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Divide these numbers in scientific notation.
(9.6*10^-8) divided by (3*10^-7)

Answer: Choice C

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Explanation:

Recall that the form

[tex]z = r*\left[\cos\left(\theta\right)+i*\sin\left(\theta\right)\right][/tex]

can be abbreviated to

[tex]z = r*\text{cis}(\theta)[/tex]

The "cis" stands for the first letters of "cosine i sine" in that order.

The original fairly messy quotient can be shortened down to

[tex]\frac{90\text{cis}(\pi/4)}{2\text{cis}(\pi/12)}[/tex]

We have 90cis(pi/4) all over 2cis(pi/12) as one big fraction.

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Now we'll use this rule to divide two complex numbers

[tex]z_1 = r_1*\text{cis}(\theta_1)\\\\z_2 = r_2*\text{cis}(\theta_2)\\\\\frac{z_1}{z_2} = \frac{r_1}{r_2}*\text{cis}(\theta_1-\theta_2)\\\\[/tex]

As you can see, we divide the r1 and r2 values to form the final coefficient out front. The theta angles are subtracted to form the new argument.

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Let's apply that idea to what your teacher gave you

[tex]z_1 = 90*\text{cis}(\pi/4)\\\\z_2 = 2*\text{cis}(\pi/12)\\\\\frac{z_1}{z_2} = \frac{90}{2}*\text{cis}(\pi/4 - \pi/12)\\\\\frac{z_1}{z_2} = 45\text{cis}(3\pi/12 - \pi/12)\\\\\frac{z_1}{z_2} = 45\text{cis}(2\pi/12)\\\\\frac{z_1}{z_2} = 45\text{cis}(\pi/6)\\\\[/tex]

That last step then converts directly to the expression shown in choice C.

Answer:

Step-by-step explanation:

Answer:

1) 9/10 + 4/5 + 5/6 = 2 8/15

2) 14/15 + 2/9 + 1/5 = 1 16/45

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Solution:

[tex] \bold{1)} \: \tt \frac{9}{10} + \frac{4}{5} + \frac{5}{6} \\ \\⟹ \tt \frac{9}{10} + \frac{4}{5} \\ = \tt \frac{9 \times 1}{10 \times 1} + \frac{4 \times 2}{5 \times 2} = \frac{9 + 8}{10} = \frac{17}{10} \\ \\ ⟹\tt \frac{17}{10} + \frac{5}{6} \\ = \tt \frac{17 \times 3}{10 \times 3} + \frac{5 \times 5}{6 \times 5} = \frac{51 + 25}{30} = \frac{76}{30} \: or \: 2 \frac{16}{30} = 2 \frac{8}{15} \\ \\ \\ \\ \bold{2)} \tt \: \: \frac{14}{15} + \frac{2}{9} + \frac{1}{5} \\ \\⟹ \tt \frac{14 \times 3}{15 \times 3} + \frac{2 \times 5}{9 \times 5} = \frac{42 + 10}{45} = \frac{52}{45} \\ \\⟹ \tt \frac{52}{45} + \frac{1}{5} \\ = \frac{52 \times 1}{45 \times 1} + \frac{1 \times 9}{5 \times 9} = \frac{52 + 9}{45} = \frac{61}{45} = 1 \frac{16}{45} [/tex]

4a(a - b) + 3b(b - a)

= 4a² - 4ab + 3b² - 3ab

= 4a² - 4ab - 3ab + 3b²

= 4a² - 7ab + 3b²

= (a - b) (4a - 3b)

________

Hope it helps ⚜

Answer: 16.308

Step-by-step explanation:brainiest please

Answer:

i think the details given for the question is in sufficient or question is wrong

Answer:

[tex]a_{14} = 10496[/tex]

Step-by-step explanation:

A geometric sequence is of the form:

[tex]ar^0, ar^1, ar^2, ar^3, \cdot \cdot \cdot[/tex]

So the given values can be represent as:

[tex]1. \quad ar^5 = \frac{41}{256}\\2. \quad ar^{10} = -164[/tex]

So you have a system of equations with two unknows [tex]a[/tex] and [tex]r[/tex]. Then you can find one unknow in terms of the other.

[tex]a = \frac{-164}{r^{10}}[/tex]

Now replace [tex]a[/tex] in the first equation

[tex]\frac{-164}{r^{10}}r^5 = \frac{41}{256}\\\frac{-164}{r^{5}} = \frac{41}{256}\\r^5 = \frac{256 \cdot -164}{41} = -\frac{41984}{41}\\r = \sqrt[5]{-\frac{41984}{41}}\\[/tex]

You don't have to worry about the negative number inside the root, because is a odd root then you can find odd negative numbers that give me the desire result.

