We can see from the diagram that the length of the rectangle is 2 lots of the radius of one quarter circle. The width is made up of one radius, therefore the width is half of the length.
This means that the width of the rectangle is 9cm, and the radius of each quarter circle is 9cm.
To find the shaded area, we find the area of the rectangle and subtract from the areas of each circle, which are equal:
A = lw - 1/2(pi x r^2)
A = 9 x 18 - 1/2(81pi)
A = 162 - 81/2 pi
A = 34.8cm (3sf)
Geometric series are in the form of

Where a is the first term and r is the common ratio .
And it is given that




r=-3,2
So the first five terms are

= 2-6+18-54+162 or 2+4+8+16+32
= 122 or 62
100% - 20% = 80%
$26.95 * 80% = $21.56
You multiply by 80% because you are taking 20% off and now want to know what 80% of the price will be.
Using the rational root theorem, it is found that your friend is correct.
<h3>What is the rational root theorem?</h3>
- It is a theorem that states that for a polynomial with integer coefficients, with q being the factors of the leading coefficient and p being the factors of the constant, every <u>possible rational root</u> is the format
.
In this problem:
- The leading coefficient is 1, hence it's only factor is
, thus guaranteeing that every possible rational zero is an integer, which means that your friend is correct.
To learn more about the rational root theorem, you can take a look at brainly.com/question/10937559
9514 1404 393
Answer:
(a) one parallelogram
(b) opposite sides are 3 inches and 4 inches. Opposite angles are 45° and 135°
(c) yes, all side lengths can be determined, see (b)
Step-by-step explanation:
Opposite sides of a parallelogram are the same length, so if one side is 3 inches, so is the opposite side. Similarly, if one side is 4 inches, so is the opposite side. If sides have different lengths, they must be adjacent sides. The given numbers tell us the lengths of all of the sides.
The 4 inch sides are adjacent to the 3 inch sides. Thus the angle between a 4 inch side and a 3 inch side must be 45°. Opposite angles are congruent, and adjacent angles are supplementary, so specifying one angle specifies them all.
Only one parallelogram can be formed with these sides and angles. (The acute angle can be at the left end or the right end of the long side. This gives rise to two possible congruent orientations of the parallelogram. Because these are congruent, we claim only one parallelogram is possible. Each is a reflection of the other.)