Answer:
56
Step-by-step explanation:
To divide 364 into two parts in the ratio 15:11, add 15+11 to get 26. Now divide 364 by 26 to get 14. This counters 14 for each part, and we have 26 parts. If each part is x, and x=14, x times 15 will equal 15x=210, so the first number is 210. x times 11 will equal 11x=154, so the second number is 154. 210-154=56, so the first number is 56 bigger than the second.
Answer:
Step-by-step explanation:
14) 2x - 10 = 80 {alternate interior angles are equal}
2x = 80 + 10
2x = 90
x = 90/2
x = 45°
15) 3x + 120 = 180 { co interior angles are supplementary}
3x = 180 - 120
3x = 60
x = 60/3
x = 20°
16) 3x + 15 = 135 {corresponding angles are equal}
3x = 165 - 15
3x = 150
x = 150/3
x = 50°
Answer:
7 1/17
Step-by-step explanation:
A figure can be helpful.
The inscribed semicircle has its center at the midpoint of th base. It is tangent to the side of the isosceles triangle, so a radius makes a 90° angle there.
The long side of the isosceles triangle can be found from the Pythagorean theorem to be ...
BC² = BD² +CD²
BC² = 8² +15² = 289
BC = √289 = 17
The radius mentioned (DE) creates right triangles that are similar to ∆BCD. In particular, we have ...
(long side)/(hypotenuse) = DE/BD = CD/BC
DE = BD·CD/BC = 8·15/17
DE = 7 1/17 ≈ 7.059
Answer:
-19
Step-by-step explanation:
Evaluate -x^2 - 5 x y + 5 y^3 where x = -2 and y = -1:
-x^2 - 5 x y + 5 y^3 = -(-2)^2 - -2 (-5) + (-1)^3×5
(-2)^2 = 4:
-4 - -5 (-2) + 5×(-1)^3
(-1)^3 = -1:
-4 - -5 (-2) + 5×-1
-5 (-2) = 10:
-4 - 10 - 5
-4 - 10 - 5 = -(4 + 10 + 5):
-(4 + 10 + 5)
| 1 | 0
| | 5
+ | | 4
| 1 | 9:
Answer: -19
