how do I simplify the following to "a+bi" form: (1+2i)^3

Answer:

[tex]2 ^ { 4 } x \div 2x=64\\2^{4}x^{2}=128 \\16x^{2}=128 \\x^{2} = 128 \div 16\\x^{2}=8 \\x = \pm 2\sqrt{2}[/tex]

Answer: no solution  or  x ∈ Ø

Step-by-step explanation:

(2⁴ × x) ÷ 2x = 64

16x ÷ 2x = 64

[tex]\frac{16x}{2x} = 64[/tex]

8 = 64

8 = 64, x [tex]\neq[/tex] 0

8 = [tex]8^{2}[/tex]

2 = ㏒₈ 8

2 = 1

Answer:

An Acre is a propduct of any rectangular plot of land giving a total of 4,046sqm OR 43,560sq ft. An Acre consist of 6 plots each measuring 6 x 120ft. In Lagos State, the standard size of a plot is 60 x 120ft (18m x 36m ie 648sqm), while in some other cities of the country, plots are measured in 50 x100ft.

Step-by-step explanation:

Answer:

slope = - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

x + y = - 7 ( subtract x from both sides )

y = - x - 7 ← in slope- intercept form

with slope m = - 1

Parallel lines have equal slopes

then the slope of a line parallel to it is - 1

i think the answer is 336 bc 384+288=672 then divide

2 is 336,

(so sorry if im  wrong)

Answer: B

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Cos^2 2x=1/4

Cos 2x =+-1/2

2x=z

Cos z=+-1/2

z1=pi/3

z2=11pi/3

z1 and z2 are possible.

x1=pi/6

x2=11pi/6

For the exponential expression, [tex]16^{1/4}[/tex] the simplified value is 2.

First, we need to remember a rule for exponential expressions, it says that:

[tex]x^{1/n} = \sqrt[n]{x}[/tex]

Then we can rewrite the given exponential expression as:

[tex]16^{1/4} =\sqrt[4]{16}[/tex]

So, we just need to find a number that when multiplied by itself 4 times, is equal to 16.

We know that:

2*2 = 4

Then:

2*2*2*2 = 2⁴ = 4*4 = 16

Then we can conclude that:

[tex]16^{1/4} =\sqrt[4]{16} = 2[/tex]

So the simplified value of the exponential expression is 2.

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Answer:

5, 18, 44, 96, 200

Step-by-step explanation:

Given

First term : 5

Second term : a₂ = 2(a₁ + 4)

Third term : a₃ = 2(a₂ + 4) = 2(18 + 4) = 2(22) = 44

Fourth term : a₄ = 2(a₃ + 4) = 2(44 + 4) = 2(48) = 96

Fifth term : a₅ = 2(a₄ + 4) = 2(96 + 4) = 2(100) = 200

Hence, the first 5 terms of the sequence are :

Answer:

5, 18, 44, 96, 200

Step-by-step explanation:

[tex]\textsf{Given sequence}: \quad a_n=2(a_{n-1}+4)[/tex]

[tex]\textsf{Given first term}: \quad a_1=5[/tex]

[tex]\implies a_1=5[/tex]

[tex]\implies a_2=2(a_{1}+4)=2(5+4)=2(9)=18[/tex]

[tex]\implies a_3=2(a_{2}+4)=2(18+4)=2(22)=44[/tex]

[tex]\implies a_4=2(a_{3}+4)=2(44+4)=2(48)=96[/tex]

[tex]\implies a_5=2(a_{4}+4)=2(96+4)=2(100)=200[/tex]

The table is a linear function, and the rule for the input/output table is f(x) = 1 + 3x

From the table, we can see that:

