6. Sofia rearranged the equation 3x+7+2x-8=21
into 3x+2x+7-8=21 in order to combine like
terms more easily. Which of the following properties
did she use to make this manipulation?
(1) The commutative property of addition
(2) The additive property of equality
(3) The distributive property
(4) The associative property of multiplication

Answer:

0, 1, 2, or 3

Step-by-step explanation:

        0 + 7 = ≥ 10

        It is true.

        1 + 7 = ≥ 10

        It is true.

        2 + 7 = ≥ 10

        It is true.

        3 + 7 = ≥ 10

        It is true.

        4 + 7 = ≥ 10

        It is false.

3/5 = 0,6, it is 0.6 × 100 = 60%

Therefore, 3/5 is expressed as 60% in terms of percentage.

Percentage:

In mathematics, a percentage is a number or ratio that represents a fraction of 100. This is one way of representing a dimensionless ratio between two numbers. Other methods include ratios, fractions, and decimals. Percentage is often indicated by writing a "%" sign after the number.

According to the Question:

To convert a fraction to a decimal, it's always best to look at the denominator first. If the denominator only has prime factors of 2 and 5, you can easily pick a number multiplied by the denominator and convert it to a denominator that is a power of 10, and the result is the final prime number. If you have prime factors other than 2 and 5, converting to decimal takes longer and can result in infinite but repeating decimals.

In this case, the denominator is 5, so you can easily convert to decimal by multiplying the denominator and numerator by 2.

(3 × 20) / (5 × 20) = 60/100

Now,

To convert a fraction to a percentage, simply multiply by 100 and put a % sign next to the result.

As 3/5 = 0,6, it is 0.6 × 100 = 60%

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Answer: You can make 5/3 * (1/1) = 5 servings with a cup of macaroni.

And, with 5 servings, you can make 5 * (3/1) = 15 1/3 servings of pasta salad.

Step-by-step explanation:

Answer:

Answer: x=12

6 x 12=72

Answer:

x = 12 .....................

Step-by-step explanation:

.

Answer:

To find the length of a side of each square that should be cut out to give a box of maximum volume, we need to use optimization. Let's call the length of each square x cm.

To form the box, we will cut out squares of side length x from each corner of the rectangular cardboard sheet, and then fold up the sides to form the box. The dimensions of the base of the box will be (10-2x) cm by (16-2x) cm, and the height of the box will be x cm.

Therefore, the volume of the box will be:

V = (10-2x) * (16-2x) * x

V = 4x^3 - 52x^2 + 160x

To find the length of a side of each square that should be cut out to give a box of maximum volume, we need to find the value of x that maximizes V. To do this, we can take the derivative of V with respect to x, and set it equal to 0:

dV/dx = 12x^2 - 104x + 160 = 0

We can solve for x by factoring the quadratic expression:

3x^2 - 26x + 40 = 0

(3x - 10)(x - 4) = 0

So the critical points are x = 10/3 and x = 4. Since we're looking for a maximum, we need to find which of these critical points gives the highest value of V. We can do this by evaluating V at both points:

V(10/3) ≈ 51.85

V(4) = 128

Therefore, the value of x that gives the maximum volume is x = 4 cm.

So we should cut out squares of side length 4 cm from each corner of the cardboard sheet to make a box of maximum volume.

The requried maximum height of the box should be 2 for the maximum volume.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Let the side measure of the square cut b x,
Now,

The length of the box will be = 16 - 2x
width of the box will be  = 10 - 2x
The height of the box will be  = x

The volume of the box is given as,
V = (16-2x)(10-2x)(x)
V = 4x³ - 52x² + 160x

Differentiate the above equation with respect to x,, and equate it to zero to get the maximum value of x for the maxium volume,
12x² - 104x + 160 = 0
x = 2 and 6.667

We can neglect x = 6.667 because at 6.667 the volume has a negative magnitude.

Thus, the requried maximum height of the box should be 2 for the maximum volume.

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The amount of baking soda he used is 1.5 teaspoons.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

Given that

When 5 cups of flour are used in a recipe, 2.5 teaspoons of baking soda are required.

