consider the right triangle below:
the length of the missing leg, ac = ____ meters
round your answer to the nearest tenth

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.

Learn more about Scheme function: https://brainly.com/question/33167627

#SPJ11

we know that 76% of the specialty soaps are made with fresh herbs, and we also know that there are a total of 350 specialty soap bars, so how many are made with fresh herbs?  well, just 76% of those 350

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{76\% of 350}}{\left( \cfrac{76}{100} \right)350}\implies 266\)

Answer:

-17 =s

Step-by-step explanation:

-8s +4 = -7s +21

Add 8s to each side

-8s+8s +4 = -7s+8s +21

4 = s+21

Subtract 21 from each side

4-21 = s+21-21

-17 =s

Answer:

s = -17

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

-8s + 4 = -7s + 21

Step 2: Solve for s

Answer:

x = 2 or x = 3

Step-by-step explanation:

we have the expression:

First we must remove the square root, for this we pass the 2 to the left:

and we move the square root to the left as an exponent of two:

We develop the square binomial:

and clear the right side for the equation to be equal to zero:

combining like terms:

Because it is a quadratic equation we will have two answers, which we can find by the general formula or by factoring:

To factor we open two parenthesis, both with an x, and look for two numbers that when multiplied result in +6 and when added result in -5, those numbers are -2 and -3, so the factoring is:

And now we use the Zero Product Property, whic is if two thing are multiplied and result in zero one of the two or both things must zero, in this case:

and

the solutions are: x = 2 or x = 3; both satisfy the equation.

The solutions for the given equation are x=2 or x=3. Therefore, option C is the correct answer.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is x=2+√(x-2).

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

For the given equation squaring on both side, we get

x-2=√(x-2)

(x-2)²=(x-2)

x²-4x+4=x-2

x²-5x+6=0

By using middle term method, we get

x²-3x-2x+6=0

x(x-3)-2(x-3)=0

(x-3)(x-2)=0

x=3 or x=2

Therefore, option C is the correct answer.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ2

14 inches is closest to the length of the diagonal in inches. Therefore, the answer is 14.

Given, the dimensions of a rectangular piece of paper are 8.5 and 11 inches.

We need to find which measurement is closest to the length of the diagonal in inches.

To find the diagonal, we will use the Pythagorean theorem.

It states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

So, the diagonal of the rectangle = √(8.5² + 11²) = √(72.25 + 121) = √193.25 ≈ 13.89 inches.

Approximately, 14 inches is closest to the length of the diagonal in inches. Therefore, the answer is 14.

To know more about Pythagorean theorem, visit:

https://brainly.com/question/14930619

#SPJ11

Statement (c) is correct for a simple graph. Every trail is a path, and every path is a trail.

In graph theory, a simple graph is an undirected graph with no loops or multiple edges between the same pair of vertices. A path in a graph is a sequence of vertices where each consecutive pair is connected by an edge. A trail in a graph is a path that allows for repeated vertices and edges.

Statement (a) is not correct because not every path is a trail. A path does not allow for repeated vertices or edges, whereas a trail does.

Statement (b) is not correct because not every trail is necessarily a path. A trail may contain repeated vertices or edges, but a path does not.

Statement (d) is not correct because paths and trails do have a relation. A trail is a more general concept that encompasses paths by allowing for repetition of vertices and edges.

Therefore, statement (c) is the correct statement. In a simple graph, every trail is a path, and every path is a trail.

Learn more about vertices here : https://brainly.com/question/29154919

#SPJ11

Answer:

\(\frac{27y^6}{8x^{12}}\)

Step-by-step explanation:

1) Use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3x^{-5+2}{y^3}}{2z^0yx}) ^3\)

2) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3\times\frac{1}{x^3} y^3}{2x^0yx} )^3\)

3) Use Rule of Zero: \(x^0=1\).

\((\frac{\frac{3y^3}{x^3} }{2\times1\times yx} )^3\)

4) use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3y^3}{2x^{3+1}y} )^3\)

5) Use Quotient Rule: \(\frac{x^a}{x^b} =x^{a-b}\).