The output of the table  is 1 more than 3 times the input

If the input is x, then the output y is:

y = 1 +3 * x

Evaluate

y = 1 + 3x

Hence, the rule for the input/output table is f(x) = 1 + 3x

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[tex]\cfrac{40.5}{8.1} ~~ \begin{cases} 40.5\implies \frac{405}{10}\\\\ 8.1\implies \frac{81}{10} \end{cases}\implies \cfrac{ ~~ \frac{405}{10} ~~ }{\frac{81}{10}}\implies \cfrac{405}{10}\cdot \cfrac{10}{81}\implies \cfrac{405}{81}\cdot \cfrac{10}{10} \\\\\\ \cfrac{5\cdot 81}{81}\cdot \cfrac{10}{10}\implies \cfrac{5}{1}\cdot \cfrac{81}{81}\cdot \cfrac{10}{10}\implies \cfrac{5}{1}\cdot 1\cdot 1\implies \cfrac{5}{1}[/tex]

[tex]\begin{array}{ccll} pens&\$\\ \cline{1-2} 10 & 8\\ 2& x \end{array} \implies \cfrac{10}{2}=\cfrac{8}{x}\implies 5=\cfrac{8}{x}\implies 5x=8\implies x=\cfrac{8}{5}\implies x=1.6[/tex]

To solve this problem, we have to find the net displacement and the net force and the multiply the dot product together and get the work done.

The work done on moving the object is 27ft*lbs

To find the work done on this object, let's find the net force on the object.

Data;

The unit vector of the force is

[tex]\sqrt{4^2 +(-2)^2} =\sqrt{16 + 4} = \sqrt{20}[/tex]

[tex]\frac{4}{\sqrt{20} }, \frac{-2}{\sqrt{20} }[/tex]

The net force acting on the object is

[tex]F = 4(\frac{4}{\sqrt{20} }, \frac{-2}{\sqrt{20} })\\F= (\frac{16}{\sqrt{20} }, \frac{-8}{\sqrt{20} } )[/tex]

The displacement on the object is 7ft through (0,4) to (5, -1)

The unit vector on displacement is

[tex]\sqrt{5^2 + (-1-4)^2} = \sqrt{25+25} = \sqrt{50}[/tex]

[tex]\frac{5}{\sqrt{50} }, \frac{-5}{\sqrt{50} }[/tex]

The net displacement will be

[tex]7(\frac{5}{\sqrt{50} }, \frac{-5}{\sqrt{50} }) = \frac{35}{\sqrt{50} }, \frac{-35}{50}[/tex]

The work done will be F.d

[tex]w = f. d \\[/tex]

[tex]w = (\frac{16}{\sqrt{20} }, \frac{-8}{\sqrt{20} } ) * \frac{35}{\sqrt{50} }, \frac{-35}{50}\\w = 17.71+ 8.854\\w = 26.567 = 27ft*lbs[/tex]

The work done on moving the object is 27ft*lbs

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Answer: the answer is B 27ft

Step-by-step explanation: its cam btw

Answer:

150%

Step-by-step explanation:

half of 6 is three, and 9 has a value of 3 more than 6. meaning that 9/6 = 150%

Answer: [tex]150[/tex]% [tex]([/tex][tex]0.54[/tex][tex])[/tex]

Step-by-step explanation:

For fraction: divide 6 by 100 and remove the % sign.

{[tex]6[/tex]}% [tex]=\frac{6}{100}[/tex]

For decimal: move the decimal point 2 places to the left and remove the % sign.

{[tex]6[/tex]}% [tex]=0.06[/tex]

[tex]100[/tex]% [tex]=9[/tex]

[tex]\frac{6}{100}[/tex] × [tex]9=0.06[/tex] × [tex]9=0.54[/tex]

[tex]6[/tex]% [tex]of~9~is~0.54[/tex]

Answer:

C

Step-by-step explanation:

Line does not go over 1 on the y-axis

Answer:

155.24

Step-by-step explanation:

[tex]\text{Apply sine rule,}\\\\~~~~~~~~\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}\\\\\\\implies \dfrac{b }{\sin B} = \dfrac{c}{ \sin C}\\\\\\\implies b = \dfrac{c \cdot \sin B}{\sin C}\\\\\\\implies b = \dfrac{197\sin 52^\circ}{\sin 51^{\circ}}~~~~~~~~~;\left[\angle C = 180^{\circ} - 77^{\circ} -52^{\circ} = 51^{\circ} \right]\\\\\\\implies b \approx 200[/tex]

