Mathematics College

Laura and Sean find the product of 3x4 using different methods.
Laura: It's 2 thirds of 4.
²×4 = 3 +
Use words, pictures, or numbers to compare their methods in the space below.
Sean: It's 4 groups of 2 thirds.
2|3
+
= 4x
8
83 this is also worth 100 points

Laura And Sean Find The Product Of 3x4 Using Different Methods.Laura: It's 2 Thirds Of 4.4 = 3 +Use Words,

Answers

Answer 1

Both Laura and Sean arrive at the same answer of 8/3 by using different methods.

Laura starts by multiplying 2/3 by 4 to find the total amount of 2/3 in 4 units.

Sean starts by finding the total amount of 2/3 in one group and then multiplying that amount by the number of groups, 4.

Both methods lead to the same answer, so it doesn't matter which method is used. The important thing is that the answer is correct.

Related Questions

A golden retriever weighing 85lb was prescribed a medication. If the dosage is 1mg for every 5lb, how much medicine was the dog given?

Answers

The dog should be given 17 mg of dosage.

What is the unitary method?

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here: A golden retriever weighing 85 lb was given a dosage of 1 mg per 5 lb

For every 5 lb 1 mg of the product is given

Thus for 85 lb the number of doasages would be

N= 85/5

   = 17 mg

Hence, The dog should be given 17 mg of dosage.

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xa rectangular box is to have a square base and a volume of 40 ft3. rectangular box with a square base the material for the base costs 29 cents/ft2, the material for the top costs 24 cents/ft2, and the material for the sides costs 10 cents/ft2. if x denotes the length of one side of the base (in feet), find a function in the variable x giving the total cost of materials used in constructing the box in cents. total cost, as a function of x

Answers

The total cost of materials used in constructing the box in cents is given by the expression: Total Cost = [tex]1176/x2 + 960x[/tex].

Let x represent the length of the side of the square base, then the area of the base is given by [tex]x2[/tex]. If the volume of the box is given to be 40ft3, then the height of the box is given by [tex]40/x2[/tex]. The total cost of material used in constructing the box is given by the cost of the base, the cost of the top, and the cost of the sides. The total cost of material in cents is given by the expression:

Total Cost = [tex]29x2 + 24(40/x2) + 10(4x)(40/x2)[/tex]

The cost of the base is given by [tex]29x2[/tex], since the material for the base costs 29 cents/ft2. The cost of the top is given by [tex]24(40/x2)[/tex], since the material for the top costs 24 cents/ft2. The cost of the sides is given by [tex]10(4x)(40/x2)[/tex], since the material for the sides costs 10 cents/ft2.

Therefore, the total cost of materials used in constructing the box in cents is given by the expression:

Total Cost = [tex]29x2 + 24(40/x2) + 10(4x)(40/x2) = 1176/x2 + 960x[/tex]

The total cost of materials used in constructing the box in cents is given by the expression: Total Cost = [tex]1176/x2 + 960x.[/tex]

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Fill in the blanks to follow the steps in solving the equation:

5x − 12 − 6x = −10x + 7 − 1

Answers

Answer:

see explanation

Step-by-step explanation:

5x - 12 - 6x = - 10x + 7 - 1

step 1 : combine like terms

- x - 12 = - 10x + 6

step 2 : collect x- terms on the left side of the equation

add 10x to both sides

9x - 12 = 6

step 3 : collect constants on the right side of the equation

add 12 to both sides

9x = 18

step 4 : isolate x by dividing both sides by 9

x = 2

Final answer:

To solve the equation 5x - 12 - 6x = -10x + 7 - 1, combine like terms and isolate the x term and we get x=2

Explanation:

To solve the equation 5x - 12 - 6x = -10x + 7 - 1, we need to combine like terms on both sides of the equation. Let's start by combining the x terms on the left side:
(5x - 6x) - 12 = -10x + 7 - 1
Simplifying further:
-x - 12 = -10x + 6
Next, we want to get all the x terms on one side of the equation. We can do this by adding 10x to both sides:
-x - 12 + 10x = -10x + 6 + 10x
Simplifying further:
9x - 12 = 6
Now, we want to isolate the x term. Let's add 12 to both sides:
9x - 12 + 12 = 6 + 12
Simplifying further:
9x = 18
Finally, divide both sides of the equation by 9 to solve for x:
x = 2

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A chemical company makes two brands of antifreeze. The first brand is 70% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 180 gallons of a mixture that contains 75% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answers

The antifreeze used by each brand will be V₁ = 72 gal. and V₂ = 108 gal.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that

ω₁ = 70% ÷ 100% = 0.7; 70% pure antifreeze.

ω₂ = 95% ÷ 100% = 0.95.

ω₃ = 85% ÷ 100% = 0.85.

V₁ = ?; volume of 70% antifreeze.

V₂ = ?; volume of 95% antifreeze.

V₃ = V₁ + V₂.

V₃ = 180 gal.

The quantity will be calculated as:-

V₁ = 180 gal - V₂.

ω₁ · V₁ + ω₂ ·V₂ = ω₃ · V₃.

0.70 · (180 gal - V₂) + 0.95 · V₂ = 0.85 · 180 gal.

126gal - 0.7V₂ + 0.95V₂ = 153 gal.

0.25V₂ = 27 gal.

V₂ = 27 gal ÷ 0.25.

V₂ = 108 gal.

V₁ = 180 gal - 108 gal.

V₁ = 72 gal.

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17% of the group wanted to go out on Friday instead of doing homework. The group had 19 members. How many wanted to go out?

Answers

Multiply 19 by 17% and you get 3.23.

3 people wanted to go out, a person cannot be .23.

Hope this helps

Answer:

Step-by-step explanation:

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Evaluate and simplify the following complex fraction. -2/-7|4/-9

Answers

The solution of the complex function is ( 71- 8i ) / (16 +8i).

What is a complex function?

The area of mathematical analysis that studies functions of complex numbers are known as complex analysis, often known as the theory of functions of a complex variable.

Given that the function is ( 2 -7i) / ( 4 - 9i). The complex function will be solved as below:-

E = ( 2 -7i) / ( 4 - 9i)

E = ( 2 -7i) x ( 4 + 9i ) / ( 4 - 9i) x ( 4 + 9i )

E = ( 8 - 8i + 63 ) / ( 4 - 9i )²

E = ( 71 - 8i ) / ( 16 - 8i )

Therefore, the solution of the complex function is ( 71- 8i ) / (16 +8i).

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