Answer:
690 sq in
Step-by-step explanation:
SA = LA + 2B where LA is the lateral area and B is the area of the base
The triangular base has an area of
B = 1/2bh 1/2(5)(12) = 30
LA = ph where p is the perimeter of the base and h is the height of the prism
LA = (12 + 5 + 13)(21) = 30(21) = 630
SA = 630 + 2(30) = 630 + 60 = 690 sq in
Answer:
g(x) = |x| -9
Step-by-step explanation:
In the form ...
g(x) = a|x -h| +k
the parameters are ...
- a: the vertical scale factor (1)
- h: the right shift of the vertex (0)
- k: the upward shift of the vertex (-9)
The vertex of |x| is (0, 0). The vertex of g(x) is (0, -9), so there has been a vertical shift of -9 and no horizontal shift. The slopes of the lines on the graph of g(x) have a magnitude of 1, so the vertical scale is not changed from the original function (a=1).
Then the translated function is ...
g(x) = |x| -9
Answer:
x = total pencils = 400 pencils
Step-by-step explanation:
Let
x = total pencils
Pencils sold in the morning = 3/5x
Remaining pencil = x - 3/5x
= 5x-3x/5
= 2/5x
Pencils sold in the afternoon = 1/4 of the remainder
= 1/4 * 2/5x
= 2/20x
= 1/10x
Pencils sold in the afternoon = 1/10x
3/5x + 200 = 1/10x
3/5x - 1/10x = 200
(6x-x)/10 = 200
5/10x = 200
1/2x = 200
x = 200 ÷ 1/2
= 200 × 2/1
x = 400 pencils
x = total pencils = 400 pencils
Answer:
64 + 64sqrt(3)
174.9 cm²
Step-by-step explanation:
AD/2 = 8cos(60) = 4
AD = 8 cm
Height of each triangle = 8sin(60)
= 4sqrt(3)
sqrt: square root
Area = 8² + 4(½ × 8 × 4sqrt(3))
= 64 + 64sqrt(3) cm²
= 174.8512517 cm²
Step-by-step explanation:
(c)
By area of similar triangle theorem:
