Answer: The answer is A :)
Step-by-step explanation:
Answer:
Notice that each edge of the cube is 2 yards long, and the height of the pyramid is 2 yards long too.
The slant height refers to the height of a triangle on its face, which forms a right triangle with the height of the pyramid and half side. Using Pythagorean's Theorem, we have
![s^{2}=1^{2} +2^{2}\\ s=\sqrt{5}](https://tex.z-dn.net/?f=s%5E%7B2%7D%3D1%5E%7B2%7D%20%20%2B2%5E%7B2%7D%5C%5C%20s%3D%5Csqrt%7B5%7D)
Therefore, the slant height is the square root of 5, in yards units. (A)
The surface of the composite figure is the sum of the surface area of both volumes.
![S_{composite}=S_{cube} +S_{pyramid}\\ S_{composite}=5(2)^{2} +(2)^{2} +\frac{1}{2} (8)(\sqrt{5} )=20+4+4\sqrt{5} \\ S_{composite}\approx 32.9 yd^{2}](https://tex.z-dn.net/?f=S_%7Bcomposite%7D%3DS_%7Bcube%7D%20%20%2BS_%7Bpyramid%7D%5C%5C%20S_%7Bcomposite%7D%3D5%282%29%5E%7B2%7D%20%2B%282%29%5E%7B2%7D%20%2B%5Cfrac%7B1%7D%7B2%7D%20%288%29%28%5Csqrt%7B5%7D%20%29%3D20%2B4%2B4%5Csqrt%7B5%7D%20%5C%5C%20S_%7Bcomposite%7D%5Capprox%2032.9%20yd%5E%7B2%7D)
Therefore, the surface of the composite figure is 32.9 square yards. (B)
The concrete needed will fill the empty space between the cube and the pyramid, so we have to find the difference between their volumes.
![V_{concrete}=V_{cube} -V_{pyramid}=2^{3}-\frac{1}{3}(2)^{2} (2)=8-\frac{8}{3} \\V_{concrete} \approx 5.33 yd^{3}](https://tex.z-dn.net/?f=V_%7Bconcrete%7D%3DV_%7Bcube%7D%20-V_%7Bpyramid%7D%3D2%5E%7B3%7D-%5Cfrac%7B1%7D%7B3%7D%282%29%5E%7B2%7D%20%282%29%3D8-%5Cfrac%7B8%7D%7B3%7D%20%5C%5CV_%7Bconcrete%7D%20%5Capprox%205.33%20yd%5E%7B3%7D)
Therefore, we need 5.33 cubic yards of concrete to make the planter. (C)
Answer:
first one
Step-by-step explanation:
The sides of the isosceles triangle are two equal legs and the remaining side is called base.
Answer:
2a. One Solution
2b. Infinite Solutions
2c. No Solution
Step-by-step explanation:
In all the problems club terms with x on one side and the constants on the other side.
2a. 6x + 4x - 6 = 24 + 9x
⇒ 10x - 6 = 24 + 9x
Subtracting 9x and adding 6 on both sides;
⇒ 10x - 9x = 24 + 6
⇒ x = 30
The only possible value of x that could satisfy the equation is 30. So, there is only one possible solution to the equation.
2b. 25 - 4x = 15 - 3x + 10 - x
Clubbing like terms;
25 - 15 - 10 = 4x - 3x - x
⇒ 25 - 25 = 4x - 4x
⇒ 0 = 0
Note that any value of 'x' could satisfy this equation. So, there are infinite solutions to the equation.
2c. 4x + 8 = 2x + 7 + 2x - 20
⇒ 4x - 2x - 2x = - 20 + 7 + 8
⇒ 4x - 4x = -5
⇒ 0 = -5
This is absurd. No value of 'x' can satisfy this. So, there are no solutions to this equation.