The diagonal of the figure forms a right angle triangle with the diagonal of the base and the height of the figure.
Diagonal of base = √(3² + 4²)
= 5ft
Diagonal of solid² = Diagonal of base² + height²
height = √((√41)² + 5²)
height = 8.12 feet
Volume = width x length x height
Volume = 3 x 4 x 8.12
= 97.44 cubic feet
Answer:
<em>Similar: First two shapes only</em>
Step-by-step explanation:
<u>Triangle Similarity Theorems
</u>
There are three triangle similarity theorems that specify under which conditions triangles are similar:
If two of the angles are congruent, the third angle is also congruent and the triangles are similar (AA theorem).
If the three sides are in the same proportion, the triangles are similar (SSS theorem).
If two sides are in the same proportion and the included angle is equal, the triangles are similar (SAS theorem).
The first pair of shapes are triangles that are both equilateral and therefore have all of its interior angles of 60°. The AAA theorem is valid and the triangles are similar.
The second pair of shapes are parallelograms. The lengths are in the proportion 6/4=1,5 and the widths are in proportion 3/2=1.5, thus the shapes are also similar.
The third pair of shapes are triangles whose interior acute angles are not congruent. These triangles are not similar
Answer:
6.8 hours of pool use for a total monthly charge of $69.80
Step-by-step explanation:
6.8(6)+29=69.80
Value of n is greater than (-2) and less than or equal to 3.
n = {-1,0,1,2 3}
3x +5 > 16
Subtract 5 from both sides
3x > 16 - 5
3x > 11
x > 11/3
x> 3.67
X= 4 is the smallest value
First we find the slope m as follows:
So the equation is of the form:
y = 5x + b
When x = 1, y = 5. Therefore b = 0.
So the equation is:
y = 5x
