A square with 1,536 soldiers are not possible, i.e. the square root of 1,536 is about 39.191, which means that 1,536 is not a square a number. In order for it to be a square number, we have to round up 39.191 (because it says "how many more soldiers") to 40 and 40×40=1,600 and 1,600-1,536, so we need 64 more soldiers.
The greatest 4 digit number is simple. If the square root of 10,000 is 100, than, one can assume that because 100-1=99, the resulting answer of 99×99 is less than 10,000, meaning that is is 4 digits. 99×99=9,801.
Step-by-step explanation:
5ˣ⁻² = 6
Take log of both sides.
log 5ˣ⁻² = log 6
Use log exponent property.
(x − 2) log 5 = log 6
Solve for x.
x − 2 = log 6 / log 5
x = 2 + (log 6 / log 5)
x = 3.1133
Answer:
384 cm²
Step-by-step explanation:
The shape of the figure given in the question above is simply a combined shape of parallelogram and rectangle.
To obtain the area of the figure, we shall determine the area of the parallelogram and rectangle. This can be obtained as follow:
For parallelogram:
Height (H) = 7.5 cm
Base (B) = 24 cm
Area of parallelogram (A₁) =?
A₁ = B × H
A₁ = 24 × 7.5
A₁ = 180 cm²
For rectangle:
Length (L) = 24 cm
Width (W) = 8.5 cm
Area of rectangle (A₂) =?
A₂ = L × W
A₂ = 24 × 8.5
A₂ = 204 cm²
Finally, we shall determine the area of the shape.
Area of parallelogram (A₁) = 180 cm²
Area of rectangle (A₂) = 204 cm²
Area of figure (A)
A = A₁ + A₂
A = 180 + 204
A = 384 cm²
Therefore, the area of the figure is 384 cm²
Answer:
∠DEF = 250°
Step-by-step explanation:
1. This shape is a hexagon (6 sides), so the interior angles should all add to 720°. Also worth noting: the problem says the <em>obtuse</em> angle DEF; this means it's the angle INSIDE the shape, not outside.
2. Add all the known angles, then subtract from the total degrees:
50 + 96 + 144 + 42 = 332
720 - 332 = 338
3. Because BC is parallel to ED, we can subtract 180 - 42 for the value of ∠EDC, which is 138°.
4. Add all the known values and subtract from 720 for the value of ∠DEF:
50 + 96 + 144 + 42 + 138 = 470
720 - 470 = 250°
