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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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Which best explains why the orthocenter of an obtuse triangle is outside the triangle?

Nezavi [6.7K]

Answer: All three of the altitudes lie entirely outside the triangle.

Step-by-step explanation:

The orthocenter is the center of the triangle formed by creating all the altitudes of each side.

The altitude of a triangle is formed by creating a line from each vertex that is perpendicular to the opposite side.

In acute traingle , the orthocenter lies inside it.

In right angled triangle, the orthocenter lies on the triangle.

In obtuse triangle , the orthocenter lies outside the triangle because all the three altitudes meet outside .

So, the best explains why the orthocenter of an obtuse triangle is outside the triangle : All three of the altitudes lie entirely outside the triangle.