\((\frac{3y^{3-1}x^{-4}}{2} )^3\)

6) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3y^2\times\frac{1}{x^4} }{2} )^3\)

7) Use Division Distributive Property: \((\frac{x}{y} )^a=\frac{x^a}{y^a}\).

\(\frac{(3y^2)^3}{2x^4}\)

8) Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{(3^3(y^2)^3}{(2x^4)^3}\)

9) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{(2x^4)^3}\)

10)  Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{26y^6}{(2^3)(x^4)^3}\)

11) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{8x^12}\)

#SPJ1

Answer:

\(\displaystyle \frac{27y^{6}}{8x^{12}}\)

Step-by-step explanation:

\(\displaystyle \biggr(\frac{3x^{-5}y^3x^2}{2z^0yx}\biggr)^3\\\\=\biggr(\frac{3x^{-5}y^2x}{2}\biggr)^3\\\\=\frac{(3x^{-5}y^2x)^3}{2^3}\\\\=\frac{3^3x^{-5*3}y^{2*3}x^3}{8}\\\\=\frac{27x^{-15}y^{6}x^3}{8}\\\\=\frac{27y^{6}x^3}{8x^{15}}\\\\=\frac{27y^{6}}{8x^{12}}\)

Notes:

1) Make sure when raising a variable with an exponent to an exponent that the exponents get multiplied

2) Variables with negative exponents in the numerator become positive and go in the denominator (like with \(x^{-15}\))

3) When raising a fraction to an exponent, it applies to BOTH the numerator and denominator

Hope this helped!

The amount Thabang will receive if they decided to share their money according to hour is 380, 50 cents pieces of the container.

We know that Thabang save money by putting coins in a money box. The money box has 600 coins that consist of 20 cents and 50 cents.

We also know that Thabang worked three hours and Nidhu worked for two hours.

Therefore, let the number of 50 cents coins in the container be "x".

We know that the total number of coins in the container is 600, so we can write, x + 220 = 600

Solving for x, we get,

x = 600 - 220

x = 380

Therefore, there are 380, 50 cents pieces in the container. The amount Thabang will receive if they decided to share their money according to hour is 380, 50 cents pieces of the container.

To learn more about equations, click here:

brainly.com/question/29538993

#SPJ4

Complete question: Thabang save money by putting coins in a money box. The money box has 600 coins that consist of 20 cents and 50 cents. Thabang and his friend Nidhu share a job of cleaning a neighbor's yard and they were paid R400. Thabang worked three hours and Nidhu worked for two hours. Determine the amount Thabang will receive if they decided to share their money according to hours.​

1. The mean of a dataset represents the average value of the entire set of numbers. It is calculated by adding up all the values and dividing by the number of values in the dataset. Knowing the standard deviation of a dataset adds information about how much the values deviate from the mean.

A high standard deviation indicates that the values are more spread out from the mean, while a low standard deviation indicates that the values are closer to the mean. It can help to identify outliers and the overall variability of the dataset.

2. A p-value is a statistical measure that helps to determine whether the null hypothesis (there is no significant difference between two groups) is true or false.

It is the probability of obtaining a result as extreme or more extreme than the observed result, assuming that the null hypothesis is true. A p-value of less than 0.05 (typically) is considered statistically significant, which means that there is strong evidence to reject the null hypothesis and accept the alternative hypothesis (there is a significant difference between the two groups).

3. Alpha is the level of significance that is set to determine whether a p-value is statistically significant or not. It is typically set at 0.05, which means that if the p-value is less than 0.05, then the result is considered statistically significant and the null hypothesis is rejected.

If the p-value is greater than 0.05, then the result is not statistically significant and the null hypothesis cannot be rejected. In summary, alpha and p-value are related because alpha sets the threshold for determining whether a p-value is statistically significant or not.

