Answer:
![\[\frac{1}{24}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B1%7D%7B24%7D%5C%5D)
Step-by-step explanation:
Let the total number of batteries produced daily be represented by x.
7/8 of the batteries are packaged immediately.
So the total number of packaged batteries = ![\[\frac{7x}{8}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B7x%7D%7B8%7D%5C%5D)
Remaining batteries = ![\[x-\frac{7x}{8}\]](https://tex.z-dn.net/?f=%5C%5Bx-%5Cfrac%7B7x%7D%7B8%7D%5C%5D)
= ![\[\frac{x}{8}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7Bx%7D%7B8%7D%5C%5D)
Two third of the remaining batteries are sent to charity.
So the total number of batteries sent to charity= ![\[\frac{2}{3} * \frac{x}{8}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B2%7D%7B3%7D%20%2A%20%5Cfrac%7Bx%7D%7B8%7D%5C%5D)
= ![\[\frac{x}{12}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7Bx%7D%7B12%7D%5C%5D)
Remaining batteries are faulty.
So the total number of faulty batteries = ![\[\frac{x}{8} - \frac{x}{12}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7Bx%7D%7B8%7D%20-%20%5Cfrac%7Bx%7D%7B12%7D%5C%5D)
= ![\[\frac{3x - 2x}{24}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B3x%20-%202x%7D%7B24%7D%5C%5D)
= ![\[\frac{x}{24}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7Bx%7D%7B24%7D%5C%5D)
So the faction of batteries which are faulty =
= ![\[\frac{x}{24} \div x\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7Bx%7D%7B24%7D%20%5Cdiv%20x%5C%5D)
=
Step-by-step explanation:
let no. of hours be x.
45x - 12 ≥ 117
45x ≥ 129
x ≥ 2.8667 (5sf)
therefore, 3 hours (round up to next whole number).
Topic: inequalities
If you like to venture further, do check out my insta (learntionary) where I regularly post useful math tips! Thank you!
(a).
The product of two binomials is sometimes called FOIL.
It stands for ...
the product of the First terms (3j x 3j)
plus
the product of the Outside terms (3j x 5)
plus
the product of the Inside terms (-5 x 3j)
plus
the product of the Last terms (-5 x 5)
FOIL works for multiplying ANY two binomials (quantities with 2 terms).
Here's another tool that you can use for this particular problem (a).
It'll also be helpful when you get to part-c .
Notice that the terms are the same in both quantities ... 3j and 5 .
The only difference is they're added in the first one, and subtracted
in the other one.
Whenever you have
(the sum of two things) x (the difference of the same things)
the product is going to be
(the first thing)² minus (the second thing)² .
So in (a), that'll be (3j)² - (5)² = 9j² - 25 .
You could find the product with FOIL, or with this easier tool.
______________________________
(b).
This is the square of a binomial ... multiplying it by itself. So it's
another product of 2 binomials, that both happen to be the same:
(4h + 5) x (4h + 5) .
You can do the product with FOIL, or use another little tool:
The square of a binomial (4h + 5)² is ...
the square of the first term (4h)²
plus
the square of the last term (5)²
plus
double the product of the terms 2 · (4h · 5)
________________________________
(c).
Use the tool I gave you in part-a . . . twice .
The product of the first 2 binomials is (g² - 4) .
The product of the last 2 binomials is also (g² - 4) .
Now you can multiply these with FOIL,
or use the squaring tool I gave you in part-b .
Answer:
x = -56
Step-by-step explanation:
x/7 = -8
Multiply each side by 7
x/7 *7 = -8*7
x = -56
Answer:
14 pints were drank
Step-by-step explanation:
22 pints - 8 pints =
