Modeling Circular Motion, Picture attached to the question.
The boat is traveling at a rate of 1 meter per second.

How long does it take the barnacle to get back to its starting point?

Answer:

27

Step-by-step explanation:

Choose two outputs that are 3 values apart and find their ratio:

... f(3)/f(0) = 216/8 = 27

Answer:

4

Step-by-step explanation:

You may recognize these as factors of the difference of two squares:

... a² -b² = (a+b)(a-b)

where a=1 and b=i√3.

Then the product is ...

... 1² -(i√3)² = 1 - 3i² = 1 +3 = 4

_____

Of course, i = √-1, so i² = -1.

Answer: 4

Step-by-step explanation:

u=(1+i√3) =2       v=(1-i√3)=2        Uv = (2)(2)=4

Answer:

B: The mean study time of students in Class B is less than students in Class A.

Step-by-step explanation:

To find out why answer B is the right answer, I will give you facts from each option.

Option A is false. The mean study time in Class A is 4.8. Meanwhile in Class B it is 4. For Class A, sum up the 20 study times which is 96 and divide them by 20, you will get 4.8 hours of mean study time. For Class B, the sum of the 20 study times is 80, which divided by 20 will be 4.

Option B is True. See previous explanation.

Option C is False. The median study time in Class B is 4. The median study time in Class A is 4.8,

Option D is False. The range in Class A is from 2 to 8. The range in Class B is from 2 to 7.

Option E is False: The mean and median study time of these classes is different.

Answer:

B: The mean study time of students in Class B is less than students in Class A.

Step-by-step explanation:

Answer:

x ∈ {-2, 1, 4}

Step-by-step explanation:

The graph shows y = 0 when x = -2 or 1 or 4. Hence these values of x are the zeros of the function.

Answer:

D) [tex](x-5)^2 + (y-2)^2 = 49[/tex]

Step-by-step explanation:

Center is (5,2) and radius = 7

We use center - radius form of equation of circle

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

Where (h,k) represents the center

and r is the radius of the circle

We know center is (5,2)  so h= 5  and k =2

r= 7

Plug in all the values

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

[tex](x-5)^2 + (y-2)^2 = 7^2[/tex]

[tex](x-5)^2 + (y-2)^2 = 49[/tex]

Given zeros -4, -3, and 1, and a y-intercept of -11, the corresponding third-degree polynomial function can be formulated as y = (11/12)(x + 4)(x + 3)(x - 1).

To construct a third-degree polynomial function, we first need to define the polynomial based on its zeros. Given that the zeros are -4, -3, and 1, we can write the polynomial function in the form [y = a(x + 4)(x + 3)(x - 1)], where 'a' is the coefficient that affects the y-intercept. Because the y-intercept is -11, we set the value of y to -11 when x equals 0 to solve for 'a'. Thus the equation becomes [ -11 = a * 4 * 3 * -1], which simplifies to [a = -11/(-12) = 11/12]. Therefore, the polynomial function with the stated properties is [y = (11/12)(x + 4)(x + 3)(x - 1)] .

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The third-degree polynomial with zeros at -4, -3, and 1 and a y-intercept of -11 can be written as P(x) = 0.917(x+4)(x+3)(x-1).

To construct a third-degree polynomial with zeros at -4, -3, and 1, we write the factored form of a polynomial P(x), with the zeros plugged into the factors: P(x) = a(x+4)(x+3)(x-1). The term 'a' is a coefficient that we can find using the provided y-intercept of -11.

Because the y-intercept happens when x = 0, we substitute x = 0 and y = -11 into the polynomial: -11 =a(0+4)(0+3)(0-1). Solving for 'a' gives a = 11/12 or 0.917.

Thus, the resulting third-degree polynomial in lowest terms is P(x) = 0.917(x+4)(x+3)(x-1).

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Answer:

A. (2x + 5)(2x - 5)

Step-by-step explanation:

Factor out the polynomial given.

(4x² - 25) = (2x - 5)(2x + 5)

Check: Use the FOIL method.

(2x)(2x) = 4x²

(2x)(5) = 10x

(2x)(-5) = -10x

(-5)(5) = -25

Simplify. Combine like terms: 4x² + 10x - 10x - 25 = 4x² - 25

A. (2x + 5)(2x - 5) is your answer

~

So for this, we will be applying the difference of squares rule, which is [tex]x^2-y^2=(x+y)(x-y)[/tex] . In this case:

[tex]\sqrt{4x^2}=2x\\\sqrt{25}=5\\\\4x^2-25=(2x+5)(2x-5)[/tex]

In short, your answer is A. (2x + 5)(2x - 5).