Learn more about hypothesis from:

https://brainly.com/question/26185548

#SPJ11

1. The two shapes that make up this figure are rectangular pyramid and rectangular prism.

2. The surface area of shape 1 is 390.3 cm².

3. The surface area of shape 2 is 504 cm².

4. The total surface area of this figure is 894.3 cm².

By critically observing the figure, we can logically deduce that shape 1 represents a rectangular pyramid while shape 2 represent a rectangular prism.

Part 2.

In Mathematics, the surface area of a rectangular pyramid can be calculated by using this mathematical equation:

Total surface area of rectangular pyramid = \(lw+l\sqrt{(\frac{w}{2})^2 +h^2} +w\sqrt{(\frac{l}{2})^2 +h^2}\)

where:

By substituting the given side lengths into the formula for the surface area of a triangular prism, we have the following;

Total surface area of rectangular pyramid = \((12 \times 10)+12\sqrt{(\frac{10}{2})^2 +11^2} +10\sqrt{(\frac{12}{2})^2 +11^2}\)

Total surface area of rectangular pyramid = 390.3 cm².

Part 3.

In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

Surface area of a rectangular prism = 2(lh + lw + wh)

Surface area of a rectangular prism = 2(12 × 6 + 12 × 10 + 10 × 6)

Surface area of a rectangular prism = 2(72 + 120 + 60)

Surface area of a rectangular prism = 504 cm².

Part 4.

Total surface area of this figure = 390.3 cm² + 504 cm².

Total surface area of this figure = 894.3 cm²

Read more on surface area of a rectangular prism here: brainly.com/question/28185251

#SPJ1

The unit circle can be divided into 6 equal arcs using t-values that are multiples of π/3.

To determine the number of equal arcs that can be formed by dividing the unit circle using t-values that are multiples of π/3, we need to consider the angular measure between each division point.

A circle has a total angular measure of 360 degrees or 2π radians. Since we are using t-values that are multiples of π/3, each division point will have an angular measure of π/3.

To find the number of equal arcs, we divide the total angular measure of the circle (2π radians) by the angular measure between each division point (π/3 radians):

Number of equal arcs = (Total angular measure of the circle) / (Angular measure between each division point)

Number of equal arcs = (2π radians) / (π/3 radians)

Simplifying the expression, we get:

Number of equal arcs = (2π radians) * (3/π radians)

Number of equal arcs = 6

Therefore, the unit circle can be divided into 6 equal arcs using t-values that are multiples of π/3. Each arc will have an angular measure of π/3.

To learn more about unit circle, click here: brainly.com/question/29298870

#SPJ11

Answer:

8,000 feet

Step-by-step explanation:

10/5,000 = 0.002

so 16 divided by what equals 0.002?

16/ 8,000=0.002

Answer:

The area of the triangle is 27

Answer:

blue

Step-by-step explanation:

The x-intercept of a function is where is crosses the x-axis. By looking at the graph, you can notice the graph passes the x-axis at a value a bit more than

x = 4. Therefore, the only possible answer is blue.

The range of the function g(x) = |x - 12| - 2 is {y | y > -2}, indicating that the function can take any value greater than -2.

To find the range of the function g(x) = |x - 12| - 2, we need to determine the set of all possible values that the function can take.

The absolute value function |x - 12| represents the distance between x and 12 on the number line. Since the absolute value always results in a non-negative value, the expression |x - 12| will always be greater than or equal to 0.

By subtracting 2 from |x - 12|, we shift the entire range downward by 2 units. This means that the minimum value of g(x) will be -2.

Therefore, the range of g(x) can be written as {y | y > -2}, which means that the function can take any value greater than -2. In other words, the range includes all real numbers greater than -2.

