Answer:
Please check the explanation.
Step-by-step explanation:
We know that when a consistent system has infinite solutions, then the graphs of the equations are exactly the same. In other words, these equations are called dependent equations.
All points of dependent equations share the same slope and same y-intercept.
For example,
6x-2y = 18
9x-3y=27
represent the dependent equations.
Writing both equations in slope-intercept form
y=mx+c
where m is the slope and c is the y-intercept
Now
6x-2y=18
2y = 6x-18
Divide both sides by 2
y = 3x - 9
Thus, the slope = 3 and y-intercept = b = -9
now
9x-3y=27
3y = 9x-27
Divide both sides by 3
y = 3x - 9
Thus, the slope = 3 and y-intercept = b = -9
Therefore, both equations have the same slope and y-intercept. Their graphs are the same. Hence, they are called dependent equations.
Answer:
The volume of the new crate is exactly 174.4% of the old crate.
Step-by-step explanation:
Volume of a rectangular prism:
The volume of a rectangular prism of dimensions x, y and z is given by:
She decided that the dimensions of the new crate needs to be increased by 40% of the original length.
Each dimension is increased by 40%, which means that each is multiplied by 1 + 0.4 = 1.4. So
Percentage:
The new volume is 2.744 the original volume. Considering the original volume is 100% = 1, it increased by 2.744 - 1 = 1.744 = 1.744*100% = 174.4%.
The volume of the new crate is exactly 174.4% of the old crate.
Given:
savings 12% of her salary.
savings $4,200
This year's salary: x + 3,000
Last year's salary: x
4,200 represents 12% of her salary.
4,200 / 12% = 35,000 is her salary this year.
x + 3,000 = 35,000
x = 35,000 - 3,000
x = 32,000 her salary last year.
Answer:
triangle A andC are the same
So the Correct answer would be all three of them.
This includes 27:18, 12:8, and 21:14.
The math behind this includes proportions.
For instance, if you multiple 3 by 9, you get 37. You have to multiple 2 by 9 now, and you should get 18. This is how all three of the answers are correct!
