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MaRussiya [10]
3 years ago
8

Which of the following are roots of the following polynomial x^3-11x^2+33x+45

Mathematics
1 answer:
Mandarinka [93]3 years ago
8 0
For x^3-11x^2+33x+45 , we can make it an equation so <span>x^3-11x^2+33x+45=0. Next, we can find out if -1 or -3 is a factor. If -1 is a factor, than (x+1) is factorable. Using synthetic division, we get 

      x^2-12x+45
       ___ ________________________
x+1 | x^3-11x^2+33x+45

      - (x^3+x^2)
       _________________________
            -12x^2+33x+45
          - (-12x^2-12x)
          ______________
            45x+45
         -(45x+45)
___________
0


Since that works, it's either B or D. We just have to figure out when
</span> x^2-12x+45 equals 0, since there are 3 roots and we already found one. Using the quadratic formula, we end up getting (12+-sqrt(144-180))/2=
(12+-sqrt (-36))/2. Since sqrt(-36) is 6i, and 6i/2=3i, it's pretty clear that B is our answer
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HELP!!! A cell phone is 132 mm long and 57 mm wide. What is ratio of the width and length in simplest form.
GalinKa [24]

The ratio of width to length in simplest form is 19 : 44

<em><u>Solution:</u></em>

Given that, A cell phone is 132 mm long and 57 mm wide

Length of cell phone = 132 mm

Width of cell phone = 57 mm

We have to find the ratio of width and length in simplest form

\frac{Width}{Length} = \frac{57}{132}\\\\\text{Reduce to lowest terms }\\\\\frac{width}{length} = \frac{57 \div 3}{132 \div 3}\\\\\frac{Width}{Length} = \frac{19}{44}

In ratio form, we know that,

\frac{a}{b} = a : b

Writing in ratio form, we get

Width : length = 19 : 44

Thus the ratio of width to length in simplest form is 19 : 44

6 0
3 years ago
A thermometer reading 5 degrees celsius is brought into a room with a constant temperature of 35 degrees celsius.
Softa [21]
If it starts at 5 degrees celsius and raises to 15 degrees celsius in 3 minutes it increases by about 3 1/3 every minute.
times that by 5 and you get 16 2/3. times that by 10 and you get 33 1/3
7 0
3 years ago
A researcher wishes to conduct a study of the color preferences of new car buyers. suppose that 50% of this population prefers t
Amanda [17]
We will use the Binomial probability formula to find the answer

The formula is given by ⁿCₓ (p)ˣ (1-p)ⁿ-ˣ

We have
n, the number of trial = 16
x, the sample we aim to try = 7
p, the probability of success = 0.5

Substitute these values into the formula

P(7) = ¹⁶C₇ (0.5)⁷ (1-0.5)¹⁶⁻⁷
P(7) = 0.1746 (rounded to four decimal places)
3 0
3 years ago
Rick bought 3 shirts for $18 each, 2 pair of socks for $3.99 a pair, and a pair of slacks, for $45.00. The sales tax is 8.5%. Ho
ivolga24 [154]
Price of 3 shirts=$18*3=$54
Price of 2 pair of socks=2*$3.99=$7.98
Price of a pair of slack=$45
Total amount- $54+$7.98+ $45-$106.98
Sales tax rate = 8.5%
8.5% of total amount-8.5% of $106.98=
(8.5/100)*106.98-9.0933
Total amount Rick paid=$106.98+9.0933=$116.0733
Regards
6 0
3 years ago
A wallet is originally $11.00. With a 40% discount, what is the sales price? Show your work.
NeX [460]

Answer:

$6.6

Step-by-step explanation:

you want to find out what 40% of the original price is ($11)

100% = 11

10%= 1.1

to get 40% you times it by 4

40%= 4.4

you then have to take away the sale reduction from the original

11- 4.4 =$6.6

8 0
3 years ago
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