Answer:
2 1/3
Step-by-step explanation:
21/9 is 2.33 or 2 1/3
Answer:
The two that are blank are 2 and 7
Step-by-step explanation:
Answer:
4) x = - 12
5) x = 4
Step-by-step explanation:
4)
Since points T and S are mid points of sides ML and MN of triangle MLN.
Therefore, by mid point theorem,
TS is half of LN
so,

5) In the same way x = 4 will be the correct answer in question number 5.
Answer:
a. A(x) = (1/2)x(9 -x^2)
b. x > 0 . . . or . . . 0 < x < 3 (see below)
c. A(2) = 5
d. x = √3; A(√3) = 3√3
Step-by-step explanation:
a. The area is computed in the usual way, as half the product of the base and height of the triangle. Here, the base is x, and the height is y, so the area is ...
A(x) = (1/2)(x)(y)
A(x) = (1/2)(x)(9-x^2)
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b. The problem statement defines two of the triangle vertices only for x > 0. However, we note that for x > 3, the y-coordinate of one of the vertices is negative. Straightforward application of the area formula in Part A will result in negative areas for x > 3, so a reasonable domain might be (0, 3).
On the other hand, the geometrical concept of a line segment and of a triangle does not admit negative line lengths. Hence the area for a triangle with its vertex below the x-axis (green in the figure) will also be considered to be positive. In that event, the domain of A(x) = (1/2)(x)|9 -x^2| will be (0, ∞).
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c. A(2) = (1/2)(2)(9 -2^2) = 5
The area is 5 when x=2.
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d. On the interval (0, 3), the value of x that maximizes area is x=√3. If we consider the domain to be all positive real numbers, then there is no maximum area (blue dashed curve on the graph).
Answer:
B) 1/4 × 3/6 = 3/24
Step-by-step explanation:
1/4 of the rectangles are colored blue(ish).
3/6 of the rectangles are colored yellow(ish).
The colors overlap in 3/24 of the rectangles.
The problem statement with these numbers in it is that of choice B.