Answer: Lower left corner
We have 29 people who chose fishing out of 18+29 people who filled out the survey. We don't use 60 because not everyone filled out the survey, and we're only focusing on survey participants. The "times 100" at the end will move the decimal point 2 spots to the right, and convert it to percent form.
For example, if you had 2 people who liked fishing out of 8 total then 2/8 = 0.25 = 25% of the people like fishing.
Answer:
1. x = 3, 1/2 (solutions); (x - 3)(2x - 1) (factors)
2. x = -1/3, -2 (solutions); (3x + 1)(x + 2) (factors)
Step-by-step explanation:
<u>1. 2x^2 - 7x + 3</u>
To solve problem 1, you will need to identify your a, b, and c values in this quadratic function.
Since this problem is in standard form, it will be easy to identify these values. The standard form of a quadratic function is ax^2 + bx + c.
The a value is 2, the b value is -7, and the c value is 3 if we use our standard form and see which numbers are plugged into it.
Since we know that
we can use the quadratic formula:
Substitute the a, b, and c values into the quadratic formula:
Now simplify using the laws of pemdas:
Simplify even further:
Now split this equation into two equations to solve for x:
12/4 can be simplified to 3, and 2/4 can be simplified to 1/2.
This means your solutions to problem 1 is 3, 1/2.
There is also another way to solve for the quadratic functions, and this was by factoring.
If you factor 2x^2 - 7x + 3 using the bottoms-up method, you will get (x - 3)(2x - 1).
After factoring, solving for the solutions is simple because all you have to do is set each factor to 0.
After solving for x by adding 3 to both sides, or by adding 1 to both sides then dividing by 2, you will end up with the same solutions: x = 3 and x = 1/2.
<u>2. 3x^2 + 7x + 2</u>
To save time I'll be using the bottoms-up factoring method, but remember to refer back to problem 1 (quadratic formula) if you prefer that method.
Factor this quadratic function using the bottoms-up method. After factoring you will have (3x + 1)(x + 2). These are your factors.
Now to solve for x and find the solutions of the quadratic function, you will set both factors equal to 0.
Solve.
<u>First factor:</u> 3x + 1 = 0
Subtract 1 from both sides.
3x = -1
Divide both sides by 3.
x = -1/3
<u>Second factor:</u> x + 2 = 0
Subtract 2 from both sides.
x = -2
Your solutions are x = -1/3 and x = -2.
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Answer:
y = -3/8x -23/8
Step-by-step explanation:
The slope is found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (-4 -(-1))/(3 -(-5)) = -3/8
Then the point-slope equation of the line is ...
y -k = m(x -h) . . . . line with slope m through point (h, k)
For m = -3/8 and (h, k) = (-5, -1), the line is ...
y +1 = -3/8(x +5)
In slope-intercept form, this is ...
y = -3/8x -23/8