Answer:

gago putangina mo bold

panget

Answer:

1-nonlinear it is not consistant

2- a increasing, b constant, c decreasing

3- 'a' walking away from hole, 'b' rests, 'c' goes back to hole (b could also be gather, as in food)

4- 8cm per second

work 16cm/2sec=8cm/1sec

Step-by-step explanation:

Answer:

$450

Step-by-step explanation:

[tex] \underline{ \boxed {\sf \color{cyan}{x = \frac{129}{2}}}}[/tex]

[tex]\pink{━━━━━━━━━━━━━━━━━━━━━━━━━━━━━}[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\Longrightarrow\sf{2x- 17 =51 +61}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\Longrightarrow\sf{2x- 17= 112}[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\Longrightarrow\sf{2x- 17 + 17 = 112 + 17}[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\Longrightarrow\sf{2x = 129}[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\Longrightarrow\sf{\frac{ \cancel2x}{ \cancel2}=\frac{129}{2}}[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\Longrightarrow\sf{x = \frac{129}{2}}[/tex]

[tex]\pink{━━━━━━━━━━━━━━━━━━━━━━━━━━━━━}[/tex]

[tex]{\pink{\boxed{\blue{2x - 17 = 51 + 61}}}}[/tex]

2x - 17 = 51 + 61

[tex]{\blue{\boxed{{Take -17 \: \: to \: \: the \: \: other \: \: side \: \: and }}}}[/tex]

[tex]{\blue{\boxed{{its \: \: sign \: \: will \: \: change \: \: \: into \: \: + }}}}[/tex]

2x = 112 + 17

2x = 129

[tex]{\blue{x = {\pink{ \frac{129}{2} }}}}[/tex]

answer is 31 dimes, 11 nickels

see picture attachment for the math

equation is .05N + .10D = 3.65

value of nickels and dimes

using D + N = 42

change to find value of N = 42 - D

plug value of N into the equation and solve

Answer:

26.2

X = 22.27/(1 - 0.15)

X = 22.27/0.85

X = 26.2

Answer:

because the Gravity of the eart.

Step-by-step explanation:

the times is equarl and plus is to mynos sorna iloveyou mwa.

Answer:V≈3.29×105in³

Step-by-step explanation:im smart

The correct answer is option D which is a = 5, b = 2, c = - 1.

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given that:-

The general form of the equation is given as:-

Y = ax² + bx + c

We have a quadratic equation:-

y = 5x² + 2x - 1

By comparing the equation with the general form the value of a, b and c is calculated:-

a  =  5

b  =  2

c  =  -1

Therefore the correct answer is option D which is a = 5, b = 2, c = - 1.

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The population (number of bacteria in the colony), 950 hours from that time, will be 260 bacteria

From the question, we are to determine what the population will be after 950 hours

From the given information,

The number of bacteria in a colony doubles every 475 hours

The current population is 65 bacteria

∴ After 475 hours, the new population will be 2 × 65 bacteria

New population after 475 hours = 130 bacteria

After another 475 hours (that is, 950 hours from the initial time),

The population will be 2 × 130 bacteria = 260 bacteria

Hence, the population, 950 hours from that time, will be 260 bacteria

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Step-by-step explanation:

a=60°{vertically opposite angles}

b=180°-(52+110)°=18°

c=180°-(60+18)°=102°

d=180°-102°=78°

e=180°-(78+51)°=51°

Answer: 7 BATCHES

Step-by-step explanation: to produce one batch it takes 7/10 of oatmeal

Now the factory uses 4 9/10 batch of oatmeal

1=7/10 OATMEAL

X=4 9/10 OATMEAL

X=(7/10*1)/4 9/10

=4 9/10*10/7

=490/70

=7

Answer:

5 dimes and 10 nickels

Step-by-step explanation:

0.1d + 0.05n = 1

d + n = 15

d + 0.5n = 10

d + n = 15

0.5n = 5

n = 10

d + n = 15

d + 10 = 15

d = 5

Answer: 5 dimes and 10 nickels