Answer:
Area =
Step-by-step explanation:
Recall that the area of any regular polygon is expressed via the formula:
Area = perimeter * apothem /2
The perimeter is easy to find since in our case it would be 24 cm * 5 (five sides of the same 24 cm length). Perimeter = 120 cm
In order to find the dimension of the apothem (which is pictured as an orange segment in the attached image) we use the fact that the apothem joins the center of the polygon at the exact middle of each side (thus rendering two 12 cm segments), and forming a 90 degree angle. Seeing from the picture, we can use the information on the small right angle triangles that are formed by the apothem and the sides of the triangles drawn joining the center of the polygon with its vertices.
Recall that the five equal angles around the center point, have to measure 360 degrees / 5 = 72 degrees, so, half of this (which is one of the acute angles of the small right angle triangles we are going to use to find the apothem) has to be 36 degrees.
We can then use the definition of tangent of one of the acute angles in a right angle triangle:
the tangent of the angle (36 degrees) equals the quotient of the side opposite to it (12 cm) divided by the adjacent side (apothem). Using this relationship we can solve for the apothem:
Now we can find the area using the area formula above:
Area = perimeter * apothem / 2
Area = 120 cm * 16.516583 cm / 2
Area = 990.99 cm^2
which we can round to approximately 991 square cm
So first, we need to find the measure of x. Let's do that first.
1. You need to find the expression for angle DBC. We can't just have 36 degrees. We need the actual expression.
So, subtract 6x + 5 from 10x - 7. This will give us the expression we need.
→ (10x - 7) - (6x + 5) = 4x - 12
2. Have 36 and 4x - 12 equal each other. This will help us find the value of x.
→ 36 = 4x - 12 ⇒ x = 12 <Hopefully you know how I got that. If not, I solved it by adding 12 on both sides to isolate the variable to get 48 = 4x. Then, I divided both sides by 4 to get 12.>
3. Now we know the value of x. Using the expression 6x + 5, substitute 12 for x.
→ 6 (12) + 5 ⇒ 72 + 5 = 77
Therefore, the measure of angle ABD is 77 degrees.
The difference in the dogs weight from 2 years ago is -0.83
Answer:
.76 meters
Step-by-step explanation:
The area of a circle is pi*r^2
3.14*.85^2 = 2.26865
Dividing this into thirds gives us approximately .75621666666
Round to the nearest hundredth.
.76
Label the answer.
.76 meters
Remember the difference of 2 perfect squares
(a²-b²)=(a-b)(a+b)
1/81=(1/9)²
so
x⁸=(x⁴)²
x⁸-1/81=(x⁴)²-(1/9)²=(x⁴-1/9)(x⁴+1/9)
oh look, 1/9=(1/3)²
x⁴=(x²)²
we can factor that first one again
x⁴-1/9=(x²)²-(1/3)²=(x²-1/3)(x²+1/3)
so factored completely is (x²-1/3)(x²+1/3)(x⁴+1/9)
you could go further and force taht first term to be another difference by doing 1/3=(√(1/3))², but I wouldn't
(x²-1/3)(x²+1/3)(x⁴+1/9) is factored