Answer:
x = 24
Step-by-step explanation:
10(x+12)=15x (Given)
10x + 120 = 15x (Distributive property of equality)
-5x = -120 (Subtraction property of equality)
x = 24 (Division property of equality)
In the given diagram, we can note that the tree divides the hypotenuse of the triangle as well as the side where the tree is based into halves.
In a triangle, when a line is drawn joining between the midpoints of two sides, this line is always parallel to the third side and equals half its length.
Applying this concept to the given diagram here, we will find that the tree is joining the midpoints of two sides of the triangle. this means that the tree is parallel to the building and the height of the tree is half the height of the building.
Therefore:
height of tree = 0.5 * 120 = 60 ft
First, multiply 30 with 25
30 x 25 = Area
Area = 750 square yards
one bag gives you 100 square yards
Divide the two numbers
750/100 = 7.5
Since you cannot buy half a bag, you must round up
8 bags is needed
hope this helps
<h3>
Answer: 133</h3>
=============================================================
Explanation:
The quickest way to get this answer is to add the angles given to get 87+46 = 133
This is through the use of the remote interior angle theorem.
Note how the angles 87 and 46 are interior, or inside the triangle. And also, they are not adjacent to the exterior angle we want to find. So that's where the "remote" portion comes in.
----------------
The slightly longer method involves letting x be the measure of the missing interior angle of the triangle.
The three interior angles add to 180
87+46+x = 180
133+x = 180
x = 180 - 133
x = 47
The missing interior angle of the triangle is 47 degrees.
Angle 1 is adjacent and supplementary to this 47 degree angle, so,
(angle1)+(47) = 180
angle1 = 180-47
angle1 = 133 degrees
This example helps confirm that the remote interior angle theorem is correct.
