Answer: The system of equations are
30x + 15y = 330
x = y + 2
Step-by-step explanation:
Let x represent the number of hours that Caleb worked.
Let y represent the number of hours that Landon worked.
Caleb can iron 30 shirts per hour, and Landon can iron 15 shirts per hour. This means that the number of shirts that Caleb would iron in x hours is 30x and the number of shirts that Landon would iron in y hours is 15y. They ironed 330 shirts between them. This means that
30x + 15y = 330 - - -- - - - - - - - - - - -1
Caleb worked 2 more hours than Landon. This means that
x = y + 2 - - - -- - - - - - - -2
Answer:
the answer would be (-4,1)
Answer:
![\boxed{ \bold{ \huge{ \boxed{ \sf{3 {i}^{2} + 6i}}}}}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Cbold%7B%20%5Chuge%7B%20%5Cboxed%7B%20%5Csf%7B3%20%7Bi%7D%5E%7B2%7D%20%20%2B%206i%7D%7D%7D%7D%7D)
Step-by-step explanation:
![\sf{(2 + i)(i + 2i)}](https://tex.z-dn.net/?f=%20%5Csf%7B%282%20%2B%20i%29%28i%20%2B%202i%29%7D)
Use the distribute property to multiply each term of the first binomial by each term of the second binomial.
⇒![\sf{2(i + 2i) + i(i + 2i)}](https://tex.z-dn.net/?f=%20%5Csf%7B2%28i%20%2B%202i%29%20%2B%20i%28i%20%2B%202i%29%7D)
⇒![\sf{2i + 4i + {i}^{2} + 2 {i}^{2} }](https://tex.z-dn.net/?f=%20%5Csf%7B2i%20%2B%204i%20%2B%20%20%7Bi%7D%5E%7B2%7D%20%20%2B%202%20%7Bi%7D%5E%7B2%7D%20%7D)
Collect like terms
⇒![\sf{3 {i}^{2} + 6i}](https://tex.z-dn.net/?f=%20%5Csf%7B3%20%7Bi%7D%5E%7B2%7D%20%20%2B%206i%7D)
Hope I helped!
Best regards!
Idk just use a scientific calculator
Answer:
smallest integer=9,
total number of integers are in the sequence = 19.
Step-by-step explanation:
- let a be the first term and the number of terms be n. as they are consecutive,the common difference will be 1. these will form Arithmetic Progression series.
- the sum of n terms in AP series is :
![\frac{n}{2} (a+l)](https://tex.z-dn.net/?f=%5Cfrac%7Bn%7D%7B2%7D%20%28a%2Bl%29)
[ where, l: last term]
- or, sum of n terms in AP series is :
![\frac{n}{2}(2a+[n-1]d)](https://tex.z-dn.net/?f=%5Cfrac%7Bn%7D%7B2%7D%282a%2B%5Bn-1%5Dd%29)
[where, d: common difference]
using the first formula,
342 = ![\frac{n}{2} (a+3a)](https://tex.z-dn.net/?f=%5Cfrac%7Bn%7D%7B2%7D%20%28a%2B3a%29)
342= ![\frac{n}{2} (4a)](https://tex.z-dn.net/?f=%5Cfrac%7Bn%7D%7B2%7D%20%284a%29)
342=2an .......equation 1.
using the second formula,
342=![\frac{n}{2} (2a+{n-1}l)](https://tex.z-dn.net/?f=%5Cfrac%7Bn%7D%7B2%7D%20%282a%2B%7Bn-1%7Dl%29)
684=n[2a+n-1]
684=2an+n^2-n
from equation 1,
342=n^2-n .......equation 1
-n-342=0
after solving, the solution to the above equation is 19.
substituting this in equation 2,
171=a[19]
a=9
so, smallest integer= a = 9,
total number of integers are in the sequence = n = 19.