Which pair of adjacent angles is complementary?

Final answer:

The sine of the angle between the ground and the line connecting the top of the shadow to the top of the tree, given a 50-foot tree and a 9-foot shadow, is approximately 0.984, calculated using the definition of sine in a right triangle and the Pythagorean theorem.

Explanation:

The question involves finding the sine of the angle between the ground and the line connecting the top of the shadow to the top of the tree, given that a 50-foot tree casts a 9-foot long shadow. In this scenario, we can visualize a right triangle where the tree represents the opposite side (height), the shadow represents the adjacent side (base), and the hypotenuse is the line from the top of the tree to the end of the shadow on the ground.

To find the sine of the angle, we use the definition of sine in a right triangle, which is sine(angle) = opposite / hypotenuse. However, before we can do that, we need to determine the length of the hypotenuse using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a² + b² = c²).

Let's calculate:

a (opposite) = 50 feet (Height of the tree)

b (adjacent) = 9 feet (Length of the shadow)

c (hypotenuse) = √(50² + 9²) = √(2500 + 81) = √2581 = 50.8 feet (approximately)

Now, we can calculate the sine of the angle:

sine(angle) = opposite / hypotenuse = 50 / 50.8 ≈ 0.984

Therefore, the sine of the angle between the ground and the line connecting the top of the shadow to the top of the tree is approximately 0.984.

Answer:

The total weight of the water in a full tank, to the nearest pound is 3527 pounds per cubic foot

Step-by-step explanation:

Given:

Diameter  of the hemispherical tank = 6 feet

Weight of water per cubic foot =  62. 4 pounds

To Find:

The total weight of the water in a full tank, to the nearest pound?

Solution:

We know that the volume of a sphere is:

[tex]V =\frac{4}{3}\pi r^3[/tex]

where  

r = is the radius

In the question we are given with diameter,

So

[tex]radius = \frac{diameter}{2}[/tex]

radius = [tex]\frac{6}{2}[/tex]

Radius = 3

We need the volume of the hemisphere

So the volume of the hemisphere will be half of the volume of teh sphere

[tex]\frac{V}{2} = \frac{2}{3}\pi r^3[/tex]

Thus the volume of the hemisphere is

[tex]V =\frac{2}{3} \pi r^3[/tex]

Now substituting the values

[tex]V = \frac{2}{3} \pi(3)^3[/tex]

[tex]V = \frac{2}{3}\pi(27)[/tex]

[tex]V = \frac{54 \pi}{3}[/tex]

[tex]V = \frac{169.56}{2}[/tex]

V=  56.52 cubic foot

Now, the total weight of water of:

W =  56.52 x 62.4

W= 3526.848 pounds per cubic foot

To the nearest pounds

W= 3527 pounds per cubic foot

Answer:

3529

Step-by-step explanation:

If you are here from delta math this is the Answer

Answer: Yes.

Step-by-step explanation: if y=12, then 24-12=24 aka 24-y=12

Answer:

Frosts second mile and steadys 6th mike

Step-by-step explanation:

Part A: The two plans will cost the same amount when the distance to the airport is 12 miles.

Part B: For a 20-mile distance, Mr. Gardner should choose Fost Shuttle, costing $10 compared to $12 for Steady Shuttle.

Let's solve Part A first:

Part A:

Let's denote the distance to the airport as d miles.

For Fost Shuttle:

Cost = Pick-up fee + Cost per mile × Distance

Cost = $5 + $0.25 × d

For Steady Shuttle:

Cost = Pick-up fee + Cost per mile × Distance

Cost = $2 + $0.50 × d

Now, we'll set up an equation to find when the two plans cost the same amount:

[tex]\[5 + 0.25d = 2 + 0.50d\][/tex]

Solving for d:

[tex]\[0.25d - 0.50d = 2 - 5\]\[-0.25d = -3\]\[d = \frac{-3}{-0.25}\]\[d = 12\][/tex]

So, the two plans will cost the same amount when the distance is 12 miles.