Anna wants to reduce the recipe to only 3 cups of flour.

We have to determine

How much baking powder should he use?

According to the question

Let x be the amount of baking soda he used,

A recipe for waffles calls for 5 cups of flour and 2.5 teaspoons of baking powder.

If Jason uses 3 cups of flour.

Then,

The amount of baking soda he used is

x/3 = 2.5/5

solving we get,

x = 1.5

Hence, The amount of baking soda he used is 1.5 teaspoons.

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Answer: 3.8 minutes!

Step-by-step explanation:

The answer is 3.8 minutes. To solve for t, we need to set up an inequality where the calories burned in routine #1 is equal to or greater than the calories burned in routine #2. We can write this as 22 + 5.75t ≥ 8.5t. Then, we can subtract 8.5t from both sides to get 22 ≥ -2.75t. Finally, we can divide both sides by -2.75 to get t ≤ -8/2.75, which simplifies to t ≤ 3.8. Therefore, Jane needs to run for 3.8 minutes in Routine #1 in order to burn at least as many calories as Routine #2.

Answer:

Jane needs to run for 8 minutes or less in Routine #1 for it to burn at least as many calories as Routine #2. If she runs for more than 8 minutes in Routine #1, then Routine #2 will burn more calories.

Step-by-step explanation:

In Routine #1, the total number of calories burned is:

C1(t) = 22 + 5.75t

The first term represents the calories burned while walking, and the second term represents the calories burned while running.

In Routine #2, the total number of calories burned is:

C2(t) = 8.5t

This represents the calories burned while running, as there is no walking in Routine #2.

We want to find the values of t for which C1(t) is greater than or equal to C2(t). So we can set up the following inequality:

C1(t) ≥ C2(t)

Substituting the expressions for C1(t) and C2(t), we get:

22 + 5.75t ≥ 8.5t

Simplifying the inequality, we get:

22 ≥ 2.75t

Dividing both sides by 2.75, we get:

t ≤ 8

So Jane needs to run for 8 minutes or less in Routine #1 for it to burn at least as many calories as Routine #2. If she runs for more than 8 minutes in Routine #1, then Routine #2 will burn more calories.

Answer:

y=1/3x+4

Step-by-step explanation:

Yep

The value of x is 9. A quadrilateral having four equal, right-angled angles is called a rectangle.

The following formula determines a rectangular prism's volume:

V = l × b × h

To achieve, we substitute the dimensions.

V = 6 × 3 × 12 in^3

The rectangular pyramid's volume is,

V = 1/3 × 6 × 12 × x in^3

Comparing the two volumes results in,

1/3 × 6 ×  12 × x = 6 × 3 × 12

We divide through by 6 × 12 to get,

x/3 = 3

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Answer:

the answer is y=/0.375x

Step-by-step explanation:

The number of minutes that you walk directly from the parking lot to the house will be 12.73 minutes.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The house is located 1480 ft down a paved path that parallels the beach, which is 740 ft wide. Along the path, you can walk 330 ft/min, but on the beach, you can only walk 130 ft/min.

The distance between the house and the parking is given as,

d² = 740² + 1480²

d² = 547,600 + 2,190,400

d² = 2,738,000

d = 1,654.69 feet

Then the time taken is given as,

T = 1,654.69 / 130

T = 12.73 minutes

The number of minutes that you walk directly from the parking lot to the house will be 12.73 minutes.

