If it takes 2 cups of rice to make 5 servings, how many cups of rice are needed to make 12 servings?

[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]

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: 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

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: 2 hours and 30 minutes

Step-by-step explanation:

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:

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.

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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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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Answer:

15

Step-by-step explanation:

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?

The length of the segment AB is 3.5 cm  

What is a line segment ?

A line segment in geometry is bounded by two separate points on a line. Another way to describe a line segment is as a piece of the line that joins two points. A line segment has two fixed or distinct endpoints while a line has no endpoints and can stretch in both directions indefinitely.

We have segments ratio as shown:

BC/AB = CD/ED

=> (AC - AB)/AB = (EC - ED)/ED

=> (14-AB)/AB = (84-21)/21 = 3

    Let AB=x

=>  (14-x)/x = 3

=> 14-x = 3x

=> 14 = 3x+x = 4x

=> 14/4 = x

=> x=3.5 cm

AB=x = 3.5 cm  

The length of the segment AB is 3.5 cm  

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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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Answerk bzijnjlngljntgojengojnetgihnrtgkte4wg

Answer:

Find the indicated side of the

triangle.

b

30°

12

a = -

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:

4(4x+1)

Step-by-step explanation:

16x+4
Factor out 4,
4(4x+1)

Answer:

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

Step-by-step explanation:

Given that, the coordinates of the endpoints of ij are i(3,5) and j(17,19). point k is on ij and divides it such that ik:jk is 3:4.

The coordinates of the point k are (9,10)

The concept of section formula asserts that if a line segment is divided into two pieces in a certain ratio, the coordinates at the point of division may be obtained using the formula:

(mx2 + nx1)/(m+n), (my2 + ny1)/(m+n) = K

where (x1, y1) and (x2, y2) are the line segment's endpoint coordinates, and m:n is the provided ratio by which the line segment is divided.

The ends of the line segment IJ in this example are I(3,5) and J(17,19), and the ratio by which it is divided is 3:4, implying that IK:JK is 3:4.

As a result, m:n = 3:4, implying that m = 3 and n = 4.

When we enter these values into the formula, we get:

K = (3 x 17 + 4 x 3)/(3+4), (3 x 19 + 4 x 5)/(3+4)

When we simplify this expression, we get:

K = ( 51 + 12)/(7), (57 + 20)/(7)

K = (63)/(7),(77)/(7)

K = 9,10

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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:

Answer: (a) To find the position vector of point D, we need to find the midpoint of the line segment AB. We can do this by taking the average of the position vectors of points A and B:

D = (A + B) / 2 = ((2i + 3j - 4k) + (4i - 2j + 3k)) / 2 = (3i + 0.5j - 0.5k)

So, the position vector of point D is (3i + 0.5j - 0.5k).

(b) To find the value of a, we use the fact that the distance between points A and C is 4. We can find the distance between two points by finding the magnitude of the difference between their position vectors. The position vector of point C is (ai + 5j – 2k), so the difference between the position vectors of points A and C is (ai + 5j – 2k) - (2i + 3j - 4k) = (a-2)i + 2j - (-2k).

The magnitude of this difference is given by:

|(ai + 5j - 2k) - (2i + 3j - 4k)| = √((a-2)^2 + 2^2 + 2^2) = 4

So, we have:

√((a-2)^2 + 2^2 + 2^2) = 4

(a-2)^2 + 2^2 + 2^2 = 16

(a-2)^2 = 16 - 4 - 4

(a-2)^2 = 8

a-2 = ±2√2

Since a < 0, we have:

a = 2 - 2√2

So, the value of a is 2 - 2√2.

Step-by-step explanation:

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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The prediction about what might happen if you have ten birds will be 5. You'll have either seven or eight angry neighbors

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, it should be noted that as the number of birds increase, the number of angry neighbor increased too. Therefore, the prediction about what might happen if you have ten birds will be that you'll have either seven or eight angry neighbors.

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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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Answer: B

Step-by-step explanation:

Answer D

Step-by-step explanation:

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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Ratio of the base of two triangles is 16:9 , if ratio of heights of two triangles is 3:4 and area 4:3.

It is given that the ratio of heights of two triangles is 3:4 and the ratio of area of two triangles is 4:3

We have to find the ratio of their base

The basic formula for the area of a triangle is equal to half the product of its base and height or  [tex]\frac{1}{2} \times base \times height[/tex]

Let b₁ , b₂ are the base of two triangles respectively

So, ratio of areas of triangles : [tex]\frac{\frac{1}{2}\times b_{1} \times3}{\frac{1}{2}\times b_{2} \times4}[/tex]

[tex]\frac{4}{3} = \frac{\frac{1}{2}\times b_{1} \times3}{\frac{1}{2}\times b_{2} \times4}[/tex]

[tex]\frac{b{1}}{b_{2}} =\frac{16}{9}[/tex]

So, ratio of the base of two triangles is 16:9

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