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Irina18 [472]
3 years ago
9

If 80 is divided by the sum of 4 and a certain number , the result is 16 .find the number

Mathematics
1 answer:
nata0808 [166]3 years ago
3 0

Answer:

x = 60

Step-by-step explanation:

80/ 4+x = 16

(4 + x) * 80/ 4+x = 16 = 16 (4 + x)

80 = 16 + 4 + x

80 = 20 + x

60 = x or x = 60

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Find the two square roots of each complex number by creating and solving polynomial equations.
son4ous [18]

Answer:

1) w₁=4 - i w₂= -4 + i

2) w₁= 3 - i w₂= -3  + i

3) w₁= 1 + 2i w₂= - 1 - 2i

4) w₁= 2- 3i w₂= -2 + 3i

5) w₁= 5 - 2i w₂= -5 + 2i

6) w₁= 5 - 3i w₂= -5 + 3i

Step-by-step explanation:

The root of a complex number is given by:

\sqrt[n]{z}=\sqrt[n]{r}(Cos(\frac{\theta+2k\pi}{n}) + i Sin(\frac{\theta+2k\pi}{n}))

where:

r: is the module of the complex number

θ: is the angle of the complex number to the positive axis x

n: index of the root

1) z = 15 − 8i  ⇒ r=17 θ= -0.4899 rad

w₁=\sqrt{17}(Cos(\frac{-0.4899}{2}) + i Sin(\frac{-0.4899}{2}))=4-i

w₂=\sqrt{17}(Cos(\frac{-0.4899+2\pi}{2}) + i Sin(\frac{-0.4899+2\pi}{2}))=-1+i

2) z = 8 − 6i  ⇒ r=10 θ= -0.6435 rad

w₁=\sqrt{10}(Cos(\frac{ -0.6435}{2}) + i Sin(\frac{ -0.6435}{2}))= 3 - i

w₂=\sqrt{10}(Cos(\frac{ -0.6435+2\pi}{2}) + i Sin(\frac{ -0.6435+2\pi}{2}))= -3  + i

3) z = −3 + 4i  ⇒ r=5 θ= -0.9316 rad

w₁=\sqrt{5}(Cos(\frac{-0.9316}{2}) + i Sin(\frac{-0.9316}{2}))= 1 + 2i

w₂=\sqrt{5}(Cos(\frac{-0.9316+2\pi}{2}) + i Sin(\frac{-0.9316+2\pi}{2}))= -1 - 2i

4) z = −5 − 12i  ⇒ r=13 θ= 0.4426 rad

w₁=\sqrt{13}(Cos(\frac{0.4426}{2}) + i Sin(\frac{0.4426}{2}))= 2- 3i

w₂=\sqrt{13}(Cos(\frac{0.4426+2\pi}{2}) + i Sin(\frac{0.4426+2\pi}{2}))= -2 + 3i

5) z = 21 − 20i  ⇒ r=29 θ= -0.8098 rad

w₁=\sqrt{29}(Cos(\frac{-0.8098}{2}) + i Sin(\frac{-0.8098}{2}))= 5 - 2i

w₂=\sqrt{29}(Cos(\frac{-0.8098+2\pi}{2}) + i Sin(\frac{-0.8098+2\pi}{2}))= -5 + 2i

6) z = 16 − 30i ⇒ r=34 θ= -1.0808 rad

w₁=\sqrt{34}(Cos(\frac{-1.0808}{2}) + i Sin(\frac{-1.0808}{2}))= 5 - 3i

w₂=\sqrt{34}(Cos(\frac{-1.0808+2\pi}{2}) + i Sin(\frac{-1.0808+2\pi}{2}))= -5 + 3i

6 0
3 years ago
72 is what percent of 240 ?
PilotLPTM [1.2K]

Answer:

72 = 30%

Step-by-step explanation:

240 = 100%

24 = 10%

12 = 5%

2.4 = 1%

72 / 24 = 3

72 = 30%

Let me know if I got it wrong :)

4 0
3 years ago
Read 2 more answers
(x-2)times (x^2+8x-1)
DerKrebs [107]

Answer:

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Step-by-step explanation:

(x-2)*(x^2+8x-1)

=x(x^2+8x-1)-2(x^2+8x-1)

=x^3+8x^2-x-2x^2-16x+2

collect like terms

= x^3+6x^2-17x+2

6 0
3 years ago
5. The cost per person to rent a chartered bus varies inversely to the number of people a who ride the bus. If 40 people pay $9.
777dan777 [17]
Answer d $380.00 or answer a $24.00
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2 years ago
Rashi borrowed rs 12000 from a bank . if the bank charges interest at the rate of 11 percent p.a. what amount will he pay to ban
Vlada [557]

Answer:

INTEREST=Rs 3960

Step-by-step explanation:

INTEREST=PTR/100

INTEREST=12000*3*11/100

INTEREST=3960

3 0
3 years ago
Read 2 more answers
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