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Answer:

300 w

Step-by-step explanation:

swim this question we have an equation w = 21 25 - 2012 I square which represents the power w where w is the power in watts and 120 volt circuit is there which has a resistance of 12 ohm when current I is flowing through the circuit the voltage resistance and current is what is the maximum power in war that can be delivered in this circuit so we have to find out the maximum value of power that can exist in the circuit with 120 volts AC circuit and 12 homes of resistance ok so to find the maximum value of this in an equation we need to find vi we can the best way is we can find out the Maxima Abhishek creation and how do you

find the maximum to find the maximum we can differentiate this equation with respect to I and when the equator when we will equip the differentiation of this equation 20 the value of I that will obtain that will be obtained after doing this will be the maximum for this equation let me show you how that is differentiate DW by D I can we differentiate this this equation with respect to I we get 120 - 24 I know what we have to do this week with this 20 now 120 - 24 I = 20 with this I = 25 we get the value of equal to 55 is the maximum for this equation which means that if we put the value of I

45 we replace if the Avengers equation replace iPhone 5 will get the maximum value of w which is what you wanted right we wanted the maximum power in watts letters replace I buy 5 this equation the equation is 120 I -12 I square be replaced by 5 we get the answer as 300 w this is our answer

The requried number that consists of the line of symmetry is 3. Option B is correct.

A line of symmetry is defined as the line that bisects the entity in two equal symmetrical halves.

here,
Given numbers,
2, 3,  7.8, 4, 9 since the line of symmetry for the given number would be that line that bisects the shapes of the given number in a mirror-like symmetry so, the only number given the mirror-like symmetry when a line passes through its center is 3.

Thus, the requried number that consists of the line of symmetry is 3. Option B is correct.

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The figure below illustrates constructing: A. a bisector of a segment.

In Mathematics, a line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points. Additionally, a line segment typically has a fixed length.

In Mathematics, an angle bisector can be defined as a type of line, ray, or segment, that bisects or divides a line segment exactly into two (2) equal angles.

By critically observing the construction illustrated in the image attached above, we can logically deduce that it represents the bisector of line segment AB.

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The values for x by completing the given steps to solve for |x/6 - 7/12| = 11/6 is x=29/2 or x= -15/2.

A modulus function is a function which gives the absolute value of a number or variable. It produces the magnitude of the number of variables.

Given is a modulus function, |x/6 - 7/12| = 11/6

Solving for x,

Negative Direction;

x/6 - 7/12 = -11/6

x/6 = -22/12 + 7/12 = - 15/12

x = (-15/12)6 = -15/2

x = -15/2

Positive Direction;

x/6 - 7/12 = 11/6

x/6 = 22/12 + 7/12 = 29/12

x = (29/12)6 = 29/2

x = 29/2

Hence, the values for x by completing the given steps to solve for |x/6 - 7/12| = 11/6 is x=29/2 or x= -15/2.

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The question is not complete the similar question is solved.

So the solution of the given question is,  the correct answer is D) Both data sets represent multiplicative relationships. from the given conditions.

In mathematics, a multiplicative relationship between two variables means that the ratio of their values remains constant as the values of the variables change. In other words, the product of the two variables is a constant. For example, if we have two variables x and y such that xy = k, where k is a constant, then x and y have a multiplicative relationship. If we increase the value of one variable, we must decrease the value of the other variable proportion in order to maintain the constant product. This type of relationship is often seen in situations involving rates, ratios, and proportions, such as in growth or decay processes, population dynamics, and financial calculations.

In Table A, y is 2.5 times x, and in Table B, y is 3 times x. In both tables, the relationship between x and y is a constant ratio, which is a characteristic of multiplicative relationships. In Table A, the ratio of y to x is always 2.5, meaning that y is always 2.5 times greater than x. In Table B, the ratio of y to x is always 3, meaning that y is always 3 times greater than x. Therefore, both tables represent multiplicative relationships between x and y.

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Answer: 3 + 3 adds up to 6, which is less than 10.

Step-by-step explanation:

The 4-2-1 rule is a guideline used to help determine the amount of water an individual needs to drink each day.

The rule states that an individual should drink 4 liters of water for every 50 pounds of body weight, 2 liters of water for every 50 pounds of body weight if they are exercising, and 1 liter of water for every 50 pounds of body weight if they are in a hot or dry environment.

