Answer:
<em>Greatest number of boxes to pack all items into them equally will be 12 where each box contain 10,12,9 files, notebooks and pencils respectively.</em>
Step-by-step explanation:
To find the greatest number of boxes that Riley could pack the items into, we have to find the HCF of 144, 120 and 108.
We will find the HCF through prime factorization.
<em>("Prime Factorization" is finding which prime numbers multiply together to make the original number)</em>
<u>Step 1:</u>
Find the prime factorization of each of the given numbers.
<u>Step 2:</u>
The product of all common prime factors is the HCF of the given numbers.
First number is 120:
120 = 2*2*2*3*5
Second number is 144:
144 = 2*2*2*2*3*3
And last number is 108:
108 = 2*2*3*3*3
Now we will match the numbers which are common in all three values. In other words we will find the common factors.
<em>The common factors in 120,108 and 144 are:</em>
<em>2*2*3</em>
If we multiply 2*2*3 we get 12
Hence, HCF of ( 120,108,144 ) = 12
<em>Therefore, Greatest number of boxes to pack all items into them equally will be 12 where each box contain 10,12,9 files, notebooks and pencils respectively.</em>
Answer:
<em>Area of Regular Polygon: ( About ) 716.6 m^2; Option B</em>
Step-by-step explanation:
<em> ~ In this situation we can apply the formula 1/2 * a * P, provided a ⇒ apothem, and P ⇒ Perimeter of the shape ~</em>
<u>Here we are not directly provided with the apothem, so we have to first plan out our procedure step-by-step:</u>
Let us first divide this dodecagon into 12 triangles, each equilateral provided that this is a regular polygon ( implied ). Now let us draw an altitude to one of these triangles, and provided these are equilateral triangles Coincidence Theorem can be applied to this specific triangle. That would mean this altitude is both an angle bisector and a median, which can help us determine the tan degree of the mini triangle formed by the altitude, and the length of one of the sides of this mini triangle.
1. Knowing that the altitude splits the base of the triangle into the two congruent parts ⇒ one of the congruent parts should be ⇒ 8/2 = 4 meters
2. Now the triangles formed through spliting this figure are all ≅, so one of the angles of the triangle is 360/12 = 30 degrees. The mini triangle formed should thus have a measure of 30/2 as the altitude is an angle bisector ⇒ tan 15.
3. From this you can create a proportion, with a ⇒ apothem:
tan 15/ 1 = 4/a ⇒ tan 15 * a = 4 ⇒ a = 4/tan 15° ⇒ <em>a = ( About ) 14.93</em>
4. The perimeter of this shape would be 8 * 12 ⇒ <em>96 meters</em>
5. Now let us solve for the area of this regular polygon through substitution into the formula 1/2 * a * P ⇒ 1/2 * 14/93 * 96 = <em>( About ) 716.64 meters^2</em>
<em>Answer ⇒ Area of Regular Polygon: ( About ) 716.6 m^2</em>
Answer:
113.04
Step-by-step explanation:
6*6=36
36*3.14=113.04
Answer:
Area = 12.82 miles²
Step-by-step explanation:
Area of a triangle with two adjacent sides and the inscribed angle between these side is given by,
Area = ![\frac{1}{2}ab[\text{sin(C)}]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dab%5B%5Ctext%7Bsin%28C%29%7D%5D)
By substituting the values of sides a, b and the angle C,
Area = ![\frac{1}{2}(5.7\times 9.3)[\text{sin}(14^{\circ})]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%285.7%5Ctimes%209.3%29%5B%5Ctext%7Bsin%7D%2814%5E%7B%5Ccirc%7D%29%5D)
= 12.82 square miles
Answer:
3x
Step-by-step explanation:
The GCF would be 3x, if you took out 3x from those numbers you'd be left with x^2, 2x, and 5, which can't be reduced any further.
