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2 years ago

What is the area of the trapezoid shown? A = units

Mathematics

1 answer:

Natalija [7]2 years ago

6 0

Answer: The answer is 75

Step-by-step explanation: The area of a Trapezoid is the base x height x length

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Find the vertical and horizontal asymptotes, domain, range, and roots of f (x) = -1 / x-3 +2.

gladu [14]

Answer:

Vertical asymptote: $x=3$

Horizontal asymptote: $f(x) =2$

Domain of f(x) is all real numbers except 3.

Range of f(x) is all real numbers except 2.

Step-by-step explanation:

Given:

Function:

$f (x) = -\dfrac{1 }{ x-3} +2$

One root, $x = 3.5$

To find:

Vertical and horizontal asymptote, domain, range and roots of f(x).

Solution:

First of all, let us find the roots of f(x).

Roots of f(x) means the value of x where f(x) = 0

$0= -\dfrac{1 }{ x-3} +2\\\Rightarrow 2= \dfrac{1 }{ x-3}\\\Rightarrow 2x-2 \times 3=1\\\Rightarrow 2x=7\\\Rightarrow x = 3.5$

One root, $x = 3.5$

Domain of f(x) i.e. the values that we give as input to the function and there is a value of f(x) defined for it.

For x = 3, the value of f(x) $\rightarrow \infty$

For all, other values of $x$ , $f(x)$ is defined.

Hence, Domain of f(x) is all real numbers except 3.

Range of f(x) i.e. the values that are possible output of the function.

f(x) = 2 is not possible in this case because something is subtracted from 2. That something is $\frac{1}{x-3}$ .

Hence, Range of f(x) is all real numbers except 2.

Vertical Asymptote is the value of x, where value of f(x) $\rightarrow \infty$ .

$-\dfrac{1 }{ x-3} +2 \rightarrow \infty$

It is possible only when

$x-3=0\\\Rightarrow x=3$

$\therefore$ vertical asymptote: $x=3$

Horizontal Asymptote is the value of f(x) , where value of x $\rightarrow \infty$ .

$x\rightarrow \infty \Rightarrow \dfrac{1 }{ x-3} \rightarrow 0\\\therefore f(x) =-0+2 \\\Rightarrow f(x) =2$

$\therefore$ Horizontal asymptote: $f(x) =2$

Please refer to the graph of given function as shown in the attached image.

5 0

3 years ago

Which systems of equations is in standard form?

kakasveta [241]

Answer:

2c-3y-4=0

Step-by-step explanation:

Standard form is when the answer is equal to zero.

3 0

3 years ago

How to write b plus 2 in algebraic

maxonik [38]

Answer:

b+2 ..................

Step-by-step explanation:

.......

3 0

3 years ago

Desenhe em uma folha dois quadrados de lado 1dm. Trace uma diagonal em cada um e recorte-os

Kobotan [32]

Answer:

The given question is

Draw two 1 dm squares on a sheet of paper. Draw a diagonal on each one and cut them out.

So, you need to draw square with sides of 1 dm. However, first, you need to transform from dm to cm.

We know that 1 decimenter (dm) equals 10 centimeters (cm).

That means the square sides are 10 centimerers long. So, you need to draw two squares like the first image attached shows.

Then, to draw their diagonals, you need to draw a line segment from one corner to its opposite corner, you should have an inclined line acroos each square. As the second image attached shows.

There you have it. Two squares of 1 dm side with on diagonal each.

6 0

3 years ago

70 POINTS!

siniylev [52]

You can solve this question with pythagorean theorem > ${a}^{2} + {b}^{2} = c^{2}$

Based on the information, you already have one side (a or b, doesn't matter, 12) and the hypotenuse (the cut, c, 15)

So:
1. $12^{2} + b^{2} = 15^{2}$
2. 144+ $b^{2}$ = 225
3. $b^{2}$ = 225 - 144 = 81
4. $b= \sqrt{81}$
5. $b=9$

7 0

3 years ago

What is the area of the trapezoid shown? A = units​

What is the area of the trapezoid shown? A = units