If you solve for x you get:
x=(<span><span><span>5/2)</span>y</span>+<span>10
</span></span>
If you solve for y you get:
y=(<span><span><span>2/5)</span>x</span>−<span>4</span></span>
Given:
Equilateral triangle: height = 2.6 inches ; base or side length = 3 inches
Rectangle: length = 6 inches ; width = 3 inches
1 name plate has 2 equilateral triangle and 3 rectangles.
Surface area of an equilateral triangle = √3/4 * a² = √3/4 * 3² = 3.9 in²
3.9 in² x 2 = 7.8 in²
Surface area of a rectangle = 6 in * 3 in = 18 in²
18 in² x 3 = 54 in²
7.8 in² + 54 in² = 61.8 in²
61.8 in² x 30 nameplates = 1,854 in² Choice A.
2
+
4
5
=
−
1
4
x
2
+
45
=
−
14
x
x2+45=−14x
2
+
4
5
−
−
1
4
=
0
The formula for the problem is: An = 8(n-1) - 2
<span>The table shows the outputs, y, for different inputs, x:
Input (x) 1 3 5 7
Output (y) 8 6 5 4
Part A: Do the data in this table represent a function? Justify your answer. (3 points)
Yes, the data in the table represent a function. The reason is that given an input (value of x), in the domain of the function (which is 1, 3, 5, 7), you can state the correspondant output (value of y) without ambiguity.
Part B: Compare the data in the table with the relation f(x) = 4x + 8. Which relation has a greater value when x = 3? (2 points)
x = 3 => f(3) = 4(3) + 8 = 12 + 8 = 20
While the image of 3 in the data is y = 6.
So, the function f(x) = 4x + 8 has a greater value when x = 3.
Part C: Using the relation in Part B, what is the value of x if f(x) = 76? Be sure to show all your work.
f(x) = 76 = 4x + 8 => 4x = 76 - 8 = 68
=> x = 68/4 = 17
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