Answer:
(x^2 + 2x - 21) sq units
Step-by-step explanation:
Area of the shaded region = Area of the larger rectangle - Area of smaller rectangle
Area of the larger region = x(x+2)
Area of the larger region =x^2 + 2x
Area of the smaller rectangle = 3 * 7
Area of the smaller rectangle = 21 sq. units
Area of the shaded region = x^2 + 2x - 21
Hence the required expression is (x^2 + 2x - 21) sq units
9514 1404 393
Answer:
470.16 cm²
Step-by-step explanation:
The apothem of the base is used for two purposes: to find the area of the base, and to find the slant height of each face.
The apothem of the base for side length s is ...
s/2 = a·tan(π/8)
a = s/(2·tan(π/8)) ≈ 7.24 cm
The slant height of a triangular face is found using the Pythagorean theorem. The apothem of the base and the height are legs of the right triangle whose hypotenuse is the slant height. For slant height x, we have ...
x² = 10² + a² = 100 +52.46
x ≈ √152.46 ≈ 12.35
__
The area of the 8 triangular faces will be ...
A = 1/2Px . . . . where P is the perimeter of the pyramid
The area of the base will be ...
A = 1/2Pa
So, the total surface area is ...
A = 1/2P(a + x) = (1/2)(8)(6 cm)(7.24 +12.35 cm) ≈ 470.16 cm²
1)
8² + 15² = 17²
64 + 225 = 289
This is true, so the triangle is a right triangle.
2)
4² + 12² = 13²
16 + 144 = 169
This is false, so the triangle is not a right triangle.
3)
20² + 21² = 27²
400 + 441 = 729
This is false, so the triangle is not a right triangle.
4)
28² + 45² = 53²
784 + 2,025 = 2,809
This is true, so the triangle is a right triangle.
The answer is 98 small and 57 large cups.
s - the number of small cups
l - the number of large cups
<span>Ashley sold a total of 155 cups: s + l = 155
</span><span>Ashley earned</span><span>for $265: 1.25 * s + 2.50 * l = 265
</span>s + l = 155
1.25 * s + 2.50 * l = 265
________
s = 155 - l
1.25 * s + 2.50 * l = 265
________
1.25 * (155 - l) + 2.50 * l = 265
193.75 - 1.25 * l + 2.50 * l = 265
193.75 + 1.25 * l = 265
1.25 * l = 265 - 193.75
1.25 * l = 71.25
l = 71.25 / 1.25
l = 57
______
s = 155 - l
l = 57
s = 155 - 57
s = 98
We know the rule of change: a b/c= (ac+b):c
So we have 2 7/8= (2x8+7):8= 23/8
and the second: 2 1/4 = (2x4+1):4= 9/4
We do the division: 23/8: 9/4= 23/8 x 4/9= (23x4):(8x9)= 23/18= 1 5/18
