Answer:
Prime: x^2 + 17x - 30.
Difference of 2 squares: 256x^4 - 49x^2.
GCF: 4x^2 - 24x + 144.
Perfect Square trinomial: 4a^6 - 28a^3 + 49
Factoring Trinomial: b^2 + 5b - 36.
Step-by-step explanation:
1. x^2 + 17x - 30 will not factor.
2. 256x^4 - 49x^2 = (16x^2 + 7x)(16x^2 - 7x)
3. 4x^2 - 24x + 144 = 4(x^2 - 6x + 36).
4. 4a^6 - 28a^3 + 49 = (2a^3 - 7)^2.
5. b^2 + 5b - 36 = (b + 9)(b - 4).
Answer:
Let the first trip be x
Second trip is 2x-4
Third trip is 2(2x-4)
Fourth trip is 3x + 18
x + (2x-4) + 2(2x-4)+3x+18 = 426
x + 2x -4 + 4x - 8 + 3x + 18 = 426
10x + 6 = 426
10x = 426-6
x = 420/10 = 42 km
Second trip was
2x-4 = 2(42)-4 = 84-4 = 80 km
Third trip was
2 * 80 = 160 km
Fourth trip was
3(42) + 18 = 144 km
Answer:
Step-by-step explanation:
Volume of the box = x³ +11x² + 20x – 32 I think the ' is a typo for ³
the width is x-1 and the height is x+8
Find an expression for the length
Vol = LWH solve L
Vol / (WH) = L so
L = (x³ +11x² + 20x – 32) / (x-1) (x+8)
so it would help to factor the numerator
(x³ +11x² + 20x – 32) I'm willing to bet (x-1) and (x+8) are factors
but I will plot the equation to find the three roots
(x³ +11x² + 20x – 32) = (x-1) (x+8) (x+4)
L = (x³ +11x² + 20x – 32) / (x-1) (x+8)
= (x-1) (x+8) (x+4) / (x-1) (x+8) the (x-1) and (x+8) cancel out leaving
L = (x + 4)
Answer:
$172,806.37.
Step-by-step explanation:
Total = [ P(1+r/n)^(nt) ] + [ PMT × (((1 + r/n)^(nt) - 1) / (r/n)) ] * (1 + r/n)
is the formula for the amount left after the first 7 years where the money is deposited at the beginning of each month and P = initial amount, PMT = monthly payment, r = rate as a decimal and t = time in years.
Total after the first 7 years
= [ 200(1+0.09/12)^(7*12) ] + [ 200 × (((1 + 009/12)^(7*12) - 1) / (0/09/12) ] * (1 + 0.09/12)
= 374.64 + (200 * 0.8732019633) / (0.09/12) * (1 + 0.09/12)
= 374.64 + 23485.386 * 1.0075
= $24.036.17
Total after a further 22 years:-
= 24.036.17(1 + 0.09/12)^(12*22)
= $172,806.37 (answer).
X^4-3x^3-28x^2+36x+144=(x-6)(x^3+3x^2-10x-24)
x-6 is a factor