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3 years ago

What is the area of the two rectangles shown below?

Mathematics

2 answers:

DedPeter [7]3 years ago

6 0

Answers are in bold.

For the first one:

The total area of both shaded and unshaded portions is equal to $3x(4x+7)$ , which simplifies to $12x^2}+21x$ . The area of the middle white portion is $(5x)(2x)$ , which simplifies to $10x^2$ . To find the area of the shaded portion, we do $12x^2}+21x - 10x^2$ . Combining like terms, we get $2x^2+21x$ as our expression for the area of the shaded portion of the first rectangle.

For the second one:

The total area of both shaded and unshaded portions is equal to $6n(8n+14)$ , which simplifies to $48n^2}+84n$ . The area of the middle white portion is $10n(4n+1)$ , which simplifies to $40n^2+10n$ . To find the area of the shaded portion, we do $48n^2+84n-40n^2+10n$ . Combining like terms, we get $4n^2+94n$ as our expression for the area of the shaded portion of the second rectangle.

Phoenix [80]3 years ago

4 0

Answer:

-- I don't know if you'll still need mine, but here's what I got --

1st (shaded) box = Area is 441

2nd (shaded) box = Area is 1,764

Step-by-step explanation:

First of all, It stated, "To determine the area of the (shaded) portion" but it didn't mention the white box so I ignored it and pay attention only to the "shaded box" as mentioned in the assignment

1st (shaded) box

1. write it out like so, $4x + 7 = 3x$

2. next to get "x" alone subtract 7 to the other side once done you would have this, $4x=3x-7$

3. then subtract 3x to both sides... $3x-3x=cancelsout$ >> $4x-3x=1x=x$ >> you're now left with, $x=-7$

To find the area we need one more step...

$4x+7=4(-7)+7=-28+7=-21$ and $3x=3(-7)=-21$ then multiply to get the area, negative crosses each other out once multiplying so -21 times -21 gives you 441

-------

2nd (shaded) box repeat from above

1. $8n+14=6n$

2. $8n=6n-14$

3. $2n=-14$ , here is different as there is still one more step, we need to divide to get "n" alone.

4. $\frac{2n=-14}{2} = n=-7$

Now plugin to get the area, $6n=6(-7)=-42\\8n+14=8(-7)+14=-56+14=-42\\$ once multiplied you get 1,764

Once again I could be wrong but this is what I got after reading the little description from your attached assignment.

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Granola bars are sold in three packs which cost $2.34. Which equation represents the proportional relationship between b the num

Elena L [17]

Okay gotcha. i missed the three packs info. answer is option C

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4 years ago

PLEASE PLEASE HELP PLEASE PLEASE

Lilit [14]

Answer:

14.8

Step-by-step explanation:

The Pythagorean theorem applies.

... x² = 7² + 13² . . . . . the square of the hypotenuse is the sum of the squares of the legs

... x² = 218

... x = √218 ≈ 14.8

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3 years ago

Brian can get to class by taking either a Commuter North bus, a Bursley Baits bus, or a Northwood Express bus. If he takes Commu

jolli1 [7]

Answer:

a) P(C/L) = 0.6668

b) P(C/L') = 0.1875

Step-by-step explanation:

Let's call C the event that Brian takes Commuter North, B the event that Brian takes Bursley Baits, N the event that Brian takes Northwood Express, L the event that Brian is late and L' the event that Brian is not late.

First, there is equal probability of taking any given bus so, P(C)=P(B)=P(N)=1/3

Now, the probability P(C/L') that Brian took a Commuter North bus given that he is late is calculated as:

P(C/L) = P(C∩L)/P(L)

Where P(L) = P(C∩L) + P(B∩L) + P(N∩L)

Then, the probability P(C∩L) that Brian takes a Commuter North bus and it is late is calculated as:

P(C∩L)= (1/3)*(0.5) = 0.1667

Because, there is a probability of 1/3 to takes Commuter North Bus and if Brian takes Commuter North there is a 0.5 chance to be late.

At the same way, we get:

P(B∩L) = (1/3)(0.2) = 0.0667

P(N∩L) = (1/3)(0.05) = 0.0167

So, P(L) and P(C/L) are equal to:

P(L) = 0.1667 + 0.0667 + 0.0167 = 0.25

P(C/L) = 0.1667/0.25 = 0.6668

For part b, the probabilities of C, B and N changes and are equal to:

P(C) = 0.3

P(B) = 0.1

P(N) = 0.6

Then, the probability P(C/L') that he took a Commuter North bus given that Brian was not late to class is calculated as:

P(C/L') = P(C∩L')/P(L')

Where P(L') = P(C∩L') + P(B∩L') + P(N∩L')

So, P(C∩L'), P(B∩L') and P(N∩L') are equal to:

P(C∩L') = 0.3*(0.5) = 0.15

P(B∩L') = 0.1*(0.8) = 0.08

P(N∩L') = 0.6*(0.95) = 0.57

It means that P(L') and P(C/L') are equal to:

P(L') = 0.15 + 0.08 + 0.57 = 0.8

P(C/L') = 0.15/0.8 = 0.1875

5 0

3 years ago

Read 2 more answers

Five is 10% of what number?

bonufazy [111]

So,

10% is also known as one-tenth.

If 5 is one-tenth of something, that means that we can multiply 5 by 10 to get ten-tenths of that something.

5 * 10 = 50

The number is 50.

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3 years ago

Yoko needs 300 copies of her resume printed. Dakota Printing charges 19.50$ for the first 200 copies and 9$ for every 100 additi

enyata [817]

Answer:

29.79 should be the answer

Step-by-step explanation:

200 copies 19.50 + 9.00 for 100 copies = 28.50 + 4% = 29.79

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3 years ago