For Part B:

Given the distance is 20 miles, let's calculate the cost for each company:

For Fost Shuttle:

Cost = $5 + $0.25 × 20 = $5 + $5 = $10

For Steady Shuttle:

Cost = $2 + $0.50 × 20 = $2 + $10 = $12

Comparing the costs, Mr. Gardner should choose Fost Shuttle as it costs $10 compared to $12 for Steady Shuttle.

Answer:

Ms. Griffiths lives on 3rd floor

Step-by-step explanation:

The elevator moves 10.2 seconds from one floor to another and stops for 45.8 seconds for people to exit. Thus, add: 10.2 seconds + 45.8 seconds = 56 seconds

If it takes her 158 seconds to travel from the lobby to her apartment, then 158 seconds/56 seconds = 2.8 = 3 (approximately).

Therefore, she lives on 3rd floor.

Mathematically, the values ought to be 168 seconds /56 seconds = 3.

Answer:

The migration of the African-Americans to Harlem in the USA empowered the African-Americans in the society in the early 1900s. This was one of the greatest accomplishments of the African-Americans in history.

Explanation:

The "Harlem Renaissance" was originally called the "New Negro Movement." During the "Reconstruction Era," many of the African Americans felt a newfound empowerment in the society. They started leaving the South, where most of them were enslaved and maltreated. Many of them moved to other places such as "Harlem" in New York City. It became an ideal destination for many "Negros" and their number increased over time. This then became an African-American neighborhood.

African-Americans started producing plays with actors of their descent. Several Negro poets emerged describing the life of the African-Americans. Negros became more literate and able when it comes to expressing themselves in the society. They even had their own newspaper known as "The New Negro Movement."

Answer:

y=-6x-2

Step-by-step explanation:

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

m=(10-(-2))/(-2-0)

m=(10+2)/(-2)

m=12/-2

m=-6

y-y1=m(x-x1)

y-(-2)=-6(x-0)

y+2=-6(x)

y+2=-6x

y=-6x-2

Answer:

If you want the mixed number,it is 7 1/9

Step-by-step explanation:

Divide using long division. The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction.

Answer:

Step-by-step explanation:

total capacity = 62.5 GB

available capacity = 35.0 GB

35 is what percent of 62.5

35 = x% * 62.5

35 / 62.5 = x%

0.56 = x%

56% = x <=====

56% of the memory capacity is still available.

To calculate the percentage of memory capacity that is still available, we can use the available capacity and total capacity information provided.

Given:

Capacity: 62.5 GB

Available: 35.0 GB

To find the percentage, we divide the available capacity by the total capacity and multiply by 100:

Percentage = (Available / Capacity) x 100

Percentage = (35.0 GB / 62.5 GB) x 100

Percentage ≈ 56%

Therefore, 56% of the memory capacity is still available.

Learn more about Percentage here:

https://brainly.com/question/32197511

#SPJ2

By calculating the shipping fees for regular and rush delivery for a 26.5 pound computer, we find that regular shipping saves approximately 14.90 dollars.

We must first calculate the fee for each method and then subtract the regular "shipping fee" from the rush delivery fee to find the savings.

Using the given expression, the regular shipping fee for a 26.5 pound computer is: 0.5*26.5 + 4.49 = 17.74 dollars. Meanwhile, the rush delivery fee for the same computer, using the other given expression, would be: 0.99*26.5 + 6.49 = 32.635 dollars.

Subtracting the regular fee from the rush fee, we find: 32.635 - 17.74 = 14.895 dollars. Therefore, you save about 14.90 dollars by choosing regular shipping over rush delivery.

https://brainly.com/question/32022597

#SPJ2

The correct answer is: When triangle ABC is translated 2 units to the left and 1 unit down to create triangle A'B'C' , the coordinates for B' are (-1, 0). The true statement is D.

Let's analyze each statement:

A; When triangle ABC is reflected over the y-axis to create triangle A'B'C' , the coordinates for B' are (1, -1) .

