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)
the percent increase in the price of a gallon of milk from 1985 to 2005 is 59%
Define percent increase
Percent increase can be described as the rise in the value of an item, in this case the value is milk.
Write out the parameters
In 1985 the price of a gallon of milk is $2.20
In 2005 the price is $3.50
Formula for percent increase
new price-old price/new price × 100
Calculate the percent increase
new price= $3.50
old price= $2.20
= 3.50-2.20/2.20
= 1.3/2.20
= 0.59 × 100
= 59%
Hence the percent increase from 1985 t0 2005 is 59%
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Answer: um i think you asked the question wrong. But ok.
Step-by-step explanation:
= 47 miles per hour
This is a fraction equal to
47 miles ÷ 1 hours
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 1
47 miles ÷ 1
1 hours ÷ 1
=
47 miles
1 hour
=
47 miles
hour
= 47 miles per hour
Answer:
15
Step-by-step explanation:
Let the smallest integer be x. The integers will be x, x+1, x+2, all the way up to x+6.
119 = 7x + (1+2+3+4+5+6)
119 = 7x + 21
7x = 98
x = 14
The second smallest integer will be x+1, so x+1 = 15.
Answer: 24 and 37
Step-by-step explanation:
Let the numbers be x and y . Also let us pick x as the larger number.
From the first statement :
x + y = 61 ............................ equation 1
From the second statement :
x = y + 13 ............................equation 2
Solving the resulting linear equations by substitution method, substitute x = y + 13 into equation 1, then
x + y = 61 becomes
y + 13 + y = 61
2y + 13 = 61
2y = 48
y = 24
Substitute y = 24 into equation 2 , then
x = y + 3 becomes
x = 24 + 13
x = 37
Therefore the numbers are 24 and 37
