Answer:
<u>The average speed or proportionality constant (y to x) of Jean biking from Pine Buff to Newberry to go to the charity event was 15 miles per hour</u>
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Distance from Pine Bluff to Newberry (y axis) = 75 miles
Time it took Jean to rode her bicycle (x axis) = 5 hours
2. The proportionality constant (y to x) is?
We can calculate the answer this way:
Proportionality constant (y to x) = Distance from Pine Bluff to Newberry (y axis)/Time it took Jean to rode her bicycle (x axis)
Substituting with the real values, we have:
Proportionality constant (y to x) = 75/5
Proportionality constant (y to x) = 15 miles per hour
<u>The average speed or proportionality constant (y to x) of Jean biking from Pine Buff to Newberry to go to the charity event was 15 miles per hour</u>
Answer:
rise over run
Step-by-step explanation:
you look at the distance between the 2 points by looking at how many points its goes up or down, and you look at how points it goes from the left to the right or vice versa. but if you don't have a graph to look at, you will want to use the slope formula. look up the slope formula and plug it in.
So focusing on x^4 + 5x^2 - 36, we will be completing the square. Firstly, what two terms have a product of -36x^4 and a sum of 5x^2? That would be 9x^2 and -4x^2. Replace 5x^2 with 9x^2 - 4x^2: 
Next, factor x^4 + 9x^2 and -4x^2 - 36 separately. Make sure that they have the same quantity inside of the parentheses: 
Now you can rewrite this as 
, however this is not completely factored. With (x^2 - 4), we are using the difference of squares, which is 
. Applying that here, we have 
. x^4 + 5x^2 - 36 is completely factored.
Next, focusing now on 2x^2 + 9x - 5, we will also be completing the square. What two terms have a product of -10x^2 and a sum of 9x? That would be 10x and -x. Replace 9x with 10x - x: 
Next, factor 2x^2 + 10x and -x - 5 separately. Make sure that they have the same quantity on the inside: 
Now you can rewrite the equation as 
. 2x^2 + 9x - 5 is completely factored.
<h3><u>Putting it all together, your factored expression is
</u></h3>
800 + 16x = 720 + 21x. Cancel out the 720 to get 80 + 16x = 21x. Subtract 16x from both sides to get 80 = 5x. Divide by 5 to get 16 = x, or x = 16. 16 hours. The charge is 800 + 16(16), = 720 + 21(16) which = 800 + 256 = 720 + 336 which = 1,056 = 1,056. Hope this helped!
