ben baked 6 times as many cookies as francis. francis baked 42 cookies. how many cookies did ben bake

Answer:

Step-by-step explanation

c

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Explanation:

We use De Moivre's Theorem. It says that if you started with

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

then raising both sides to the nth power leads to

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

The term out front r is raised to the nth power. We also have copies of n inside the trig functions.

The square root operation undoes the squaring operation, so we'll be dealing with n = 2.

If you were to go through each answer choice, then you'll find that squaring choice B will lead to the original expression given.

[tex]z = \sqrt{3}*\left[\cos\left(\frac{\pi}{4}\right)+i*\sin\left(\frac{\pi}{4}\right)\right]\\\\\\z^2 = (\sqrt{3})^2*\left[\cos\left(2*\frac{\pi}{4}\right)+i*\sin\left(2*\frac{\pi}{4}\right)\right]\\\\\\z^2 = 3*\left[\cos\left(\frac{\pi}{2}\right)+i*\sin\left(\frac{\pi}{2}\right)\right]\\\\\\[/tex]

Note that working this process in reverse means we apply the square root and we'll go from the expression in choice B to the original expression again.

The complex number Z =  √3[cosπ/4 + i sinπ/4] represents the complex number √(3[cosπ/2 + i sinπ/2]) after using the De Moivre's theorem option (B) is correct.

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number in the trigonometric form:

Z = √(3[cosπ/2 + i sinπ/2])

It is required to find the square root of the complex number.

To find the square root of the complex number we can use the De Moivre's theorem:

If

Z = r[cosθ + i sinθ]

Zⁿ = rⁿ[cosnθ + i sinnθ]

Using the above theorem:

Z =  √3[cos[(1/2)π/2] + i sin[(1/2)π/2]]

Z =  √3[cosπ/4 + i sinπ/4]

Thus, the complex number Z =  √3[cosπ/4 + i sinπ/4] represents the complex number √(3[cosπ/2 + i sinπ/2]) after using the De Moivre's theorem option (B) is correct.

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First find the slope:

   m = ( 2 - 1 ) / ( 0 - (-1) ) = 1 / 1 = 1

Set up slope-intercept form:

  y = 1·x +2

Now move x and y to the left and leave 2 on the right:

  -x + y = 2

This is also equivalent to x - y = -2, so that just depends if you want your x coefficient to be positive or negative.

Answer:

Standard form: x - y = -2

Step-by-step explanation:

The standard form of linear equations is Ax + By = C, where A, B, and C are integers; A and B ≠ 0, and A is a non-negative integer.

Given the two points, we must first solve for the value of the slope.

Let (x₁, y₁) = (-1, 1)

    (x₂, y₂) = (0, 2)

Substitute these values into the following slope formula:

m = (y₂ - y₁)/(x₂ - x₁)

m = (2 - 1)/[0 - (-1)]

m = 1/(0 + 1) = 1

Therefore, the value of the slope, m = 1.

Next, we need to determine the y-intercept, which is the point on the graph where it crosses the y-axis.  The y-intercept is also the value of y when x = 0.  One of the given points happens to be the y-intercept, (0, 2). Its y-coordinate is the value of b in the slope-intercept form, y = mx + b. Substitute the slope and the y-intercept into the equation:

y = mx + b

y = x + 2

Next, we need to rewrite the slope-intercept form into its standard form, Ax + By = C:

y = x + 2

Subtract x from both sides:

- x + y = x - x + 2

-x + y = 2

Multiply both sides of the equation by -1, so that the coefficient of x becomes a positive integer:

(-1) (-x + y) = 2(-1)

x - y = -2  ⇒ This is the standard form where A = 1, B = -1, and C = -2

Answer:

355 ounces

Step-by-step explanation:

Okay! We're going to have to use some conversion factors for this problem, since we're working with two different units (pounds and ounces). We know that there are 16 ounces in a pound - that's our first conversion factor. We can use it to write up a little equation to help us:

[tex]\frac{22lbs}{1} *\frac{16oz}{1lb} + 3 = x[/tex]

"x" is the total amount of ounces. Does everything in that equation make sense? The first multiplication part tells us how many ounces are in 22 pounds, and the second part (+ 3) adds the 3 ounces that were there from the beginning. Now, it's time to calculate.

[tex]\frac{22bs}{1} *\frac{16oz}{1lb} + 3 = x\\[/tex]

[tex]\frac{352oz}{1} + 3 = x[/tex]

[tex]352+3 = x[/tex]

[tex]x=355[/tex]

So, there are 355 ounces in a bike that weighs 22 pounds and 3 ounces. Hopefully that's helpful! :)

Answer:

16

Step-by-step explanation:

- 4 ( 5 - ( 36 ÷ 4 ) )

= - 4 ( 5 - 9 )

= - 4 ( - 4 )

= - 4 * - 4

= 16

Answer:

The answer is B.

