Answer:
14
Step-by-step explanation:
The square will have area
.. (9 cm)^2 = 81 cm^2.
The two triangles together will have area
.. (9 cm)*(12 cm) = 108 cm^2.
The sum of the areas of those three shapes is
.. 81 cm^2 +108 cm^2 = 189 cm^2
Answer:
(C)18 units
Step-by-step explanation:
- Point G is the centroid of triangle ABC.
- C is a vertex of the triangle
- D is the midpoint of the side opposite the vertex.
From Centroid Theorems, we know that the distance from the centroid to the vertex is twice as long as the distance from the centroid to the midpoint of the side opposite the vertex.
Therefore:
CG=2DG
Let the length of segment DG =x
The length of segment CG is 6 units greater, therefore: CG=x+6
Substituting into CG=2DG:
x+6=2x
2x-x=6
x=6 Units
Therefore:
CD=CG+GD
=6+6+6
=18 Units
<u><em>The correct option is C.</em></u>
Let x and y be the sides of the rectangular corral. Therefore,
Area, A = x*y = xy
Additionally, let the side bordering the barn be x. Then,
Circumference, C = x+y+y = x+2y = 4000 ft => x = 4000 - 2y
Substituting for x in the area equation,
A = (4000-2y)y = 4000y - 2y^2
For maximum area, dA/dy = 0
Then,
dA/dy = 4000 - 4y = 0 => 4000 = 4y => y = 4000/4 = 1000 ft
And x = 4000 - 2y = 4000 - 2*1000 = 4000 - 2000 = 2000 ft
The dimensions of the corral are: 2000 ft by 1000 ft.
Area, A = xy = 2000*1000 = 2000,000 ft^2
Answer:
B. 140
Step-by-step explanation:
A radius is a segment connecting the center of a circle to the outer perimeter of the circle. One property of radii is that all radii from the same circle are congruent. Thus, one can conclude that the triangle with the angle (C) is an isosceles triangle because its sides are radii of the same circle, thus they must be congruent.
One property of an isosceles triangle is the base angle theorem. This states that the angles opposite the congruent sides in an isosceles triangle are cognrunet. Moreover, a property of all triangles is that the sum of angles in any triangle is (180) degrees. Therefore, one can combine this information with the base angles theorem to form an equation and solve for the unknown, (C).
20 + 20 + (m<C) = 180
Simplify,
40 + m<C = 180
Inverse operations,
m<C = 140
