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3 years ago

How do you do this?

Mathematics

2 answers:

lora16 [44]3 years ago

6 0

X/5 = 24/8
(because the triangles are similar)

x/5 = 3

x = 5*3 = 15 Answer

a/27 = 8/24 = 1/3
a = 9 Answer

astraxan [27]3 years ago

3 0

3)a/8 = 27/24 => a = 8*27/24 = 9

x/24 = 5/8 => x = 24*5/8 = 15

4)C≡X, A≡Z, B≡Y

5)C=2πR=15π=>R=7,5

A = πR² = 56,25π cm²

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Garrett and Carter went to the movies last weekend. Together they bought 2 drinks and 2 popcorns. They spent a total of $12.50.

Tatiana [17]

Since Garrett and Carter bought popcorn and drinks, we have to figure out how much money is 1 drink and 1 popcorn. I figured the best way is to figure out half of $12.50 because 2 drinks and 2 popcorn cost that amount of money. You divide $12.50 by 2 to figure out half of that amount. The quotient equals to $6.25.

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4 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

Read 2 more answers

Helpp plz i'll mark brainliest (see picture). <br> The second part is, What is the value of y?

Art [367]

Answer:

116*

Step-by-step explanation:

36* + 28* = 64*

180* - 64* = 116*

4 0

3 years ago

A line passes through (2,-1) and (4,5)

MrRissso [65]

Answer:

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

The line passes through (2,-1) and (4,5),

y2 = 5

y1 = - 1

x2 = 4

x1 = 2

Slope,m = (5 - - 1)/(4 - 2) = 6/2 = 3

To determine the intercept, we would substitute x = 4, y = 5 and m= 3 into y = mx + c. It becomes

5 = 3 × 4 + c

c = 5 - 12 = - 7

The equation becomes

y = 3x - 7

5 0

3 years ago

Write the equation of a line for the graph:

zzz [600]

Answer: y=1/3x-2

Step-by-step explanation:

To find the equation of the line, we need the slope and y-intercept. To find the slope, we can take any two points on the graph and use the formula $m=\frac{y_2-y_1}{x_2-x_1}$ . To find the y-intercept, we find the point that crosses the y-axis. The two points on the graph are (0,-2) and (3,-1).

$m=\frac{-1-(-2)}{3-0} =\frac{1}{3}$

Now, we know the slope is 1/3.

The graph crosses the y-axis at (0,-2). Therefore the y-intercept is -2. This tells us that the equation is y=1/3x-2.

6 0

3 years ago