Answer:
y = 3x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
3x - y + 12 = 0 ( subtract 3x + 12 from both sides )
- y = - 3x - 12 ( multiply through by - 1 )
y = 3x + 12 ← in slope- intercept form
with slope m = 3
Parallel lines have equal slopes , thus
y = 3x + c ← is the partial equation
To find c substitute (2, 5) into the partial equation
5 = 6 + c ⇒ c = 5 - 6 = - 1
y = 3x - 1 ← equation of parallel line
The function is equal to (x+2) / (x+2)(x-2), so when you simplify, it would be 1/(x-2). This means that there is a hole in the graph at x=-2, and a vertical asymptote at x=2.
11 inches would be the long side. Since we know 3 is the height, divide 330 by it and then divide that (110) by 11. This will give you the width which is 10. The area of the problem was already found. The area was 110 in^2
ANSWER
80 units²
EXPLANATION
One way to solve this is to find the area of the blue square and the subtract the areas of the red triangles:
The blue square is 12 units long by 12 units wide. Its area is:
Then, the area of the big triangle, which has a base 12 units long and a height of 10 units, is:
The smaller triangle has a base of 4 units and a heigth of 2 units. Its area is:
So the total area of the figure is:
Answer:
The number of pounds of:
Decaffeinated coffee = x = 5 pounds
Regular coffee = y = 9 pounds
Step-by-step explanation:
A 14 -pound mixture of coffee that contains both decaffeinated and regular coffee costs $37. The decaffeinated coffee costs $2 per pound, and the regular coffee costs $3 per pound.
Let the number of pounds of:
Decaffeinated coffee = x
Regular coffee = y
Hence, our system of equations =
x + y = 14..... Equation
x = 14 - y
2x + 3y = 37....... Equation 2
We substitute 14 - y for x in Equation 2
= 2(14 - y) + 3y = 37
= 28 - 2y + 3y = 37
= - 2y + 3y = 37 - 28
= y = 9 pounds
Solving for x
x = 14 - y
x = 14 - 9
x = 5 pounds
Therefore,
The number of pounds of:
Decaffeinated coffee = x = 5 pounds
Regular coffee = y = 9 pounds
