Answer:
C
Step-by-step explanation:
the area of a triangle is
baseline × height / 2
so, we know in our case
b(b+12) = 189 cm²
b² + 12b - 189 = 0
let's try to solve this by completing the square.
that means we try to find the expression
(b + k)² + c
that is equal to
b² + 12b - 189
(b + k)² + c = b² + 2kb + k² + c = b² + 12b - 189
so,
2k = 12
k = 6
and then
k² + c = -189
6² + c = -189
36 + c = -189
c = -225
(b + 6)² - 225 = 0
(b + 6)² = 225
b + 6 = 15
b = 9
so, the baseline b = 9 cm.
the height b+12 = 9+12 = 21 cm.
5/6 = 0.833333 .... (non-terminating)
56/90
" / " means divide
56 divided by 90 = 0.62 with a line over the 2 because it is repeating
2000 + 1500g ≤ 15000
1500g ≤ 15000 - 2000
1500g ≤ 13000
g ≤ 13000/1500
g ≤ 8 2/3
Therefore, the crane can safely lift a maximum of 8 2/3 cubic meters of gravel.
Read the problem and answer choices. You want to get from ABCD to EFGH, so you need to figure out how to do that with reflection, translation, and dilation—in that order.
The reflection part is fairly easy. ABC is a bottom-to-top order, and EFG is a top-to-bottom order, so the reflection is one that changes top to bottom. It must be reflection across a horizontal line. The only horizontal line offered in the answer choices is the x-axis. Selection B is indicated right away.
The dimensions of EFGH are 3 times those of ABCD, so the dilation scale factor is 3. This means that prior to dilation, the point H (for example), now at (-12, -3) would have been at (-4, -1), a factor of 3 closer to the origin. H corresponds to D in the original figure, which would be located at (0, -2) after reflection across the x-axis.
So, the translation from (0, -2) to (-4, -1) is 4 units left (0 to -4) and 1 unit up (-2 to -1).
The appropriate choice and fill-in would be ...
... <em>B. Reflection across the x-axis, translation </em><em>4</em><em> units left and </em><em>1</em><em> unit up, dilation with center (0, 0) and scale factor </em><em>3</em><em>.</em>
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You can check to see that these transformations also map the other points appropriately. They do.