Visually, if we were to plot the graph of g(x), it would be a V-shaped graph with the vertex at (12, -2) and the arms extending upward infinitely. The function will never be less than -2 since we are subtracting 2 from the absolute value.

for similar questions on  range of the function.

https://brainly.com/question/29017978

#SPJ8

Correct answer is option A. T

Answer:

-17

Step-by-step explanation:

\( - 3{(y + 2)}^{2} - 5 + 6y \\ - 3(y + 2)(y + 2) - 5 + 6y \\ ( - 3y - 6)(y + 2) - 5 + 6y \\ - 3 {y}^{2} - 6y - 6y - 12 - 5 + 6y \\ - 3 {y}^{2} - 12y - 12 - 5 + 6y \\ - 3 {y}^{2} - 12y + 6y - 12 - 5 \\ - 3 {y}^{2} - 6y - 17\)

\(-3y^{2}-6y-17\)

The values for numbers #21 through #26 are as follows:

#21: 2.33% or 0.0233. #22: $56.4842. #23: 1.85% or 0.0185. #24: $56.4148. #25: 3.64% or 0.0364. #26: $57.4397

#21: 2.33% (arithmetic mean as a fraction: 0.0233)

#22: $56.4842 (result of the calculation)

#23: 1.85% (geometric mean as a fraction: 0.0185)

#24: $56.4148 (result of the calculation)

#25: 3.64% (continuous mean as a fraction: 0.0364)

#26: $57.4397 (result of the calculation)

To fill out numbers #21 through #26, we need to calculate the values for each term using the given information and convert the percentages to fractions.

#21: The arithmetic mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #21 = 2.33% = 0.0233.

#22: Multiply the starting price ($53.07) by the compound factor (1 + arithmetic mean)^3. Substitute the value of #21 into the calculation. Therefore, #22 = $53.07 x (1 + 0.0233)^3 = $56.4842.

#23: The geometric mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #23 = 1.85% = 0.0185.

#24: Multiply the starting price ($53.07) by the compound factor (1 + geometric mean)^3. Substitute the value of #23 into the calculation. Therefore, #24 = $53.07 x (1 + 0.0185)^3 = $56.4148.

#25: The continuous mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #25 = 3.64% = 0.0364.

#26: Multiply the starting price ($53.07) by the continuous factor e^(continuous mean x 3). Substitute the value of #25 into the calculation. Therefore, #26 = $53.07 x e^(0.0364 x 3) = $57.4397.

Hence, the values for numbers #21 through #26 are as calculated above.

To learn more about fraction, click here: brainly.com/question/28372533

#SPJ11

Answer:

see explanation

Step-by-step explanation:

(a)

OC = OB ( both radii of the circle )

Thus Δ BOC is isosceles with congruent base angles.

∠ BOC = ∠ BCO = 50°

(b)

∠ ACB = 90° ( angle in a semicircle ), then

∠ ACO = 90° - 50° = 40°

OA = OC ( both radii of the circle )

Thus Δ ACO is isosceles with congruent base angles.

∠ BAC = ∠ ACO = 40°

Answer:

V represents final velocity

MORE TO KNOW -

Answer: -7, -6.5, -6.2, -4.5, 0

I hope this helps, stay safe, and have a great rest of your day. :)

Answer:

-7, -6.5, -6.2, -4.5, 0

Step-by-step explanation:

Answer:

135 degrees

Step-by-step explanation:

The two column proof is completed by

Statement                                            Justification

1. DE || KL                                        1. Given

2. < DFE ≅ < LF-K                            2. Vertical Angles Theorem

3. < DEF ≅ < LKF                            3. Alternate Interior Angles Theorem

4. Δ FDE ≅ Δ FLK                           4. AAS postulate

According to the AAS Postulate, triangles are congruent if two angles and the non-included side of one triangle are congruent with two angles and the non-included side of another triangle.

In the given problem the side is non included and the angels are congruent and hence completes the proof

Learn more on two column proof:

https://brainly.com/question/14304869

#SPJ1

Answer:

2

Step-by-step explanation:

p/2-5

You can use PEMDAS to help:

Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

So, first we have to substitute 14 for p to get:

14/2-5

Next, comes division before subtraction, so we can rewrite the equation as this:

(14/2)-5

7-5

=2

The value of x in the triangle is 2√13.

