Coach Jones has a rope that is 36 feet long. He wants to divide it into 9 equal parts. Write an equation to find how long each part will be. Use a ? to represent the unknown number. Then solve the equation and explain how you determined the length of each part.

The two expressions that would have the same product as 3.5 x 5.12 are:

184.32 x 1/12

76.8 x 3/12

The product of a number is the value that is derived when two or more numbers are multiplied by each other.

Product of 3 and 5.12 is 15.36.

In order to determine what number should be multipled by 1/12 to yield 15.36, multiply 15.36 by 12: 15.36 x 12 = 184.32

In order to determine what number should be multipled by 3/12 to yield 15.36, multiply 15.36 by 4: 15.36 x 4 = 76.8

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The SSS Similarity Theorem states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are similar. This theorem is also known as the Side-Side-Side Similarity Theorem or the SSS Similarity Postulate.

What is the similarity theorem of triangles?

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle similarity is indicated here by the symbol (~).

SSS or Side-Side-Side Similarity.
If all three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.
Thus, if AB/XY = BC/YZ = AC/XZ then ΔABC ~ΔXYZ.
From this result, we can conclude that-
∠A = ∠X, ∠B = ∠Y and ∠C = ∠Z
Hence, we have described the SSS similarity theorem.

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The perimeter of the hexagon is the sum of its side lengths

The perimeter of the hexagon is 48.5 ft

The given parameters are:

\(\mathbf{Area = 169.74}\) --- the area of the hexagon

\(\mathbf{a = 7}\) -- the apothem

Let the perimeter of the hexagon be p.

So, the area is calculated as:

\(\mathbf{Area = \frac 12 pa}\)

Substitute values for Area and (a)

\(\mathbf{169.74 = \frac 12 \times p \times 7}\)

Multiply both sides by 2

\(\mathbf{339.48= p \times 7}\)

Divide both sides by 7

\(\mathbf{48.5= p }\)

Rewrite as:

\(\mathbf{p = 48.5}\)

Hence, the perimeter of the hexagon is 48.5 ft

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To solve for x at an angle, you must first understand what type of angle you are working with. If the angle is a right angle, you can use the Pythagorean theorem to solve for x. If the angle is an obtuse angle, you can use the law of cosines to solve for x. If the angle is an acute angle, you can use the law of sines to solve for x.

To solve for x at a right angle using the Pythagorean theorem, you must have the lengths of the two neighboring sides of the triangle. The sum of the squares of the two sides is equal to the square of the hypotenuse, according to the Pythagorean theorem. By rearranging the components and solving for x, this equation may be used to find x.

To use the law of cosines to solve for x at an obtuse angle, you must know the lengths of all three sides of the triangle. According to the law of cosines, the square of one side's length equals the sum of the squares of the other 2 sides minus twice the product of the other 2 sides multiplied by the cosine of the obtuse angle. You can use this equation to solve for x by rearranging the terms and solving for x.

To apply the law of sines to solve for x in an acute angle, you should first know the lengths of the triangle's two sides as well as the acute angle's measurement. According to the law of sines, the ratio of one side's length to the sine of the opposite angle equals the ratio of the other side's length to the sine of the acute angle. By rearranging the terms and solving for x, you may use this equation to solve for x.

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Answer:

mud

Step-by-step explanation:

Answer:

160 square inches

Step-by-step explanation:

You can split the irregular figure up into regular shapes:

the top 4x6 inch rectangle

the middle section can be a 18x6 rectangle (added 7+11 for the length)

the bottom 4x7 rectangle (sibtracted 10-6 for the width)

Then, find the area of each section with the equation A = lw.

A= 4(6) = 24 square inches

A = 18(6) = 108 square inches

A = 4(7) = 28 square inches

Add these areas up to get the total area of the irregular figure.

24 + 108 + 28 = 160 square inches

Answer:

8.57142857143

Step-by-step explanation:

12(5) = 60/7 = About 8.6

1/5=2/10=5/25

To get 2/10, since, in the denominators, to go from 5 to 10, you multiply 5 by 2, I multiplied 1 and 2 to get the answer.

For 5/25, to go from 1 to 5 you multiply 1 by 5, so you multiply 5 by 5, and that's 25, so the denominator for that fraction is 25.

Answer:

y = 1/2x -.5

Step-by-step explanation:

We know that is the line is parallel to the equation then the slopes are going to be the same we just have to find the a different y-intercept.

It's a simple as this just plug the points into the equation you have like this.

(-7,-4) (PLUG IN)

-4 = 1/2(-7) +b (I do plus be so we can get another y intercept)

-4 = -3.5 + b (add 3.5 on each side)

-.5 = b

the equation parallel to the first one is...

y = 1/2x -.5

Answer:

x = 9

Step-by-step explanation:

Assuming the rectangles are similar

13           x

------ = ---------

130         90

Using cross products

13*90 = 130*x

Divide each side by 130

13*90/130 = x

x = 9

Answer:

d cuz it said negative and only negative is d

The object will be 78.4 meters high after 2 seconds of launch.

