Plotting the 4 points and doing visual inspection will tell us if the quadrilateral is a parallelogram. We can also do analytical techniques which are to determine the slope and the distance between the points. Doing either of these two will give us
<span>B. Yes,TUVW quadrilateral s a parallelogram because there are two pairs of parallel sides.
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Answer:
There are 19 big marbles
Step-by-step explanation:
10a + 3b = 209
a = 3b
3b = 3b
10a + a = 209
11a = 209
a = 209/11
a = 19
Answer:
volume ≈ 930 cm³ (nearest cubic cm)
Step-by-step explanation:
The base of the prism which is a pentagon is regular. The apothem which is a line drawn from the center to any side of the pentagon is 4 cm. The height of the prism is 16 cm.
The volume of a prism = Bh
where
B = base area
h = height of the prism
The base of the prism can be divided into 5 congruent triangles.But the base of the triangles is unknown.
The sum of interior angle of a pentagon is 540°. That means each angle is 108° . The triangle divide the angle into 2. Making the 2 base angle as 54° each. The last angle of the triangle at the center is 72°(remember sum of angle in a triangle is 180° which is 54° + 54° + 72° = 180°) .
The angle form the center can be divided by the line of height of the triangles. The angle will then be 36°. Using tangential ratio half of the length of the base of the triangle can be known. Therefore,
tan 36° = opposite/adjacent
tan 36° = opposite/4
opposite = 4 tan 36°
The full base of the triangles = 2(4 tan 36°)
area of each triangle = 1/2 × 2(4 tan 36°) × 4 = 16 tan 36°
Base area of the prism(pentagon) = 5 × 16 tan 36° = 80 tan 36°
Volume of the prism = Bh
where
h = 16 cm
B = 80 tan 36°
volume = 80 tan 36° × 16 = 1280 tan 36° = 1280 × 0.726542528
volume = 929.974435847 cm³
volume ≈ 930 cm³ (nearest cubic cm)
<span>To convert 12.5 to a fraction, consider the decimal portion of the number, .5. Since .5 is in the tenth spot of the decimal, it may be read as five-tenths, or 5/10. To reduce it to lowest terms, find the lowest common denominator, 5, and divide each by that number to get 1/2, or one-half. Thus, the number is now 12 1/2. To convert this mixed number into an entirely rational fraction, multiply the whole number, 12, by the denominator, 2, to get 24, then add the numerator, to end up with 25. This is the new numerator, so the rational number is 25/2. To check the work, divide 25 by 2 on a calculator or as a decimal equation, yielding 12.5.</span>