You can go at this in different ways. In the attached, we multiplied the number of pounds by the sale price per pound ($5.25/4.2). You can also figure the price per pound of each proposed purchase and compare with the sale price.

... sale price = $5.25/(4.2 lb) = $1.25/lb

(A) $7.60/(6 lb) = $1.25/lb (yes)

(B) $4.25/(3.4 lb) = $1.25/lb (yes)

(C) $4.20/(3.5 lb) = $1.20/lb (no)

(D) $8.70/(5.8 lb) = $1.50/lb (no)

(E) $2.50/(2 lb) = $1.25/lb (yes)

Options A (6 pounds for $7.50), B (3.4 pounds for $4.25), and E (2 pounds for $2.50) are proportional to the sale price as their unit prices match, whereas options C (3.5 pounds for $4.20) and D (5.8 pounds for $8.70) do not match the unit price and are thus not proportional.

To determine if the proportions are equivalent to the sale price of green beans, we need to calculate the unit price for each scenario and compare it to the unit price that Mrs. Reynolds paid during the sale. Mrs. Reynolds bought 4.2 pounds of green beans for $5.25. The unit price is found by dividing the total cost by the total weight in pounds:

Unit price = $5.25 / 4.2 pounds = $1.25 per pound.

Now, let's calculate the unit price for each of the given scenarios and see if they match the unit price Mrs. Reynolds paid:

Based on these calculations, options A, B, and E are proportional to the sale price Mrs. Reynolds paid, while options C and D are not.

Answer:

y = .025x +20

The y intercept is the value when x = o, or the starting value.  In this case, it is the temperature in degrees F at a depth of 0 meters.

Step-by-step explanation:

We have a point a (0,20) and a point at (2 , 20.05)

We can find the slope from

m = (y2-y1)/(x2-x1)

   = (20.05-20)/(2-0)

   = .05/2

     =.025

One of the points (0,20) is the y intercept  since x=0

We can use the slope intercept form of the equation

y= mx+b

y = .025x +20

The y intercept is the value when x = o, or the starting value.  In this case, it is the temperature in degrees F at a depth of 0 meters.

Answer:

.

Step-by-step explanation:

Answer:

4 people

Step-by-step explanation:

You Know that 1/3 of an hour is 20 min, and u find out that 1/4 of an hour is 15 min. So then it takes 45 min for 1 person. 3 1/3 hour= 3 hr 20 min= 200 min. 200/45=4.44...= 4 people

Answer:

hello :

- 3π/4  = (-3×180°)/4 =  - 540°/4 = - 135°

Step-by-step explanation:

Answer: [tex]\bold{-\dfrac{3}{4}\pi}[/tex]

Step-by-step explanation:

Set up a proportion using π = 180°  →   [tex]\dfrac{\pi}{180} = \dfrac{x}{-135}[/tex]

Multiply both sides by -135 to solve for x  →  [tex]\dfrac{-135\pi}{180} = x[/tex]

Simply the fraction by dividing by [tex]\dfrac{45}{45}[/tex] →  [tex]-\dfrac{3}{4}\pi = x[/tex]

Assume x is a whole number. Then 2x+1 is a whole number, and 7(2x+1) is a whole number that is a multiple of 7.

13 is not a multiple of 7, so we have reached a contradiction, and our assumption must be false.

x cannot be a whole number.

see attachments below

In Algebra, angles are measured counterclockwise (CCW), generally using the +x axis as a reference. Thus any angle with an arrow shown in the CW direction will have a negative measure.

Know that clockwise measured angles are negative and anticlockwise measured angles are positive in sign.

Thus,

It is a standard convention used in mathematics that if you measure an angle clockwise(like the clock's hand moves), then the measured angle will be written with negative sign.

If the angle is measured anticlockwise, then the measured angle is written with positive sign.

Thus, by these conclusions, we have:

Learn more about sign of angles here:

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16.0

The mnemonic SOH CAH TOA reminds you of the relationship ...

... Tan = Opposite/Adjacent

... tan(32°) = 10/AC

Multiply by AC and divide by tan(32°) to get ...

... AC = 10/tan(32°) ≈ 16.0033 ≈ 16.0

Answer:

a) m = -6/5

b) m = -5/6

Step-by-step explanation:

The slopes of parallel lines are the same. The parallel line will have a slope equal to that of the line it is parallel to, -6/5.

__

The slopes of perpendicular lines are the opposite of the reciprocal of one another. The perpendicular line will have a slope that is the negative reciprocal of the slope of the one it is perpendicular to: -1/m = -1/(6/5) = -5/6.

