Look at one of the vertices of the heptagon where two squares meet. The angles within the squares are both of measure 90 degrees, so together they make up 180 degrees.
All the angles at one vertex must clearly add up to 360 degrees. If the angles from the squares contribute a total of 180 degrees, then the two remaining angles (the interior angle of the heptagon and the marked angle) must also be supplementary and add to 180 degrees. This means we can treat the marked angles as exterior angles to the corresponding interior angle.
Finally, we know that for any convex polygon, the exterior angles (the angles that supplement the interior angles of the polygon) all add to 360 degrees (recall the exterior angle sum theorem). This means all the marked angles sum to 360 degrees as well, so the answer is B.
<h3><u>4(2x^2 + 3x + 12)</u></h3>
We can factor a 4 out of this expression.
4(2x^2 + 3x + 12)
Now that the expression is simplified, we can see if splitting the middle term is possible.
<em><u>Display factors of 24.</u></em>
1 * 24
-1 * - 24
2 * 12
-2 * -12
3 * 8
-3 * - 8
4 * 6
-4 * -6
All factors of 24 have been listed, and none of these digits satisfy the criteria.
Trinomial cannot be further factored.
The Final Answer for the Square Root of 27
To an accuracy of at least .01%, the square root of 27 is 5.196.
Step-by-step explanation:
Step-by-step explanation:
-2, -8/3, -10/3, -4, -14/3
Write as multiples of 1/3.
-6/3, -8/3, -10/3, -12/3, -14/3
This is an arithmetic sequence where the first term is -6/3 and the common difference is -2/3.
Therefore, the recursive formula is:
aᵢ₊₁ = aᵢ − 2/3, a₁ = -2
small frames ($8): s
large frames ($15): L
Cost: 8s + 15L = 239 ⇒ 1(8s + 15L = 239) ⇒ 8s + 15L = 239
Quantity: s + L = 22 ⇒ -8( s + L = 22) ⇒ <u> -8s -8 L = -176 </u>
7L = 63
L = 9
Quantity: s + L = 22 ⇒ s + (9) = 22 ⇒ s = 13
Answer: 13 small frames, 9 Large frames
