X=40 degrees because it s on the circle. arc AD+arc DC=180 arc DC is 100 so AD is 80. That means x must be 40.
Answer:
Area of shaded rectangle = 42 cm²
55%
Step-by-step explanation:
The length of the shaded area is equal to the length of the white rectangle.
Therefore, length of shaded rectangle = 7 cm
The width of the shaded rectangle is equal to the length of the white rectangle <u>minus</u> two widths of the white rectangle.
Therefore, width = 7 - (2 x 0.5) = 6 cm
Area of shaded rectangle = width x length
= 6 x 7
= 42 cm²
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Perimeter of a square = 4 × side length
If the perimeter of the square is 40 cm,
then the side length = 40 ÷ 4 = 10 cm
Area of a square = side length x side length
⇒ area of this square = 10 x 10 = 100 cm²
To determine the shaded area, calculate the areas of the 2 white triangles and subtract these from the area of the square.
Area of a triangle = 1/2 x base x height
⇒ area of left triangle = 1/2 x (10 - 7) x 10 = 15 cm²
⇒ area of right triangle = 1/2 x 10 x (10 - 4) = 30 cm²
Therefore, shaded area = 100 - 15 - 30 = 55 cm²
To calculate the percentage, divide the shaded area by the area of the square and multiply by 100:
(55 ÷ 100) × 100% = 55%
Answer:
Because the sides BO and MA are marked with one line through the middle, which means those sides are congruent, angle A and Angle O are marked with one line, the angles are congruent, and angles W and N are marked with two lines, which means they are congruent. Therefore the triangles are congruent
Answer:
vvvIf the perimeter of the rectangle is 60 in, find its area.
Step-by-step explanation:
This question is in reverse (in two ways):
<span>1. The definition of an additive inverse of a number is precisely that which, when added to the number, will give a sum of zero. </span>
<span>The real problem, in certain fields, is usually to show that for all numbers in that field, there exists an additive inverse. </span>
<span>Therefore, if you tell me that you have a number, and its additive inverse, and you plan to add them together, then I can tell you in advance that the sum MUST be zero. </span>
<span>2. In your question, you use the word "difference", which does not work (unless the number is zero - 0 is an integer AND a rational number, and its additive inverse is -0 which is the same as 0 - the difference would be 0 - -0 = 0). </span>
<span>For example, given the number 3, and its additive inverse -3, if you add them, you get zero: </span>
<span>3 + (-3) = 0 </span>
<span>However, their "difference" will be 6 (or -6, depending which way you do the difference): </span>
<span>3 - (-3) = 6 </span>
<span>-3 - 3 = -6 </span>
<span>(because -3 is a number in the integers, then it has an additive inverse, also in the integers, of +3). </span>
<span>--- </span>
<span>A rational number is simply a number that can be expressed as the "ratio" of two integers. For example, the number 4/7 is the ratio of "four to seven". </span>
<span>It can be written as an endless decimal expansion </span>
<span>0.571428571428571428....(forever), but that does not change its nature, because it CAN be written as a ratio, it is "rational". </span>
<span>Integers are rational numbers as well (because you can always write 3/1, the ratio of 3 to 1, to express the integer we call "3") </span>
<span>The additive inverse of a rational number, written as a ratio, is found by simply flipping the sign of the numerator (top) </span>
<span>The additive inverse of 4/7 is -4/7 </span>
<span>and if you ADD those two numbers together, you get zero (as per the definition of "additive inverse") </span>
<span>(4/7) + (-4/7) = 0/7 = 0 </span>
<span>If you need to "prove" it, you begin by the existence of additive inverses in the integers. </span>
<span>ALL integers each have an additive inverse. </span>
<span>For example, the additive inverse of 4 is -4 </span>
<span>Next, show that this (in the integers) can be applied to the rationals in this manner: </span>
<span>(4/7) + (-4/7) = ? </span>
<span>common denominator, therefore you can factor out the denominator: </span>
<span>(4 + -4)/7 = ? </span>
<span>Inside the bracket is the sum of an integer with its additive inverse, therefore the sum is zero </span>
<span>(0)/7 = 0/7 = 0 </span>
<span>Since this is true for ALL integers, then it must also be true for ALL rational numbers.</span>
