Answer is D. Not too sure, but I believe it's D.
Answer:
Moira didn't add
to both sides of the equation in the fourth step she applied (this is:
).
She can correct it applying the Addition property of equality and add
to both sides of the equation then she must apply the Division property of equality (See the procedure below).
Step-by-step explanation:
Given the equation:
![12x + 10 = 54 - 10x](https://tex.z-dn.net/?f=12x%20%2B%2010%20%3D%2054%20-%2010x)
The steps to solve it are:
1. According to the Subtraction property of equality, you we can subtract 10 from both sides of the equation:
![12x + 10-10 = 54 - 10x-10\\\\12x = 44 - 10x](https://tex.z-dn.net/?f=12x%20%2B%2010-10%20%3D%2054%20-%2010x-10%5C%5C%5C%5C12x%20%3D%2044%20-%2010x)
2. Based on the Addition property of equality, you we can add
to both sides of the equation:
![12x +10x= 44 - 10x+10x\\\\22x=44](https://tex.z-dn.net/?f=12x%20%2B10x%3D%2044%20-%2010x%2B10x%5C%5C%5C%5C22x%3D44)
3. Finally, applying the Division property of equality, we must divide both sidesby 22:
![\frac{22x}{2}=\frac{44}{22}\\\\x=2](https://tex.z-dn.net/?f=%5Cfrac%7B22x%7D%7B2%7D%3D%5Cfrac%7B44%7D%7B22%7D%5C%5C%5C%5Cx%3D2)
Therefore, she made an error in fourth step she applied:
Because she didn't add
to both sides of the equation.
She can correct it applying the Addition property of equality and add
to both sides of the equation and then she must apply the Division property of equality (As you can observe in the procedure shown above).
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:
Answer:
![\text{Segment midpoint formula}](https://tex.z-dn.net/?f=%5Ctext%7BSegment%20midpoint%20formula%7D)
Step-by-step explanation:
![(\frac{x1 + x2}{2},\frac{y1+y2}{2})](https://tex.z-dn.net/?f=%28%5Cfrac%7Bx1%20%2B%20x2%7D%7B2%7D%2C%5Cfrac%7By1%2By2%7D%7B2%7D%29)
For example:
![\text{Points: } (4,9) (8,4)](https://tex.z-dn.net/?f=%5Ctext%7BPoints%3A%20%7D%20%284%2C9%29%20%288%2C4%29)
As long as you appropriately place the X and Y points, it doesn’t matter which
etc you use.
![(\frac{4+8}{2},\frac{9+4}{2}) = 6, 6.5](https://tex.z-dn.net/?f=%28%5Cfrac%7B4%2B8%7D%7B2%7D%2C%5Cfrac%7B9%2B4%7D%7B2%7D%29%20%3D%206%2C%206.5)
![\text{X midpoint: 6}\\\text{Y midpoint: 6.5}](https://tex.z-dn.net/?f=%5Ctext%7BX%20midpoint%3A%206%7D%5C%5C%5Ctext%7BY%20midpoint%3A%206.5%7D)
Answer:
Each side of the square in centimetres = 10.80 centimetres
Step-by-step explanation:
To convert from one unit to another or in between units we make use of conversion factors or conversion formulas
The conversion factor for the conversion of units in centimetres to units in inches is given as about 2.54 centimetres being equivalent to 1 inch
Therefore;
1 inch = 2.54 centimetres
4.25 inches = 2.54 × 4.25 = 10.795 ≈ 10.80 centimetres
Therefore, each side of the square in centimetres = 10.80 centimetres.