Let t = 4 and u = 6 + 2i. Find t – u

Answer:

[tex]3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n[/tex]

[tex]4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n[/tex]

[tex]2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n[/tex]

[tex]3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n[/tex]

Step-by-step explanation:

Given

See attachment for complete question

Required

Match equivalent expressions

Solving (a):

[tex]3 + 12 + 48 + 192 + 768[/tex]

The expression can be written as:

[tex]3 \to 3*4^{0[/tex] --- 0

[tex]12 \to 3 * 4^{1[/tex] ---- 1

[tex]48 \to 3 * 4^{2[/tex] --- 2

[tex]192 \to 3 * 4^{3[/tex] ---- 3

[tex]768 \to 3 * 4^{4[/tex] ---- 4

For the nth term, the expression is:

[tex]Term = 3 * 4^{n[/tex] ---- n

So, the summation is:

[tex]3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n[/tex]

Solving (b):

[tex]4 + 32 + 256 + 2048 + 16384[/tex]

The expression can be written as:

[tex]4 \to 4 * 8^0[/tex] --- 0

[tex]32 \to 4 * 8^1[/tex] ---- 1

[tex]256 \to 4 * 8^2[/tex] --- 2

[tex]2048 \to 4 * 8^3[/tex] ---- 3

[tex]16384 \to 4 * 8^4[/tex] ---- 4

For the nth term, the expression is:

[tex]Term \to 4 * 8^n[/tex] ---- n

So, the summation is:

[tex]4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n[/tex]

Solving (c):

[tex]2 + 6 + 18 + 54 + 162[/tex]

The expression can be written as:

[tex]2 \to 2 * 3^0[/tex] --- 0

[tex]6 \to 2 * 3^1[/tex] ---- 1

[tex]18 \to 2 * 3^2[/tex] --- 2

[tex]54 \to 2 * 3^3[/tex] ---- 3

[tex]162 \to 2 * 3^4[/tex] ---- 4

For the nth term, the expression is:

[tex]Term \to 2 * 3^n[/tex] ---- n

So, the summation is:

[tex]2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n[/tex]

Solving (d):

[tex]3 + 15 + 75 + 375 + 1875[/tex]

The expression can be written as:

[tex]3 \to 3 * 5^0[/tex] --- 0

[tex]15 \to 3 * 5^1[/tex] ---- 1

[tex]75 \to 3 * 5^2[/tex] --- 2

[tex]375 \to 3 * 5^3[/tex] ---- 3

[tex]1875 \to 3 * 5^4[/tex] ---- 4

For the nth term, the expression is:

[tex]Term \to 3 * 5^n[/tex] ---- n

So, the summation is:

[tex]3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n[/tex]

Answer :

Evaluate

Isolate the variable by dividing each side by factors that don't contain the variable.

x = 2 i √ 5 , − 2 i √ 5

Step-by-step explanation:

[tex]\boxed{B.\:5x\:+\:12}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]4 + x + x + 2x + 5 + 3 + x \\ = (x + x + 2x + x) + 12 \\ since \: they \: are \: like \: terms, \: we \: can \: add \: them \\ = 5x + 12[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]

Answer:

1/2 = 0.5

Step-by-step explanation:

Given that the game company gave each customer a single game for testing

There is definitely just two outcomes, i.e. the customer will either recommend the game or Not recommend the game.

since we do not have additional information regarding what might influence the decision of the customer, hence the probability of either recommending the tested game or not recommending the game will be equal

∴P ( recommending tested game ) = 1 - 0.5 = 0.5

[tex]x = 2.857[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]6x - 9 - 2(1 - x) = x + 9 \\ ⇢ 6x - 9 - 2 + 2x = x + 9 \\ ⇢ 8x - x = 9 + 11 \\ ⇢ 7x = 20 \\ ⇢  x = \frac{20}{7} \\ ⇢ x = 2.857[/tex]

[tex]{ \bf{ \underbrace{To\:verify:}}}[/tex]

[tex]6 \times 2.857 - 9 - 2(1 - 2.857) = 2.857 + 9 \\ ➪ \: 17.142 - 9 - 2 \times( - 1.857) = 11.857 \\➪ \: 8.142 + 3.714 = 11.857 \\➪ \: 11.856 = 11.857 \\ ➪ \: 11.86 = 11.86 \\ ➪ L.H.S.=R. H. S [/tex]

Hence verified.

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]

Answer: D) Groundwater collects only where the soil and geological features allow water to seep down into underground chambers.

In other words, as long as there are gaps to allow water through, then that would lead to underground aquifers. Another important component is the amount of rain water that happens. Sources such as rivers, lakes and streams are also a contributing factor.

Stuff like earthquakes, volcanic activity, and continental movement doesn't really have much an effect on where or how aquifers form. It's really all about the soil type and how the landscape is formed, and of course the other factors mentioned in the previous paragraph.

