Answer:
Only A, the first equation is true.
Step-by-step explanation:
A. (y + 6)(y – 7) + 42 = y² + 6y –7y – 42 + 42 = y² – y. This means A is true
B. (x + 3)(X – 8) = x² + 3x – 8x – 24 = x² – 5x – 24. This means B is false.
Answer:
The area of an octagon whose perimeter is 120 cm is 1086.4 
Step-by-step explanation:
An octagon is a polygon with eight sides. If the lengths of all the sides and the measurement of all the angles are equal, the octagon is called a regular octagon.
There is a predefined set of formulas for the calculation of perimeter, and area of a regular octagon.
The perimeter of an Octagon is given by
and the area of an Octagon is given by
We know that the perimeter is 120 cm, solving for side length (a) in the perimeter formula we get
Now, we calculate the area
Answer:
GCF=2 LCM=140
Step-by-step explanation:
Answer:
triangle A
Step-by-step explanation:
the area is 16cm²
8×4/2 = 32/2 = 16
Answer:
a solution is 1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) + π/4
Step-by-step explanation:
for the equation
(1 + x⁴) dy + x*(1 + 4y²) dx = 0
(1 + x⁴) dy = - x*(1 + 4y²) dx
[1/(1 + 4y²)] dy = [-x/(1 + x⁴)] dx
∫[1/(1 + 4y²)] dy = ∫[-x/(1 + x⁴)] dx
now to solve each integral
I₁= ∫[1/(1 + 4y²)] dy = 1/2 *tan⁻¹ (2*y) + C₁
I₂= ∫[-x/(1 + x⁴)] dx
for u= x² → du=x*dx
I₂= ∫[-x/(1 + x⁴)] dx = -∫[1/(1 + u² )] du = - tan⁻¹ (u) +C₂ = - tan⁻¹ (x²) +C₂
then
1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) +C
for y(x=1) = 0
1/2 *tan⁻¹ (2*0) = - tan⁻¹ (1²) +C
since tan⁻¹ (1²) for π/4+ π*N and tan⁻¹ (0) for π*N , we will choose for simplicity N=0 . hen an explicit solution would be
1/2 * 0 = - π/4 + C
C= π/4
therefore
1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) + π/4
