A rectangle's length is three times its width. Let w denote the rectangle's width. What polynomial represents the rectangle's area?

Answers

Answer 1

Answer: Width = ' W '
Length = 3 times as long = 3W

Area = (length) x (width) = (3W) x (W) = 3W²

Answer 2

Answer: Width = W
Length = 3W

Area = Length * Breadth

= 3W * W

= 3W²

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Kyle has 125 marbles. Fifty of these marbles are red and the reat are other colors. What is the ratio of the nunber of red marbles to the total of marbles expressed in simplest terms?

Jessica took out a, $84,000 loan to buy her grandmother a house. After 10 years, she had paid $31.500 in interest. What was herinterest rate?

Answers

3.75%
_________
please mark brainliest if correct

How is using a conversion factor different from using proportions to convert measurement units? Explain which is easier and why.

Answers

A conversion factor is basically a simplified ratio. For example, we want to convert 50 cm to meters
With a ratio,
1 m: 100 cm
x m : 50 cm
1/100 = x/50
x = 50 * 1/100
x = 0.5 m
Whereas, the conversion factor says,
cm/100 = meters
50/100 = 0.5m
The conversion is easier to use since it skips many steps and produces an answer directly.

Answer: Please don't copy and paste my answer. Conversion is simpler if you have the conversion factor.

Step-by-step explanation:

Conversion factor is easier because it uses a known conversion.

for example: 1 foot = 12 inches or 12 inches = 1 foot

or 1 cm= __ mm or 1 m= ___ cm

please don't copy my work or anyone else's. Read what is here and put it in your own words.

Converting measurements using proportions is a little more difficult because you do not know the conversion factor immediately and you have to find it based on information you are given.

For example: lets say I'm playing Minecraft with my 5 friends and I want to make chests for every one in the group, but I haven't played in a long time so i forget the amount of wood needed to make a chest. It's easier for me to make the chests if i already have enough pieces of wood first rather than gathering, then making, then gathering more etc.

I do remember that i will have to go cut down trees to get logs of wood to turn into pieces to make the chest. If i collect 5 logs and go to the crafting table, I am able to turn those logs into 4 pieces per log so I have 5 logs = 20 pieces total.

Then I use all those pieces to craft chests and i discover that I am only able to make 2 chests and I have 4 pieces of wood left over. That means that it takes 8 pieces of wood to make 1 chest. To recap, I now know that 1 log= 4 pieces of wood and it takes 8 pieces of wood to make a chest, so I can say that 2 logs is what i should gather per chest i want to make.

Don't get confused here, I started working this out as a proportion conversion, not conversion factor... I'm just saying that when using a proportion that you still have to find a conversion rate of some kind. So, I guess in a way, we have changed using proportion conversion into a conversion factor because we now know the ratio of 2 logs = 1 chest ( 2 logs of wood= 8 pieces of wood= 1 chest, so 2 logs = 1 chest).

I want to make a chest for every one so now I have to figure out how many logs I need. There area total of 6 of us ( me and 5 friends). 6 people= 6 chests.

so 2 logs= 1 chest and ___ logs = 6 chests

you can also write this as 2/1 = x/6 where x represents the number of logs

2/1= 2 so you can simplify to 2=x/6

multiply each side by 6 to solve for x

12=x

i need to find 12 logs to make a total of 6 chests

So, now that you've read through all of this, the difference is really pretty small between using conversion factor and proportion to convert measurement. Conversion factor is where you already know the conversion and proportion means that you have to find the conversion factor to solve the equation. Don't copy and paste this. Every one is going to obviously say that conversion factor is easier. However, you have to use proportion if you do not already have a set, standard conversion.

Hope that helps!

3x+6+4=6×2+10lve for x

Answers

3x + 6 + 4 = 6 × 2 + 10
3x + 6 + 4 = 12 + 10
3x + 10 = 12 + 10
3x + 10 = 22
3x = 22 - 10
3x = 12
x = 12/3
x = 4

The answer is: x = 4.

3x+10=12+10
3x+10=22
-10 -10
3x=12
x= 4

Mark Pryor, who lives in the Eastern Time Zone, placed a phone call at 7:00 A.M. to his uncle, who lives in the Pacific Time Zone. What time was it in the Pacific Zone when he called? Include A.M. or P.M. in your answer.

Answers

In the Pacific Zone was 4: 00 A.M. when he placed the phone call.

Hope it is helpful :)

What is a fraction of a circle of 120 degree

Answers

Since the fraction of 120 at a circle is 120/360 which is 1/3

The function g(x) = 2x2 – 28x + 3 written in vertex form is g(x) = 2(x – 7)2 – 95. Which is one of the transformations applied to the graph of f(x) = x2 to produce the graph of g(x) = 2x2 – 28x + 3?shifted up 3 units
shifted left 7 units
shifted right 7 units
shifted down 3 units

Answers

The function $g(x) = 2x^2 - 28x + 3$ written in vertex form is $g(x) = 2(x - 7)^2 - 95.$

You have to do such transformation to obtain the graph of the function g(x) from the graph of the function f(x) (the graph of f(x) is red on the diagram below):

1. translate graph of the function y=f(x) right 7 units to get graph of the function $f_1(x)=(x-7)^2$ (blue curve);

2. shrink twice in y-direction the graph of $f_1(x)$ to obtain the graph of the function $f_2(x)=2(x-7)^2$ (green curve);

3. translate graph of the function $f_2(x)$ down 95 units to get the graph of the function $y=g(x)=2(x-7)^2-95$ (orange curve).

From these steps the only possible choice of transformations is C - shifted right 7 units.

The vertex form tells us the answer. This is the general vertex form a parabola:
y = a(x-h)^2 + k

a indicates any stretching or shrinking
h indicates any shifting to the left (if h is positive) or the right (if h is negative)
k indicates any shifting up (if k is positive) or down (if k is negative)

Therefore, the transformation that apply is only
shifted right 7 units

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