Let f(x) = 2√3x and g(x) = -4√3x. Find (f-g)(x), then evaluate when x = 12.

Answer: 2 hours and 30 minutes

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the length of JL in the right triangle JKL, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides equals the square of the length of the hypotenuse (the longest side). In this case, JL is the hypotenuse and JK and KL are the two shorter sides.

Since K is a right angle in triangle JKL, we can find the lengths of JK and KL using the given information. We have KM = 6 and JM = 8, so we can use those values to find JK and KL:

JK = √(JM^2 - KM^2) = √(8^2 - 6^2) = √(64 - 36) = √(28) = 2√(7)

KL = KM = 6

Finally, to find JL, we can use the Pythagorean theorem:

JL = √(JK^2 + KL^2) = √( (2√(7))^2 + 6^2) = √(4 * 7 + 36) = √(52) = 2√(13)

So, JL = 2√(13).

Answer:

(9y + 4)(5x + 7)

Step-by-step explanation:

Yes, this sample of the trees in the county likely to be representative if each forest is the same size.

Representative sample, the sample must accurately reflect the population studied in demographics and characteristics of the chosen subjects.

For example, a representative sample will reflect only those within the study population and should not extend to those outside the study. If Jose is interested in studying the exercise habits of college athletes, only the population of college athletes should be considered for the selection of a representative sample. Jose will not choose athletes from high school or career athletes as part of his representative sample.

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The graph is translated to the right 2 units. This is because the expression inside the function is now 6x - 4, which means the function has a horizontal shift to the right by 4/6 = 2/3 units.

What is Graph?

In mathematics, a graph is a collection of points, called vertices or nodes, and a collection of lines, called edges, that connect pairs of vertices. Graphs are used to represent relationships between objects, such as the connections between different parts of a network or the dependencies between different variables in a system. They are commonly used in fields such as computer science, operations research, and engineering to model and solve problems involving complex systems.

The correct transformations are:

The graph is translated to the right 2 units. This is because the expression inside the function is now 6x - 4, which means the function has a horizontal shift to the right by 4/6 = 2/3 units.

The graph is translated up 2 units. This is because there is a constant term of +2 added to the function, which means the function has a vertical shift upwards by 2 units.

Therefore, the correct answers are:

The graph is translated to the right 2 units.

The graph is translated up 2 units.

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The algebra word problem method shows that Richard is 22 years old and Teo is 6 years old.

Algebra is used in our daily lives without us even recognizing it. Students can relate to and comprehend the significance of mathematics in the real world by solving algebraic word problems in worksheets.

Algebraic word problems usually comprise interpreting words into numbers, variables, their coefficients, and the use of appropriate arithmetic operations.

From the information given, we can the following system of equations as follows:

r + t = 28     --- (1)

r =  2t + 10   --- (2)

(2t + 10) + t = 28

3t + 10 = 28

3t = 28 - 10

3t = 18

t = 18/3

t = 6

From (1),  r + t = 28

r + 6 = 28

r = 28 - 6

r = 22

Therefore, we can conclude that Richard is 22 years old and Teo is 6 years old.

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On solving the provided question, we can say that  Here, 21 and 22 only share a single element, which is 1. Since they are co-prime factor, their HCF equals 1.

Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.

21 and 22:

1, 3, 7, and 21 are the factors of 21.

1, 2, 11, and 22 are the factors of 22.

Here, 21 and 22 only share a single element, which is 1. Since they are co-prime, their HCF equals 1.

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The population of a large US city is 1.70321 × 10⁶ in Scientific Notation.

It may be referred to as scientific form or standard index form.

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

We know that, a number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

According to the question,

the population of a large US city is 1,703,210. we need to show this number in Scientific Notation.

The number is written in two parts,

The digits, with the decimal point placed after the first digit, followed by × 10 to a power that puts the decimal point where it should be

Therefore,

1,703,210 = 1.70321 × 10⁶.

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Answer:

285.50

Step-by-step explanation:

The total for the ratio of 1:4 is 5.  The ratio to the woman to the total is

4:5 or

[tex]\frac{4}{5}[/tex] = [tex]\frac{x}{2855}[/tex]  Cross multiply and solve for x

4(2855) = 5x

11420 = 5x  Divide both sides by 5

2284 =x

The woman's portion of the total is 2284.

The woman takes the 2284 and divides it in a ratio of 5:1:2.  The total is 8.

The daughter will receive the ratio of 1:8 of the total.

[tex]\frac{1}{8}[/tex] = [tex]\frac{x}{2284}[/tex]  cross multiply and solve for x

8x = 2284    Divide both sides by 8

x = 285.50

The daughter's portion is 285.50

Answer:

15

Step-by-step explanation:

Answer:

Find the indicated side of the

triangle.

b

30°

12

a = -

Step-by-step explanation:

Answer:

B. m-3=m+3

Step-by-step explanation:

Because the others have a solution such as 0 and -1.

