We are asked to solve for the volume of the composite figures and the answer is the summation of the two volumes such as the volume of a triangular prism and volume of a rectangular prism. In order to solve this, we need to recall the following formulas:
the volume of triangular prism = 1/2* b*h*l and solving the volume, we have it:
the volume of triangular prism = 1/2 * 15* 16*20 = 3600 units³
the volume of rectangular prism = l*w*h and solving the volume, we have it:
the volume of rectangular prism = 20*15*12 = 2400 units³
The total volume of the composite figure is the summation of the two volumes such as:
total volume = 3600 + 2400
total volume = 6000 units²
The answer is 6,000 units².
Answer:
o calculate the volume of a cone, start by finding the cone's radius, which is equal to half of its diameter. Next, plug the radius into the formula A = πr^2, where A is the area and r is the radius. Once you have the area, multiply it by the height of the cone.Step-by-step explanation:
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Answer:
B. (3, 0)
Step-by-step explanation:
The x-intercept is the point where the graph of the function meets the x-axis.
At x-intercept, y=0 or f(x)=0
So look through the table and find where f(x)=0.
From the table, f(x)=0 at x=3.
We write this as an ordered pair.
Therefore the x-intercept is (3,0)
The correct choice is B.
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Answer with explanation:</h3>
It is given that:
Circle 1 has center (−4, −7) and a radius of 12 cm.
Circle 2 has center (3, 4) and a radius of 15 cm.
Two circles are said to be similar if by some translation and dilation it could be placed over the other to form the same circle.
The circles are similar because the transformation rule ( x,y ) → (x+7,y+11) can be applied to Circle 1 and then dilate it using a scale factor of 5/4
( Since, as the center of circle 1 is (-4,-7)
so,
(-4+7,-7+11) → (3,4)
( Since, the radius of circle 1 is 12 and that of circle 2 is 15 cm.
so, let the scale factor be k .
that means :
)
The general vertex form of the a quadratic function is y = (x - h)^2 + k.
In this form, the vertex is (h,k) and the axis of symmetry is x = h.
Then, you only need to compare the vertex form of g(x) with the general vertex form of the parabole to conclude the vertex point and the axis of symmetry.
g(x) = 5(x-1)^2 - 5 => h = 1 and k = - 5 => theis vertex = (1, -5), and the axis of symmetry is the straight line x = 1.
<span>Answer: the vertex is (1,-5) and the symmetry axis is x = 1.</span>