Given:
The equation is:
It cuts the x-axis and y- axis at the point A and B respectively.
The area of ∆AOB =12 sq.units.
To find:
The value of <em>k</em>.
Solution:
We have,
Substituting 
to find the y-intercept.
Substituting 
to find the x-intercept.
Area of a triangle is:
The height of the ∆AOB is 
because distance cannot be negative and the base of the ∆AOB is 
. So, the area of the ∆AOB is:
It is given that, the area of ∆AOB = 12 sq.units.
Therefore, the value of k is either 24 or -24.
Answer:
x(x+3)(x−10)
Step-by-step explanation:
Hope this was helpful let me know if it was!
Answer:the total number of horses in the herd is 36
Step-by-step explanation:
Let x represent the total number of horses in the herd.
One fourth of the herd of horses was seen in the forest. This means that the number of horses that was seen in the forest would be
1/4 × x = x/4
Twice the square root of the herd had gone to the mountain slopes. This means that the number of horses that had gone to the mountain slopes would be
2 × √x = 2√x
Three times five horses remained on the riverbank. This means that the number that remained would be
3 × 5 = 15
Therefore
x/4 + 2√x + 15 = x
x - x/4 - 15 = 2√x
(4x - x - 60)/4 = 2√x
(3x - 60)/4 = 2√x
Cross multiplying,
3x - 60 = 8√x
Squaring both sides of the equation, it becomes
(3x - 60)(3x - 60) = 64x
9x² - 180x - 180x + 3600 = 64x
9x² - 360x - 64x + 3600 = 0
9x² - 424x + 3600 = 0
Applying the quadratic equation
x = (- b ±√b² - 4ac)/2a
x = ( - - 424 ± √-424² - 4(9 × 3600)/2 × 9
x = (424 ± √179776 - 129600)/18
x = (424 ±√50176)/18
x = (424 + 224)/18 or
x = (424 - 224)/18
x = 36 or x = 11.11
the number of horses must be whole number. Therefore, the number of horses is 36
