Sam and Andre shared a number of pennies in the ratio 8:3. They received a total of 671 pennies. How many more pennies did Sam receive than Andre?

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:

I am not certified because I also struggle with these but-

it might be

A. t = -5h-4

Step-by-step explanation:

For the answer A in the paragraph it states that the temperature was 4 degrees BELOW 0 meaning we shall put as -4° and each HOUR it keep going down 5 degrees so I would suppose it would be answer A.

Co-ordinates will be

Answer:

3c

Step-by-step explanation:

10c - 7c = 3c

Answer:

You press a little crow looking thing on the bottom of the persons answer

Step-by-step explanation:

Answer: 17%

Step-by-step explanation:

1. First divide the percentages by 100 to turn the percentages into a decimal (28/100) x (63/100) = 0.1764

2. Then turn that decimal into a percentage again.

0.1764 x 100 = 17.64 but if you’re rounding to the nearest tenth without any decimals it’ll just be 17%

Answer:

She lives in the Southern Hemisphere.

Step-by-step explanation:

Answer:

  158 minutes

Step-by-step explanation:

If m represents the number of minutes Rafael rode, his total bill is ...

  0.08m +6.00 = 18.64 . . . . cost to start plus cost based on time

  0.08m = 12.64 . . . . . . . . . . subtract 6

  m = 12.64/0.08 = 158 . . . . divide by 0.08

Rafael rode the scooter for 158 minutes.

Step-by-step explanation:

m +2 = 4

m = 2

x = 1

y +1 = 2

y = 1

z = -1

Answer:

12÷20.5= 0.5953658537

Dilation is the transformation that changes the size of a shape.

4 is a positive number so the shape will increase in size.

So after dilating every side by 4:

0,1

-0.5,0

1,0

We get

0,4

-2,0

4,0

Answer: y = -48/7 + 4x/7

Answer:

1) a number squared, reduced by 12

2) the quantity of twice a number divided by 3, increased by 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

The first expression reads "x squared less (or minus) 12."

The second expression becomes "the quotient 2x/3 plus one."    Note that 2x/3 must be computed before "one" is added, due to order of operations rules.

The third expression reads "8 less than the cube of x."

Answer:

B' (3, 1 )

Step-by-step explanation:

Given

A (- 1, 3 ) → A' (- 3, 7 )

x- coordinate goes from - 1 → - 3 , that is - 2

y- coordinate goes from 3 → 7 , that is + 4

Translation rule is (x, y ) → (x - 2, y + 4 ) , then

B (5, - 3 ) → B' (5 - 2, - 3 + 4 ) → B' (3, - 1 )

Answer:

use Pythagoras theorem a^2+b^2 = c^2 where c is the longest side of the triangle (hypotenuse)

3^2 + 4^2 = c^2 (c is the length of the ladder)

9 + 16 = c^2

25 = c^2

c = √25 (square root)

c = 5

Answer:

blahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Step-by-step explanation:

what goes around always come back around

Answer:

1.66667

Step-by-step explanation:

using online slope calculater

Answer:

1

Step-by-step explanation:

d5 7yvjn3f5crc6tv6tvt7gv7g

Answer:

4.6

Step-by-step explanation:

23/5=4.6

Answer:

24960(y-1)

I'm so glad to help you with this question hope you get it

Answer:

= 78

Step-by-step explanation:

Step One:

1 + 4= 5

Step Two:

5+9= 14

Step Three:

14+64= 78

= 78

Hope it helps :)

Answer: 441

Step-by-step explanation:

The formula for an arithmetic sum is

[tex]$\frac{\text{number of terms}}2 \cdot (\text{first term + last term})$[/tex]

We know that the [tex]\text{first term + last term} = -1 + 64 = 63[/tex]. So now all we need is the [tex]\text{number of terms}[/tex]. Well, if you draw each number onto the number line, you get something like

---|------|------|------|------|------|-----|------|-----|------|-----|------|-------|----------

 -1      0      1      2      3     4     5     6     7     8     9     10     11  ...

You can see that your numbers are spaced 5 apart, and they go from -1 all the way up to 64. So what you're really asking is, "how many segments of five can I draw from -1 up to 64?" The length of the line from -1 to 64 is 65 (think about it), so the number of line segments is 65/5 = 13. However, we didn't count 64 itself, since there's no line segment past it! So really there are 14 terms in this sequence. Thus the total sum is

[tex]$\frac {14}2 \cdot (63) = \boxed{441}.$[/tex]

Answer:

1738 kilometers

Step-by-step explanation:

Answer:

snap for secsy pics

Step-by-step explanation:

cat.lover

Answer:

a+b+2

Step-by-step explanation:

Measure the distance between the two end points, and divide the result by 2. This distance from either end is the midpoint of that line. Alternatively, add the two x coordinates of the endpoints and divide by 2. Do the same for the y coordinates.

Answer:

C, just use the formula.

Step-by-step explanation:

Answer:

your friend has 6 more marbles

Step-by-step explanation:

7×2=14

10×2=20

20-14=6

Answer:

6

Step-by-step explanation:

First you multiply 7 by 2 because there is 2 marbles in each bag and there is 7 bags so that is 14 marbles

Then you multiple 2 by 10 because there is 10 bags with 2 marbles each which is 20.

20-14=6

Can I get brainliest?

Answer:

b = 14 cm , h = 112 cm

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

Given height is 8 times base , then h = 8b and A = 784 , then

[tex]\frac{1}{2}[/tex] × b × 8b = 784

b × 4b = 784

4b² = 784 ( divide both sides by 4 )

b² = 196 ( take square root of both sides )

b = [tex]\sqrt{196}[/tex] = 14

Then base b = 14 cm and height h = 8 × 14 = 112 cm

Step-by-step explanation: