The simplified form is: =4p2−18p+8
Step by Step:
(4p−2)(p−4)
=(4p+−2)(p+−4)
=(4p)(p)+(4p)(−4)+(−2)(p)+(−2)(−4)
=4p2−16p−2p+8
=4p2−18p+8
Answer:
See below.
Step-by-step explanation:
1)
So we have:
![\exists x\in\mathbb{N},y\in\mathbb{Z}|x^2=y^2](https://tex.z-dn.net/?f=%5Cexists%20x%5Cin%5Cmathbb%7BN%7D%2Cy%5Cin%5Cmathbb%7BZ%7D%7Cx%5E2%3Dy%5E2)
This can be interpreted as:
"There exists a natural number <em>x</em> and an integer <em>y</em> such that x² is equal to y²."
2)
So we want even numbers are in the set of integers.
![\{2n:n\in\mathbb{Z}\}\in\mathbb{Z}](https://tex.z-dn.net/?f=%5C%7B2n%3An%5Cin%5Cmathbb%7BZ%7D%5C%7D%5Cin%5Cmathbb%7BZ%7D)
This is interpreted as:
"The set of even numbers (2n such that n is an integer) is in the set of integers"
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:
b
Step-by-step explanation:
Answer:
I think it’s d
Step-by-step explanation: