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The distributive property of multiplication over addition can be used when you multiply a number by a sum. The distributive property lets you multiply a sum by multiplying each addend separately and then add the products:

[tex] a\cdot (b+c)=a\cdot b+a\cdot c. [/tex]

The distributive property of multiplication over subtraction can be used when you multiply a number by a difference. The property states that the product of a number and the difference of two other numbers is equal to the difference of the products:

[tex] a\cdot (b-c)=a\cdot b-a\cdot c. [/tex]

Therefore, you can see what sign is in the brackets, if sign is "+", then you have to add, if sign is "-", then you have to subtract.

The addition or subtraction in the distribution property depends on the sign between the two real numbers in the expression.

Further explanation:

The distributive property states that if a number [tex]a[/tex] is multiplied with the sum of the two numbers [tex]b[/tex] and [tex]c[/tex] then the result is same as if the numbers are multiplied separately.

[tex]\fbox{\begin\\\ \math a(b+c)=(a\cdot b)+(a\cdot c)\\\end{minispace}}[/tex]          ....(1)

The distributive property states that if a number [tex]a[/tex] is multiplied with the difference of the two numbers [tex]b[/tex] and [tex]c[/tex] then the result is same as if the numbers are multiplied separately.

[tex]\fbox{\begin\\\ \math a(b-c)=(a\cdot b)-(a\cdot c)\\\end{minispace}}[/tex]             ....(2)

For example: Consider [tex]5[/tex] as [tex]a[/tex], [tex]6[/tex] as [tex]b[/tex] and [tex]2[/tex] as [tex]c[/tex].

Substitute [tex]5[/tex] for [tex]a[/tex], [tex]6[/tex] for [tex]b[/tex] and [tex]2[/tex] as [tex]c[/tex] in the equation (1) as follows:

[tex]\begin{aligned}5(6+2)&=(5\cdot 6)+(5\cdot 2)\\5\cdot 8&=30+10\\40&=40\end{aligned}[/tex]  

Now, substitute [tex]5[/tex] for [tex]a[/tex], [tex]6[/tex] for [tex]b[/tex] and [tex]2[/tex] as [tex]c[/tex] in the equation (2) as follows,

[tex]\begin{aligned}5(6-2)&=(5\cdot 6)-(5\cdot 2)\\5\cdot 4&=30-10\\20&=20\end{aligned}[/tex]

Therefore, the addition or subtraction in the distributive property is based on the sign between the two real numbers. If the sign between the real number is positive then the numbers are added and if the sign between the real number is negative then the numbers are subtracted.

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Answer details

Grade: Middle school

Subject: Mathematics

Chapter: Real numbers

Keywords: Distributive property, a(b+c)=ab+ac, a(b-c)=ab-ac, real numbers, positive value, negative value, multiply, add, sum, difference.

Chad bought 8 dozens of note pads, which totals 96 note pads. When he divides these into 6 boxes, each box will contain 16 note pads.

To solve the problem of dividing 8 dozen note pads equally into 6 boxes, we first need to know the total number of note pads Chad has. As one dozen is equal to 12 objects, Chad has 8 x 12 = 96 note pads. Then, we divide this total by the number of boxes to find out how many note pads go into each box.

So, 96 note pads / 6 boxes = 16 note pads per box.

Answer:

Sales tax for the refrigerator is $31.53.

Step-by-step explanation:

The price of a refrigerator = $525.50

Sales tax rate = 6%

Sales tax on the price of refrigerator = 6% × 525.50

                                                             = [tex]\frac{6}{100}[/tex] × 525

                                                             = 0.06 × 525.50

                                                             = $31.53

Sales tax for the refrigerator is $31.53.

The rate of change represents the cost per lawn mowed. which is the correct answer would be an option (B).

It quantifies how much the function changed per unit on average throughout that time interval. The slope of the straight line connecting the interval's ends on the function's graph is used to calculate it.

The graph is given in the question.

According to the given graph, we can see that the y-axis is labeled cost (dollars) and that the x-axis is labeled lawns mowed.

The rate of change of a graph is given by the y value divided by the x value.

As per this situation, the rate of change describes the cost per lawn mowed.

Therefore, the rate of change represents the cost per lawn mowed.

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The problem is solved by setting up a ratio of green lights to white lights. Given 30 green lights, and knowing the ratio is 6 green lights for every 4 white lights (or 3:2), we find that there are 20 white lights.

The problem can be solved by setting up a ratio. We know that for every 6 green lights, there are 4 white lights. Therefore the ratio of green lights to white lights is 6:4, or simplified to 3:2. Given that there are 30 green lights on the string, we can set up the equation (3/2 = 30/x), where x represents the number of white lights. Solving for x (multiplying both sides by 2 and then dividing both sides by 3) gives us x = 20. Therefore, there are 20 white lights on the string.

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The width of the car on the scale drawing is 16 inches.

To find the width of the car on the scale drawing, we can set up a proportion using the scale of the drawing and the actual width of the car.

The scale of the drawing is 1 inch = 1/2 foot. The actual width of the car is 8 feet. So the proportion is: x/1 inch = 8/1/2 foot.

To solve for x, we multiply both sides of the proportion by 1 inch: x = 8/1/2 inch. Simplifying the right side of the equation, we get x = 16 inches. Therefore, the width of the car on the scale drawing is 16 inches.

The width of the car on the scale drawing is 16 inches.

To find the width on the scale drawing, we need to use the scale provided in the question. The scale is given as 1 inch = 1/2 foot. This means that for every inch on the drawing, it represents 1/2 foot of the actual object.

Given that the actual width of the car is 8 feet, we need to convert this measurement to inches using the scale factor. Since 1 foot is equal to 12 inches, 1/2 foot is equal to 6 inches (because 12 inches / 2 = 6 inches).

Now, we can set up a proportion to find the width on the scale drawing:

[tex]\[ \frac{1 \text{ inch}}{1/2 \text{ foot}} = \frac{\text{width on drawing}}{8 \text{ feet}} \][/tex]

To solve for the width on the drawing, we multiply both sides of the equation by 8 feet: [tex]\[ \text{width on drawing} = \frac{1 \text{ inch}}{1/2 \text{ foot}} \times 8 \text{ feet} \][/tex]

Since 8 feet is equal to 16 halves of a foot (because 8 * 2 = 16), we can simplify the equation:

[tex]\[ \text{width on drawing} = 1 \text{ inch} \times 16 \][/tex]

[tex]\[ \text{width on drawing} = 16 \text{ inches} \][/tex]

Therefore, the width of the car on the scale drawing is 16 inches.

Answer:

Your correct answer is A. Without a table or graph, you might forget what an equation represents.

Step-by-step explanation:

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She can make 48 cups juice

One variable linear equation is an equation that has a variable and the exponent number is one.  

Can be stated in the form:  

[tex]\large{\boxed{\bold{ax=b}}[/tex]

or  

ax + b = c, where a, b, and c are constants, x is a variable  

Whereas the two-variable linear equation is a linear equation that has 2 variables and the exponent is one  

Can be stated in the form:  

[tex]\large{\boxed{\bold{ax+bx=c}}}[/tex]

x, y = variable  

Let x = cups of concentrate

w = cups of water

If we translate this sentence into equation:

w = 5x .. equation 1

If we translate this sentence into equation:

w = 32+x .. equation 2

We can make a comparison from equation 1 and 2

[tex]\displaystyle \frac{water}{concentrate} =5[/tex]

[tex]\displaystyle \frac{32+x}{x} =5[/tex]

[tex]\displaystyle 32+x=5x[/tex]

[tex]\displaystyle 32=4x[/tex][tex]\large{\boxed{x=8\:cups}}[/tex]

so x = concentrate = 8 cups

then water :

[tex]\displaystyle water={5\times8}[/tex]

water = 40 cups

Total juice she can make :

= 40 + 8 cups

=  48 cups

the slope-intercept form of the linear equation  

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a graph of a linear equation  

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system of linear equations  

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Keywords : one variable, linear equation , juice, cups, concentrate, water

The area of rectangular shelf with length 5 feet and width 3 feet is 15 feet².

