Rewrite as a logarithmic equation. e^9=y

Hey there! Hello!

Not sure if you still need these answers, but I'd love to help out if you do!

Now, I want you to go ahead and think of some stuff that's true for squares. To name a few, the opposite sides are going to be parallel to one another, all the angles are 90°, all the sides are the same length, and both diagonals are going to be perpendicular and equal in length. I'm sure there's even more, but I'll leave that to you. (BTW, by diagonals, I mean the lines that go through the the opposite diagonal corners).

What about rectangles? The opposite sides are going to be parallel to one another, the diagonals are going to be equal in length, and the angles are going to be 90°.

Now, rhombi. All sides are going to be equal, opposite sides are going to be parallel, the diagonally opposite angles will be equal to each other, and the diagonals bisect each other at 90°.

And lastly, parallelograms. Pretty similar to rhombi in that they have parallel opposite sides and that the opposite diagonal angles are equal to each other, but there's one thing that makes a parallelogram not a rhombus.

If you differentiate the stuff I described, you'll be golden. There's a lot to choose from, and I personally like to have options. Hope this helped you out, feel free to ask me any additional questions you have! :-)

3 0

2 years ago

The image above is of a virtual roller coaster showing the initial path of the

KIM [24]

Answer:

Part 1) The end points of the initial incline are the points (0,0) and (4,6)

Par 2) The slope of the initial incline (red) is m=1.5

Part 3) The linear equation of the initial (red ) incline would be y=1.5x

Part 4) The end points of the first decline are the points (4,6) and (6,2)

Part 5) The slope of the first decline (blue) is m=-2

Part 6) The linear equation of the first decline (blue) would be y=-2x+14

Part 7) Two end points of the second incline (green) are the points (6,2) and (10,5)

Part 8) The slope of the second incline (green) is m=0.75

Part 9) The slope of the first decline is the steepest of the three

Part 10) see the explanation

Part 11) The track is not a function

Part 12) see the explanation

Part 13) The domain is all real numbers greater than or equal to 0 and less than or equal to 12

Part 14) The range is all real numbers greater than or equal to 0 and less than or equal to 8

Step-by-step explanation:

Part 1) Two end points of the initial incline(red) are ( , ) and ( , )

Observing the graph

The end points of the initial incline are the points (0,0) and (4,6)

Part 2) The slope of the initial incline (red) is

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

(0,0) and (4,6)

substitute the values in the formula

$m=\frac{6-0}{4-0}=1.5$

Part 3) The linear equation of the initial (red ) incline would be y = __x +__

we know that

The initial red incline represent a proportional relationship, because is a line that passes through the origin

therefore

The linear equation is

$y=mx$

we have

$m=1.5$

substitute

$y=1.5x$

Part 4) Two end points of the first decline (blue) are ( , ) and ( , )

Observing the graph

The end points of the first decline are the points (4,6) and (6,2)

Part 5) The slope of the first decline (blue) is

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

(4,6) and (6,2)

substitute the values in the formula

$m=\frac{2-6}{6-4}=-2$

Part 6) The linear equation of the first decline (blue) would be y= __ x + __

The equation of the line in slope intercept form is

$y=mx+b$

we have

$m=-2$

so

$y=-2x+b$

with the point (4,6) find the value of b

substitute the value of x and the value of y in the linear equation

$6=-2(4)+b$

$6=-8+b$

$b=6+8=14$

therefore

The linear equation is

$y=-2x+14$

Part 7) Two end points of the second incline (green) are ( , ) and ( , )

Observing the graph

The end points of the second incline are the points (6,2) and (10,5)

Part 8) The slope of the second incline(green) is

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

(6,2) and (10,5)

substitute the values in the formula

$m=\frac{5-2}{10-6}=0.75$

Part 9) Which incline is steepest of the three?

we have

The slope of the initial incline (red) is m=1.5

The slope of the first decline (blue) is m=-2

The slope of the second incline (green) is m=0.75

we know that

The steepest slope is that of the line that is closest to being vertical. This could be a line that has positive slope OR negative slope...the steepest one should be determined by examining the ABSOLUTE VALUES of these three slopes.

This means that the slope of the first decline is the steepest of the three

Part 10) How mathematically can you tell it is the steepest?

we know that

The slope with highest absolute value is the steepest. Positive slope means the function is ascending left to right, negative slope means it is descending left to right.

In this problem

The slope of the first decline is the highest absolute value (absolute value is 2)

Part 11) For the last (orange) section of the track is the track a function

we know that

The <u>vertical line test </u>is a method that is used to determine whether a given relation is a function or not

In this problem the track section does not pass the vertical line test.

therefore

The track is not a function

Part 12) How do you know it is or isn’t a function for this region?

we know that

A function can only have one output, y, for each unique input, x.

In this problem, applying the vertical line test, the vertical line you draw intersects the graph more than once for any value of x, so the graph is not the graph of a function.

Part 13) What is the domain for the roller coaster in total

we know that

The domain is the interval -----> [0,12]

$0 \leq x\leq 12$

All real numbers greater than or equal to 0 and less than or equal to 12

Part 14) What is the range for the roller coaster in total

we know that

The range is the interval ----> [0,8]

$0 \leq y\leq 8$

All real numbers greater than or equal to 0 and less than or equal to 8

3 0

2 years ago

During the fall, you charge $8 to go to a house and rake the leaves and an additional $6

kifflom [539]

Answer:

4 hours

Step-by-step explanation:

32 = 6x + 8

24 = 6x

4 = x

8 0

2 years ago