The given polynomial is
f(x) = x³ + 6x² + 12x + 35
According to the Remainder Theorem, if x = a is a zero, then
f(a) = 0, and (x-a) is a factor.
Test (x-1):
f(1) = 1 + 6 +12 + 35 = 54
Not a factor.
Test (x-3):
f(3) = 3³ +6*3² + 12*3 + 35 = 152
Not a factor.
Test (x+3):
f(-3) = (-3)³ + 6*(-3)² + 12*(-3) + 35 = 26
Not a factor.
Test (x+5):
(-5)³ + 6*(-5)² + 12*(-5) + 35 = 0
It is a factor.
Answer: (x+5) is a factor.
Answer:
x=2.5&.5
Step-by-step explanation:
The quadratic formula is (-b+or-sqrt(b^2-4ac)/2a
12+or-sqrt((-12^2)-4(4)(5))
12+or-sqrt(144-80)
12+or-sqrt(64)
(12+8)/8 and (12-8)/8
x=2.5 and x=.5
We will calculate this by using ratios and because these two triangles are similar, which is very important.
Explanation:
We see that the FG = 9 corresponds to the VU = 21. Therefore, FH = 18 corresponds to the UW = x.
9 : 21 = 18 : x
x = (21*18)/9
x = 378/9
x = 42.
The correct answer is B. 42.
Answer:
7x - 3y = 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 )
Rearrange 3x + 7y = 15 into this form
Subtract 3x from both sides
7y = - 3x + 15 ( divide all terms by 7 )
y = - 
x + 
← in slope- intercept form
with slope m = -
Given a line with slope m the the slope of a line perpendicular to it is
= - 
= - 
= 
, thus
y = x + c ← is the partial equation of the line
To find c substitute (4, 9) into the partial equation
9 = 
+ c ⇒ c - 
y = x - ← in slope- intercept form
Multiply through by 3
3y = 7x - 1 ( subtract 3y from both sides )
0 = 7x - 3y - 1 ( add 1 to both sides )
1 = 7x - 3y, that is
7x - 3y = 1 ← in standard form
