a. Find SL
Explain your reasoning.

b. Explain how the captain can use a similar process to find the distance between the boat and the shoreline.​

Lisa manages to cycle 56.52 m before falling off if the diameter of the wheel of a unicycle is 0.6m.

The circumference of a circle refers to the straight line distance around it. In other words, if you open a circle and draw a straight line, the length of that line will be the circumference. The circumference is the total distance around the circle. Then find the perimeter using the formula C = 2πr.

Given,

Diameter of the wheel of a unicycle = 0.6 m

Radius of the wheel of a unicycle = 0.3 m

Number of revolutions before falling off = 32

Circumference (C) = 2 x pi x radius

= 2 × π × r

= 2 × 3.14 × 0.3

= 1.884 m

Total distance travelled by Lisa = 30 × 1.884

= 56.52 m

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Answer:

y = 3(x-1) + 3

This is because the 1 equals h in this equation and 3 equals k, which will give you the point (1,3)

The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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Answer:

\(\frac{\sqrt[4]{30} }{3}\)

Step-by-step explanation:

Answer:

The amount in the account after 11 years is $134,963.29

Step-by-step explanation:

Here, we want to determine the amount in the account after 11 years

What we have to do here is to substitute P for the amount invested which is $73,700

r is the rate given as 5.5% = 5.5/100 = 0.055

t is the time given as 12 years

substituting these values, we have;

V = 73,700 * e^(12* 0.055)

V = $134,963.29

Answer:

The answer is B

Step-by-step explanation:

Since we already know that angle A and D are congruent, if angles C and F were also congruent, we can prove the triangles are similar through AA, meaning the triangles have 2 sets of corresponding congruent angles. The other option D doesn’t work because if we were going off on using the sides as a way to prove similarly, than all 3 sides of one triangle would need to be proportional and corresponding to the other 3 of the other triangle (which is not given, so that info isn’t enough, option D only gives us 2 sides of each triangle)

Hope this helped ~~

Answer:

x=6

Step-by-step explanation:

(5x+30)+80=140

5x+110=140

5x=30

x=6

answer: B

Answer:

5 nights

Step-by-step explanation:

39 divided by 3 = 13

so we divided 65 by 13 hence your answer 5 nights

The required scale factor for the resized image is 110.25:1.

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
The original photo is 4 inches by 6 inches.
The dimensions of the resized image is 3.5 ft by 5.25 ft,
1 feet = 12 inches

As of the definition mentioned above

Scale factor = 3.5 × 12 × 5.25 × 12 / 4×6
Scale factor = 110.25:1

Thus, the required scale factor for the resized image is 110.25:1.

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2+2+3=7

7/3=2.33

2.33/3=0.78 hours

46 minutes 12 second

It would take them 46 minutes 12 seconds to clean the car if they worked together.

Answer:

45 min

Step-by-step explanation:

Answer:

$7.03

Step-by-step explanation:

Answer:

26.5%

Step-by-step explanation:

Answer:

i am only here for the points

Step-by-step explanation:

Answer:

Roughly 16 million bacteria.

Step-by-step explanation:

Multiply the rate of the bacteria going through mitosis times the amount of daughter cells per hour, for this case.

r x (m)ms x hr = bacteria in one day

Hope this helps!

note: ms and hr are millisecond and hour

The cost of nails can be represented as 12.99n, and the cost of screws can be represented as 14.99s.

The cost of buying nails and screws can be represented by a system of inequalities where "n" represents the number of boxes of nails and "s" represents the number of boxes of screws.

The cost of one box of nails is $12.99 and the cost of one box of screws is $14.99. Hence, the cost of "n" boxes of nails is represented by 12.99n and the cost of "s" boxes of screws is represented by 14.99s. The carpenter has a budget of $60 and can spend no more than that.

Therefore, the combined cost of buying nails and screws must be less than or equal to $60. This requirement can be represented by the inequality 12.99n + 14.99s <= 60.

To make the calculation easier, we can also express the inequality as n + s <= 4.62, where 4.62 is obtained by dividing $60 by $12.99. This system of inequalities represents the carpenter's budget constraint and helps to determine the number of boxes of nails and screws that can be purchased within the budget.

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x intercept(y=0)

4y-3x=108

4×0-3x=108

-3x=108

x=108/-3

x=-36

y intercept(x=0)

4y-3×0=108

4y=108

y=108/4

y=27

Answer:

The answer is 28 1/3. So, the bottom right option

Answer:

6

Step-by-step explanation:

15 = 5/2x

15 = 5x/2

30 = 5x

x = 6

Step-by-step explanation:

If f(x)=2x²-5x-3 g(x)=2x²+5x+2 then (f/g)(x) = (x - 3) / (x + 2).

