Answer:
4x-20 is the same as x+x+x+x-20
Answer:
(x + 0, y − 2), reflection over y = 1
Step-by-step explanation:
H will be shifted down 2 units and then reflected over y = 1, which maps H into itself
Answer:
I. Circumference of circular flower bed = 31.42 ft.
II. Area of circular flower bed = 78.55 ft²
Step-by-step explanation:
Given the following data;
Diameter = 10 ft
Radius = diameter/2
Radius = 10/2
Radius, r = 5 ft
I. To find the circumference of the circular flower bed;
Circumference of circle = 2πr
Substituting into the formula, we have
Circumference of circular flower bed = 2*3.142*5
Circumference of circular flower bed = 31.42 ft
II. To find the area;
Area of circle = πr²
Substituting into the formula, we have;
Area of circular flower bed = 3.142*5²
Area of circular flower bed = 3.142*25
Area of circular flower bed = 78.55 ft²
Answer: The value of k for which one root of the quadratic equation kx2 - 14x + 8 = 0 is six times the other is k = 3.
Let's look into the solution step by step.
Explanation:
Given: A quadratic equation, kx2 - 14x + 8 = 0
Let the two zeros of the equation be α and β.
According to the given question, if one of the roots is α the other root will be 6α.
Thus, β = 6α
Hence, the two zeros are α and 6α.
We know that for a given quadratic equation ax2 + bx + c = 0
The sum of the zeros is expressed as,
α + β = - b / a
The product of the zeros is expressed as,
αβ = c / a
For the given quadratic equation kx2 - 14x + 8 = 0,
a = k, b = -14, c = 8
The sum of the zeros is:
α + 6α = 14 / k [Since the two zeros are α and 6α]
⇒ 7α = 14 / k
⇒ α = 2 / k --------------- (1)
The product of the zeros is:
⇒ α × 6α = 8 / k [Since the two zeros are α and 6α]
⇒ 6α 2 = 8 / k
⇒ 6 (2 / k)2 = 8 / k [From (1)]
⇒ 6 × (4 / k) = 8
⇒ k = 24 / 8
⇒ k = 3
Answer:
x is 13
y is 39
Step-by-step explanation:
