Simplify the following expression:

(3i + 4) - i + 4(6 + 2i)

A. 27 + 11i

B. 28 + 10i

C. 14 + 8i

D. 14 + 4i

Answer:

a) 15/8   b) 25/18

Step-by-step explanation:

a) First bring all the fractions to a common denominator (I'm going to use 8th's). 5/8 is already simplified, 1/2=4/8, and 3/4=6/8. Then, simply add the numerators and leave the denominator:  [tex]\frac{5+4+6}{8} =\frac{15}{8}[/tex]

Since this can not be simplified any further, your final answer is 15/8.

b) Start by bringing all the fractions to a common denominator (for this problem, we'll use 18th's). 2/3=12/18, 1/6=3/18, and 5/9=10/18. Then just add all the numerators and leave the denominator the same: [tex]\frac{12+3+10}{18} = \frac{25}{18}[/tex]

Since this cannot be simplified further either, your final answer is 25/18.

Hope this helps! :)

Answer:

so to add we need to find lcm

Step-by-step explanation:

a) 5/8 + 1/2+3/4                            lcm of 2,4 and 8 = 8

5/8 = 5/8

1x4
2x4  =  = 4/8

3x2
4x2    = 6/8

5/8 + 4/8 + 6/8 = 15/8


b) 2/3 + 1/6 + 5/9                       lcm of 3 , 6 and 9 = 18

2x6
3x6  = 12/18

1x3
6x3      = 3/18

5x2
9x2 = 10/18

12/18 + 3/18 + 10/18 = 25/18

Step-by-step explanation:

hope you have a great day

The value of x will be;

⇒ x = 13.9

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle is shown in figure.

Now,

Since, We know that;

The sine rule is;

⇒ sin A / a = sin B / b = sin C / c

By given figure, we get;

⇒ sin 83°  / x = sin 68° / 13

⇒ sin 83° × 13 / sin 68° = x

⇒ x = 0.99 × 13 / 0.92

⇒ x = 13.9

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The answers to the given question are as follows:-

1.  Cos(∠mA)  =  [tex]\dfrac{3}{5}[/tex]

2. Sin(∠mA)   = [tex]\dfrac{\sqrt{20}}{\sqrt{35}}[/tex]

3. Tan(∠mB)  =  [tex]\dfrac{b}{a}[/tex]

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

The angles will be calculated by using trigonometric identities.

1. For the first triangle:-

Cos∠mA = [tex]\rm \dfrac{Base}{Hypotenuse}[/tex]

We can see in the first triangle base is 3 and the hypotenuse is 5.

Cos∠mA =  [tex]\dfrac{3}{5}[/tex]

2. For the second triangle:-

Sin∠mA = [tex]\rm \dfrac{Perpendicualr }{Hypotenuse}[/tex]

We can see in the first triangle Perpendicular is √20 and the hypotenuse is √35.

Sin∠mA =  [tex]\dfrac{\sqrt{20}}{\sqrt{35}}[/tex]

3. For the third triangle:-

Tan∠mB = [tex]\rm \dfrac{Perpendicualr }{Base}[/tex]

We can see in the first triangle Perpendicular is b and the Base is a.

Tan∠mA =  [tex]\dfrac{b}{a}[/tex]

Therefore  answers to the given question are as follows:-1. Cos(∠mA)  =  [tex]\dfrac{3}{5}[/tex]2. Sin(∠mA)   = [tex]\dfrac{\sqrt{20}}{\sqrt{35}}[/tex] and 3. Tan(∠mB)  =  [tex]\dfrac{b}{a}[/tex]

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Answer:

1.) ∞

2.) -∞

3.) 0

4.) 0

Step-by-step explanation:

As you approach x = -2 from the left, the "y" values are going to infinity. You never actually get a "y" value that equals x = -2 because of the vertical asymptote.

As you approach x = -2 from the right, the "y" values are going to -infinity. You never actually get a "y" value because there is a vertical asymptote.

As you approach x = 2, both sides converge to y = 0. At this point, there is a smooth, uninterrupted line.

The actual "y" value at x = 2 is 0 because the function goes straight through this point. So, you can just read this point as usual.

Answer:

A graph shows zeros to be ±3. Factoring those out leaves the quadratic

 (x-2)² +1

which has complex roots 2±i.

The function has roots -3, 3, 2-i, 2+i.

Step-by-step explanation:

Answer:

See below ~

Step-by-step explanation:

The function is :

f(x) = x⁴ - 4x² - 5

=============================================================

Plotting on a graph :

⇒ Once plotted on graph, check where the line of the function intersects the x-axis

⇒ Those will be the zeros of the function

===========================================================

Solution :

⇒ x = -2.236

⇒ x = 2.236

Th amount of money that Diana is left with is $8,430.23.

