A 7-pack of movie tickets costs $41.84. What is the unit price, rounded to the nearest cent?

What is the solution for r in the following system of equations?<br> 2x + 3y = 16<br> 2 + 2y = 10

klio [65]

Answer:

(2,4)

*View attached graph*

Step-by-step explanation:

2x + 3y = 16

2 + 2y = 10

-2 - 2

2y = 8

/2 /2

y = 4

2x + 3y = 16

2x + 3(4) = 16

2x + 12 = 16

- 12 - 12

2x = 4

/2 /2

x = 2

(x,y) -> (2,4)

Hope this helps!

8 0

2 years ago

Please somebody help me i need the answer

Daniel [21]

Answer:

B 2.25

Step-by-step explanation:

4 0

3 years ago

Which of the following is equivalent to (125^2/ 125^4/3)

zysi [14]

Option D:

The expression equivalent to the given expression is 25.

Solution:

The image of the question is attached below.

Given expression:

$$\left(\frac{125^{2}}{125^{\frac{4}{3}}}\right)$

To find which expression is equivalent to the given expression:

$$\left(\frac{125^{2}}{125^{\frac{4}{3}}}\right)$

125 can be written as 5 × 5 × 5 = 5³

$$=\frac{(5^3)^{2}}{(5^3)^{\frac{4}{3}}}$

Using the exponent rule: $\left(a^{m}\right)^{n}=a^{(m n)}$

$$=\frac{5^6}{5^{\frac{12}{3}}}$

$$=\frac{5^6}{5^4}$

Using the exponent rule: $\frac{a^{m}}{a^{n}}=a^{m-n}$

$=5^{(6-4)}$

= 5²

= 25

$$\left(\frac{125^{2}}{125^{\frac{4}{3}}}\right)=25$

The expression equivalent to the given expression is 25.

Option D is the correct answer.

7 0

3 years ago

Consider the functions f(x) = 2x and g(x) = <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx-3%7D" id="TexFormula1" title="\

bagirrra123 [75]

Question 1:

For this case we must find $(f_ {0} g) (4)$ knowing that:

$f (x) = 2x\\g (x) = \frac {1} {x-3}$

By definition we have that, be two functions f (x) and g (x), then the composite function of f with g is:

$(g_ {0} f) (x) = g [f (x)]$

In this case, they ask us for the function composed of g with f:

$(f_ {0} g) (x) = f [g (x)]$

So, we have:

$(f_ {0} g) (x) = 2 (\frac {1} {x-3})\\(f_ {0} g) (4) = 2 (\frac {1} {4-3})\\(f_ {0} g) (4) = 1$

ANswer:

$(f_ {0} g) (4) = 1$

Question 2:

For this case, we must find the inverse function of $g (x) = \frac {1} {x-3}$ , given by: $g ^ {- 1} (x)$

To do this, replace g(x) with y:

$y = \frac {1} {x-3}$

We exchange variables:

$x = \frac {1} {y-3}$

We solve for "y":

$y-3 = \frac {1} {x}\\y = \frac {1} {x} +3$

Replace "y" with $g ^ {-1} (x)$

So, we have:

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

Answer:

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

Question 3:

For this case, we have by definition, the domain of a function f (x), is the set of all the values for which the function is defined.

We must find the domain of the following function:

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

It is observed that the function is not defined for $x = 0$

Then the domain is given by all the values of x, except 0.

${x | x \neq 0}$ for any integer n

Answer:

All numbers, except $x = 0$

4 0

3 years ago

Read 2 more answers

Consider the segment AB with A positioned at (6,2). The midpoint of AB, M is located at (5, -3). What are the coordinates of poi

GREYUIT [131]

Answer:

I didn't "do the math" yet at all, but draw it out on an X,Y axis... Thinking about it logically... If point A is in the upper right quadrant of the axis, because both X and Y coordinates are positive numbers, so you go right on the horizontal axis and up on the vertical axis... Then the midpoint is in the lower right quadrant of the due to the X coordinate being a positive, thus you go right on the horizontal axis, but the Y coordinate is a negative, so you go down vertically... So point B cannot be above both the midpoint or point A, ruling out (7,7) and (4,5) as both Y coordinates of those answers (7 or 5) are higher than point A's Y coordinate of 2... B would have to be below point A because the midpoint is below point A with a Y coordinate of -3... So this leaves either option (5,-0.5) or option (4,-8)... However.... While (5,-0.5) has a lower Y coordinate than point A with -0.5, its Y coordinate is above the Y coordinate of the midpoint as well, since -0.5 is above -3... So this doesn't jive as point B cannot be between point A and the midpoint to point B... This logically leaves (4,-8) left to be the answer... And if you drew on an X,Y axis the coordinates (6,2) as well as (5,-3) and (4,-8), then connect the dots, you'd find (5,-3) sits about half ways between (6,2) and (4,-8)...

So (4,-8) is probably the answer...

The best way to come to this conclusion mathematically is finding the slope (rise over run) of point A and the midpoint between point A and point B, then continuing the slope down, etc... But this particular question with the multiple choice answers ruled all but 1 answer out...

To find the slope you take rise over run, which is the Y of the 2nd coordinate minus the Y of the 1st coordinate, divided by (or over) the X of the 2nd coordinate minus the X of the 1st coordinate....

IE: ( Y2 - Y1 ) / ( X2 - X1 ) = Rise / Run

So.... The 2nd coordinate's Y value is -3, and the 1st coordinate's Y value is 2... Subtract 2 from -3, and you get -5...

Then the 2nd coordinate's X value is 5, and the first coordinate's X value is 6... Subtract 6 from 5, and you get -1...

Divide -5 over -1, which equals the same as 5 over 1... The rise is 5, the run is 1, the slope is 5 steps vertically for every 1 step horizontally...

Or visually... ( -3 - 2 ) / ( 5 - 6 ) which is -5 / -1... Since both sides are negative, that's the same as 5 / 1... which is 5 vertical steps (rise) for every 1 horizontal step (run), or a slope of 5...

So add the slope rise of 5 to the Y coordinate of the midpoint, -3, and you get 2, which is the Y coordinate of point A... And add slope run of 1 to the midpoint X coordinate, 5, and you get 6, the X coordinate of point A... Now subtract the slope rise of 5 from the midpoint, -3, and you get -8... So that tells you that point B has to have a Y coordinate of -8.... And now subtract the slope run of 1 from the midpoint X coordinate, 5, and you get 4... The X coordinate of point B... Giving you a point B coordinate of (4,-8)...

5 0

4 years ago