Answer:
x = -1 ± √6 / 5
Step-by-step explanation:
Solve + 2x = 1
move 1 to the left side of the equation by subtracting it from both sides.
+ 2x - 1 = 0
Use the quadratic formula to find the solutions.
-b± / 2a
Substitute the values a = 5 , b = 2, and c = -1 into the quadratic formula and solve for x
-2±/ 2 ⋅ 5
Simplify.
x = -2 ± 2 / 10
x = -1 ± / 5
Exact Form:
x = -1 ± / 5
Answer:
(x - 3)² + (y + 9)² = 25
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
Given area = 25π , that is
πr² = 25π ( divide both sides by π )
r² = 25 ( take the square root of both sides )
r = = 5
With centre (h, k) = (3, - 9 ) and r = 5 , then
(x - 3)² + (y - (- 9) )² = 5² , that is
(x - 3)² + (y + 9)² = 25
Answer:
The system of inequalities " x + 2 y ≤ 5 and 3 x + y ≤ 4 " is represented by the graph ⇒ D
Step-by-step explanation:
To find the answer let us find the equation of each line
Blue line:
∵ The line passes through points (5 , 0) and (0 , 2.5)
- Find the slope of the line
∵ m = Δy/Δx
∴
∴ m = -0.5
- The form of the equation is y = m x + b, where b is the
y-intercept (value y at x = 0)
∵ y = 2.5 at x = 0
∴ b = 2.5
- Write the equation of the line
∴ y = - 0.5 x + 2.5
- Multiply both sides by 2
∴ The equation of the blue line is 2 y = - x + 5
- The shading is under the line and the line is solid, that means
2 y is less than or equal - x + 5
∴ The inequality of the blue line is 2 y ≤ - x + 5
Red line:
∵ The line passes through points (3 , -5) and (0 , 4)
- Find the slope of the line
∴
∴ m = -3
∵ y = 4 at x = 0
∴ b = 4
- Write the equation of the line
∴ y = -3 x + 4
∴ The equation of the red line is y = -3 x + 4
- The shading is below the line and the line is solid, that means
y is less than or equal -3 x + 4
∴ The inequality of the red line is y ≤ -3 x + 4
Let us find which answer is the same with this system of inequalities
∵ 2 y ≤ - x + 5
- Add x to both sides
∴ x + 2 y ≤ 5 ⇒ same as the first inequality of answer D
∵ y ≤ -3 x + 4
- Add 3 x to both sides
∴ 3 x + y ≤ 4 ⇒ same as the second inequality of answer D
The system of inequalities " x + 2 y ≤ 5 and 3 x + y ≤ 4" is represented by the graph