To reflect over the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. If the coordinates for B are (x, y), then after reflecting, the x-coordinate becomes -x. Since B has coordinates (1, 1), after reflection, B' will have coordinates (-1, 1). So, statement A is false.

B; When triangle ABC is rotated 90 degrees clockwise about point A to create triangle A'B'C' , the coordinates for B' are (3,3]

Rotation of 90 degrees clockwise about a point involves swapping x and y coordinates and negating the new x-coordinate. The point A is not given, but assuming it's (0, 0), if B has coordinates (x, y), then after rotation, B' will have coordinates (y, -x). If A is (0, 0) and B is (3, 1), after rotation, B' will have coordinates (1, -3), not (3, 3). So, statement B is false.

C; When triangle ABC is dilated from the origin by a scale factor of 1/4 to create triangle A'B'C', the coordinates for B' are (4,4)

Dilating by a scale factor of 1/4 means multiplying each coordinate by 1/4. If B has coordinates (x, y), then after dilation, B' will have coordinates (1/4 * x, 1/4 * y). Since B has coordinates (4, 4), after dilation, B' will have coordinates (1, 1). So, statement C is false.

D; When triangle ABC is translated 2 units to the left and 1 unit down to create triangle A'B'C' , the coordinates for B' are (-1, 0)

Translation involves adding/subtracting values to x and y coordinates. If B has coordinates (x, y), then after translation by (-2, -1), B' will have coordinates (x - 2, y - 1). Since B has coordinates (1, 1), after translation, B' will have coordinates (-1, 0). So, statement D is true.

E; When triangle ABC is dilated from the origin by a scale factor of 5 to create triangle A'B'C', the coordinates for B' are (5,5)

Dilating by a scale factor of 5 means multiplying each coordinate by 5. If B has coordinates (x, y), then after dilation, B' will have coordinates (5 * x, 5 * y). Since B has coordinates (4, 4), after dilation, B' will have coordinates (20, 20), not (5, 5). So, statement E is false.

So, the true statement is D.

The vertical asymptote of the function f(x) = 3 log(x + 3) is x = -3

Step-by-step explanation:

A symptote is a line that a curve approaches but never touches

∵ f(x) = 3 ㏒(x + 3)

∵ The argument is (x + 3)

- Equate the argument by zero

∵ x + 3 = 0

- Subtract 3 from both sides

∴ x = -3

- The vertical asymptote of a logarithmic function is at the zero

  of the argument

∴ The vertical asympotote of f(x) is x = -3

The vertical asymptote of the function f(x) = 3 log(x + 3) is x = -3

Learn more:

You can learn more about the logarithmic functions in brainly.com/question/11921476

#LearnwithBrainly

Answer:

-3

Step-by-step explanation:

plato

Answer:        [tex]x=9[/tex]

Step-by-step explanation:

Alright, lets get started.

[tex]log_{6}4x^2-log_{6}x=2[/tex]

Using the property of logs : [tex]log (m) - log(n)=log\frac{m}{n}[/tex]

[tex]log_{6}\frac{4x^2}{x}=2[/tex]

[tex]log_{6}4x=2[/tex]

Using the property of logs : [tex]if \ log_{a}m=n, \ then \ a^n=m[/tex]

So,

[tex]6^2=4x[/tex]

[tex]4x=36[/tex]

Dividing 4 in both sides

[tex]x=9[/tex]   ......................   Answer

Hope it will help :)

Answer:

x = 9

Step-by-step explanation:

Determine the defined range

[tex]log^6 (4x^2) - log^6 (x) = 2, x = (0, + ∞)[/tex]

Use log^a (x) - log^a (y) = log^a (x/y) to simplify the expression

[tex]log6 (\frac{4x^{2} }{x} )= 2[/tex]

Simplify the expression

log^6 (4x) = 2

Convert the logarithm into an exponential form using the fact that log^a (x) = b is equal to x = a^b

[tex]4x=6^{2}[/tex]

Evaluate the power

4x = 36

Divide both sides of the equation by 4

x = 9, x = (0, + ∞)

Check if the solution is the defined range

x = 9

Final answer:

The independent variable in the scenario is the time spent baking, and the dependent variable is the number of cookies baked. The size of the oven might be another independent variable if comparing productivity between different bakeries.

