Answer:
Step-by-step explanation:
-3 = 2x+6y
2x+6y = 0
By transitivity, -3 = 0, a contradiction. No solution.
If you graph the lines, you will see they are parallel, therefore never intersect.
If you want to inscribe a polygon inside a circle, you have a formula that doesn't have to use the apothem. The formula is:
A = (nr²/2)sin(360/n)
Since the polygon is a hexagon, it has 6 sides. Thus, n = 6. Knowing the area, we can determine the radius of the circle, r.
166.28 = (6r²/2)sin(360/6)
r = 8 inches
Thus, the radius of the circle is 8 inches.
Answer:
m∠Q = 121°
m∠R = 58°
m∠S = 123°
m∠T = 58°
Step-by-step explanation:
The sum of the interior angles of a quadrilateral = 360°
Create an expression for the sum of all the angles and equate it to 360, then solve for x:
∠Q + ∠T + ∠S + ∠R = 360
⇒ 2x + 5 + x + 2x + 7 + x = 360
⇒ 6x + 12 = 360
⇒ 6x = 360 - 12 = 348
⇒ x = 348 ÷ 6 = 58
So now we know that x = 58, we can calculate all the angles:
m∠Q = 2x + 5 = (2 x 58) + 5 = 121°
m∠R = x = 58°
m∠S = 2x + 7 = (2 x 58) + 7 = 123°
m∠T = x = 58°
Answer:
670 animals
Step-by-step explanation:
First, round both numbers to the nearest ten. Remember that the numbers 4 and under round down (e.g. 143 = 140) and the numbers 5 and above round up (e.g. 145 = 150).
218 = rounds up = 220
454 = rounds down = 450
Finally, add the rounded numbers together.
220 + 450 = 670
The zoo has approximately 670 animals.
