F ( x ) = x² ( x² - 4 x + 3 ) =
= x² ( x² - 3 x - x + 3 ) =
= x² ( x ( x - 3 ) - ( x - 3 ) ) =
= x² ( x - 3 ) ( x - 1 ) = 0
x² = 0 ⇒ x = 0
x - 3 = 0 ⇒ x = 3
x - 1 = 0 ⇒ x = 1
The zeroes of the function are: x = 0, x = 1 and x = 3.
Answer:
B ) The number 0 is a zero of multiplicity 2; the numbers 1 and 3 are zeroes of the multiplicity 1.
if what you are asking is 6 times 1 then the answer is 6 because it could be like 6 groups of one
1+1+1+1+1+1=6
it could also be like 1 group of 6
6=6
if you mean something else, i dont get it sorry!
Answer:
Step-by-step explanation:
To find this equation in standard form, first, write it in factored form. This looks like . Then, multiply the polynomials using the FOIL (First, Outside, Inside, Last) method.
- Following the FOIL method, you should multiply the first terms in each binomial, , which equals .
- Then, the outside terms, . This equals .
- Next, the inside terms, .
- Finally, the last terms, , this equals .
Then, add all of the terms together . To get the standard form, combine like terms, this comes out to .
#1)
A) b = 10.57
B) a = 22.66
#2)
A) a = 1.35 (across from the 15° angle)
∠C = 50.07° (the angle at the top of the triangle)
∠B = 114.93°
B) ∠A = 83°
b = 10.77 (across from angle B)
a = 15.11 (across from angle A)
Explanation
#1)
A) Since b is across from the 25° angle and we have the hypotenuse, we have the information for the sine ratio (opposite/hypotenuse):
sin 25 = b/25
Multiply both sides by 25:
25*sin 25 = (b/25)*25
25*sin 25 = b
10.57 = b
B) We will first use the cosine ratio. Side a is the side adjacent to the angle and we have the hypotenuse, and the cosine ratio is adjacent/hypotenuse:
cos 25 = a/25
Multiply both sides by 25:
25*cos 25 = (a/25)*25
25*cos 25 = a
22.66 = a
Now we will use the Pythagorean theorem. We know from part a that side b = 10.57, and the figure has a hypotenuse of 25:
a²+(10.57)² = 25²
a² + 111.7249 = 625
Subtract 111.7249 from both sides:
a²+111.7249-111.7249=625-111.7249
a² = 513.2751
Take the square root of both sides:
√a² = √513.2751
a = 22.66
#2)
A) Let A be the 15° angle, B be the angle to the right and C be the angle at the top of the triangle. This means side a is across from angle A, side B is across from angle B, and side c is across from angle C.
Using the law of cosines,
a²=3²+4²-2(3)(4)cos(15)
a²=9+16-24cos(15)
a²=25-24cos(15)
a²=1.8178
Take the square root of both sides:
√a² = √1.8178
a = 1.3483≈1.35
Now we can use the Law of Sines to find angle C:
sin 15/1.35 = sin C/4
Cross multiply:
4*sin 15 = 1.35* sin C
Divide both sides by 1.35:
(4*sin 15)/1.35 = (1.35*sin C)/1.35
(4*sin 15)/1.35 = sin C
Take the inverse sine of both sides:
sin⁻¹((4*sin 15)/1.35) = sin⁻¹(sin C)
sin⁻¹((4*sin 15)/1.35) = C
50.07 = C
To find angle B, add angle A and angle C together and subtract from 180:
B=180-(50.07+15) = 180-65.07 = 114.93
B) To find angle A, add angle B and angle C together and subtract from 180:
180-(52+45) = 180-97 = 83
Now use the Law of Sines to find side b (across from angle B):
sin 52/12 = sin 45/b
Cross multiply:
b*sin 52 = 12*sin 45
Divide both sides by sin 52:
(b*sin 52)/(sin 52) = (12*sin 45)/(sin 52)
b = 10.77
Find side a using the Law of Sines:
sin 83/a = sin 52/12
Cross multiply:
12*sin 83 = a*sin 52
Divide both sides by sin 52:
(12*sin 83)/(sin 52) = (a*sin 52)/(sin 52)
15.11 = a
Our word problem: <em>$0.20 per text message, $55 for 1,000 minutes of talk time per month."</em>
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Since a person has to pay 20 cents whenever they send a text message, and we do not know how many messages they will send, that is an unknown value, so we will label the number of messages they send as x.
Since they are limited to 1,000 minutes of talk time per month and they have to pay $55, we have to set this as an inequality, since we do not know if they will use up all 1,000 minutes of talk time. We have to use the less than or equal to sign to indicate that they cannot talk more than 1,000 minutes.
≤ 55
Text messages: $0.20x
Talk time: ≤ $55
We cannot put both of these into one expression.