Pls, Help! 25 Points! TY!!!

A) give stating reasons five other angles each equal to x b) prove that AECF is a parallelogram

Gennadij [26K]

Simple Proof:

a) In the image, we know that ABCD is a parallelogram and that means opposite angel measures should be the same. We know that angel DCB is made up by angel 1 and 2, and angel DAB and DCB are equal and angel DAB is made up by angel 1 and x. So now we can conclude that angel x is equal to angel 2.

b) According to the definitions of a parallelogram, opposite angel measures have to be the same, while AECF have angle 1 to angel 1 and angel 2 to angel 1. We can conclude that AECF is NOT a parallelogram. (Sorry, you didn't give me the full question so some information remains unclear. )

7 0

3 years ago

A. Use composition to prove whether or not the functions are inverses of each other.

kogti [31]

A. In a composition of two functions the first function is evaluated, and then the second function is evaluated on the result of the first function. In other word, you are going to evaluate the second function in the first function.

Remember that you can evaluate function at any number just replacing the variable in the function with the number. For example, let's evaluate our function $f(x)$ at $x=1$ :

$f(x)=\frac{1}{x-3}$

$f(1)=\frac{1}{1-3}$

$f(1)=\frac{1}{-2}$

Similarly, to find the composition of $f(x)$ and $g(x)$ , we are going to evaluate $f(x)$ at $g(x)$ . In other words, we are going to replace $x$ in $f(x)$ with $\frac{3x+1}{x}$ :

$f(x)=\frac{1}{x-3}$

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

Remember that two functions are inverse if after simplifying their composition, we end up with just $x$ . Let's simplify and see what happens.

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

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

$f(g(x)=\frac{1}{\frac{1}{x} }$

$f(g(x)=x$

Now let's do the same for $g(f(x))$ :

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

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

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

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

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

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

We can conclude that $g(x)$ is the inverse function of $f(x)$ , but $f(x)$ is not the inverse function of $g(x)$ .

B. The domain of a function is the set of all the possible values the independent variable can have. In other words, the domain are all the possible x-values of function.

Now, interval notation is a way to represent and interval using an ordered pair of numbers called the end points; we use brackets [ ] to indicate that the end points are included in the interval and parenthesis ( ) to indicate that they are excluded.

Notice that when $x=0$ , $g(x)=\frac{3(0)+1}{0} =\frac{0}{0}$ , so when $x=0$ , $g(x)$ is not defined; therefore we have to exclude zero from the domain of $f(g(x))$ .

We can conclude that the domain of the composite function $f(g(x))$ in interval notation is (-∞,0)U(0,∞)

Now let's do the same for $g(f(x))$ .

Notice that the composition is not defined when its denominator equals zero, so we are going to set its denominator equal to zero to find the values we should exclude from its domain:

$x(x-3)=0$

$x=0$ and $x-3=0$

$x=0$ and $x=3$

Know we know that we need to exclude $x=0$ and $x=3$ from the domain of $g(f(x))$ .

We can conclude that the domain of the composition function $g(f(x))$ is (-∞,0)U(0,3)U(3,∞)

4 0

3 years ago

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How many 0.35 L glasses can be filled from a 1.5 L bottle of water?

11111nata11111 [884]

I’m not sure but I think the answer is 3

4 0

3 years ago

When the center of Earth is 3.8 × 105 kilometers from the center of the moon, the force of gravity between Earth and the moon is

kolezko [41]

Given:
r = 3.8x10⁵ km = 3.8x10⁸ m, the distance between the earth and moon,
F = 20.46x10²⁵ N, the gravitational force between the earth and the moon,
G = 6.674x10⁻¹¹ m³/(kg-s²), gravitational constant
M = 5.972x10²⁴ kg, the mass of the earth.

Let m = mass of the moon.
Then
F = (G*M*m)/r^2
or
m = (F*r^2)/(G*M)

In SI units,
m = [20.46×10²⁵ * (3.8×10⁸)²]/[6.674×10⁻¹¹ * 5.972×10²⁴]
= 7.4125×10²⁸ kg

Answer: 7.4125x10²⁸ kg

5 0

3 years ago

Write the equation of a line perpendicular to y=-2x+1 that passes through the point (2,3)

Cloud [144]

Answer:

y = 1/2x + 2

Step-by-step explanation:

First you have to determine the slope which is the opposite reciprocal of the slope of the line given.

So we take the slope -2 and reciprocate and by flipping the numerator and denominator which makes it -1/2.

Then we have to make it the opposite, like making a negative into a positive or a positive into a negative. So that would make it positive 1/2.

We now have the slope which is 1/2 and not we have to make sure it goes through point (2,3).

To do that, we must adjust the y-intercept until it goes through that point. We result in getting the y-intercept of 2.

The answer is y = 1/2x + 2

3 0

3 years ago

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