Explanation:

In the context of the question where a baker bakes 40 cookies in an hour, we are being asked to identify the dependent and independent variables in this scenario. First, let's define these terms:

In this particular case, the independent variable could be the time spent baking, because it is what the baker controls. The dependent variable is the number of cookies baked, which depends on the amount of time the baker spends baking. If, for example, the baker decides to bake for two hours instead of one, we would expect the number of cookies baked to potentially double, assuming productivity remains constant.

In a different scenario, where comparing the productivity of bakers with different oven sizes – such as a Canadian worker with an industrial-size oven versus a U.S. worker with a smaller oven – the size of the oven could be seen as the independent variable affecting the dependent variable of productivity measured by the output of loaves of bread in an hour.

Answer:

Step-by-step explanation:

(7,2) , (0,0)

slope = (y2 - y1) / (x2 - x1) = (0 - 2) / (0 - 7) = -2/-7 = 2/7

y = mx + b

slope(m) = 2/7

(0,0)...x = 0 and y = 0

now sub

0 = 2/7(0) + b

0 = b

ur equation is : y = 2/7x + 0.....same as y = 2/7x <====

The equation of the line is y = ( 2/7 )x where the slope is m = 2/7

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 7 , 2 )

Let the second point be Q ( 0 , 0 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 2 - 0 ) / ( 7 - 0 )

m = 2/7

Now , the equation of line is y - y₁ = m ( x - x₁ )

On simplifying , we get

y - 0 = ( 2/7 ) ( x - 0 )

y = ( 2/7 )x

Hence , the equation of line is y = ( 2/7 )x

To learn more about equation of line click :

https://brainly.com/question/14200719

#SPJ6

Through algebra, we found that Xavier's current age is 61, which makes Yolanda 65. Subtracting the 40 years of marriage from their current ages, we determined that Yolanda was 25 years old when they got married.

The question given by the student is a problem that can be solved with simple algebra. To find out how old Yolanda was when they married, we first need to establish the current ages of Xavier and Yolanda based on the information given.

Let's denote Xavier's current age as x years. Consequently, Yolanda's current age will be x + 4 years (since she is 4 years older than Xavier). According to the problem, the sum of their ages now is 126 years. We can set up the following equation based on this information:

x + (x + 4) = 126

By solving the equation:

Combine like terms: 2x + 4 = 126

Subtract 4 from both sides: 2x = 122

Divide both sides by 2: x = 61

This means that Xavier is now 61 years old, and Yolanda is x + 4, which is 65 years old. Since they have been married for 40 years, we subtract 40 from their current ages to get their ages at the time they got married. So, Yolanda was 25 years old when she got married.

Answer:

Therefore the Speed of a wave is 340 m/s.

Step-by-step explanation:

Given:

Wave Length = 5 m

Frequency = 68 hertz

To Find:

Speed = ?

Solution:

Wave Speed:

Wave speed is the distance a wave travels in a given amount of time, such as the number of meters it travels per second.

Wave speed is related to wavelength and wave frequency.

The Formula is given by

[tex]Speed = Wavelength\times Frequency[/tex]

Substituting the values we get

[tex]Speed = 5\times 68=340\ m/s[/tex]

Therefore the Speed of a wave is 340 m/s.

Answer:

D.  -2.

Step-by-step explanation:

2(x-4) + 3x - x2 for x = 3

= 2(3-4) + 3(3) - 3^2

= 2(-1) + 9 - 9

= -2 + 9 - 9

= -2.

