Answer:
First coin Second coin outcome
H T HT
T H TH
T T TT
Step-by-step explanation:
First coin Second coin outcome
H T HT
T H TH
T T TT
Answer:
Step-by-step explanation:
The equation for a straight line is
y = mx + b
where m is the slope of the line and b is the y-intercept.
The line passes through the points (-12, 0) and (0, 6)
(a) Calculate the slope of the line
(b) Write the equation
The y-intercept is at x = -6.
The diagram shows the graph of the line passing through the two intercepts.
Answer:
7 -1 6 | -8
7 -5 7 | 1
0 1 -4 | -5
Step-by-step explanation:
Note that there are four columns in this system, representing the variables x, y and z and constants. So the given matrix pattern is appropriate: It has three columns for the coefficients of x, y and z and one column for the constants.
We need only identify the coefficients and transfer them into the appropriate boxes of the matrix pattern.
We get:
7 -1 6 -8
7 -5 7 1
0 1 -4 -5
x = - 1
given = x + 3
square both sides
1 - 3x = (x + 3 )² ( expand right side using FOIL )
1 - 3x = x² + 6x + 9 ( subtract 1 - 3x from both sides )
0 = x² + 9x + 8
0 = ( x + 1)(x + 8)
equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = -1
x + 8 = 0 ⇒ x = - 8
As a check
substitute these values into the equation and if both sides are equal then they are the solutions
x = - 1 : = 2 and - 1 + 3 = 2 ← true
x = - 8 : = 5 and - 8 + 3 = -5 ← false
thus the only solution is x = - 1
Step-by-step explanation:
180° = 2x + 70 + 4x + 10
180° = 2x + 4x + 70 + 10
180° = 6x+ 80
180 - 80 = 6x
100 = 6x
6x = 100
x = 16.66
x ≈ 17°