To calculate how much water you need to drink using the 4-2-1 rule, simply follow these steps:

1. Determine your body weight in pounds.
2. Divide your body weight by 50 to get the number of 50-pound increments in your weight.
3. Multiply the number of 50-pound increments by 4 to get the amount of water you need to drink if you are not exercising or in a hot or dry environment.
4. Multiply the number of 50-pound increments by 2 to get the amount of water you need to drink if you are exercising.
5. Multiply the number of 50-pound increments by 1 to get the amount of water you need to drink if you are in a hot or dry environment.
6. Add the amounts from steps 3, 4, and 5 together to get the total amount of water you need to drink each day.

For example, if you weigh 150 pounds, you would need to drink 4 liters of water for every 50 pounds of body weight (150 / 50 = 3), 2 liters of water for every 50 pounds of body weight if you are exercising (3 x 2 = 6), and 1 liter of water for every 50 pounds of body weight if you are in a hot or dry environment (3 x 1 = 3). Therefore, you would need to drink a total of 13 liters of water each day (4 + 6 + 3 = 13).

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Answer:

<P = 41

Step-by-step explanation:

we can consider this first figure as a quadrilateral and the trianlgle attached to be is equilateral triangle (as it is already shown in the figure that sides are equal)

we know that each angle of equalateral triangle is 60°

we can see that angle 79° is attached to it and even other angle is also attached

let the other angle be x

we can notice that x and the angle of equi triangle make a linear pair

so 180 - 60

= 120°

the opposite angle to the angle x will be also equal as angles on the same side of qual sides will be equal

now we know that total angle sum of quadrilateral is 360°

so

79 + 120 + 120 + <P = 360

319 + <P = 360

<P = 360 - 319

<P = 41

A relation in math is a set of ordered pairs containing two elements, one from each set. The first element is from the domain and the second from the range.

Relations can be expressed as a set of ordered pairs, as a graph, or as a mapping diagram. A function is a special type of relation in which, for every element in the domain, there is one and only one element in the range. This is expressed mathematically by stating that for every x in the domain, there is one and only one y in the range such that y = f(x). To calculate a relation, the domain and range values are paired with each other, and the ordered pairs are written down. For example, if the domain is {2,3,4,5} and the range is {7,8,9,10}, then the relation would be {(2,7),(3,8),(4,9),(5,10)}.

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Other things constant, how will an increase in the wage of teenagers affect the market for fast food hamburgers will cause the supply of fast food hamburgers will increase, leading to an increase in price of hamburgers. Option A

supply is the amount of a resource that firms, producers, laborer, providers of financial assets, or other economic agents are willing and able to provide to the marketplace or to an individual.

The law of supply in economics states that supply will increase as price increases, due to the fact that producers want to maximize profits. In this instance, the law assumes that all other factors are equal and price is the only independent element, meaning supply is completely dependent on the price.

Hence, an increase in the wages of teenager will lead to an increase in the quantity of hamburgers demanded, which will also leads to an increase in supply.

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The height of flagpole C is approximately 6.1 feet.

Distance is a numerical measurement of how far apart or how far away objects or locations are from each other. It is a physical quantity that is usually expressed in units such as meters, kilometers, miles, or feet. Distance is a scalar quantity, meaning it only has magnitude and no direction.

The distance between two points is typically calculated using a formula, such as the distance formula in Euclidean geometry, which involves taking the square root of the sum of the squares of the differences in the coordinates of the two points.

Let's start by drawing a diagram of the situation:

          A

          |

          |

          |

          |

          |

          |

          |

-----------S-----------C

We can see that the triangles ASC and ABC are similar, since they have the same angles (90 degrees at S and a common angle at A). Therefore, we can use proportions to find the height of flagpole C:

AC   SC

-- = --

AB   AS

Substituting the given values, we get:

AC   10

-- = --

AB   AB + 12

We can solve for AB by noting that the height of flagpole A is the sum of the heights of AB and BC:

13.2 = AB + BC

Solving for BC, we get:

BC = 13.2 - AB

Substituting this into the first equation, we get:

AC   10

-- = --

AB   AB + 12

AC = 10(AB)/(AB + 12)

Now we can substitute the value we found for AB:

AC = 10(13.2 - BC)/(13.2 - BC + 12)

AC = 10(13.2 - BC)/25.2

We still need to find BC, which we can do by using the fact that the triangles ABC and ASC are similar:

BC/AB = SC/AS

Substituting the given values, we get:

BC/AB = 10/22

BC = 10AB/22

Substituting this into the equation for AC, we get:

AC = 10(13.2 - 10AB/22)/25.2

Now we can solve for AB:

13.2 = AB + 10AB/22

AB = 7.92

Finally, we can substitute this into the equation for AC:

AC = 10(13.2 - 10(7.92)/22)/25.2

AC = 6.1

Therefore, the height of flagpole C is approximately 6.1 feet.