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The length of rectangular shelf = 5 feet

The width of rectangular shelf = 3 feet

We know that;

Area of rectangle = Length × Width

So, We get;

The area of rectangular shelf = 5 × 3

                                             = 15 feet²

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To find the height of the tube with a given surface area and radius, use the formula for the surface area of a cylinder and solve for height.

The surface area of a cylinder (A) is given by the formula:

A = 2πrh + 2πr²

Given: A = 455.28 in², r = 4.2 in

Substitute the values and rearrange the formula to solve for h:

455.28 = 2π(4.2)h + 2π(4.2)²

Calculate the height, h, to find the answer.

The height of the tube is B. 50 inches.

The result of the expression 18(26) using the distributive property is 468

Given the product of integers 18(26), we are to write it using the distributive property.

Given 3 integers A, B and C

A(B+C) = AB + AC

This shows that the variable A was distributed over A and B

Applying this in the given question;

18(26) = 18 (20 + 6)

18(26) = 18 (20) + 18(6)

18(26)  = 360 +  108

18(26)  = 468

Hence the result of the expression 18(26) using the distributive property is 468

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Answer: 38 and there would be more likely 1 less kid in each group

Step-by-step explanation:

The question, from the Physics subject for a High School grade level, involves calculating the equivalent resistance of three identical resistors in parallel. The equivalent resistance in this scenario is one third of a single resistor, represented as R/3.

The question is regarding the equivalent resistance when three resistors are used in comparison to a single resistor. In the context given, if it is three times easier for current to flow through three identical resistors (R) than through a single one, the equivalent resistance is R/3. This is because resistors in parallel share the current, and hence the total resistance is divided by the number of resistors in parallel, if they are identical.

For example, if the current through three resistors in parallel is I, each resistor carries a current of I/3, and if they are identical, that means each has a resistance R. Therefore, the total current I flows through a resistance R/3, which is one third of the resistance faced by the current in the case of a single resistor.

Answer:  The correct option is (C) [tex]y=4x-13.[/tex]

Step-by-step explanation:  We are given to write a rule for the linear function given in the graph.

Since the graph is a straight line, so we are to find the equation of the line to find the rule.

From the graph, we note that

the points (3, -1) and (4, 3) lie on the straight line.

So, the slope of the line will be

[tex]m=\dfrac{3-(-1)}{4-3}\\\\\\\Rightarrow m=4.[/tex]

Since the line passes through the point (4, 3), so the equation of the line is given by

[tex]y-3=m(x-4)\\\\\Rightarrow y-3=4(x-4)\\\\\Rightarrow y=4x-16+3\\\\\Rightarrow y=4x-13.[/tex]

Thus, the required rule for the linear function is

[tex]y=4x-13.[/tex]

Option (C) is correct.

75% of 20 peaches is 15 peaches. To find this, divide 15 by 0.75.

To find the total number of peaches represented by 75%, you can divide the known amount (15 peaches) by 0.75. This is because 75% can be written as the decimal 0.75.

Dividing 15 peaches by 0.75 gives us:

15 ÷ 0.75 = 20 peaches

So, 75% of 20 peaches is 15 peaches.

To find the total number of peaches where 75% of them is 15 peaches, a proportion is set up and solved to discover that the total is 20 peaches.

The question "21. 75% of ________ peaches is 15 peaches" is asking us to find the total number of peaches if 75% of that total is equivalent to 15 peaches. To solve this, we need to set up a proportion where 75% is to 15 peaches as 100% is to the total number of peaches. We represent the total number of peaches by the variable x.

Here is the proportion set up as an equation: 0.75 * x = 15. To find x, divide both sides of the equation by 0.75, which gives us x = 15 / 0.75. When we calculate this, we get x = 20. So, the total number of peaches is 20.

To check our work, we can confirm that 75% of 20 is indeed 15 by multiplying 20 by 0.75, which equals 15. Hence, the statement "21. 75% of 20 peaches is 15 peaches" is correct and answers the student's question.

The answer to this question is 10267.