Answer:
see explanation
Step-by-step explanation:
(a)
x² - 6x + 4 = 0 ( subtract 4 from both sides )
x² - 6x = - 4
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 3)x + 9 = - 4 + 9
(x - 3)² = 5 ( take the square root of both sides )
x - 3 = ± ( add 3 to both sides )
x = 3 ± ← exact solutions
(b)
4x² + 16x + 9 = 0
To complete the square
The coefficient of the x² term must be 1
Factor out 4 from 4x² + 16x
4(x² + 4x) + 9 = 0
add/subtract ( half the coefficient of the x- term )² to x² + 4x
4(x² + 2(2)x + 4 - 4 ) + 9 = 0
4(x + 2)² - 16 + 9 = 0
4(x + 2)² - 7 = 0 ( add 7 to both sides )
4(x + 2)² = 7 ( divide both sides by 4 )
(x + 2)² = ( take the square root of both sides )
x + 2 = ± = ± ( subtract 2 from both sides )
x = - 2 ± ← exact solutions
Answer:
Step-by-step explanation:
Let the equation of the line 'a' is,
y = mx + c
Here, m = slope of the line
c = y-intercept
For line 'a',
Slope of the line =
m =
m =
y-intercept = 20
Therefore, equation of the line 'a' is,
y =
Similarly, equation of the line 'b' is,
y = m'x + c'
Slope of the line =
m' =
m' =
y-intercept = 0
Therefore, equation of the line is 'b' is,
y =
1). Line 'b' represents a proportional relationship → FALSE
2). The constant of proportionality of y to x for line 'a' is → FALSE
3). The ratio of y-coordinate to x-coordinate of one of the points on line b is 25 : 8 → FALSE
4). let a passes through the point so the constant of proportionality is → TRUE
$139 - $121 = $18
(139-121) / 4 = b
BTW
he would only be able to buy 4 buns because he only has $18 dollars left and 4 buns x 4 dollars = a total cost of 16 dollars so
Luke would only be able to buy 4 buns and have $2 left over
Answer:
Part 1) The maximum number of pounds of regular coffee that you can buy is 7.5 pounds.
Part 2)
Step-by-step explanation:
Part 1)
Let
x-----> the number of pounds of regular coffee
we know that
The inequality that represent the situation is
Solve for x
Divide by 2 both sides
The maximum number of pounds of regular coffee that you can buy is 7.5 pounds.
The solution of the inequality is the interval ------> (-∞,7.5]
but the number of pounds cannot be a negative number
therefore
The solution is the interval -----> [0,7.5]
see the attached figure
Part 2) we have
Adds m and n
Group terms that contain the same variable
Combine like terms
y = csc x doesnt have any zeros.