For 0° ≤ x < 360°, what are the solutions to cos(x/2) – sin(x) = 0?
A{0°, 60°, 300°}
B{0°,120°, 240°}
C{60°, 180°, 300°}
D{120°,180°, 240°}
Precalc

The total segment AE is 46.

"SAS" is when we know two sides and the angle between them.

To solve an SAS triangle we use "The Law of Cosines" to calculate the unknown side.

The Law of Cosines = a² = b² + c² − 2bc cosA

where

'b' and 'c' are two given sides

'A' is the angle between side 'b' and 'c' and

a' is the unknown side which we have to find.

In ΔABC , b=21, c=20, a= AC

By the Cosine law

a² = 21²+20² - 2*21*20 cos90°

a² =441 + 400 - 0 (∵cos 90° =0)

a² = 841

a=√841

a=29= AC.

Now, in ΔCDE, b=8, c=15 and a = CE

By the Cosine law

a² = 8² + 15²- 2*8*15cos90°

a² = 64 + 225 - 0 (∵cos 90° =0)

a²= 289

a = 17 = CE.

AE = AC + CE

AE = 29+17= 46.

Therefore, the total segment AE is 46.

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Step-by-step explanation:

your welcome

....................

Answer:

1st and 2nd option

Step-by-step explanation:

All the other options were basically N, P, and Q which were on the same line. However, point R isn't on the same line as point N or point Q.

Answer:

28y - 4z

Step-by-step explanation:

Hey there!

In order to simplify this, we need to first distribute the numbers outside of the parentheses to the numbers inside the parentheses:

20y + 8z + 8z - 20z + 8y

Now we combine like terms:

28y - 4z

Answer:

\(\implies \footnotesize \text{ Average Speed} = \dfrac{ \text{Total Distance}}{ \text{Total time}} \\ \)

\(\implies \footnotesize \text{ Average Speed} = \dfrac{ 6.7 \: km}{ \frac{1}{2} \: hr }\)

\(\implies \footnotesize \text{ Average Speed} = 6.7 \times 2 \: km/h\)

\(\implies \footnotesize \textbf{ Average Speed = 13.4 \: km/h}\)

His rate is 13.4km/ hour

Data;

To solve this problem, we have to convert his speed from km/min to km/h

\(60min =1 hour\\\)

Since his rate is 6.7kmin 30 minutes, let's convert it to hour

\(6.7km = 30min\\x km = 1min\\x = \frac{6.7}{30} \\x = 0.223km/min\)

But to convert minutes to hours, we have to divide the time by 60

\(0.223\frac{km}{min}*60/1 = 13.4\)

From the calculation above, his rate is 13.4km/ hour

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No idea

Sorryyyyy

I dont know

The maximum number of non-overlapping regions into which a circle can be divided by 9 chords is 46.

The maximum number of non-overlapping regions that a circle can be divided into by n chords is given by the formula:

N = (n^2 + n + 2) / 2

Substituting n = 9 into the formula, we get:

N = (9^2 + 9 + 2) / 2

N = (81 + 9 + 2) / 2

N = 92 / 2

N = 46

Therefore, the maximum number of non-overlapping regions into which a circle can be divided by 9 chords is 46.

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John borrowed $7000 at an interest rate of 4.5% compounded monthly for a period of 6 years. We can calculate the monthly payments, determine how much of the first payment goes towards paying interest, and find the unpaid balance after the first payment.

To calculate the monthly payments, we can use the formula for calculating the monthly payment on a loan. In this case, the loan amount is $7000, the interest rate is 4.5% (or 0.045 as a decimal), and the loan duration is 6 years. Plugging these values into the formula, we can calculate the monthly payment.

To determine how much of the first payment goes towards paying interest, we can calculate the interest on the loan for the first month using the monthly interest rate and subtract it from the monthly payment.

After making the first payment, the unpaid balance can be found by subtracting the principal amount that was paid off from the initial loan amount.

