The first few steps in solving the quadratic equation 9x2 + 49x = 22 − 5x by completing the square are shown. 9x2 + 49x = 22 − 5
2 answers:
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Hey there!
The easiest way I could think to do this is by converting your mixed number to an improper fraction and multiplying the fraction by 2, or 2 over 1.
To multiply fractions, you can just multiply the numerators and denominators and simplify, if applicable.
Since you can't simplify this fraction in its improper form, just convert it back into a mixed number.
So, your answer will be
.
Hope this helped you out! :-)
The easiest way I could think to do this is by converting your mixed number to an improper fraction and multiplying the fraction by 2, or 2 over 1.
To multiply fractions, you can just multiply the numerators and denominators and simplify, if applicable.
Since you can't simplify this fraction in its improper form, just convert it back into a mixed number.
So, your answer will be
Hope this helped you out! :-)
Answer:
14.86 knots.
Step-by-step explanation:
<em>Given that:</em>
The boats leave the port at noon.
Speed of boat 1 = 12 knots due east
Speed of boat 2 = 8 knots due south
At 2 pm:
Distance traveled by boat 1 = 24 units due east
Distance traveled by boat 2 = 16 units due south
Now, speed of boat 1 changes to 9 knots:
At 3 pm:
Distance traveled by boat 1 = 24 + 9= 33 units due east
Distance traveled by boat 2 = 16+8 = 24 units due south
Now, speed of boat 1 changes to 8+7 = 15 knots
At 5 pm:
Distance traveled by boat 1 = 33 + 2 9= 51 units due east
Distance traveled by boat 2 = 24 + 2 15 = 54 units due south
Now, the situation of distance traveled can be seen by the attached right angled .
O is the port and A is the location of boat 1
B is the location of boat 2.
Using pythagorean theorem:
so, the total distance between the two boats is 74.28 units.
Change in distance per hour =
Since is the square of x and 6x is twice the product between x and 3, the second square must be 3 squared, i.e. 9.
So, if we think of 15 as 9+6, we have
Which is the required vertex form. This form tells us imediately that the vertex is the point (3,6).
Since the leading coefficient is 1, the parabola is facing upwards (it's U shaped), so the vertex is a minimum.