We have,

There are two similar triangles.

So,

The ratio of the corresponding sides is equal.

Now,

4/x = x/(9 + 4)

4/x = x / 13

4 x 13 = x²

x² = 4 x 13

x = √(4 x 13)

x = 2√13

Thus,

The value of x in the triangle is 2√13.

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ1

The angle of elevation is 72.5° and the height at which the ladder will elevate on the building is 19.06 ft.

Here we have to find the angle of elevation of the ladder and the height the ladder will reach on the building if the ladder is leaned against a building.

Data given:

length of the ladder = 20 ft

the base of the ladder = 6ft

we have to find the angle of elevation.

cos Ф = base/ hypotenuse

= 6/20

Ф = \(cos^{-1}\) ( 6/20)Ф

    = 72.5°

Now we have to find how high the ladder reaches on the building when leaned against a building.

sin(72.5°) = x/ 20

x = 0.953 ×20

x = 19.06 ft

Therefore the angle of elevation is 72.5° and the ladder will elevate to 19.06.

To know more about the angle of elevation refer to the link given below:

https://brainly.com/question/88158

#SPJ4

True/False question cannot be answered with a "main answer". However, the archaeologists do believe that the cities of Sodom and Gomorrah were near the Dead Sea.

The location of Sodom and Gomorrah is a subject of debate among archaeologists and scholars. Some believe that they were located near the Dead Sea, while others propose different locations. However, the prevailing theory is that they were situated near the Dead Sea, which is a salt lake bordered by Jordan to the east and Israel and Palestine to the west.

The true/false question you have posed cannot be answered with a long answer as it is a binary question. However, if you want to know more about the archaeology and history of Sodom and Gomorrah, there is a wealth of information available online and in scholarly articles and books. The story of Sodom and Gomorrah is a biblical tale that recounts the destruction of two cities by God due to their wickedness. The story appears in both the Book of Genesis in the Hebrew Bible and in the Quran. Archaeological evidence suggests that there were settlements in the area of the Dead Sea around the time the story of Sodom and Gomorrah is said to have occurred, but there is no conclusive proof that these were the cities referred to in the Bible. Some scholars argue that the story is a myth, while others believe that there is a historical basis for it. Regardless of the veracity of the tale, the story of Sodom and Gomorrah has captured the imagination of people for centuries and continues to be a subject of scholarly inquiry.

To know more about archaeologists visit :-

https://brainly.com/question/31720195

#SPJ11

Statement is true because the corresponding sides are congruent. The answer is: BA = LN.

What is Triangle?

A triangle is a closed, two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and is used in many areas of mathematics, science, and engineering.

Since triangle ABC and triangle LMN have congruent corresponding sides, we know that they are similar triangles. This means that their corresponding angles are also congruent.

We are given that angle BAC is 58 degrees and angle MLN is 78 degrees. Since corresponding angles are congruent, this means that angle BAC is congruent to angle MLN.

Therefore, triangle ABC and triangle LMN are similar triangles with two pairs of corresponding congruent angles. This means that all corresponding sides are proportional.

Since AC = LN and BA = ML, we know that the ratio of the lengths of corresponding sides is:

AC / LN = BA / ML

Substituting the given values, we get:

1 = 1

This statement is true because the corresponding sides are congruent.

Therefore, the answer is: BA = LN.

Learn more about Triangle

https://brainly.com/question/17335144

#SPJ1

The term that is not possible in the domain of a sequence is:

-5

The domain of a function is the set that contains all possible input values for the function. For a sequence, the domain is the set that contains all the indexed of the terms, starting at 0 and going until the nth term.

For example, suppose we have the following sequence: 3, 5, 7, ...

From what was explained above, which also can be visualized with the example, an index term of a sequence cannot be negative, hence the term that is not possible in the domain of a sequence is:

-5.

Which is the only negative number of the options.

More can be learned about the domain of a function at https://brainly.com/question/10891721

#SPJ1