We get the gradient of the lines which is perpendicular to the given lines as 1/3, -8, 0 and -3/2.
We are given some equation of the lines and we need to find the gradient of the lines which are perpendicular to them.
For this, we will first find the slope of the lines and then reciprocal it and change their signs to obtain the gradient of the perpendicular lines.
a) y = -3 x + 11
Here we can see that the slope of the line is:
m = -3
So, the gradient of the perpendicular line will be:
m' = 1 / 3
b) - x / 4 + 2 y = 0
2 y = x / 4
y = x / 8
slope = m = 1 / 8
Gradient = m' = - 8
c) y = - 3
Slope = m = 0
Gradient = m' = 0
d) y = 2(x - 1) / 3
y = 2/3 x - 1/3
slope = m = 2/3
Gradient = m' = -3/2.
Therefore, we get the gradient of the lines which is perpendicular to the given lines as 1/3, -8, 0 and -3/2.
Learn more about gradients here:
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Answer:
c. sin 30 is positive and sin -30 is negative
Step-by-step explanation:
Picture the unit circle (which is attached). <u>Sine is like the y-coordinate.</u> And -30 and 30 on the unit circle both form equally-sized triangles, but -30 is underneath the x-axis, so it has a <u>negative y-coordinate.</u> 30 is above the x-axis, so it has a <u>positive y-coordinate.</u>
Answer:
v = 17.4 meters
Step-by-step explanation:
This is a triangle with height (red dotted line) given.
The area of a triangle is given by the formula:
![A=\frac{1}{2}bh](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7Dbh)
Where
A is the area
b is the base length
h is the height
Given height = 12, and
area = 104.4
THe base is labeled as "v", so we find v by replacing into formula:
![A=\frac{1}{2}bh\\104.4=\frac{1}{2}(v)(12)\\104.4=6v\\v=\frac{104.4}{6}\\v=17.4](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7Dbh%5C%5C104.4%3D%5Cfrac%7B1%7D%7B2%7D%28v%29%2812%29%5C%5C104.4%3D6v%5C%5Cv%3D%5Cfrac%7B104.4%7D%7B6%7D%5C%5Cv%3D17.4)
The base, v, is 17.4 meters
Answer:
C) 33%
Step-by-step explanation:
To solve for the percentage of success, we first need to find out how many numbers we are working with. In this case, there are 9 numbers (0,1,2,3,4,5,6,7,8).
Since there are 3 "successful" numbers, (0,1,2), we can write the probability as a fraction
3/9 (represents number of successes over number of possible outcomes)
This simplifies to be 33%
12x^4 +6 +2x^3 +1x -6x^2 -3
12x^4 +2x^3 -6x^2 +1x + 3
i'm not completely sure this is the right answer but i gave it a shot! let me know if i was right or wrong