Step-by-step explanation:

0.0605

Answer:

1 and 3/20 total, 15/20 of the fish are yellow tangs which would also be 75%.

Step-by-step explanation:

2/5 and 3/4 need to be converted into a fraction with a similar denominator. 5x4= 20, so 20 is our denominator.

To find the numerator, we need to multiply 2 by 4, which equals 8, and 3 by 5 which equals 15.

8/20 + 15/20 = 23/20 or 1 3/20

Answer:

Observation

Step-by-step explanation:

He walked around seeing if every fifth person bought lunch

Survey - Requires asking questions

Simulation - Needs prior data to make an estimation

Experiment - Testing something

Observation - Just observing and watching

Study - Looking up data

The method he used to collect his data is observational method.

Observational study is usually chosen when the researches the system is likely to produce different result if interfered.

Sample survey is done if the population is too big to analyze or destructible as the analysis occurs.

Controlled experiment is done manually, specifically to deduce conclusions. Its steps are fixed.

Random experiment is done specifically to deduce conclusions, but it is done in a random manner.

We are given that;

He saw every fifth person in cafeteria

Now,

An observational study is a method of collecting data by observing and recording the behavior or characteristics of individuals or groups without interfering or manipulating any variables. Nico did not ask any questions or change any conditions, he just observed whether every fifth person in the cafeteria bought lunch or brought their own.

Therefore, by sampling the answer will be observational method.

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143.25 °

is the correct answer.

please mark my answer as brainest and follow me to get the answer faster.

Answer:

=34

Step-by-step explanation:

4x+12x-6=4(4x+7) ur question

using BODMAS

4x+12x-6=16x+28

16x-6=16x+28

16x-16x=28+6

0=34

but make sure your question is right, can you go through it again

Answer: main

Step-by-step explanation:

Answer:

yeah it's main it cuts up through oak and elm

Step-by-step explanation:

We have,

We've to find the amount shared and what each of them received.

★ Amount Shared = Amount received by Edwin + Amount received by Franklin ★

As, Edwin and Franklin share money in the ratio 3:7. So, let's say that,

Also, Franklin received $20 more than Edwin. So,

→ Amount received by Franklin = 20 + Amount received by Edwin

→ 7x = 20 + 3x

Solving the equation further.

→ 7x - 3x = 20

→ 4x = 20

→ x = 20/4

→ x = 5

Hence,

→ Amount received by Edwin = $ 3x

→ Amount received by Edwin = $ 3(5)

→ Amount received by Edwin = $ 15 [Ans]

And,

→ Amount received by Franklin = $ 7x

→ Amount received by Franklin = $ 7(5)

→ Amount received by Franklin = $ 35 [Ans]

Lastly,

→ Total amount shared = 3x + 7x

→ Total amount shared = $35 + $15

→ Total amount shared = $50 [Ans]

Answer:

3/4 ÷ 1/8 = 6

Step-by-step explanation:

first you would have to figure out how to make them even factors.

6/8 ÷ 1/8

Then you would divide, and get 6.

Answer:

-5 + -8 = -13

Step-by-step explanation:

-5 + -8 = -13

in total you owe $13 but seperat it’s $5 and $8.

also you show a debt with Integers by using negative numbers.

Answer:

Write an equation the represents the words.

6x - 7 = 4x + 9

To solve for x (the number), isolate it from the other variables.

Subtract 9 from both sides.

6x - 7 - 9 = 4x

Combine like terms.

6x - 16 = 4x

Subtract 6x from both sides.

-16 = 4x - 6x

Combine like terms.

-16 = -2x

Divide both sides by -2.

-16/-2 = x

x = 8

The number is 8.

Hope this helps! :)

Answer:

The number is 8.

Step-by-step explanation:

Hello there!

We're given an unknown number, let's call this number n

We know that 7 less than 6 times n is equal to 9 more than 4 times n

Let's break that statement down, starting with "7 less than 6 times n"

6 times n should be 6n, since 6 * n = 6n

"7 less" means subtraction.

So "7 less than 6n" should be 6n-7

Now with "9 more than 4 times n"

4 times n should be 4n, as 4 * n = 4n

"9 more" means addition

So "9 more than 4n" should be 4n+9

The statement says that 6n-7 is equal to 4n + 9, and so when we write it as an equation:

6n - 7 = 4n + 9

Now we can solve the equation

Subtract 4n from both sides

2n - 7 = 9

Add 7 to both sides

2n = 16

Divide both sides by n

n=8

The number is 8

PS. we can substitute 8 back into the equation as n to see if it works:

6(8)-7=4(8)+9

Multiply

48-7=32+9

41= 32 + 9

41=41

It works :))

Hope this helps!

