Answer:
E
Step-by-step explanation:
if we decidedly factor this expression-
4x^2+4xy+y^2
= (2x)^2 + 2*2xy + y^2
= (2x + y)^2
as you can see it is a perfect square so it can be grouped into (2x+y)^2
hence your solution is option e
Answer: Choice C) 10.5
The distance from A to C is 7 units (count out the spaces between the two points, or subtract y coordinates 4-(-3) = 4+3 = 7)
Let AC = 7 be the base of the triangle. You might want to rotate the image so that AC is laying horizontally rather than being vertical.
Now move to point P. Walk 3 spaces to the right until you land on segment AC. This shows that the height of the triangle is 3 when the base is AC = 7.
base = 7, height = 3
area of triangle = (1/2)*base*height
area of triangle = 0.5*7*3
area of triangle = 10.5 square units
Answer: It's a tie between f(x) and h(x). Both have the same max of y = 3
The highest point shown on the graph of f(x) is at (x,y) = (pi,3). The y value here is y = 3.
For h(x), the max occurs when cosine is at its largest: when cos(x) = 1.
So,
h(x) = 2*cos(x)+1
turns into
h(x) = 2*1+1
h(x) = 2+1
h(x) = 3
showing that h(x) maxes out at y = 3 as well
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Note: g(x) has all of its y values smaller than 0, so there's no way it can have a max y value larger than y = 3. See the attached image to see what this graph would look like if you plotted the 7 points. A parabola seems to form. Note how point D = (-3, -2) is the highest point for g(x). So the max for g(x) is y = -2
Let's say that x represents hours that Elizabeth volunteers over 1 week. Katie volunteers x+3 and Siobhan x-1 hours per week. The equation that arises from condition in text is:
3*(x+3) = 3*(x + x-1)
x+3 = 2*x - 1
2*x - x= 3+1
x=4.
Elizabeth volunteers 7 hours
Katie volunteers 4 hours
Siobhan volunteers 3 hours
Answer: 21.13 miles
Explanation: The question asks “drive in all”. They gave you the miles driven, which is 8.7 and 12.43. If you add them together, you will get 21.13 miles.