Answer:
The equation would be y = 3/2x + 3
Step-by-step explanation:
First we have to find the slope of the original line. We can do this by solving for y.
2x + 3y = 15
3y = -2x + 15
y = -2/3x + 5
Now that we have the slope of -2/3, we know the slope of the new line will be 3/2. This is because perpendicular lines have opposite and reciprocal slopes. We can use that and a point in point-slope form to find the equation.
y - y1 = m(x - x1)
y + 3 = 3/2(x + 4)
y + 3 = 3/2x + 6
y = 3/2x + 3
Answer:
Yes the sequence is arithmetic
The common difference is 6
Step-by-step explanation:
Determine whether the following sequences are arithmetic. If so, identify the common difference.
9, 15, 21, 27, ...
The sequence given in the above question is arithmetic because it follows the formula
Un = a + (n -1)d
Where
a= First term
n = Number of terms
d = Common difference
The common difference is calculated as the
Second term - First term
15 - 9
= 6
or the Third term - Second term
21 - 15
= 6
or the Fourth term - Third term
= 27 - 21
= 6
Therefore, the Common difference = 6
Answer:
x = 36.9
Step-by-step explanation:
Use the sine function if you know the length of the opposite side and the hypotenuse. Plug your values into the equation: sine (x) = opposite ÷ hypotenuse. Say that the length of the opposite side is 6 and the length of the hypotenuse is 10. Divide 6 by 10, which is equal to 0.6. Now you know that sine (x) = 0.6 which is the same as x = sine^-1 (0.6).
Steps:
sin (x) = 6/10
sin(x) = 0.6
then we do sin^-1(0.6), which equals 36.869897645844 ° (degrees)
36.869897645844 ° (degrees) rounded to the nearest tenth is 36.9
so x = 36.9