Answer:
32.5 miles in 30 minutes.
Step-by-step explanation:
There are a total of 4 - 30 minute segments in a period of two hours. Therefore, in this question, we can simply divide the total distance that Mr Edwards travelled during those two hours by the 4 segments, and that would give us the distance travelled in a single segment of 30-minutes.
130 / 4 = 32.5 miles
Finally, we can see that Mr Edwards travelled 32.5 miles in 30 minutes.
- A square handkerchief has a side of 2x + 3.
- So, it is given that the handkerchief is a square.
- So, in other words we have to find out the area of a square.
- We know, area of a square = side²
- Therefore, the area of the handkerchief
- = (2x + 3)²
- = (2x)² + 2(2x)(3) + (3)²
- = 4x² + 12x + 9
<u>Answer</u><u>:</u>
<u>The </u><u>area </u><u>of </u><u>the </u><u>square </u><u>handkerchief</u><u> </u><u>is </u><u>4x² + 12x + 9</u><u>.</u>
Hope you could understand.
If you have any query, feel free to ask.
Part 1
Let:
y be the total cost
x be the number of tickets
a be fair admission
Since the fair charges $1.25 per ticket, the equation of the line would look like:
y = 1.25x + a
Since Johnny spent $43.75 and bought 25 tickets, we find a by replacing y with 43.75 and x with 25:
43.75 = 1.25×25 + a
Now solve for a
43.75 = 31.25 + a
43.75 - 31.25 = a
a = 12.50
Going back to the first equation:
y = 1.25x + 12.50
Part 2:
a) Let (9,8) be (x1,y1) and (4,-12) be (x2,y2)
The formula for slope is:
![m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{ - 12 - 8}{4 - 9} \\ m = \frac{ - 20}{ - 5} \\ m = 4](https://tex.z-dn.net/?f=m%20%3D%20%20%5Cfrac%7By2%20-%20y1%7D%7Bx2%20-%20x1%7D%20%20%5C%5C%20m%20%3D%20%20%5Cfrac%7B%20-%2012%20-%208%7D%7B4%20-%209%7D%20%20%5C%5C%20m%20%3D%20%20%5Cfrac%7B%20-%2020%7D%7B%20-%205%7D%20%20%5C%5C%20m%20%3D%204)
b) For the point-slope equation, I'll use (9,8)
Using the formula:
![y - y1 = m(x - x1) \\ y - 8 = 4(x - 9)](https://tex.z-dn.net/?f=y%20-%20y1%20%3D%20m%28x%20-%20x1%29%20%5C%5C%20y%20-%208%20%3D%204%28x%20-%209%29)
c) For the slope-intercept form, we solve for y in the point-slope formula:
The horizontal sums of the survey numbers are 200, so the numbers in the left chart are the survey values divided by 200.
The vertical sum in the first column is 188, so the first column of the right chart will be 76/188 and 112/188. Likewise, the vertical sum in the second column is 212, so the numbers will be 124/212 and 88/212.
Once you find the first number in each case, the second number is that value subtracted from 1, since the total of the two must be 1.
...-1,8......................................