[tex]r = -\frac{4\sqrt[5]{41} }{\sqrt[5]{41}} \\r = -4[/tex]

For find [tex]a[/tex] only replace [tex]r[/tex] in whatever of the two equations.

[tex]-a4^5 = \frac{41}{256}\\-a1024 = \frac{41}{256}\\a = -\frac{41}{262144}[/tex]

After find [tex]a[/tex] and [tex]r[/tex] use the next formula for find the [tex]14^{th}[/tex] term.

[tex]ar^{13} = x\\-\frac{41}{262144} \cdot -4^{13} = x\\\\10496 = x[/tex]

Answer:

Im not sure

Step-by-step explanation:

Im not sure what the exact slope is, but instead of being useless, and a waste of your time, here is how to find the slope.To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The required expression is ~

[tex] \boxed{(2x + 1)(x - 5)}[/tex]

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

let's solve ~

Answer:

8

Step-by-step explanation:

v=l*w*h so 2^3=8

Answer:

(7, -6)

(-7, -6).............

..

Answer: -7,-6

Step-by-step explanation:

So if we look at a graph 7,6 is on the right upper quadrant since its completely positiv, once we relfect the x axis then it becomes 7,-6 then once we reflect across the why axis it finally becomes -7,-6

Answer:

268,840

Step-by-step explanation:

286,000 x 6% commission= 17,160. you then subtract this commission from the sold price of 286000=$17160

Answer:

y = x + 14

Step-by-step explanation:

y - 14 = x

y = x + 14

[tex](xy-1)^2-(y-1)^2\\\\=(xy - 1 - y+1)(xy-1+y-1)~~~~~~;[a^2-b^2 = (a-b)(a+b)]\\\\=(xy-y)(xy+y-2)\\\\=y(x-1)(xy+y-2)[/tex]

Answer: 6 1/3

Step-by-step explanation:

4x-14 = -2x+24

4x = -2x+24 + 14  [Add 14 to both sides]

4x + 2x = 24 + 14  [Add 2x to both sides]

6x = 38                 {Combine like terms]

 x  = (19/3) or 6 1/3

Answer:

  A.  20·60

Step-by-step explanation:

The product of force and distance is ...

  [tex]F\cdot D=(20\text{ m})\cdot\dfrac{60\text{ kg$\cdot$m}}{\text{s}^2}=\dfrac{20\cdot60\text{ kg$\cdot$m$^2$}}{\text{s}^2}=\boxed{20\cdot60\text{ J}}[/tex]

Answer:

I think by mental math it would be 2.8 feet.

Step-by-step explanation:

Answer:

The first option you have selected should be correct. if any doubt comment.

Step-by-step explanation:

boy, that is hard to decipher ...

but from what I understood after a while of reading and re-reading, the proof is based on the equal slope (0) of all 3 lines showing that all 3 lines are parallel.

remember, the slope is the ratio y/x indicating how many units y changes, when x changes a certain amount of units when going from one point to another.

so, going from N to M :

x changes by (2d - 2b) units.

y changes by 0 units (2c to 2c).

so, the slope of NM is 0/(2d - 2b) = 0.

going from K to L :

x changes by (2a - 0) = 2a units.

y changes by 0 units (0 to 0).

so, the slope of KL is 0/2a = 0.

R and S are the middle points between K and N, and between L and M.

R = ((2b+0)/2, (2c+0)/2) = (b, c)

S = ((2d + 2a)/2, (2c + 0)/2) = ((d+a), c)

so, going from R to S :

x changes by (d+a-b) units.

y changes by 0 units (c to c).

so, the slope of KL is 0/(d+a-b) = 0.

as all 3 slopes are equal (and with being 0 also parallel to the x-axis), this proves that the line RS is parallel to its bases.

Hope I helped! Have a nice day! Really hope this helps k12 students!

Answer:

1

Step-by-step explanation:

x - 5 = -2( x + 1 )

=> x - 5 = -2x - 2

=> x + 2x = 5 - 2

=> 3x = 3

∴ x = 1

Answer:

probably 2.................

