Answer:
L = (x - 2) meters
Step-by-step explanation:
The area of the rectangle = (x² - 7x + 10) m²
The width = (x - 5) m
length = ?
Area of a rectangle = length × width
x² - 7x + 10 = L(x -5)
note L = length
divide both sides by (x-5)
(x² - 7x + 10)/(x - 5) = L
L = x² - 7x + 10 / (x -5)
Factorize x² - 7x + 10
find the numbers you can multiply to give you 10 and also add to give you -7
The numbers are -2 and -5. Therefore,
x² - 2x - 5x + 10 = 0
x(x - 2) - 5(x - 2) = 0
(x-5)(x-2) = 0
Let us go back to our division
L = x² - 7x + 10 / (x -5)
x² - 7x + 10 = (x-5)(x-2)
L = (x-5)(x-2) / (x -5)
L = (x - 2) meters
Answer:
Step-by-step explanation:
take your compass on a point on your line. then draw a circle. take the 2 points in which the circle hit the line and draw 2 circles larger than half the distance between he 2 points. take the point that they intersect and and connect it to the line and you point M and it is purpendicular. does that make sense?
Answer:
C. f(5) = 13 and f(-3) = -3
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = 2x + 3
x = 5
x = -3
<u>Step 2: Evaluate</u>
x = 5
- Substitute: f(5) = 2(5) + 3
- Multiply: f(5) = 10 + 3
- Add: f(5) = 13
x = -3
- Substitute: f(-3) = 2(-3) + 3
- Multiply: f(-3) = -6 + 3
- Add: f(-3) = -3
Check the picture below.
now, let's keep in mind that, the vertex is half-way between the focus point and the directrix, it's a "p" distance from each other.
since this horizontal parabola is opening to the left-hand-side, "p" is negative, notice in the picture, "p" is 2 units, and since it's negative, p = -2.
its vertex is half-way between those two guys, so that puts the vertex at (-5, 3)
![\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ 4p(y- k)=(x- h)^2 \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=-5\\ k=7\\ p=-2 \end{cases}\implies 4(-2)[x-(-5)]=[y-7]^2 \\\\\\ -8(x+5)=(y-7)^2\implies x+5=\cfrac{(y-7)^2}{-8}\implies \boxed{x=-\cfrac{1}{8}(y-7)^2-5}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bparabola%20vertex%20form%20with%20focus%20point%20distance%7D%20%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Bllll%7D%204p%28x-%20h%29%3D%28y-%20k%29%5E2%20%5C%5C%5C%5C%204p%28y-%20k%29%3D%28x-%20h%29%5E2%20%5Cend%7Barray%7D%20%5Cqquad%20%5Cbegin%7Barray%7D%7Bllll%7D%20vertex%5C%20%28%20h%2C%20k%29%5C%5C%5C%5C%20p%3D%5Ctextit%7Bdistance%20from%20vertex%20to%20%7D%5C%5C%20%5Cqquad%20%5Ctextit%7B%20focus%20or%20directrix%7D%20%5Cend%7Barray%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cbegin%7Bcases%7D%20h%3D-5%5C%5C%20k%3D7%5C%5C%20p%3D-2%20%5Cend%7Bcases%7D%5Cimplies%204%28-2%29%5Bx-%28-5%29%5D%3D%5By-7%5D%5E2%20%5C%5C%5C%5C%5C%5C%20-8%28x%2B5%29%3D%28y-7%29%5E2%5Cimplies%20x%2B5%3D%5Ccfrac%7B%28y-7%29%5E2%7D%7B-8%7D%5Cimplies%20%5Cboxed%7Bx%3D-%5Ccfrac%7B1%7D%7B8%7D%28y-7%29%5E2-5%7D)