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Answer: 1181

Step-by-step explanation:

a. The type of figure shown is a triangular prism.

b. The surface area of the figure is 118.5 sq. in.

A triangular prism is a 3 dimensional shape which has 2 triangular surfaces and a rectangular base. It has 5 surfaces in total.

Considering the given figure in the question, we have;

a. The type of figure shown is a triangular prism.

b. The surface area of the prism can be deduced as follows;

area of one of its triangular surfaces = 1/2*base*height

                                       = 1/2*5*1.7

                                       = 4.25 sq. in.

area of its base = length x width

                   = 10x 5

                   = 50 sq. in.

area of one of its slant sides = length x width

                      = 10 x 3

                      = 30 sq. in.

Therefore, the surface area of the figure = (2*4.25) + 50 + (2*30)

                                    = 8.5 + 50 + 60

                                     = 118.5 sq. in.

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Answer: 3

Step-by-step explanation: Someone is 15 steps behind in a race, then that is sectioned into a fifth. How many steps behind are they?

Answer:

Maths

Step-by-step explanation:

We find the percent equivalent of each test.

Maths: 14 out of 17

percent = part/whole × 100%

percent = 14/17 × 100%

percent = 82.35%

English: 31 out of 39

percent = part/whole × 100%

percent = 31/39 × 100%

percent = 79.49%

Since 82.35% > 79.49%, she did better in Maths.

Answer: Maths

Answer:

4/7 to decimal rounded to nearest thousandth is 0.571

A medium-sized orange contains 68 calories. Which is one-fifth the number of calories in a slice of cheese pizza.

If one slice of cheese pizza contains 340 calories, and a medium-size orange has one-fifth that number of calories, we can find the number of calories in a medium-size orange by dividing 340 by 5. Calories in a medium-sized orange = [tex]\frac{340}{5}[/tex] calories = 68 calories. The division is an arithmetic operation used to find out how many times one number is contained within another number. The result of a division operation is called the quotient.

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Based on the information provided, it can be concluded that Licia's piece of wood is 10 1/8 long.

To determine Licia's piece of wood, let's first consider the information given:

Based on this, to find out the length of Licia's let's add the fractions provided, the process is shown as follows:

Licia piece of wood = 8 1/2 + 1 5/8= 17/2 +13/8= 81/8= 10 1/8

Therefore, Licia's piece of wood is 10 1/8

This result is equal to 10,125

1/8 = 0,125

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(a)The value of g(3) = 13/2 + π,  g(-2) = 5 - π

(b) The graph of y g(x) has points of inflection at x = 0, x = 2 and x = 3

This problem described a function g that is defined and differentiable on [-7, 5]  and with g(0) = 5. The graph of y = g′(x) on [ -7, 5] was given, consisting of three line segments and a semicircle.

[tex]g(3) = 5 + \int\limits^3_0 {g'(x)} \, dx \\g(3) = 5 + \frac{\pi.2^{2}}{4} + \frac{3}{2}[/tex]

g(3) = 13/2 + π

[tex]g(-2) = 5 + \int\limits^ 2_0 {g'(x)} \, dx \\[/tex]

g(2) = 5 - π

(b) x-coordinates of points of inflection for the graph of y  = g(x) on the interval [-7 5].

The graph of y = g(x) has points of inflection at x = 0, x = 2 and x = 3 because g′ changes from increasing to decreasing at x = 0 and 3, x = and g′ changes from decreasing to increasing at x = 2.

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The image of this question is probably this