The first step is to determine the interest earned in the first year and the total amount that was made in the 2 years.

The formula used to determine the future value with monthly compounding is:

P(1 + r)^( n x m)

Where:

Total amount made in 2 years = $8000 x ( 1 + 5% / 12)^(12 x 2) = 8839.53

Interest earned in the first year = [ $8000 x ( 1 + 5% / 12)^(12) ] - 8000 = $409.29

Amount she is left with =  8839.53 - $409.29 = $8430.23

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Answer:

3/7  /    42.8% chance

Step-by-step explanation:

There are 6 striped balls (9, 10, 11, 12, 13, 14) and 8 (1, 2, 3, 4, 5, 6, 7, 8) solid colored balls. So, 6 / 14 balls are striped.

(6 / 14  = 3 / 7)

this means that the probability of a ball being striped has the odds of 3/7

(3/7 = about 42.8% chance)

Answer:

squares: 204

rectangle: 1,296

Step-by-step explanation:

Board Size: 8 x 8

The total number of squares is thus:

[tex]1^{2} + 2^{2} + ... + n^{2}[/tex]

sum = [tex]\frac{n(n + 1)(2n + 1)}{6}[/tex]

For a chess board, with n = 8,

sum = [tex]\frac{(8)((8) + 1)(2(8) + 1)}{6}[/tex]

sum = 204

the number of rectangles on a chess board,

to make a rectangle you need to pick any two of the vertical lines, and any two of the horizontal lines. There are 36 distinct pairs and the same number of vertical pairs, so the answer is 36 × 36 = 1,296.

Answer:

1200

Step-by-step explanation:

I'm not 100% sure but that seems like the most reasonable answer

Answer: [tex]a_{n}=64\left(\frac{1}{4} \right)^{n-1}[/tex]

Step-by-step explanation:

The common ratio is 16/64 = 1/4, so substituting into the formula, we get that [tex]a_{n}=64\left(\frac{1}{4} \right)^{n-1}[/tex]

kung 5ft and a width of 9ft and the area of prism is 174 the answer is 5ft

Answer:

288 grams

Step-by-step explanation:

Chelsea

12 × 3 = 36

48 × 4 = 192

Pierre

8 × 3 = 24

24 × 4 = 96

together

192 + 96 = 288 grams

Answer:

5 faces

Step-by-step explanation:

V – E + F = 2

We know that V = 5 and E = 8

Substitute these into the equation

5 -8+F = 2

-3+F =2

Add 3 to each side

-3+F+3 = 2+3

F=5

Based on the calculations, the sequence defined by the given function are 0.75, 1.1, 1.45​, 1.80 and 2.15.

In this exercise, you're required to create the first five (5) terms of the sequence defined by the given function as follows:

For the first term, we have:

f(1) = 0.75

For the second term, we have:

f(2) = f(2-1) + 0.35

f(2) = 0.75 + 0.35

f(2) = 1.1.

For the third term, we have:

f(3) = f(3-1) + 0.35

f(3) = 1.1 + 0.35

f(3) = 1.45.

For the fourth term, we have:

f(4) = f(3-1) + 0.35

f(4) = 1.45 + 0.35

f(4) = 1.80.

For the fifth term, we have:

f(5) = f(3-1) + 0.35

f(5) = 1.80 + 0.35

f(5) = 2.15.

Therefore, the sequence defined by the given function are 0.75, 1.1, 1.45​, 1.80 and 2.15.

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An equivalent expression is given by  (2 / x ^ 3) * sqrt (2)

We have the following expression

8 / x ^ 6

Rewriting we have

sqrt (8 / x ^ 6)

The expression consists of numbers and arithmetic operators. It does not contain equality or inequality symbols.

sqrt (2 * 4 / ((x ^ 2) * (x ^ 2) * (x ^ 2)))

(2 / (x * x * x)) sqrt (2)

(2 / x ^ 3) * sqrt (2)

An equivalent expression is given by

(2 / x ^ 3) * sqrt (2)

Therefore an equivalent expression is given by  (2 / x ^ 3) * sqrt (2).

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The distribution of the sample means when the samples of size n = 60 are randomly selected from the population is normal (approximately).

Calculating the sample mean is as simple as adding up the number of items in a sample set and then dividing that sum by the number of items in the sample set.

Here, the distribution of the sample means when the samples of size n = 60 are randomly selected from the population is normal (approximately).