Answer:

B

Step-by-step explanation:

A. 2L, 2.9L, 2.5L, 2.4L

B. 2L, 2.4L, 2.5L, 2.9L

C. 2.9L, 2.5L, 2L, 2.4L

D. 2.9L, 2L, 2.5L, 2.4L

Answer:

what is in order from least to greatest is B

Step-by-step explanation:

as we know 1L = 10dL = 100cL = 1000mL so that we have 2L then 24dL (2.4L) then 250cL (2.5L) then 2900mL (29L)

Answer:

  33. $5.75

  34. 15 ft

  35. 8

  36. 32

Step-by-step explanation:

These questions pretty much cover the sorts of things you're supposed to learn in an Algebra course. If you don't get any of it, you may have a problem with follow-on courses.

__

You are expected to understand this question gives you two relations in two unknowns. The first step is to assign a variable to each of the unknowns. We can use ...

The given relations have to do with the prices of different quantities of these:

  2x +3y = 26.25 . . . . . . cost of 2 shakes and 3 sundaes

  4x +2y = 29.50 . . . . . . cost of 4 shakes and 2 sundaes

These two equations in two unknowns can be solved several ways. Here, it is convenient to use the method of "elimination", because the coefficients of x are related by a small integer. Subtracting the second equation from 2 times the first eliminates the x-variable (hence the name of the method).

  2(2x +3y) -(4x +2y) = 2(26.25) -(29.50)

  4y = 23.00 . . . . . . simplify

  y = 5.75 . . . . . . . . . divide both sides by 4

The cost of an ice cream sundae is $5.75.

We can substitute this value into either equation and solve for x. We would find the cost of a shake to be x=4.50. However, the question only asks for the price of a sundae.

__

There are formulas for the perimeter, area, and volume of various geometric figures of a generally circular or rectangular shape. You might find it convenient to memorize them. Here, you need the formulas for the volume of a cylinder and of a cone. You also need to know that the diameter of a circle is 2 times the radius of the circle, since most of the circle-related formulas are in terms of the radius.

Volume of a cone of radius r and height h: V = 1/3πr²h

Volume of a cylinder of radius r and height h: V = πr²h

It can be convenient to remember that a cone has 1/3 the volume of a cylinder the same height.

The relation of interest here is the volume of the silo is the sum of the volumes of the bottom cylinder and the top cone.

  V = π(20 ft)²(60 ft) + 1/3(20 ft)²(x ft) = 26000π ft³

  V = 24000π ft³ +(400/3)x·π ft³ = 26000π ft³ . . . . simplify a bit

  400/3·x = 2000 . . . . . . . divide by π ft³, and subtract 24000

  x = 2000(3/400) = 15 . . . . multiply by 3/400

The height of the top portion is 15 feet.

__

This has to do with understanding the meaning of a table and of an expression relating table values. The expression f(a) = g(b) means you're looking for table entries such that the number in the f(x) column is equal to the number in the g(x) column.

We find the only common function value to be -1, so f(-6) = -1 = g(1). Comparing this to f(a) = g(b), we see that a=-6.

The question asks for |g(a)|. The table tells us g(-6) = -8. Its absolute value will be the value without the negative sign:

  |g(-6)| = |-8| = 8 = |g(a)|

__

This is a polynomial division problem. It tells you the quotient of the quadratic, divided by (ax +2), is (3x -4) with a remainder of 66. We're concerned with the leading coefficient of the divisor, 'a'.

Polynomial long division is much simpler than numerical long division, because each quotient term is the leading dividend term divided by the leading divisor term. Here, that means ...

  96x²/(ax) = 3x

Multiplying by ax gives ...

  96x² = 3ax²

Dividing by 3x², we see that ...

  (96x²)/(3x²) = (3ax²)/(3x²)

  96/3 = a = 32

The value of 'a' is 32.

Answer: 0 bricks

Step-by-step explanation:

2,913 milligrams (mg) is only 2.913 grams.  It takes 1,000 grams to make a kilogram.  2,913 mg is only 0.002913 kg.  

Answer:

66 Cents per pound

Step-by-step explanation:

1 ton = 2,000 pounds

5 tons = 10,000 pounds

10,000 pounds = $6,600

1 Pound = $0.66

Answer:

?????????

Step-by-step explanation:

What are u asking

Answer: f(x) = (x −8)2

Step-by-step explanation:

Answer:

you will half the recipe, so

50g flour

30g sugar

25g margarine

20g chocolate chips

1 egg

then add together. recipe for 15 cookies will be;

150g flour

90g sugar

75g margarine

60gr chocolate chips

3 eggs

answer is 0.2 using cross multiplication.

Answer:

in 2 seconds, the snail will only move 0.2 centimeters or 2 millimeters. And after 2.5, 0.25 centimeters, or 2.5 millimeters.

Step-by-step explanation: