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>
y<span> = 12x+76 is the answer to your question i know it was a little late but at least other people who would like to know can see it.</span>
Answer:
Step-by-step explanation:
Because of the nature of the information we are given, we have no choice but to use the equation
and solve for a.
We know by the info that the vertex is (0, 84). We also know that if the vertex is at the origin, and that the base is 42 feet wide, it spans 21 feet to the right of the origin and 21 feet to the left of the origin. That means that we have 2 coordinates from which we need to pick one for our x and y in the equation. I don't like negatives, so I am going to choose the coordinate (21, 0) as x and y. Because this parabola opens upside down, as archways of door openings do, our "a" value better come out algebraically as a negative. Let's see...From the vertex we have that h = 0 and k = 84. So filling in:
and simplifying a bit:
0 = 441a + 84 and
-84 = 441a so
Good, a is negative. Your equation is, then:
X + y = 9 Subtract x from both sides.
y = 9 - x
x^2 + y^2 = 53
x^2 + (9 - x)^2 = 53 Remove the brackets.
x^2 + 81 - 18x + x^2 = 53 Collect the like terms on the left.
2x^2 - 18x + 81 = 53 Subtract 53 from both sides.
2x^2 - 18x + 81 - 53 = 0
2x^2 - 18x + 28 = 0 This factors, but you can see it much easier if you pull out 2 as a common factor.
2(x^2 - 9x + 14) = 0
2(x - 2)(x - 7) =0 You could divide by 2 on both sides. But you can also leave it.
x - 2 = 0
x = 2
x - 7 = 0
x = 7
If x = 2 then y = 7
If x = 7 then y = 2