And That would eliminate D

Answer: B

Step-by-step explanation:

Answer:

18 and 3/4 rows of radishes

Step-by-step explanation:

6 + 4 + 7 = 17

3/4 + 3/4 + 1/4 = 7/4

7/4  = 1 3/4

17 + 1 3/4 = 18 3/4

Answer: 18 and 3/4 rows of radishes

Since all the fractions have the same denominator,

you can combine 3/4 + 3/4 + 1/4 together into 1 and 3/4

Adding in the numbers 7 + 4+ 6 and the 1 and 3/4 would amount to 18 and 3/4

The total area of the composite figure is 258 squared centimeters.

The figure in the diagram is composed of two triangle and a rectangle?

The area of a triangle = 1/2 × base × height

Area of a rectangle = length × width

From the diagram;

Triangle 1

Triangle 2

Rectangle

To find the area of the composite figure, we find the area of the two triangle and rectangle and add.

Area = area of triangle 1 + area of triangle 2 + area of rectangle.

Area = ( 1/2 × base × height ) + ( 1/2 × base × height ) + ( length × width )

Area = ( 1/2 × 4 × 12 ) + ( 1/2 × 12 × 3 ) + ( 18 × 12 )

Area = ( 2 × 12 ) + ( 6 × 3 ) + ( 18 × 12 )

Area = 24 + 18 + 216

Area = 258cm²

Therefore, the area is 258 squared centimeters.

Option C) 258cm² is the correct answer.

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Answer:

258cm^2

Step-by-step explanation:

The function among all options is y=30.5(0.7)ˣ.

The graph of a function represents a set of all points in a plane. It helps to derive the nature of the function.

The function must satisfy the points that are given in the graph.

When x=0, y=21.35(0.7)ˣ=21.35(0.7)⁰=21.35.

But the given point is (0,30.5).

Hence, it cannot be the required function.

When x=0, y=30.5(21.35)ˣ=30.5(21.35)⁰=30.5.

When x=1, y=30.5(21.35)ˣ=30.5(21.35)¹=651.175.

But the given point is (1,21.35).

Hence, it cannot be the required function.

When x=0, y=30.5(1.3)ˣ=30.5(1.3)⁰=30.5.

When x=1, y=30.5(1.3)ˣ=30.5(1.3)¹=39.65

But the given point is (1,21.35).

Hence, it cannot be the required function.

When x=0, y=30.5(0.7)ˣ=30.5(0.7)⁰=30.5.

When x=1, y=30.5(0.7)ˣ=30.5(0.7)¹=21.35.

When x=2, y=30.5(0.7)ˣ=30.5(0.7)²=14.945≈14.95.

It satisfies all three given points.

Therefore, the required function is y=30.5(0.7)ˣ.

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Answer: 29 yards

Step-by-step explanation:

    First, we want to find how much she spent. We will subtract the leftover from the original amount.

$15 - $9.49 = $5.51 spent

    Next, we will convert this value into cents.

$5.51 = 551 cents

    Last, we will divide this by the price per yard to find how many yards she bought.

551 / 19 = 29 yards

Answer:

29 yards

Step-by-step explanation:

$15.00 - $9.49= $5.51

$5.51 divide by .19 per yard = 29

Answer D

Step-by-step explanation:

1. The Venn diagrams are attached

2. When the statistics students number = 10·x + 3, we have;

The number of students that study

When the statistics students number = 2·x + 3, we have;

The number of students that study

The parameters given are;

Total number of students = 30

Number of students that study algebra n(A) = x + 10

Number of students that study statistics n(B) = 10·x + 3

Number of student that study both algebra and statistics n(A∩B) = 4

Number of student that study only algebra n(A\B) = 2·x

Number of students that study neither algebra or statistics n(A∪B)' = 3

Therefore;

The number of students that study either algebra or statistics = n(A∪B)

From set theory we have;

n(A∪B) = n(A) + n(B) - n(A∩B)

n(A∪B) = 30 - 3 = 27

Therefore, we have;

n(A∪B) = x + 10 + 10·x + 3 - 4 = 27

11·x+13 = 27 + 4 = 31

11·x = 18

x = 18/11

The number of students that study

a. Algebra

n(A) = 18/11 + 10 = 128/11

b. Statistic

n(B) = 213/11

Hence, we have;

n(A - B) = n(A) - n(A∩B) = 128/11 - 4 = 84/11

Similarly, we have;

n(B - A) = n(B) - n(A∩B) = 213/11 - 4 = 169/11

However, assuming n(B) = (2·x + 3), we have;

n(A∪B) = n(A) + n(B) - n(A∩B)

n(A∪B) = 30 - 3 = 27

Therefore, we have;

n(A∪B) = x + 10 + 2·x + 3 - 4 = 27

2·x+3 + x + 10= 27 + 4 = 31

3·x = 18

x = 6

Therefore, the number of students that study

a. Algebra

n(A) = 16

b. Statistics

n(B) = 15

Hence, we have;

n(A - B) = n(A) - n(A∩B) = 16 - 4 = 12

Similarly, we have;

n(B - A) = n(B) - n(A∩B) = 15 - 4 = 11

See the attached Venn Diagrams.

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A knitted hat pattern comes in 4 styles with 4 stitch options and 3 sizes, and there are 7 yarns appropriate for the hat. There are 112 different hats that can be made using the knitted hat pattern, disregarding size.

