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4 years ago

8

Marcus drew a quadrilateral with only 1 pair of parallel sides. Which quadrilateral did Marcus draw? parallelogram rhombus trape

zoid rectangle

1 answer:

SpyIntel [72]4 years ago

8 0

Answer:

Trapezoid

Step-by-step explanation:

We have been given that Marcus drew a quadrilateral with only 1 pair of parallel sides. We are asked to determine the quadrilateral that Marcus drew.

We know that a parallelogram has two pair of parallel sides.

We also know that rhombus is a parallelogram whose 4 sides are equal is measure and rectangle is a parallelogram with opposite sides equal.

Since parallelogram, rhombus and rectangle has two pair of parallel sides, therefore, Marcus didn't draw any of these.

We know that trapezoid has only one pair of parallel sides, therefore, Marcus drew a trapezoid.

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Step-by-step explanation:

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Which expression is NOT equivalent to −3/8 x (-4 + 1/2)

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1) Inverse function: $f^{-1}(x)=g(x)=\frac{x+4}{3}$

2) $f(1) = -1, g(-1) = 1$

3) $f(g(x))=g(f(x))=x$

Step-by-step explanation:

1)

In this first method, we want to find the inverse function of $f(x)$ .

The original function is:

$f(x) = 3x-4$

We rewrite it as

$y=3x-4$

We swap the name of the variables:

$x=3y-4$

Adding +4 on both sides:

$x+4=3y-4+4\\x+4=3y$

And dividing by 3 on both sides:

$y=\frac{x+4}{3}$

which is identical to $g(x)$ :

$g(x)=\frac{x+4}{3}$

2)

In this second method, we want to use the output of one function as input to the other function, and show that the output value is equal to the imput value.

We start using the function

$f(x)=3x-4$

We choose $x=1$ . We find:

$f(1)=3(1)-4=3-4=-1$

Now we use this output value as input in the function

$g(x)=\frac{x+4}{3}$

Substituting $x=-1$ ,

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

So, the final output value (1) is equal to the input value (1).

3)

Here we want to verify that the two are inverse functions by showing that

$f(g(x))=x$

We have

$f(x)=3x-4\\g(x)=\frac{x+4}{3}$

Substituting g(x) into f(x),

$f(g(x))=3g(x)-4 = 3(\frac{x+4}{3})-4=(x+4)-4=x$

Viceversa, we want to show that

$g(f(x))=x$

Substituting g(x) into f(x), we get

$g(f(x))=\frac{f(x)+4}{3}=\frac{(3x-4)+4}{3}=\frac{3x-4+4}{3}=\frac{3x}{3}=x$

So, the two functions are one the inverse of the other.

Learn more about inverse functions:

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