Answer:
f(x) = 3x² + 6x + 1
General Formulas and Concepts:
- Order of Operations: BPEMDAS
- Expand by FOIL (First Outside Inside Last)
- Standard Form: f(x) = ax² + bx + c
- Vertex Form: f(x) = a(bx + c)² + d
Step-by-step explanation:
<u>Step 1: Define function</u>
f(x) = 3(x + 1)² - 2
<u>Step 2: Find Standard Form</u>
- Expand by FOILing: f(x) = 3(x² + 2x + 1) - 2
- Distribute 3: f(x) = 3x² + 6x + 3 - 2
- Combine like terms (constants): f(x) = 3x² + 6x + 1
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Divide the total pieces by the number of kids:
108 pieces / 9 kids = 12 pieces per kid.
Answer:
-2
Step-by-step explanation:
The slope of the line is rise over run. The line goes up 2 and over 1. 2/1=2. The slope is negative because the line goes up and left.
Let

be the measure of one angle in our triangle; since we have two equal angles in our triangle, their measure will be

.
We know from our problem that at least one angle of our triangle measure 52°; since the sum o the interior angles of a triangle is 180°, we can use an equation to relate the quantities and solve for

to find the measure of the tow equal angles:




Now how know that the measure of the angles of our triangle are 52°, 64°, and 64°. Since we have tow equal angles in our triangle, we can conclude that our triangle is isosceles. Notice that we don't have any given side, so the sides of our isosceles triangle can vary in length.
We can conclude that the correct answer is: <span>
C. More than one triangle exists with the given conditions, and all instances must be isosceles triangles.</span>