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The region is C is the correct option because intersection region is on the region C after drawing on the coordinate plane.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

The question is incomplete:

The complete question is:

Which region represents the solution to the given system of inequalities?

y < -1/2x and y ≥ 2x+3 and the missing figure is shown in the picture please refer to the picture.

We have two inequalities:

y < -1/2x

y ≥ 2x+3

After drawing the inequalities on the coordinate plane we see that the intersection region is on the region C.

Thus, the region is C is the correct option because intersection region is on the region C after drawing on the coordinate plane.

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Answer:

B

Step-by-step explanation:

millimeter means one-thousandth of a meter meaning the number of millimeters will be larger by a factor of 1000.

Answer:

B

Step-by-step explanation:

Millimetres is A LOT smaller than meters, meaning the individual number of millimetres is larger than the individual number of meters.

Answer:

No, right answer is = 1017.36

Answer:

1017.36

Step-by-step explanation:

All your work is correct, but the final answer is not. In the problem it says to use 3.14 as pi, but when you multiplied you did:

[tex]\pi * 6^{2}*9 = 1017.88[/tex]

instead of

[tex]3.14*6^{2}*9 = 1017.36[/tex]

like you had written above. So the final is actually supposed to be 1017.36

Answer:

B

Step-by-step explanation:

Answer:

3, 2, 4, 1

Step-by-step explanation:

let me answer the last one first

compound interest is just an exponential sequence really, where the next value is some exponential amount of the previous.

hmmm that can happen in say, a bouncing ball, the 1st bounce is high, let it keep on boucing by itself and the next bounce is usually a compounded value of the previous one, since it's smaller it'd be a Decay type of equation.

hmmm it also happens in say population growth, of any organism, humans, bees, amoebas.

now let's do the others

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years \end{cases} \\\\\\ A=3000\left(1+\frac{0.026}{4}\right)^{4\cdot t}\implies \boxed{A=3000(1.0065)^t} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{after 15 years}}{t=15}\hspace{5em} A=3000(1.0065)^{15}\implies A\approx 3306.19 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ t=years\dotfill &15 \end{cases} \\\\\\ A=3000e^{0.026\cdot 15}\implies A=3000e^{0.39}\implies A\approx 4430.94[/tex]

The approximation of the slope of the graph at t = 10 days using this secant lines are 11750 and -11750, respectively.

(a) t = 10 days and a day earlier

This means that:

t = 10 and t = 9

The function is given as:

[tex]N(t) = 100000e^{\frac{-(t - 10)^2}{8}}[/tex]

Calculate N(10)

[tex]N(10) = 100000e^{\frac{-(10 - 10)^2}{8}}[/tex]

Evaluate

N(10) = 100000

Next, calculate N(9)

[tex]N(9) = 100000e^{\frac{-(9 - 10)^2}{8}}[/tex]

Evaluate

N(9) = 88249.6902585

The slope is then calculated using"

[tex]m = \frac{N(10) - N(9)}{10 - 9}[/tex]

This gives

[tex]m = \frac{100000 - 88249.6902585}{10 - 9}[/tex]

Evaluate

m = 11750.3097415

Approximate

m = 11750

(b) t = 10 days and a day later

This means that:

t = 10 and t = 100

The function is given as:

[tex]N(t) = 100000e^{\frac{-(t - 10)^2}{8}}[/tex]

In (a), we have:

N(10) = 100000

Next, calculate N(11)

[tex]N(9) = 100000e^{\frac{-(11 - 10)^2}{8}}[/tex]

Evaluate

N(11) = 88249.6902585

The slope is then calculated using:

[tex]m = \frac{N(11) - N(10)}{11 - 10}[/tex]

This gives

[tex]m = \frac{88249.6902585 - 100000}{11 - 10}[/tex]

Evaluate

m = -11750.3097415

Approximate

m = -11750

Hence, the approximation of the slope of the graph at t = 10 days using this secant lines are 11750 and -11750, respectively.

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Answer:

Total Area = 68

Step-by-step explanation:

Comment

There is 1 square at each end.

There are 2 congruent trapezoids in the middle

Draw a 7 inch line across the widest part of the middle

Area of the squares

Area = s^2

s = 3

Area = 3^2

Area = 9

But there are 2 of them                                        18

Area of the 2 trapezoids

Area = (b1 + b2)*h / 2

b1 = 3

b2 = 7    Notice that 7 was the line you drew

h = 5

Area = (3 + 7)*5/2

Area = 50 / 2

Area = 25

But there are 2 of them                                        50

Total Area                                                              68