We will put t = 2 in the equation to find the height.

s(2) = -4.9(2)² + 19.6(2) + 58.8s(2) = -4.9(4) + 39.2 + 58.8s(2) = -19.6 + 98s(2) = 78.4

Therefore, the object will be 78.4 meters high after 2 seconds of launch.

The formula to calculate the height of an object s(t) at time t seconds after launch is:s(t) = -4.9t² + 19.6t + 58.8where s is in meters.

Using this formula, we can find the height of the object after 2 seconds.

s(2) = -4.9(2)² + 19.6(2) + 58.8s(2) = -4.9(4) + 39.2 + 58.8s(2) = -19.6 + 98s(2) = 78.4

Therefore, the object will be 78.4 meters high after 2 seconds of launch.

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Answer:

a) \(C(t)=245,000\cdot(1.035)^t\)

b) Nicki's house is worth $281,143 in 4 years

Step-by-step explanation:

Exponential Growth Function

The exponential function is commonly used to model natural growing or decaying processes where the change is proportional to the actual quantity.

An exponential growth function is expressed as:

\(C(t)=C_o\cdot(1+r)^t\)

Where:

C(t) is the actual value of the function at time t

Co is the initial value of C at t=0

r is the growth positive rate, expressed in decimal

Nicki paid Co=$245,000 for a house and it's known that home prices increase by r=3.5%=0.035 each year.

a)

Substituting the given values, the equation is:

\(C(t)=245,000\cdot(1+0.035)^t\)

\(\mathbf{C(t)=245,000\cdot(1.035)^t}\)

b) The value of Nicki's house in t=4 years is:

\(C(4)=245,000\cdot(1.035)^4\)

\(C(4)=245,000\cdot 1.148=281,143\)

Nicki's house is worth $281,143 in 4 years

The number of values in each group of the data set would be equal to the degrees of freedom for each group plus one.

In order to determine the number of values in each group of the data set based on the partially completed ANOVA table, we need to consider the total number of observations and the number of groups.

The ANOVA table consists of three main components: "Source of Variation," "Sum of Squares (SS)," and "Degrees of Freedom (df)." The "Source of Variation" represents the different factors or groups in the data set, while the "Sum of Squares" measures the variability within each group. The "Degrees of Freedom" represents the number of independent pieces of information available for estimating the population parameters.

In this case, since all groups are of the same size, we can determine the number of values in each group by examining the "Degrees of Freedom" column. The degrees of freedom for each group is the group size minus one (df = group size - 1). By adding one to the degrees of freedom for each group, we obtain the number of values in each group.

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Answer:

12 inches of fabric

Step-by-step explanation:

Area of a triangle = hight x base

so 6 x 2 = 12

12 inches of fabric is your answer

Hope this helps :)

If she plans to cover the front with a piece of fabric. Then the amount of fabric that she needs will be 6 square inches.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

Sue bought a triangular-shaped piece of wood with a height is 6 inches and a base of 2 inches.

She plans to cover the front with a piece of fabric.

Then the amount of fabric that she needs will be

The amount of fabric is given by the area of the triangle.

The area of the triangle will be

Area = 1/2 x 2 x 6

Area = 6 square inches

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Answer:

\(2x - y = 1 \\ 2( - 1) - y = 1 \\ - 2 - y = 1 \\ y = - 3\)

Answer:

Step-by-step explanation:

Im not positive but,

2x - y = 1

2(-1) - ? = 1

Change it around

2(-1)= -2

-2 + 1= -1

Then (it bugged out)

Switch it back

(2×(-1))-1=

-3

-3 = y  its that or -1

I dont know if i did this right I'm using my class notes

Answer:

The answer would be based off of how many miles the dad went so if he went to say 140 miles then it would be 2 hours.

Step-by-step explanation:

Just go to your calculator and divide how many miles he went by 70 then it will give you the amout of hours he went.

Have a great day! :)

The percentage change from 150 -117 is 22%

First, we need to know that percentage is defined as the ratio of a number with 100.

It is represented with the symbol, '%'.

From the information given, we have that;

The numbers are 150 and 117

Then, the percentage change is expressed with the equation;

Percentage change = (original number - second number)/original number ×100/1

Substitute the values, we get;

Percentage change = 150 -117/150 ×100/1

Subtract the numbers, we have;

Percentage change = 33/150 ×100/1

Divide the values, we have;

= 0.22 ×100/1

Multiply the values, we have

= 22%

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Answer:

To answer the questions regarding Mokoena's and his brother's ages, we'll use the given information:

Mokoena is p years old.

His brother is twice his age.

2.1 How old is his brother?

Since his brother is twice Mokoena's age, his brother's age would be 2p.

2.2 How old will Mokoena be in 10 years?

To find Mokoena's age in 10 years, we add 10 to his current age: p + 10.

2.3 How old was his brother 3 years ago?

To find his brother's age 3 years ago, we subtract 3 from his brother's current age: 2p - 3.

2.4 What will their combined age be in q years' time?

To find their combined age in q years' time, we add q to the sum of their current ages: p + 2p + q = 3p + q.

