given by y -y₁= m(x -x₁), where m is the slope. This is also known as the point-slope form.

$\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }$

Slope of the line

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Substitute m= -4 into the equation:

y -y₁= -4(x -x₁)

Substitute a pair of coordinates into (x₁, y₁):

Let's start by substituting (1, 2).

y -2= -4(x -1)

This gives us the same equation as D, making D an incorrect option. Note that the question asks for which is not the correct equation.

Let's change the above into the slope-intercept form, where by y is the subject of formula.

Start by expanding the right-hand side:

y -2= -4x +1

+2 on both sides:

y= -4x +3

This equation is not the same as C. C is thus the correct option.

Let's check for options A and B.

The equation in option B is not the correct equation either as they have substituted (2, 1) instead of (1, 2) into (x₁, y₁). Thus, option B is also correct.

y -y₁= -4(x -x₁)

Substitute (3, -6) into (x₁, y₁):

y -(-6)= -4(x -3)

y +6= -4(x -3)

This is the same as option A, making option A incorrect too.

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2 years ago