Answer:
10:1
90 red counters
30 blue
1/3 of 90 =30
80% of 30 =24
90-30 =60 remaining red counters
30-24 =6 remaining blue counters
= 60:6 simplest form is 10:1
Answer:
y = 1/4x or y = 0.25x
Step-by-step explanation:
In this question, we are trying to write an equation with the given points.
To solve this question, we would use the slope formula: y2-y1/x2-x1
Find the slope by plugging in variables:
2-1/8-4
1/4 = m
The slope would be 1/4
Find the y intercept:
To find the y-intercept, you would need to use the slope you've found and one point, and plug it into the slope-intercept equation:
1 = 1/4(4) + b
Solve:
1 = 1/4(4) + b
1 = 1 + b
Subtract 1 from both sides
0 = b
This means that the y-intercept is 0.
Our equation will be: y = 1/4x
Answer:
stuff and more stuff
Step-by-step explanation:
They're not equivalent.
(vertical bars) represents the absolute value of x. How it works is that it turns negative numbers positive but leaves 0 and positive numbers alone (hence it gets a number's distance from 0 on the number line).
![[x]](https://tex.z-dn.net/?f=%5Bx%5D)
(square brackets) usually represents the floor function, which returns the largest integer that is less than or equal to x. (The floor of x can also be written as 
--- it depends on what your textbook/source says).
To solve 
, you first transform it into the equivalent equation 
. Then by definition of absolute value, there are only two solutions for the first equation: x = 10 or x = -10.
[x] = 10 has infinitely many solutions. For example, the floor of 10 is 10, so ![[10] = 10](https://tex.z-dn.net/?f=%5B10%5D%20%3D%2010)
, thus a solution for the second equation is x = 10
The floor of 10.1 is 10, so ![[10.1] = 10](https://tex.z-dn.net/?f=%5B10.1%5D%20%3D%2010)
, thus another solution for the second equation is x = 10.1.
The two equations do not have the same solution set (as x = 10.1 does not solve |x| - 3 = 7 but solves [x] = 10), so they're not equivalent.
Answer
Step-by-step planation:
The given expression is .
We have to check which of he given options on simplification gives the same given expression.
(A) The expression is:
=
=
which is not equivalent to the given expression, thus this option is incorrect.
(B) The expression is:
=
=
which is not equivalent to the given expression, thus this option is incorrect.
(C) The expression is:
=
=
which is not equivalent to the given expression, thus this option is incorrect.
(D) The expression is:
=
=
which is equivalent to the given expression, thus this option is correct.
(E) The expression is:
=
==
which is equivalent to the given expression, thus this option is correct.
(F) The expression is:
=
which is not equivalent to the given expression, thus this option is incorrect.
