Explain why 3(5x) is not equivalent to (3*5)(3*x).

1. Identity Property of Multiplication: [tex]\(1 \times (a+3) = a+3\)[/tex]

2. Associative Property of Multiplication: [tex]\((ab) c = c (ab)\)[/tex]

3. Associative Property of Multiplication: [tex]\(m (nr) = (mn) r\)[/tex]

4. Associative Property of Addition: [tex]\(2p + (3q+2) = (2p +3q) + 2\)[/tex]

5. Zero Property of Multiplication: [tex]\(2t \times 0 = 0\)[/tex]

6. Identity Property of Addition: [tex]\(0+ 2s = 2s\)[/tex]

1. Identity Property of Multiplication: [tex]\(1 \times (a+3) = a+3\)[/tex]

  - The identity property of multiplication states that any number multiplied by 1 equals the number itself.

2. Associative Property of Multiplication: [tex]\((ab) c = c (ab)\)[/tex]

  - The associative property of multiplication states that the grouping of factors does not affect the result of multiplication.

3. Associative Property of Multiplication: [tex]\(m (nr) = (mn) r\)[/tex]

  - Similar to statement 2, this demonstrates the associative property of multiplication.

4. Associative Property of Addition: [tex]\(2p + (3q+2) = (2p +3q) + 2\)[/tex]

  - The associative property of addition states that the grouping of terms does not affect the result of addition.

5. Zero Property of Multiplication: [tex]\(2t \times 0 = 0\)[/tex]

  - The zero property of multiplication states that any number multiplied by 0 equals 0.

6. Identity Property of Addition: [tex]\(0+ 2s = 2s\)[/tex]

  - The identity property of addition states that adding 0 to any number does not change the value of the number itself.

Complete question:

Name the property shown by each statement

1. 1 * (a+3) = a+3

2. (ab) c = c (ab)

3. m (nr) = (mn) r

4. 2p + (3q+2) = (2p +3q) + 2

5. 2t * 0 = 0

6. 0+ 2s = 2s

Final answer:

Colton will need 2 5/8 cups of vegetable oil to make 6 dozen brownies. This is calculated by tripling the original required amount of 7/8 cup of oil needed for 2 dozen brownies.

Explanation:

Colton's recipe for brownies specifies that 7/8 cup of vegetable oil is needed to make 2 dozen brownies. To find out how much oil is required for 6 dozen brownies, we need to calculate the amount of oil for triple the original quantity since 6 dozen is three times 2 dozen. First, we set up a proportion where 2 dozen corresponds to 7/8 cup of oil.

Mathematically, we can find the amount of oil needed for 6 dozen by multiplying the amount of oil for 2 dozen by 3 (since 6 is three times larger than 2):

Multiply 7/8 cup by 3.

7/8 × 3 = 21/8 cups.

Convert 21/8 cups to a mixed number to get 2 5/8 cups.

Therefore, Colton will need 2 5/8 cups of vegetable oil to make 6 dozen brownies.

Cindy's shortcut will not work because;

She made a mistake by not multiplying the 2 tens by 3 .

Now, for 24; 2 is the tens digit and 4 is the units digit.

This means according to partial products, we can rewrite 24 as; (2 × 10) + (4 × 1)

Now, to multiply 3 by (2 × 10) + (4 × 1) gives the expression;

3[(2  × 10) + (4 × 1)]

3(2  × 10) + 3(4 × 1)

This corresponds with the solution i got which is 3(4 × 1) = 12.

Now, the second part of the solution is; 3(2  × 10) = 60

But she just used 2 tens which is (2 × 10) = 20.

This means she failed to multiply 2 tens by 3 and that was her mistake.

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Answer: it's four

Step-by-step explanation:

Answer:

its -4

Step-by-step explanation:

To convert 5 quarts to cups, multiply 5 by the conversion factor of 4 cups per quart, resulting in 20 cups.