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

To find (f/g)(x), we need to divide f(x) by g(x) as follows:

f(x) = 2x² - 5x - 3

g(x) = 2x² + 5x + 2

f(x) / g(x) = (2x² - 5x - 3) / (2x² + 5x + 2)

To simplify this expression, we can factor the numerator and denominator:

f(x) / g(x) = [(2x + 1)(x - 3)] / [(2x + 1)(x + 2)]

Now, we can cancel out the common factor of (2x + 1) from both the numerator and denominator:

f(x) / g(x) = (x - 3) / (x + 2)

Therefore, (f/g)(x) = (x - 3) / (x + 2).

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Answer:m is greater than or equal to 1/2

Step-by-step explanation:

Subtract the two equations to eliminate g :

(3g + h) - (3g - 2h) = (5   1/5) - (-6   4/5)

3h = (5   1/5) + (6   4/5)

Write the mixed numbers as improper fractions with a common denominator and solve for h :

3h = (25/5 + 1/5) + (30/5 + 4/5)

3h = 26/5 + 34/5

3h = 60/5

3h = 12

h = 12/3

h = 4

Solve for g :

3g + h = 5   1/5

3g + 4 = 5   1/5

3g + 4 = 26/5

3g = 26/5 - 4

3g = 26/5 - 20/5

3g = 6/5

g = (6/5)/3

g = 2/5

False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

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The two non zero roots of the equation sin x - x² + 1/2 = 0 are - 0.375 and 1.1875.

Given the function is,

f(x) = sin x - x² + 1/2

f(0) = 0.5 > 0

and f(-1) = sin (-1) - 1 + 1/2 = - 1.3415

So the root is between 0 and - 1.

So the first iteration is,

x₁ = (-1 + 0)/2 = - 0.5

f(x₁) = f(-0.5) = sin (-0.5) - (-0.5)² + 1/2 = - 0.2294 < 0

Second iteration is,

f(0) > 0 and f(-0.5) < 0

So the root is between 0 and - 0.5.

x₂ = (- 0.5 + 0)/2 = -0.25

Now, f(-0.25) = 0.1901 > 0

So the third root is in between -0.25 and - 0.50.

So, third iteration is, x₃ = (-0.25 - 0.5)/2 = - 0.375

Hence the first root is - 0.375.

For second root:

f(x) = sin x - x² + 1/2

Now,

f(1) = 0.3415 > 0

f(1.5) = - 0.7525 < 0

First iteration is,

x₁ = (1 + 1.5)/2 = 1.25

f(1.25) = - 0.1135 < 0

Second iteration is,  x₂ = (1 + 1.25)/2 = 1.125

f(1.125) = 0.1366 > 0

So third iteration is,  x₃ = (1.125 + 1.25)/2 = 1.1875

Hence the second root 1.1875.

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There is no real number that satisfies this equation, so there are no real solutions to the given equation. the equation √2y² - √(-2y) - 1 = 0 has complex solutions or imaginary solutions.

a) Solve by factoring √7 - 12√2 + 36 = 0:

To solve this equation, we can rewrite it as (√7 - 6√2)² = 0. Applying the square of a binomial formula, we have (√7 - 6√2)² = 0. Expanding the equation, we get (√7)² - 2(√7)(6√2) + (6√2)² = 0. Simplifying further, 7 - 12√14 + 72 = 0. Combining like terms, we have -12√14 + 79 = 0. Isolating the radical term, we get -12√14 = -79. Dividing both sides by -12, we have √14 = 79/12. However, there is no real number that satisfies this equation, so there are no real solutions to the given equation.

b) State the number(s) and type of solution(s) for the equation √2y² - √(-2y) - 1 = 0:

The equation √2y² - √(-2y) - 1 = 0 can be simplified by considering the nature of the terms involved. Since the term √(-2y) involves the square root of a negative number, it indicates the presence of imaginary solutions. Therefore, the equation √2y² - √(-2y) - 1 = 0 has complex solutions or imaginary solutions.

c) The statement seems to be incomplete. The system of equations is not provided, so it is not possible to solve or provide an answer for part c. If you can provide the missing equations, I will be happy to assist you in solving the system.

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Answer:

y = (2x/3) - 3

Step-by-step explanation:

parallel means same slop

y=2x/3 + b

-9 = -6 + b

b = -3

therefore y = (2x/3) - 3

Answer:

y = 2/3x - 3

Step-by-step explanation:

let's put equation into slope-intercept form first, which is y=mx+b where 'm' is the slope and 'b' is the y-intercept

y-8 = 2/3x

y = 2/3x+8

parallel lines have equal slopes, so we know our equation must have a slope of 2/3

now use (-9,-9) to find 'b':

-9 = 2/3(-9) + b

-9 = -6 + b

-3 = b

put it together:

y = 2/3x - 3

Answer:

3x+15\(\leq\)7

Step-by-step explanation:

The equation form of the given statement would be 3n + 15 ≤ 7.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

The given statement is "Fifteen more than three times a number is

at most 7"

Let the unknown number be n.

So, the equation form;

3n + 15 ≤ 7

Where n =unknown number

Hence, the equation form of the given statement would be 3n + 15 ≤ 7.

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