Answer: 4 5/14

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\text{Let}\\\\x-\text{number of wrapping paper of Mr. Smith's class}\\y-\text{number of magazines of Mr. Davis' class}\\\$3.50x-\text{the amount obtained from the sale of wrapping paper}\\\$2.75y-\text{the amount obtained from the sale of magazines}[/tex]

[tex]\bold{SYSTEM\ of\ EQUATIONS:}\\\\\left\{\begin{array}{ccc}x+y=72&\text{subtract}\ y\ \text{from both sides}\\3.5x+2.75y=222\end{array}\right\\\\\left\{\begin{array}{ccc}x=72-y&(1)\\3.5x+2.75y=222&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\3.5(72-y)+2.75y=222\qquad\text{use the distributive property}\\\\(3.5)(72)+(3.5)(-y)+2.75y=222\\\\252-3.5y+2.75y=222\qquad\text{substract 252 from both sides}\\\\-3.5y+2.75y=222-252\qquad\text{combine like terms}[/tex]

[tex]-0.75y=-30\qquad\text{divide both sides by (-0.75)}\\\\\boxed{y=40}\\\\\text{Put it to (1):}\\\\x=72-40\\\\\boxed{x=32}\\\\\$3.5x=\$3.5\cdot32=\$112\\\\\$2.75\cdot40=\$110\\\\\$112-\$110=\$2[/tex]

Answer:

7 - 3[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Given

3 + [tex]\sqrt{x+7}[/tex] - [tex]\sqrt{3x}[/tex] ← substitute x = 9

= 3 + [tex]\sqrt{16}[/tex] - [tex]\sqrt{27}[/tex]

= 3 + 4 - [tex]\sqrt{9(3)}[/tex]

= 7 - 3[tex]\sqrt{3}[/tex]

Answer:

It is important to use mixed numbers in real life, because it can help you find the measurements for when you are buying ingredients or baking something.

Hope this helps ;)

Step-by-step explanation:

Answer:

Total: 40

Mean: 8

Step-by-step explanation:

To find the total, we add the numbers together and get 40. Then, to find the mean, we take the total and divide by the number of numbers, which is 5, to get our answer: 8

-AXZ

Answer:

1989xsquared y + 585xsquared+ 2618xy + 770x - 8075y - 2375

Step-by-step explanation:

(9x + 25) x (13x - 19) x (17y + 5)

(117x squared - 171x + 325x - 475) x (17y + 5)

(117x squared + 154x - 475) x (17y + 5)

[tex](9x + 25) (13x - 19) (17y + 5)=1989x^2y + 585x^2+ 2618xy + 770x - 8075y - 2375[/tex]

We have to simplify the expression:

(9x + 25)(13x - 19)(17y + 5)

Multiply the first two expressions as

[tex][9x(13x - 19)+25(13x - 19)](17y + 5)[/tex]

[tex]=(117x^2 - 171x + 325x - 475)(17y + 5)[/tex]

[tex]=(117x^2 + 154x - 475)(17y + 5)[/tex]

[tex]=17y(117x^2 + 154x - 475) + 5(117x^2 + 154x - 475)\\=1989x^2y + 585x^2+ 2618xy + 770x - 8075y - 2375[/tex]

Therefore after simplifying , we get

[tex](9x + 25) (13x - 19) (17y + 5)=1989x^2y + 585x^2+ 2618xy + 770x - 8075y - 2375[/tex]

Learn more:https://brainly.com/question/16684541  

Answer:theres nothimh here to answer

Step-by-step explanation:

y < –12

Solution:

Step 1: Given inequality is y + 15 < 3.

To find the solution to the inequality.

Step 2: Subtract –15 on both sides to equal the expression.

⇒ y + 15 –15 < 3 –15

Step 2: Using addition identity property, any number adding with zero gives the number itself.

⇒ y + 0 < –12

⇒ y < –12

Hence the solution to the inequality is y < –12.

Answer:

Step-by-step explanation:

It’s b

Answer:

The person up there is right just saying:)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is 1.2, you want to replace the x with the 6.3 and then the -7.5 ends up turning into a positive. You then add the two together -6.3 + 7.5 = 1.2