Answer:
p = 9
Step-by-step explanation:
(p - 1) = p - 3 ( multiply both sides by 4 to clear the fraction )
3(p - 1) = 4p - 12 ← distribute left side
3p - 3 = 4p - 12 ( subtract 3p from both sides )
- 3 = p - 12 ( add 12 to both sides )
9 = p
Answer: x = {-3, -1, 1, 7}
<u>Step-by-step explanation:</u>
f(x) = x⁴ - 4x³ - 22x² + 4x + 21
possible roots are: +/- 1, 3, 7, 21
Let's try x = 1
1 | 1 -4 -22 4 21
<u>| ↓ 1 -3 -25 -21 </u>
1 -3 -25 -21 0 <em>remainder is 0 so (x - 1) is a factor</em>
(x - 1)(x³ - 3x² - 25x - 21)
Next, let's try x = -1
-1 | 1 -3 -25 -21
<u>| ↓ -1 4 21 </u>
1 -4 -21 0 <em>remainder is 0 so (x + 1) is a factor</em>
(x - 1)(x + 1)(x² - 4x - 21)
Then, factor the third polynomial
(x - 1)(x + 1)(x + 3)(x - 7)
Now, set each factor equal to zero and solve each one.
(x - 1) = 0 ⇒ x = 1
(x + 1) = 0 ⇒ x = -1
(x + 3) = 0 ⇒ x = -3
(x - 7) = 0 ⇒ x = 7
A function of the form: A = P(1-r)ⁿ [OR if (1-r) <1, the function is decaying1)
1) y = 100(1-1/2)ⁿ = decay because 1-1/2 = 1/2 <1
2) y =0.1(1.25)ⁿ = growth because 1.25 >1
3) y = [(0.03)¹/²]²ⁿ = decay because 0.03¹/² = √0.03 = 0.17 <1
4) y = 426(0.98)ⁿ = decay because 0.98 <1
5) y = 2050(1/2)ⁿ = decay because 1/2 <1
Answer:
Acute triangle
x = 3
GH = 19
Step-by-step explanation:
C = 4900 + 175S
The graph will cross the y-axis at 4900 and show a slope of 175/1 . Good luck graphing. If you choose the right scale, the graph will be easier. Increment by by 500 on the yaxis and 25 on the x-axis.