Answer:
(2x - 1)
Step-by-step explanation:
- <em>Volume of a rectangular prism is: V = lwh, where l= lenght, w= width, h= height</em>
<h3>Given</h3>
- V = 36x³ + 60x² + x - 20
- l = (3x + 4)
- w = (6x + 5)
and
<h3>Solution</h3>
Since the volume is the polynomial of third degree and the two of the factors are of the first degree, the third factor is going to be a first degree as well in the format of (mx +n)
<u>So we have below equation:</u>
- 36x³ + 60x² + x - 20 = (3x + 4)(6x + 5) (mx + n)
<u>We can work out the value of m and n:</u>
- 3x*6x*mx = 36x³
- 18mx³ = 36 x³
- m = 2
<u>And</u>
- 4*5*n = -20
- 20n = -20
- n = -1
So we get the factor of (mx + n) = (2x - 1)
<u>Therefore </u>
<u>Proof of the polynimial is correct:</u>
- (3x + 4)(6x +5)(2x - 1) =
- (18x²+39x+20)(2x - 1) =
- 36x³ - 18x² + 78x² - 39x + 40x - 20 =
- 36x² + 60x² + x - 20
Answer:
5) Alternate Exterior angles 90º
6) Same side Interior angles. 132º if that says 48º on the page
7) Corresponding angles. too blurry but they are congruent
8) Alternating Exterior angles. too blurry but they are congruent
Step-by-step explanation:
Congruent means they are the same measurement just as a reminder :).
Answer:
k = - 2
Step-by-step explanation:
Lines g(x) and f(x) passes through the points (2, 0), (0, 2) & (4, 0), (0, 4)
Since both the lines are parallel, so slopes of lines g(x) and f(x) would be same.
Therefore,
Slope of line g = Slope of line f = (2-0)/(0 - 2) = 2/-2 = - 1
Equation of line g(x)
For point (0, 2)
y- intercept (b) = 2
y = mx + b
g(x) = - 1x + 2 [y = g(x)]
g(x) = - x + 2
Equation of line f(x)
For point (0, 4)
y- intercept (b) = 4
y = mx + b
f(x) = - 1x + 4 [y = g(x)]
f(x) = - x + 4
It is given that:
g(x) = f(x) + k
g(x) - f(x) = k
(-x + 2) - (-x + 4) = k
-x + 2 + x - 4 = k
2 - 4 = k
-2 = k
k = - 2