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Answer:

Measure of angle B is 70 degrees

Step-by-step explanation:

If they are both supplementary, it means that add up to be 180 degrees

Thus;

5x + 25 + 3x + 19 = 180

8x + 44 = 180

8x = 136

x = 136/8

x = 17

Measure of angle B will be;

3(17) + 19

= 51 + 19 = 70 degrees

Answer:

3:7

Step-by-step explanation:

which means 3 cars 7 trucks

There are 5x6=30 one-to-one functions from a set containing 5 elements to a set containing 6 elements.

A one-to-one (or injective) function is a type of mathematical function that maps each element of one set to one, and only one, element of another set. In other words, a one-to-one function is a function that has a unique output for each input. To calculate the number of one-to-one functions from a set containing 5 elements to a set containing 6 elements, we can use the formula f(x)=y, where x is the number of elements in the original set and y is the number of elements in the target set. In this case, x = 5 and y = 6, so f(x) = 6. Since each element in the original set must be mapped to a unique element in the target set, the total number of one-to-one functions is equal to the product of x and y, or 5 x 6 = 30.

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Answer:

to add on to what the other dude said its 4

Step-by-step explanation:

Answer:

Your answer is 40√3.

At x = 3, we don't have enough information to find f(3^2) or f'(3^2), so we cannot evaluate the expression for dy/dx at x = 3.

We can use the chain rule to find the derivative of y = sin(f(x^2)) with respect to x:

dy/dx = cos(f(x^2)) * d/dx[f(x^2)]

To find d/dx[f(x^2)], we can use the chain rule again:

d/dx[f(x^2)] = f'(x^2) * d/dx[x^2] = 2xf'(x^2)

So, putting it all together:

dy/dx = cos(f(x^2)) * 2xf'(x^2)

At x = 3, we don't have enough information to find f(3^2) or f'(3^2), so we cannot evaluate the expression for dy/dx at x = 3.

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Answer:

Step-by-step explanation:

Given equation:

Solve:

Your answer is 160 \(units^2\).

The true statement is: while researchers found it difficult to reject the random walk hypothesis for exchange rates on empirical grounds, there is no theoretical reason why exchange rates should follow a pure random walk.

The solution to the system of equations is X = 12/7 and Y = 16/7. To determine the best method to solve the system of equations 5X - 2Y = 4 and 2X + 2Y = 8, we can use the addition method (also known as the elimination method).

Step 1: Write down the given equations:
5X - 2Y = 4
2X + 2Y = 8

Step 2: Observe that the coefficients of Y in both equations have the same absolute value, but with opposite signs. This makes the addition method suitable, as adding the equations will eliminate the Y variable.

Step 3: Add the two equations:
(5X - 2Y) + (2X + 2Y) = 4 + 8
7X = 12

Step 4: Solve for X by dividing both sides of the equation by 7:
X = 12 / 7

Step 5: Substitute the value of X back into one of the original equations to solve for Y. We'll use the second equation:
2(12/7) + 2Y = 8

Step 6: Solve for Y:
24/7 + 2Y = 8
2Y = 8 - 24/7
2Y = (56 - 24) / 7
2Y = 32/7
Y = 16/7

So, the solution to the system of equations is X = 12/7 and Y = 16/7.

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Over a period of 8 years, with monthly deposits starting at $50 and increasing by $5 each month, and an annual effective interest rate of 10%, we can calculate the accumulated balance at the end of the 8-year period.

To calculate the accumulated balance at the end of 8 years, we need to consider the monthly deposits, the interest earned, and the compounding effects. The annual effective interest rate of 10% needs to be converted to a monthly interest rate.

First, we can calculate the monthly interest rate by dividing the annual effective interest rate by 12 (since there are 12 months in a year). In this case, the monthly interest rate would be (10% / 12) = 0.00833.

Next, we can calculate the accumulated balance using the formula for the future value of an ordinary annuity:

Accumulated Balance = P * [\((1 + r)^n\) - 1] / r

Where:

P = Monthly deposit amount

r = Monthly interest rate

n = Number of compounding periods (in this case, 8 years * 12 months = 96 months)

Plugging in the values, we have:

P = $50 (initial deposit)

r = 0.00833 (monthly interest rate)

n = 96 (number of compounding periods)

Using the formula, we can calculate the accumulated balance at the end of 8 years.

