The product is 60.
We start out with the information we have. This forms a right triangle, with one leg being 24, the other leg x, and the hypotenuse 30. Using the Pythagorean theorem we have
x²+24²=30²
x²+576=900
Subtract 576 from both sides:
x²+576-576 = 900-576
x²=324
Take the square root of each side:
√x²=√324
x=18
We know that the formula for the volume of a triangular prism is V=(1/2bh)H, where b is the base of the triangle, h is the height of the triangle, and H is the height of the prism. Substituting our known information we have:
720=(1/2*18*24)y
720=216y
Divide both sides by 216:
720/216 = 216y/216
3 1/3 = y
This means the product of x and y would be:
18(3 1/3)
18(10/3)
180/3
60
Let lucy = l & neighbour= n
l = n +4
l + n= 14 years
substitute l with n +4
(n +4) + n = 14
2n +4 =14
n=5 years
l = n + 4 lets substitute n with 5
l = 5 + 4
lucy = 9 years
<em>hey</em><em> </em><em>buddy</em><em>,</em>
<em>●</em><em>15x</em><em> </em><em>+</em><em> </em><em>5y</em><em> </em><em>=</em><em> </em><em>25</em>
<em>5y</em><em> </em><em>=</em><em> </em><em>25-15x</em>
<em>y</em><em> </em><em>=</em><em> </em><em>(</em><em>25</em><em> </em><em>-</em><em> </em><em>15x</em><em>)</em><em> </em><em>/</em><em>5</em>
<em>y</em><em> </em><em>=</em><em> </em><em>5</em><em> </em><em>-</em><em> </em><em>3x</em>
Answer:
∠D = 13°
Step-by-step explanation:
∠A and ∠D are vertical angles and thus are congruent, hence
x - 2 = - 3x + 58 ( add 3x to both sides )
4x - 2 = 58 ( add 2 to both sides )
4x = 60 ( divide both sides by 4 )
x = 15
∠D = x - 2 = 15 - 2 = 13°