Answer:
135
Step-by-step explanation:
I think you mean the LCM instead of LMC. LCM stands for Least Common Multiple. Anyway, some of the multiples of 27 are 27, 54, 81, 108, and 135. Some multiples for 45 are 45, 90, 135. We can see here that 27 and 45 share the mutiple of 135 which is the first number they have in common.
8r and 4r are like terms since they both have an r
also 3s and -3s are also like terms because of the s
Same side, interior angles of parallel lines cut by a transversal are supplementary.
The sum of the measures of supplementary angles is 180.
Angles 4 and 6 are same side, interior angles, so their measures add to 180.
m<4 + m<6 = 180
109 + m<6 = 180
m<6 = 180 - 109
m<6 = 71
Answer: m<6 = 71 deg.
Answer:
x + 3y + 9 = 0
Step-by-step explanation:
y=3x + 2
Coefficient of x = 3
Gradient (m) of line y= 3x + 2 is 3
Since the line passing through point
(3,-4) is perpendicular to line y=3x + 2
hence gradient (m) of the line is -1/3;
And hence it equation is given as;
y - y1 = m(x - x1)
y - (-4) = -1/3(x - 3)
multiplying through by 3;
3 × y + 3 × 4 = 3 × -1/3(x - 3)
3y + 12 = -1(x - 3)
3y + 12 = -x + 3
x + 3y + 12 - 3 = 0
x + 3y + 9 = 0
Answer
y = 1(x +1) - 3
Explanation
A quadratic equation of the form y = ax^2 + bx + c
This written in complete the square form provides you with the vertex (either a maximum or minimum point depending on the equation).
This results in y = a(x + p) + q
Where - p is the x value and q is the y value of turning point.
For graph 22, x = -1 and y = -3
Therefore, the equation is of the form
y = a(x + 1) - 3 (*)
We still need the value a, this can be obtained by using the y-intercept we are given.
We are told x = 0 when y = -2
Substitute this in (*) equation:
-2 = a(0+1) - 3
-2 = a - 3
a = 1
Therefore final equation is
y = 1(x +1) - 3
This should provide you with the train of thought of how the second question should also be tackled.
If unsure about why the equation
y = a(x + p) + q gives the vertex ask in comments I will respond
