One marble is selected at random from a bowl containing 15 blue marbles and 12 red marbles. What are the odds of selecting a blu
2 answers:
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Answer:
5
Step-by-step explanation:
What we have to know is that when two triangles are similar their sides will always be proportional. So we will create a proportion that goes like this... but since it doesn't tell us the exact value of triangle 1. We will have to add 3 and 12 to get 15 which is the base of the first triangle. Now we're ready to write the proportion.
Now we cross multiply and solve the equation...
So the value of x is 5.
Answer:
length of rectangle = 5
width of rectangle = 5
Area of rectangle = 25
Step-by-step explanation:
Since the length of the rectangle is "x", and the value of the area is given by the product of the length "x" times the width "10-x", indeed, the area "y" of the rectangle is given by the equation:
Now, they tell us that the area of the rectangle is such that coincides with the maximum (vertex) of the parabola this quadratic expression represents. So in order to find the dimensions of the rectangle and therefore its area, we find the x-coordinate for the vertex, and from it, the y-coordinate of the vertex, which is the rectangle's actual area.
Recall that the formula for the x of the vertex of a quadratic of the form :
is given by the formula:
which in our case gives:
Therefore, the length of the rectangle is 5, and its width (10-x) is also 5.
The area of the rectangle is therefore the product of these two values: 5 * 5 = 25
Which should coincide with the value we obtain when we replace x by 5 in the area formula: