The lines y=3x-1 and y=ax+2 are perpendicular if a=___
2 answers:
Answer:
Step-by-step explanation:
The equation of line in the form .
y = mx + c
Where m is the slope and c is the y- intercept .
As given
The lines y=3x-1 and y=ax+2 are perpendicular .
Here 3 is slope for equation of line y=3x-1 and a is slope for equation of line
y=ax+2 .
Now by using properties of the perpendicular lines property .
When two lines are perpendicular than slope of one line is negative reciprocal of the other line .
Thus
Therefore
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Question 3)
Given
The point (1, -5)
The slope m = -5/6
Using the point-slope form of the equation of a line
where
- m is the slope of the line
- (x₁, y₁) is the point
In our case:
- m = -5/6
- (x₁, y₁) = (1, -5)
substituting the values m = -5/6 and the point (1, -5) in the point-slope form of the equation of the line
Thus, the point-slope form of the equation of the line is:
Question 4)
Given
The point (-1, 5)
The slope m = -7/2
In our case:
- m = -7/2
- (x₁, y₁) = (-1, 5)
substituting the values m = -7/2 and the point (-1, 5) in the point-slope form of the equation of the line
Thus, the point-slope form of the equation of the line is:
<h3>Answer:</h3>
87.5 ounces
<h3>Explanation:</h3>There's a cute "X-diagram" tool that can be used for solving mixture problems of all kinds. (See the attachment.) The numbers on the left represent the percentages of the constituents of the mix. The number in the center is the desired percentage in the resultant mix. The numbers on the right in the X are the differences along the diagonals. (6-5=1, 5-3=2)
These are also the proportions of the constituents in the final mix. That is, there are 2 parts of spice that is 6% salt for each 1 part of spice that is 3% salt. So, we need half as much of the latter as the former.
Half of 175 ounces is 87.5 ounces, the amount of 3% spice that is needed.
_____
If you really want to write an equation, you can let x represent the amount of 3% spice needed. Then the amount of salt in the mix is ...
... 175×6% +x×3% = (175+x)×5%
Dropping the percent symbols and eliminating parentheses, we have
... 1050 +3x = 875 +5x
... (1050 -875) = (5x -3x) . . . . . add -875-2x
... 175/2 = x = 87.5 . . . . . . . . . . divide by the coefficient of x