To convert from quarts to cups, you need to use a conversion factor. The conversion factor for converting quarts to cups is 1 quart = 4 cups. Therefore, to convert 5 quarts to cups, you need to multiply the number of quarts by the conversion factor.

The calculation is as follows:

Therefore, 5 quarts is equal to 20 cups.

2x + 5 is the expression for the calculation double 2 then add 5.

The given statement is double 2 then add 5.

We have to make an expression using this statement.

We will separate the statement into two parts.

- Double 2

- Add 5

We need to assume a number and let that number be x.

So first we need to double that number as 2x and add 5.

We have,

2x + 5

Thus 2x + 5 is our expression.

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Answer:

Step-by-step explanation:

We can express the charge made by the companies as equations.

The charge made by the Company A starts at 35 cents, and cost 3 additional cents per minute. We can write this as:

[tex]charge_A(t)= 35 \ c + 3 \ \frac{c}{min} * t[/tex]

where t is the length of the call in minutes. For the company B the charge starts at 45 cents, and cost 2 additional cents per minute. This is:

[tex]charge_B(t)= 45 \ c + 2 \ \frac{c}{min} * t[/tex].

Now. At what length t' the cost of the phone call is the same? We can write the condition as:

[tex]charge_A(t')= charge_B(t')[/tex]

this means:

[tex]35 \ c + 3 \ \frac{c}{min} * t'= 45 \ c + 2 \ \frac{c}{min} * t'[/tex]

doing a little work...

[tex]35 \ c + 3 \ \frac{c}{min} * t' - 35 \ c = 45 \ c + 2 \ \frac{c}{min} * t' - 35 \ c[/tex]

[tex]3 \ \frac{c}{min} * t'= 10 \ c + 2 \ \frac{c}{min} * t'[/tex]

[tex]3 \ \frac{c}{min} * t' - 2 \ \frac{c}{min} * t'= 10 \ c[/tex]

[tex] 1 \ \frac{c}{min} * t'= 10 \ c[/tex]

[tex] \frac{1 \ \frac{c}{min} * t'}{1 \ \frac{c}{min}}= \frac{10 \ c}{1 \ \frac{c}{min}}[/tex]

[tex] t'= 10 min [/tex]

And this is the length of time we are looking for.

Alyssa can design her garage with dimensions that are factors of 240 square feet. Possible dimensions range from 1 ft x 240 ft to 15 ft x 16 ft, with more practical and reasonable options being dimensions that are narrower but still close to a square, such as 12 ft x 20 ft or 15 ft x 16 ft.

The question regarding Alyssa's garage design involves finding all the pairs of whole numbers that multiply to give an area of 240 square feet for a rectangular floor. To determine this, we must find the factors of 240 that can serve as potential lengths and widths of the garage.

Factors of 240 that represent possible lengths and widths (where the first number in each pair is the length and the second is the width) are:

However, choosing the dimensions that are reasonable for a garage floor requires considering practicality. Very long and narrow rectangles, such as 1 ft x 240 ft or 2 ft x 120 ft, are not practical for a garage. Usually, dimensions that are closer to square but still rectangular, like 12 ft x 20 ft or 15 ft x 16 ft, are more suitable and reasonable for a garage.

The fish swam 28 feet down in the 32-foot deep lake.

To find out how many feet down the fish swam, we can multiply the depth of the lake by the fraction representing the proportion it swam.

The depth of the lake is given as 32 feet, and the fish swam 7/8 of this depth.

Multiplying 32 by 7/8:

32 * (7/8) = 224/8 = 28

Therefore, the fish swam 28 feet down in the 32-foot deep lake.

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Answer:

Elias is not correct. The new rectangle will be an enlargement because the scale factor is greater than 1. To be a reduction, the scale factor must be between 0 and 1.

Scale factor less than 1 gives the expanded form of the figure so Elias is wrong.

You must specify the extent of the shape's enlargement when describing one.

The scale factor is the ratio of two dimensions such that one figure is large and another is small.

The scale factor is done due to the unpractical measurement of any figure.