To find the total number of different hats that can be made using the knitted hat pattern, we need to multiply the number of choices for each feature.

There are 4 styles to choose from and 4 stitch options, so there are 4 x 4 = 16 different combinations of style and stitch.

For each of these style and stitch combinations, there are 7 yarns that can be used, so the number of possible yarn choices is 7.

Therefore, the total number of different hats that can be made, disregarding size, is:

16 (style and stitch combinations) x 7 (yarn choices) = 112

This calculation shows how the multiplication principle of counting can be used to find the total number of outcomes in a multi-stage process where the number of choices at each stage is known. In this case, we multiplied the number of style and stitch combinations by the number of yarn choices to find the total number of different hats that can be made.

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Complete question is:

A knitted hat pattern comes in 4 styles with 4 stitch options and 3 sizes, and there are 7 yarns appropriate for the hat. Disregarding size, how many different hats can be made?

Answer:

To find the number of courts with doubles matches, we need to determine the total number of players playing doubles. If each court with a doubles match has 4 players, then the total number of players playing doubles would be 4 times the number of courts playing doubles.

Since there are 28 players in total, and each court with a singles match has 2 players, the number of players playing singles would be 28 - 4x, where x is the number of courts playing doubles.

Since each court with a singles match has 2 players, the number of courts playing singles would be 28/2 = 14.

So, 28 - 4x = 14, and solving for x, we get x = 7.

Therefore, there are 7 courts with doubles matches and 14 courts with singles matches.

Answer: j = -8

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

2j = 16 + 4j

collecting like terms, you would have

2j - 4j = 16

-2j = 16

divide both sides by 2

j = 16/(-2)

j = -8

Answer: A 90° rotation around the origin maps point (x, y) to (-y, x). So, the image of point J after a 90° rotation is J' = (-2, 2) -> (-2, -2).

A reflection across the line x = 3 maps point (x, y) to (2x - 3, y). So, the image of point J' after a reflection across x = 3 is J'' = (-2, -2) -> (4, -2).

Similarly, we can find the images of K and L:

K' = (-2, 6) -> (-6, -2)

K'' = (-6, -2) -> (-2, -2)

L' = (-8, 2) -> (2, -8)

L'' = (2, -8) -> (8, -2)

Therefore, the image of triangle JKL after the 90° rotation and reflection is triangle PQR, with vertices P = J'', Q = K'', and R = L''.

The area of triangle PQR can be found using the Shoelace Formula:

P = [(4 -2) + (-2 -2) + (8 -2) * (-2 - (-8))]/2 = [6 + 4 * 6]/2 = 30/2 = 15 square units.

So, the area of triangle PQR is 15 square units.

Step-by-step explanation:

Answerk bzijnjlngljntgojengojnetgihnrtgkte4wg

The length of the rectangle is [tex]8x^2y^3[/tex] inches when  the area of the rectangle is [tex]48x^3y^5[/tex] square inches.

To find the length of the rectangle, we can use the formula for the area of a rectangle, which is:

Area = length x width

We are given that the area of the rectangle is [tex]48x^3y^5[/tex] square inches, and its width is [tex]6xy^2[/tex] inches. Therefore, we can substitute these values into the formula to get:

[tex]48x^3y^5 = length * 6xy^2[/tex]

Simplifying this equation, we can cancel out the common factors of 6x and [tex]y^2[/tex] on both sides to get:

[tex]8x^2y^3 = length[/tex]

Therefore, the length of the rectangle is [tex]8x^2y^3[/tex] inches.

To verify our answer, we can substitute the length and width back into the formula for the area of a rectangle and check if it matches the given area:

Area = length x width = [tex](8x^2y^3) * (6xy^2) = 48x^3y^5[/tex]

Since this matches the given area, we can be confident that our answer is correct. Therefore, the length of the rectangle is [tex]8x^2y^3[/tex] inches.

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The school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets.The price of a senior citizen ticket is $17.33 and the price of a child ticket is $5.01.

What is Word Problem?

A word problem is a mathematical problem that is presented in the form of a story or scenario, often using words and symbols to describe a real-world situation. Word problems require the solver to read and understand the problem, identify the relevant information, translate the information into mathematical expressions or equations, and then solve for the unknown quantity.

Word problems can involve a wide range of mathematical concepts, including arithmetic, algebra, geometry, statistics, and calculus, and are often used to test students' problem-solving abilities and mathematical reasoning skills.

Let's call the price of a senior citizen ticket "s" and the price of a child ticket "c".

From the information given, we know:

3s + c = 38 (equation 1)

3s = 52 (equation 2)

Using equation 2, we can solve for s:

3s = 52

s = 17.33 (rounded to two decimal places)

Now we can substitute this value of s into equation 1 and solve for c:

3s + c = 38

3(17.33) + c = 38

c = 38 - 3(17.33)

c = 5.01 (rounded to two decimal places)

So the price of a senior citizen ticket is $17.33 and the price of a child ticket is $5.01.

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[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{9}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{1}}} \implies \cfrac{ -1 }{ 7 } \implies - \cfrac{1 }{ 7 }[/tex]