Answer:

x=6       x=4

Step-by-step explanation:

x^2 - 10x + 24 =0

We need to factor this equation

What numbers multiply together to give us 24 and add together to give us -10

-6* -4 = 24 and -6+-4 = -10

(x-6) (x-4) = 0

Using the zero product property

x-6 = 0   x-4=0

x=6       x=4

Answer:

1.)C

2.)A

3.)B

Step-by-step explanation:

edge 2024

Answer:

The answer is 560

Step-by-step explanation:

multiply 420 by .75 for 75%

(420).75=560

Answer:

The answer is 10

Answer:

The answer is 10

Step-by-step explanation:

Answer:

y= 5x-3

Step-by-step explanation:

We have an intercept of -3 and a slope of 5

We can use the slope intercept form of the equation

y= mx+b where m is the slope and b is the y intercept

Substituting in the known values.

y= 5x-3

Answer:

The integers are, 30 and 31

Step-by-step explanation:

Given the statement: Two consecutive integers have a sum of 61 .

Let x and x+ 1 are the two consecutive integers.

then;

as per the given condition we have;

[tex]x +(x+1) = 61[/tex]

Combine like terms;

[tex]2x+1 = 61[/tex]

Subtract 1 from both sides ;

[tex]2x + 1-1 = 61 -1[/tex]

Simplify:

2x = 60

Divide both sides by 2 we get;

x = 30

and

value of x+1 = 30+1 = 31

Therefore, the integers are, 30 and 31.

Answer:

5,41%

Step-by-step explanation:

Remark

It's hard to interpret what % increase means. I'm going to work first with the actual increase and then I'll give the % increase. The answer I give will likely be in your choices, but it could still be incorrect.

Givens

Walking distance from A to B = 10 units down + 10 units east + 10 units down + 10 units east + 10 units down + 10 units east = 60 units.

Swimming distance = 2*sqrt(10^2 + 30^2) = 63.25 units.

Solution

The difference = 63.25 - 60 = 3.25

The % increase = (3.25/60)*100 = 5.41%

The domain and range is all real numbers.

Answer:

D) Domain: (-∞, ∞)

Range: (-∞, ∞)

Step-by-step explanation:

The domain is the input values, or the x values.

We can put in any x values for this function.

Domain : (-∞, ∞)

The range is the output values or the y values.

We can get any output values for this function

Range: (-∞, ∞)

Answer:

2, 120 degrees

Step-by-step explanation:

The first step in finding the polar form is finding the modulus, r

r= sqrt( x^2 + y^2)

r = sqrt( (-1)^2 + sqrt(3)^2)

r = sqrt(1+3)

r= sqrt(4)

r =2

The next step is finding the angle

theta = arctan (y/x)

theta = arctan (sqrt(3)/-1))

theta = arctan (-sqrt(3))

theta = -60

The point (-1, sqrt(3)) is in the 2nd quadrant, but our angle is in the 4th quadrant, so we add 180 degrees

theta = -60 + 180 = 120

theta = 120 degrees

Answer:

5 hours

Explanation:

$

6.50

(

3

)

+

$

6.50

x

=

$

52.00

$

19.50

+

$

6.50

x

=

$

52.00

$

6.50

x

=

$

32.50

x

=

5

Glad i could help! Sorry if i came out kinda weird lol

Answer:

Answer:

5 hours

Explanation:

$

6.50

(

3

)

+

$

6.50

x

=

$

52.00

$

19.50

+

$

6.50

x

=

$

52.00

$

6.50

x

=

$

32.50

x

=

5

Glad i could help! Sorry if i came out kinda weird lol

Answer:

22,332

Step-by-step explanation:

Put 6 where t is in the equation and do the arithmetic.

... y = 5500 ln(9·6 +4) = 5500 ln(58) ≈ 22,332

Answer:

The answer is: 22,332 mowers will be sold 6 years after a model is introduced.

Step-by-step explanation:

Given that y = 5500 ln (9t + 4)

In order to calculate the number of mowers (y) that will be sold after 6 years, substitute t = 6 (years):

y = 5500 ln (9 × 6 + 4) = 5500 In 58

In 58 = natural logarithm of 58 = 4.0604

Therefore, y = 5500 In 58 = 5500 × 4.0604 = 22,332.44 = 22,332 mowers.

Answer:

x = 3   and x=-6/5

Step-by-step explanation:

x = one integer

y = other integer

One integer is 9 less than 5 times another

x= 5y-9

product is 18

xy = 18

Substitute in for x

(5y-9) *y = 18

Distribute

5y*y -9y = 18

5y^2 - 9y = 18

Subtract 18 from each side.

