Angle D is 180° -75° -45° = 60°. Drawing altitude MX to segment DN divides the triangle into ΔMDX, a 30°-60°-90° triangle, and ΔMNX, a 45°-45°-90° triangle. We know the side ratios of such triangles (shortest-to-longest) are ...
... 30-60-90: 1 : √3 : 2
... 45-45-90: 1 : 1 : √2
The long side of ΔMDX is 10√3, so the other two sides are
... MX = MD(√3/2) = 15
... DX = MD(1/2) = 5√3
The short side of ΔMNX is MX = 15, so the other two sides are
... NX = MX(1) = 15
... MN = MX(√2) = 15√2
Then the perimeter of ΔDMN is ...
... P = DM + MN + NX + XD
... P = 10√3 +15√2 + 15 + 5√3
... P = 15√3 +15√2 +15 . . . . perimeter of ΔDMN
4x(3x²+5y) expand by distributing terms
4x*3x²+4x*5y take out the constants
(4*3)xx²+4x*5y simplify 4*3 to 12
12xx²+4x*5y use product rule=xᵃxᵇ=xᵃ+ᵇ, and change the two variables (the x's) into ones, because if there is just one variable with no number by it, then it is a one.
12x¹⁺²+4x*5y and simplify 1+2 to 3.
12x³+4x*5y finally simplify 4x*5y to 20xy
12x³+20xy
Hope this helps, now you know the answer and how to do it. Stay healthy and safe and HAVE A BLESSED AND WONDERFUL DAY! :-)
- Cutiepatutie ☺❀❤
Answer:
x = - 9
Step-by-step explanation:
Given
= - 3 ( multiply both sides by 3 to clear the fraction )
x = - 9