Therefore, the answers are:

2.1 His brother's age is 2p.

2.2 Mokoena will be p + 10 years old in 10 years.

2.3 His brother was 2p - 3 years old 3 years ago.

2.4 Their combined age in q years' time will be 3p + q.

Step-by-step explanation:

Step-by-step explanation:

-9.382649173.62 if you do the math

Answer:

I'm not sure what answer your looking for exactly

Step-by-step explanation:

3(-3x+9x+30x) -3x³ -18²(-24x) combine like terms

3+12x-3x³-18x² subsitute x

-4: 3+(-4)-( -1728)-( -5184)=6867

-2: 3+(-24)-(216)-1296)=-1533

0: 3

Answer:

I think the answer is 16

Step-by-step explanation:

1. The expected net operating income each year from the water slide is $238,150.

2. The simple rate of return expected from the water slide is 12.5%.

Let us discuss in a detailed way:

⇒ To calculate the net operating income, we need to consider the additional revenue from increased attendance and subtract the incremental operating expenses.

The additional attendance from the water slide is estimated to be 50,000 people per year. With an admission price of $5.00 per person, the additional revenue would be $250,000 ($5.00 x 50,000).

The incremental operating expenses for the water slide amount to $126,800 ($95,000 + $5,800 + $14,600 + $11,400).

Therefore, the expected net operating income each year is $238,150 ($250,000 - $126,800).

⇒ The simple rate of return is calculated by dividing the average annual net income by the initial investment cost and expressing it as a percentage.

The average annual net income is calculated by subtracting the annual operating expenses from the additional revenue generated. In this case, the average annual net income is $113,350 ($238,150 - $124,800).

The initial investment cost is $525,000.

Using these values, the simple rate of return is 21.6% ($113,350 / $525,000).

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Let x= the average for all three classes combined. So x=85.25.

When you add two or more numbers and divide the result by the number of numbers you added together, you obtain an average.

The arithmetic mean is determined by adding a collection of numbers, dividing by their count, and obtaining the result.

average  =  total points / number of students

total points = average*number of students

Let the total number of students in  each class = a , b  and x

The total number of points the first class amassed  was   80a

The total number of points amassed by the second class was  85b

The total number of points amassed by the third class = 89c

For the first two classes we have

[ 80a + 85b ] / [ a + b] = 83

80a + 85b = 83a + 83b  

subtract  80a, 83b from both sides    

3a = 2b

a = 2/3b

For the second two classes we have

[ 85b + 89c ]  / [ b + c ]  =  87  

[  85b + 89c ]  = 87 [b + c]

85b + 89c = 87b + 87c      

subtract  85b, 87c from both sides

2c = 2b  

b  = c

For the three classes.....

Total points by all three classes /  number of class members  = the average for all three classes

[ 80a + 85b  + 89c ] /  [ a + b + c ]   =[sub for  a and c ]  

[80 (2/3)b  + 85b  + 89b]  /  [ (2/3)b  + b  + b ]  

b [ 80 (2/3)  + 85  + 89 ]  / [  b [( 2/3) + 1 + 1] ]       [cancel the b's ]

[ 80 (2/3) + 85 + 89]  [  8/3 ]

[ 160/3 + 85 + 89 ] /  [8/3] =

[ 160/3  + 255/3 + 267/3]  / [8/3]     multiply  top/bottom by 3

[160 + 255 + 267 ] / 8  =  

85.25  = average for all three classes

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Answer:

-5 > -18

Step-by-step explanation:

The lower the negative number the higher it's value

Answer:

B

Step to Step Explaintion:

The natural logarithm is commonly used to approximate growth rates in various fields such as finance, economics, and biology. However, there are potential problems that can arise when using the natural logarithm for this purpose. Some of these problems include:

1. Non-linear growth: The natural logarithm assumes a constant growth rate over time, which may not accurately represent real-world scenarios. In many cases, growth rates may change over time, leading to non-linear patterns that cannot be accurately captured using the natural logarithm.
2. Negative growth rates: The natural logarithm cannot handle negative growth rates. If a variable experiences negative growth, such as a population declining or a stock losing value, the natural logarithm will produce an undefined result. This limitation can hinder the use of the natural logarithm in situations where negative growth rates are present.
3. Sensitivity to small changes: The natural logarithm is highly sensitive to small changes in values. This means that even a slight deviation in the growth rate can result in a significant difference in the calculated approximation. This sensitivity can introduce errors and inaccuracies in the estimation of growth rates.
4. Lack of interpretability: While the natural logarithm provides a mathematical approximation of growth rates, it may not always have a clear interpretation in real-world terms. For example, if the natural logarithm yields a growth rate of 0.05, it may not be immediately obvious what this means in practical terms. This lack of interpretability can make it challenging to communicate and understand the results.

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Please mark brainliest this took a while to make!

Answer:

622

Counting the terms already shown, we would need 59 more. Since each term adds ten, let's make each term 10 added to the previous.

2,12,22,32,42,52,62,72,82,92,102,112,122,132,142,152,162,172,182,192,202,212,222,232,242,252,262,272,282,292,302,312,322,332,342,352,362,372,382, 392,402,412,422,432,442,452,462,472,482,492,502,512,522,532,542,552, 562,572,582,592,602,612,622