5y^2 - 9y -18= 18-18

5y^2 - 9y -18 = 0

Using the quadratic formula

-b ± sqrt(b^2 -4ac)

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

2a

-(-9) ±sqrt(9^2 -4*5*(-18))

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

2(5)

9 ±sqrt(81 +360))

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

10

9 ±sqrt(441)

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

10

9±21

----------

10

x = (9+21)/10   and x = (9-21)/10

x = 30/10   and x = (-12)/10

x = 3   and x=-6/5

Final answer:

The two integers in question are 21 and 6, with 21 being 9 less than 5 times 6, and their product equating to 18.

Explanation:

Finding the Two Integers

The problem states that one integer is 9 less than 5 times another integer, and their product is 18. Let's call the first integer x and the second integer y.

From the problem, we can write two equations:

x = 5y - 9 (One integer is 9 less than 5 times the other)

xy = 18 (The product of the two integers is 18)

Using substitution from the first equation, in the second equation, we replace x with 5y - 9 and solve for y:

(5y - 9)y = 18

This equation leads to a quadratic equation: 5y^2 - 9y - 18 = 0. Factoring the quadratic equation, we find two pairs of numbers that multiply to give -18 and add up to -9: (-6) and 3.

The factors of the equation are (5y + 3)(y - 6) = 0, giving us y = 6 or y = -³/₅. However, since we are looking for integers, we disregard the fraction and only consider y = 6. Plugging y = 6 back into x = 5y - 9, we get x = 5(6) - 9 which simplifies to x = 21.

Therefore, the two integers are 21 and 6.

If Alex cut his wire 18 times, he ended up with 19 equal pieces. He kept 7, so has 7/19 of his 1/3 of the wire.

Bob cut his wire 20 times, so ended up with 21 pieces, of which he kept 9. So he has 9/21 = 3/7 of his 1/3 of the wire.

Claudia kept 1/13 of her 1/3 of the wire, so has the smallest piece.

Bob kept (3/7)·(1/3)·126 cm = 18 cm.

Alex kept (7/19)·(1/3)·126 cm ≈ 15.47 cm.

Bob kept the longest part of the original wire.

Answer:

y-2 = -(x-2)

Step-by-step explanation:

To find the slope

m = (y2-y1)/(x2-x1)  where (x1,y1) and (x2,y2) are two points on the line

    = (1-3)/(4-2)

   =-2/2

   =-1

The point slope form is

y-y1 = m(x-x1)  wher m is the slope and (x1,y1) is a point on the line

y-3 = -1(x-2)

y-2 = -(x-2)

Final answer:

The median is found by arranging a data set in ascending order and locating the middle value for an odd number of values or averaging the two middle values for an even number. Quartiles divide the data into sections and are related to the median. The median offers a measure of the center that is not skewed by outliers.

Explanation:

To find the median of a data set, start by arranging the data in ascending order. If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, calculate the median by taking the average of the two middle values.

For example, for the ordered data set 3, 4, 8, 8, ... 44, 44, 47, which has 40 values, the median is between the 20th value (24) and the 21st value (24). In this case, since they are the same number, the median is 24. However, if the two numbers were different, you would add them together and divide by two to find the median.

When considering a data set like 1, 1, 2, 2, 4, 6, 6.8, 7.2, 8, 8.3, 9, 10, 10, 11.5, with an even number of values (14), the median is the average of the 7th and 8th values, in this case, (6.8+7.2)/2 = 7. The quartiles can also be determined: Q1 is the median of the lower half, and Q3 is the median of the upper half of the data set.

Measures of the center of the data, like mean, median, and mode, offer different ways to represent the data set's central tendency. The median is particularly useful in data sets with outliers, as it is not as affected by extreme values as the mean.

Answer:

The length of a 180° arc of a unit circle is π ≈ 3.14 units.

Step-by-step explanation:

Use your knowledge of the circumference of a circle (the length full around) and the fact that there are 360° in the central angle of a full circle. The distance around is proportional to the angle, so an arc of measure 180° will have a length equal to

... (180°/360°) × circumference = (1/2)×circumference

For a unit circle, the circumference is 2π (= π×diameter = 2π×radius). Half that length is π units.

Answer:

A central angle of 180 degrees corresponds to half of the unit circle, and the circumference of the unit circle is 2π units. So, the distance traveled along the unit circle from the point (1, 0) is half of the circumference, which is 1/2 * 2π = π units. Thus, the answer is 3.14 units (approximately).