Answer:
x = -4 or 2
Step-by-step explanation:
-4x² + 10x − 40 = -9x²
First, move the x terms to one side and the constant to the other.
5x² + 10x = 40
Divide by the leading coefficient:
x² + 2x = 8
Take half of the b coefficient, square it, then add to both sides.
(2/2)² = 1
x² + 2x + 1 = 8 + 1
x² + 2x + 1 = 9
Factor the perfect square:
(x + 1)² = 9
Solve for x:
x + 1 = ±3
x = -1 ± 3
x = -4 or 2
Alright, so [-2.99] is -2.99, and [2.99] is 2.99, so -2.99+2.99=0
Answer:
x = 80
Step-by-step explanation:
9+1=10 so x/8 must equal 10.
80/8 = 10 and subract by 9 = 1
Answer:
The answer is when we rotating something 90 degrees clockwise about the orgin
(x,y) goes to (y,-x)
Let x be the cost of 1 pen
then cost of 1 notebook = x + 8.20
Let y be the number of pens Tan buys
then number of notebooks Tan buys = y/4
She spent $26 more on books than on pens which means
Cost of notebooks - Cost of pens = 26
(x + 8.20) * y/4 - xy = 26
Sinplifying it
(xy + 8.20y)/4 - xy = 26
(xy + 8.20y - 4xy)/4 = 26
8.20y - 3xy = 104
She spent $394 which means
Cost of notebooks + Cost of pens = 394
(x + 8.20) * y/4 + xy = 394
Simplifying it
(xy + 8.20y)/4 + xy = 394
(xy + 8.20y + 4xy)/4 = 394
8.20y + 5xy = 1576
Now, we have two equations,
(1) 8.20y - 3xy = 104
(2) 8.20y + 5xy = 1576
Now we need to find a third equation with either x or y as the subject of any of both the previous equations.
Let's make y the subject of (2) equation
8.20y + 5xy = 1576
y(8.20 + 5X) = 1576
(3) y = 1576/(8.20 + 5x)
Let's substitute the new value of y from (3) into (1) because we rearranged (2) to from (3)
8.20y - 3xy = 104
y(8.20 - 3x) = 104
y = 104/(8.20 - 3x)
1576/(8.20 + 5x) = 104/(8.20 - 3x)
1576 * (8.20 - 3x) = 104 * (8.20 + 5x)
12923.2 - 4728x = 852.8 + 520x
12923.2 - 852.8 = 4728x + 520x
12070.4 = 5248x
12070.4/5248 = x
x = 2.3
Now find the value of y by substituting the value of x in either equation, preferably (3)
y = 1576/(8.20 + 5x)
y = 1576/(8.20 + 5 * (2.3))
y = 80
Therefore cost of 1 notebook = x + 8.20 = 2.3 + 8.20 = $10.50