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Salma must score 405 on exam B in order to do equivalently well as she did on exam A.

To determine how well Salma must score on exam B to perform equivalently to exam A, we need to compare the scores relative to their respective means and standard deviations. Since the scores on each exam are normally distributed, we can use z-scores to make the comparison.

First, we calculate the z-score for Salma's score on exam A using the formula: z = (x - mean) / standard deviation.

For exam A:

z = (69 - 64) / 10 = 0.5

Next, we find the corresponding raw score on exam B that corresponds to the same z-score of 0.5. Using the formula: x = z * standard deviation + mean.

For exam B:

x = 0.5 * 100 + 400 = 405

Therefore, Salma must score 405 on exam B in order to perform equivalently to her score of 69 on exam A. This means that if she achieves a score of 405 on exam B, it would be at the same relative position in the distribution as her score of 69 on exam A, taking into account the different means and standard deviations of the two exams.

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Given the equation

Subtract 3 from both sides

Divide both sides by 3

Raise both sides to power 5 to remove the 5th root on the left hand side

Take the cube root of both sides

Subtract 2 from both sides

x + 2 = 32

x = 32 - 2

x = 30

The solution to the equation is x = 30

Answer:

answer 3 i think  sorry if im wrong

Step-by-step explanation:

Answer:

See attached graph for rise and run lines

Slope = -1

Step-by-step explanation:

The slope-intercept equation form of a line is given by
y = mx + b where m = slope and b the y-intercept

rise/run is the slope of the line and is given by Δy/Δx where Δy represents the change in y values and Δx the corresponding change in x values

To calculate slope, take any two points on the line, find the difference between their y values and divide them by the change in x values

Two points I have chosen are (-3, 0) and (0, -3)
\(\textsf{{Slope}}=\dfrac{\ensuremath{-3}-0}{0-(-3)}=\dfrac{-3}{3}=-1\)

We can see from the graph that the y-intercept ie where the line crosses the y axis i s-3

So the equation of the line is y = -1x - 3

Here's a Scheme function that checks whether a matrix is symmetric or not:

```scheme

(define (is-symmetric-matrix matrix)

 (define (get-element matrix i j)

   (if (null? matrix)

       #f

       (if (= i 0)

           (if (null? (car matrix))

               #f

               (if (= j 0)

                   (car (car matrix))

                   (get-element (cdr matrix) i (- j 1))))

           (get-element (cdr matrix) (- i 1) j))))

 (define (is-matrix-symmetric-helper matrix i j)

   (if (null? matrix)

       #t

       (if (equal? (get-element matrix i j)

                   (get-element matrix j i))

           (is-matrix-symmetric-helper matrix i (+ j 1))

           #f)))

 (if (null? matrix)

     #t

     (is-matrix-symmetric-helper matrix 0 0)))

```

The function `is-symmetric-matrix` takes a matrix as an input, which is represented as a list of lists. It uses a helper function called `is-matrix-symmetric-helper` to compare each element of the matrix with its corresponding element in the transposed position. The `get-element` function is used to retrieve the element at position `(i, j)` in the matrix.

The `is-matrix-symmetric-helper` function recursively iterates over the matrix, comparing each element with its transposed element. If any pair of corresponding elements is found to be different, it immediately returns `#f` (False), indicating that the matrix is not symmetric. If it reaches the end of the matrix without finding any differences, it returns `#t` (True), indicating that the matrix is symmetric.

Finally, the main `is-symmetric-matrix` function first checks if the matrix is empty. If it is, it immediately returns `#t` since an empty matrix is considered symmetric. Otherwise, it calls the helper function with the initial indices `(0, 0)` and returns its result.

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Answer:

y = -1/4x + 2

Step-by-step explanation:

rise over run

Answer:

y=4/5x

Step-by-step explanation:

If you multiply the x value of 10, substitute it into the equation. Using the equation y=4/5x, you will get the y value of 8.

When you substitute the x value of 5 into the equation. You will get 4.

You do this for the rest of the x values and will get the correct y values.