The vertex of the parabola is (-3, 9)
In order to find the vertex of any quadratic, you start by finding the x-value of said vertex. This can be done using the equation below.
-b/2a
In this equation 'a' refers to the coefficient of x^2 (-1) and 'b' refers to the coefficient of x (-6). So then we can plug into that equation using those values.
-b/2a
-(-6)/2(-1)
6/-2
-3
Now that we have the x value, we can substitute that value into the equation to find the y value.
f(x) = -x^2 - 6x
f(x) = -(-3)^2 - 6(-3)
f(x) = -(9) + 18
f(x) = 9
Therefore our point is (-3, 9)
Answer:
This is a linear optimization problem that can be solved using the simplex method
Step-by-step explanation:
I believe no one else in this platform will help with this typical question
Answer:
Hello,
Answer A: 35 dimes and 5 nickels
Step-by-step explanation:
Let say
d the number of dimes
n the number of nickels
There are 25 coins: d+n=25
Total value : 0.1*d+0.05n=2.25
![\left\{\begin {array} {ccc}d+n&=&40\\10*d+5*n&=&225\ multiplied\ by\ 100\\\end {array}\right.\\\\\\\left\{\begin {array} {ccc}n&=&40-d\\10*d+5*(40-d)&=&225\\\end {array}\right.\\\\\\\left\{\begin {array} {ccc}5*d&=&225-200\\n&=&40-d\\\end {array}\right.\\\\\\\left\{\begin {array} {ccc}5*d&=&25\\n&=&40-5\\\end {array}\right.\\\\\\\left\{\begin {array} {ccc}d&=&5\\n&=&35\\\end {array}\right.\\\\Proof:\\5*0.1+35*0.05=0.5+1.75=2.25\\](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%20%7Barray%7D%20%7Bccc%7Dd%2Bn%26%3D%2640%5C%5C10%2Ad%2B5%2An%26%3D%26225%5C%20multiplied%5C%20by%5C%20100%5C%5C%5Cend%20%7Barray%7D%5Cright.%5C%5C%5C%5C%5C%5C%5Cleft%5C%7B%5Cbegin%20%7Barray%7D%20%7Bccc%7Dn%26%3D%2640-d%5C%5C10%2Ad%2B5%2A%2840-d%29%26%3D%26225%5C%5C%5Cend%20%7Barray%7D%5Cright.%5C%5C%5C%5C%5C%5C%5Cleft%5C%7B%5Cbegin%20%7Barray%7D%20%7Bccc%7D5%2Ad%26%3D%26225-200%5C%5Cn%26%3D%2640-d%5C%5C%5Cend%20%7Barray%7D%5Cright.%5C%5C%5C%5C%5C%5C%5Cleft%5C%7B%5Cbegin%20%7Barray%7D%20%7Bccc%7D5%2Ad%26%3D%2625%5C%5Cn%26%3D%2640-5%5C%5C%5Cend%20%7Barray%7D%5Cright.%5C%5C%5C%5C%5C%5C%5Cleft%5C%7B%5Cbegin%20%7Barray%7D%20%7Bccc%7Dd%26%3D%265%5C%5Cn%26%3D%2635%5C%5C%5Cend%20%7Barray%7D%5Cright.%5C%5C%5C%5CProof%3A%5C%5C5%2A0.1%2B35%2A0.05%3D0.5%2B1.75%3D2.25%5C%5C)
Answer:
Each Jersey: $6.75
Each pair of socks: $7.47
Sales tax: $1.03
Step-by-step explanation:
$22.00 total.
$1.03 sales tax.
$6.75 jersey x2 = $13.50
$13.50 + $1.03 = $14.53 jerseys & sales tax.
$22.00 - $14.53 =7.47
Answer:
2.9 to the 4th power
Step-by-step explanation: