P C
3 39
4 48
5 57
6 66
9(3)=27+12=39=c
9(4)=36+12=48=c
57=9p+12
-12 -12
45=9p
divide by 9 both sides 45/9=5=p
c=9(6)+12
c=54+12
c=66
Given:
A figure of a right triangle and an altitude form the right angle vertex to hypotenuse.
To find:
The value of x.
Solution:
From the given figure, it is clear that the altitude divides the hypotenuse in two segments x and 8.
Length of altitude = 18
If an altitude divide the hypotenuse in 2 segments, then according to the geometric mean theorem, the length of the altitude is the geometric mean of two segments of hypotenuse.
By using geometric mean theorem, we get
Divide both sides by 8.
Therefore, the value of x is 40.5.
Answer:
-125
Step-by-step explanation:
Answer:
3.87 ft = Length of unknown side of the right triangle.
Step-by-step explanation:
Given,
Hypotenuse = 4 ft
Base = 1 ft
Altitude = x
Hypotenuse² = Base² + Altitude²
4² = 1² + x²
4² - 1² = x²
16 - 1 = x²
15 = x²
√15 ft = x
3.87 ft = x
Hope it helps ⚜
Answer:
a = 7 and b = - 18
Step-by-step explanation:
If (x - 1) is a factor of f(x) then x = 1 is a root and f(1) = 0, thus
f(1) = 1³ + 10(1)² + a + b = 0 and
1 + 10 + a + b = 0 ⇒ a + b = - 11 → (1)
Similarly if
(x + 2) is a factor then x = - 2 is a root and f(- 2) = 0
f(- 2) = (- 2)³ + 10(- 2)² - 2a + b = 0, thus
- 8 + 40 - 2a + b = 0 ⇒ - 2a + b = - 32 → (2)
Solve (1) and (2) simultaneously
Subtract (1) from (2)
- 3a = - 21 ( divide both sides by 3)
a = 7
Substitute a = 7 in (1)
7 + b = - 11 ⇒ b = - 11 - 7 = - 18
The required polynomial is
f(x) = x³ + 10x² + 7x - 18