If the dimension of any figure is 2 units by using scale factor 2/1 it will become 2 × scale factor ⇒ 2 × 2/1 = 4

Similarly,

Scale factor 8/3 creates all dimensions by a factor of 8/3 = 2.67 so all dimensions will be going to expand.

Hence "Scale factor less than 1 gives the expanded form of the figure so Elias is wrong".

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To roast a five-pound roast takes 187 minutes and 30 seconds at the same rate.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that,

A 4-pound roast takes 150 minutes

So,

4-pound ⇔ 150 minutes

Divide by 4 on each side,

1-pound ⇔ 150/4 minutes

Multiply by 5

5-pound ⇔ (150×5)/4 minutes

5-pound ⇔ 187.5 minutes

5-pound ⇔ 187 minutes and 30 seconds.

Hence "To roast a five-pound roast takes 187 minutes and 30 seconds at the same rate".

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Answer:

45

Step-by-step explanation:

Answer:

Some

Step-by-step explanation:

Term and expression are two different concepts in mathematics. When numbers, symbols and operators are combined at one place to express or show some value, it is called expression. For example;

4y-3 or 3-1

It is an expression.

Where the term can be stated or defined as a single or smallest identity. Any number or variable or combination of them can be stated as term.

For example, if we take above expression 4y-3

4y-3, we can say that 4y is one term and 3 is second term.

Now the point to be noted here is, if you separately take 4y, it can be expressed as expression as well, because 4y is expressing value of something which is in accordance with the definition of expression.

If she spent $6.25 on earrings and 4 times that amount on a shirt. She take $39.50 to the mall originally.

The study of numbers and their operations, which are relevant to all other fields of mathematics, is part of the discipline of arithmetic operations. Addition, subtraction, multiplication, and division are the basic operations that make up this system.

It is given that, Jan spent the entire day shopping. She brought $8.25 home. She spent $4 times that much on a blouse and $6.25 on earrings.\

We have to find the amount she take to the mall originally.

Suppose the total amount is x,

x=$8.25 + $6.25 + $6.25×4

x=25+14.5

x=39.50

Thus, if she spent $6.25 on earrings and 4 times that amount on a shirt. She take $39.50 to the mall originally.

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The word sentence 'The quotient of two times a number k and -2.6 is 12' translates to the equation (2 × k) / -2.6 = 12. Solving for k gives k = -15.6.

The sentence describes 'the quotient of two times a number k and -2.6 is 12'. Quotient refers to the result of division. Therefore, the equation that represents this sentence is:

(2 × k) / -2.6 = 12

To find the value of k, you would multiply both sides by -2.6 and then divide by 2:

-2.6 × 12 = 2 × k => -31.2 = 2 × k

k = -31.2 / 2 => -15.6

Answer

Find out the what is the ratio of granola bars to fruit bars .

To prove

As given

A bowl contains 15 granola bars and 10 fruit bars.

The ratio of the granola bars to fruit bars is written as .

[tex]\frac{Number\ of\ granola\ bars}{Number\ of\ fruits\ bars} = \frac{15}{10}[/tex]

Simplify the above

[tex]\frac{Number\ of\ granola\ bars}{Number\ of\ fruits\ bars} = \frac{3}{2}[/tex]

Therefore

[tex]the\ ratio\ of\ the\ granola\ bars\ to\ fruit\ bars\ be\ \frac{3}{2} .[/tex]

Final answer:

The question deals with an inequality representing that the product of an unknown number and 4 is at least -12, resulting in a solution where the number must be greater than or equal to -3.

Explanation:

The question 'The product of a number and 4 is at least -12' can be translated into the inequality 4x ≥ -12, where x represents the number. To solve this, divide both sides of the inequality by 4, which follows the multiplication rules for the sign. This gives us x ≥ -3. So, the number must be greater than or equal to -3.

This is consistent with the fact that when two negative numbers multiply, the answer is positive, and when a positive and a negative number multiply, the answer is negative.