Answer:

i know answer i heard some were i think

Answer:

4x

Step-by-step explanation:

12x-9x

=4x

I hope my answer is correct

and if u like mark me as brainliest answer.

Answer:

12x - 9x

= 3x ( 4- 3)

= 3x ( 1)

= 3x

Step-by-step explanation:

Given length of diagonal of a cube = √12 cm Recall that length of diagonal of a cube = √3 × Length of edge of the cube ⇒ √12 = √3 × Length of edge of the cube ∴ Length of edge of the cube = √12 / √3 = 2√3 / √3 = 2 Thus the edge of the given cube is 2 cm

The number of gigabytes of data Josiah can use while staying within his budget is 2.2 gigabytes.

The total amount of money that can be spent on the cell phone plan is the sum of the flat cost and the variable cost.

Total cost = flat cost + variable cost

The flat cost is the cost that remains constant each month. The variable cost is the cost that increases by gigabyte used.

$43.60 = $37 + $3x

In order to determine the value of x, combine similar terms together

$43.60 - $37 = $3x

6.6 = $3x

Divide both sides by 3

6.6/3 = x

x = 2.2 gigabytes

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Answer:

180 667 777 98827

Step-by-step

the graaph has three differnt lines that connet

Answer:

a = 9.6 b = 11.2

Step-by-step explanation:

10 percent of 8 is .8

8 + (8 x .1) = 8.8

8.8 + .8 = 9.6

She will be paid 9.6 dollars after 1 full year of working, because working for one year is 12 months, and thats 10 percent of 8 twice. You can also put that as 20 percent of 8, aka 1.6

When you do 8+1.6 it equals 9.6

For the second part, that is 24 months, so 10 percent of 8 4 times. .8+.8+.8+.8 = 3.2

8+3.2 = 11.2

She will be paid 11.2 dollars after 2 full years of working.

Your answer isnt wrong, I dont know why your teacher is saying it is.

Answer:

Step-by-step explanation:

what divided by 13 is 4​

4 * 13 = 52

----------------------------

check

52 : 13 = 4

the answer is good

Answer:

52

Step-by-step explanation:

Answer:

$0.09 or 9 cents

Step-by-step explanation:

1.17/3=0.39

2.4/5=0.48

0.48-0.39=0.09

Answer:

Well you can divide them by each

1.17/3 which is 0.39 (quick mart)

2.4/5 Which is 0.48 (stop and save)

39 cent is what you pay at the cheaper store

9 cents is what you would save

-also you go to bay academy?

I haven’t seen Jupiter ed in so long hahah

Answer:

Step-by-step explanation:

24 is the multiple of 12

24 is a multiple of 12, so 24 is the correct answer of this question

9514 1404 393

Answer:

  (d)  The y-intercept of the graph of the relationship is ( 0, 1).

Step-by-step explanation:

The y-intercept of a proportional relation is always zero. If it is 1, the relationship must be non-proportional.

Answer:

-6

Step-by-step explanation:

Because 2×(-6) is - 12

Answer:

-24

Step-by-step explanation:

Answer:

Approximately [tex]12.9\; \rm km \cdot h^{-1}[/tex], assuming that this orbit is circular.

Step-by-step explanation:

The question is asking for a tangential velocity with the unit [tex]\rm km \cdot h^{-1}[/tex]. The unit of the given distance is already in [tex]\rm km[/tex] as required. Convert the unit of the orbital period to hours:

[tex]\begin{aligned}T &= 1230\; \text{day} \times \frac{24\; \rm h}{1\; \text{day}}. = 29520\; \rm h\end{aligned}[/tex].

Calculate the angular velocity [tex]\omega[/tex] of this planet from its orbital period:

[tex]\begin{aligned}\omega &= \frac{2\, \pi}{T} \\ &= \frac{2\, \pi}{29520\; \rm h} \approx 2.1285 \times 10^{-4}\; \rm h^{-1}\end{aligned}[/tex].

Given the radius [tex]r[/tex] of the orbit of this planet, the tangential velocity [tex]v_{\perp}[/tex] of this planet would be:

[tex]\begin{aligned}v_{\perp} &= \omega\, r \\ &\approx 2.1285 \times 10^{-4}\; \rm h^{-1} \times 2.22\times 10^{7}\; \rm km \\ &\approx 4.73 \times 10^{3}\; \rm km \cdot h^{-1}\end{aligned}[/tex].

If the orbit of this planet is circular, the velocity of the planet would be equal to its tangential velocity: [tex]4.73\times 10^{3}\; \rm km \cdot h^{-1}[/tex].