Answer:

10

Step-by-step explanation:

Answer:

x = 0   or   x = - 16

Step-by-step explanation:

16+x^2=0

x ( x + 16 ) = 0

using the algebra rule a . b = a = 0 and b = 0

x = 0    or   x = - 16

so the answer is  x = 0 and x = -1 6

Mark brainliest plsssssssssss

Answer:

I only know number 11 sorry :(

11. (Image attached)

Step-by-step explanation:

First, I would find the y intercept, which is 4. Next I found the slope of -3 by finding the rise of -3 (3 to left), then the run (1 up).

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Have a good day :)

Answer:

y = 3x-2

Step-by-step explanation:

Answer:

A. We cannot calculate this value.

Step-by-step explanation:

Had it on my test c:

We cannot calculate this value because the width is not given so we cannot find the area of the region option (A) is correct.

It is defined as the ratio of the population to the total area. The population density represents the average number of people living on each square unit.

We have:

If you live in a rectangular city that is 1 mile along the southern border and contains 1000 people,

As we know,

population density = number of people/area of the region

As we have a rectangular city,

The area of the city = length×width

Width is not given so we cannot find the area of the region.

Thus, we cannot calculate this value because the width is not given so we cannot find the area of the region option (A) is correct.

Learn more about the population density here:

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Answer:

Its A y=3

Step-by-step explanation:

Answer:

A- y=3

Step-by-step explanation:

3x+4y=30

3x+5y=33

-3x+-4y=-30

3x+5y=33

-4y=-30

5y=33

y=3

Answer:

Hello! answer: 78.5 in2

Step-by-step explanation:

IMPORTANT ATTENTION: Im using 3.14 for pi so answers might vary if you are using say 22/7 for pi so please know that since this problem doesn't tell to use a certain method I will use 3.14

area can be found by doing radius × radius × 3.14 so... diameter is just twice the radius so... 10 ÷ 2 = 5 5 × 5 = 25

25 × 3.14 = 78.5 therefore 78.5 is the answer HOPE THAT HELPS!

The approximate area of a circle with a diameter of 10 in is,

⇒ Area of circle = 78.5 in²

Given that;

Diameter of circle = 10 in.

Now, We know that;

⇒ Area of circle = πr²

Where, 'r' is radius of circle.

Here, Diameter of circle = 10 in.

Hence, Radius = 10 / 2 = 5 in

Thus, We get;

⇒ Area of circle = πr²

⇒ Area of circle = 3.14 x (5)²

⇒ Area of circle = 78.5 in²

Thus, The approximate area of a circle with a diameter of 10 in is,

⇒ Area of circle = 78.5 in²

Learn more about the circle visit:

https://brainly.com/question/24810873

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Answer:

#1

#2

#3

Answer:

1

Step-by-step explanation:

Because 1.38185 is below 1.5 so it rounds to 1

=> 4(7)–2(7+a)=8

Answer: $18.75

Step-by-step explanation: Each bag cost $3.75 individually.

Answer:

B.

Step-by-step explanation:

Answer:

5.7 feet i think

Step-by-step explanation:

Answer:

Step-by-step explanation:

use formula

x^3+y^3=(x+y)^3-3*x*y(x+y)

=12^3-3*27(12)

=1728-972

=756

Answer:

x^3 + y^3 = 756

Step-by-step explanation:

Given that,  x+y=12 and xy=27

We know that,

[tex]( x + y )^3 = x^3 + y^3 + 3xy(x + y)[/tex]

∴ [tex]12^3 = x^3 + y^3 + 3 * 27 * 12[/tex]

[tex]=> 1728 = x^3 + y^3 + 972[/tex]

[tex]x^3 + y^3 = 1728 - 972[/tex]

[tex]==> x^3 + y^3 = 756[/tex]

Answer:

true.

Step-by-step explanation:

hope this helps, i looked it up :)

Answer and Step-by-step explanation:

To find out how long each side is, divide 60 by 5 (since there are 5 sides in a pentagon).

60 divided by 5 = 12.

Each side is 12 meters long.

#teamtrees #PAW (Plant And Water)

Answer:

Step-by-step explanation:

Assuming you meant

570=(x+23)

570-23=x

547 = x

Answer: C. How many mountain ranges are in the U.S.

Step-by-step explanation:

A statistical question first of all has to have a quantitative response i.e., answers should be in numbers.

The only two questions here that would yield a numeric answer are options C and D.

Furthermore, a statistical question has variability in it which means that the answer is based on multiple observations not just one. The observations in option C are mountain ranges and as the question requires finding out details about multiple mountain ranges, this is a statistical question.

This is opposed to option D which addresses issues surrounding just one mountain.

Answer:

-181

Step-by-step explanation:

According to the arithmetic calculator, it should be this.

Answer:

Triangular prism

Step-by-step explanation:

Triangle baces and Rectangle sides make a Triangular prism.

Answer:

d

Step-by-step explanation:

Look at the both picture.