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2 years ago

8

A 14-foot piece of string is cut into two pieces so that the longer piece is 2 feet longer than twice the shorter piece. If the

shorter piece is x feet long, find the lengths of both pieces.

2 answers:

Maurinko [17]2 years ago

8 0

We are given that the shorter piece is x
From your description, the longer piece is 2x + 2
The total length is
x + 2x + 2 = 14
ie
3x + 2 = 14
3x = 12
x = 4

So the length of the shorter piece is 4 ft
Therefore the length of the longer piece must be
(14 - 4) ft = 10 ft

GalinKa [24]2 years ago

4 0

X = shorter piece
y = longer piece

x + y = 14
y = 2x + 2

x + (2x + 2) = 14
3x + 2 = 14
3x = 14 - 2
3x = 12
x = 12/3
x = 4.......shorter piece (x) is 4 ft

y = 2x + 2
y = 2(4) + 2
y = 8 + 2
y = 10...longer piece (y) is 10 ft

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Answer:

Choice A) $F(x) = 3\sqrt{x + 1}$ .

Step-by-step explanation:

What are the changes that would bring $G(x)$ to $F(x)$ ?

Translate $G(x)$ to the left by $1$ unit, and
Stretch $G(x)$ vertically (by a factor greater than $1$ .)

$G(x) = \sqrt{x}$ . The choices of $F(x)$ listed here are related to $G(x)$ :

Choice A) $F(x) = 3\;G(x+1)$ ;
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The expression in the braces (for example $x$ as in $G(x)$ ) is the independent variable.

To shift a function on a cartesian plane to the left by $a$ units, add $a$ to its independent variable. Think about how $(x-a)$ , which is to the left of $x$ , will yield the same function value.

Conversely, to shift a function on a cartesian plane to the right by $a$ units, subtract $a$ from its independent variable.

For example, $G(x+1)$ is $1$ unit to the left of $G(x)$ . Conversely, $G(x-1)$ is $1$ unit to the right of $G(x)$ . The new function is to the left of $G(x)$ . Meaning that $F(x)$ should should add $1$ to (rather than subtract $1$ from) the independent variable of $G(x)$ . That rules out choice B) and D).

Multiplying a function by a number that is greater than one will stretch its graph vertically.
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3 years ago

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zmey [24]

Answer:

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Part 24) The area is $A=16m^3n\ units^2$ and the perimeter is $P=24mn\ units$

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Step-by-step explanation:

Part 22) Find the perimeter and area

step 1

The area of a rectangle is equal to

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we have

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Remember that

When multiply exponents with the same base, adds the exponents and maintain the base

substitute in the formula

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step 2

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$W=3(a)(b^2)\ units$

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step 1

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substitute in the formula the given value

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