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Answer:Eureka Math Grade 6 Module 2 Lesson 1 Answer Key

March 31, 2021 / By Prasanna

Engage NY Eureka Math 6th Grade Module 2 Lesson 1 Answer Key

Eureka Math Grade 6 Module 2 Lesson 1 Example Answer Key

Example 1.

34 gallon of batter is poured equally into 2 bowls. How many gallons of batter are in each bowl?

Answer:

→ Since the whole is being put into 2 equal parts or bowls, this is the partitive model of division. What division expression can we write to match this story?

→ 34 ÷ 2

→ We can also think of this problem as asking, “3 fourths is 2 groups of what?” Let’s take a look at how to solve this using an area model. What is the whole? How much batter is being shared?

→ Three-fourths gallon

→ The story tells us that the batter is poured equally into 2 bowls. How can we show this in the model?

→ We can draw another line, horizontally, to partition the model into 2 equal units.

→ Now our model shows 3 fourths being partitioned into 2 equal parts. Could we also say that our model shows 12 of 3 fourths?

→ Yes, it’s just like in the Opening Exercise where dividing by 2 and multiplying by are the same.

→ Let’s label our model to show that. What is half of 3 fourths?

Half of 3 fourths is 3 eighths.

→ Yes, and what is 3 fourths divided by 2?

→ It’s also 3 eighths!

→ We said that we could also think of this problem as, “3 fourths is 2 groups of what?” Is it true that 3 fourths is 2 groups of 3 eighths? Use a repeated addition or multiplication sentence to support your response.

→ Yes, it’s true. 3 eighths plus 3 eighths is 6 eighths, which is equal to 3 fourths. →. It’s true.

2 × 38=68=34.

Eureka Math Grade 6 Module 2 Lesson 1 Example Answer Key 2

34 ÷ 2 = 12 of 34 = 38

38 gallon of batter in each bowl.

Step-by-step explanation:

-48.95820 is the result of the products of the decimal numbers (-2.655) and (18.44).

Given the data in the question;

(-2.655) multiply by  (18.44)

First, we determine the total decimal places in the numbers.

We have 5.

Next, we ignore the decimal places and carry out the multiplication operation as if operating on two integers.

                                - 2 6 5 5

                ×                 1 8 4 4

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

                +              1 0 6 2 0

                +           1 0 6 2 0

                +        2 1 2 4 0

                +       2 6 5 5

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

               =      - 4 8 9 5 8 2 0

Now, rewrite the result of the product with the 5 total decimal places.

= -48.95820

Therefore, the result of the multiplication operation is -48.95820.

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√664 is the perimeter of the triangle .

What is a perimeter in math?

In this graph three points are given .

Let A = ( -9 , 3)

     B = ( 5 , 7 )

     C = ( -4 , -8 )

Distance between point AB = [tex]\sqrt{( 5 + 9 )^{2} + ( 7 - 3 )^{2} }[/tex]

                                             = [tex]\sqrt{( 14)^{2} + ( 4)^{2} }[/tex]

                                             = [tex]\sqrt{196 + 16}[/tex]

                                              = √212

Distance between point BC = [tex]\sqrt{( -4 -5)^{2} + ( -8 -7 )^{2} }[/tex]

                                               = [tex]\sqrt{( -9)^{2} + ( -15)^{2} }[/tex]

                                               = [tex]\sqrt{ 81 + 225}[/tex]

                                               = √306

Distance between point CA = [tex]\sqrt{ ( -4 + 9)^{2} + ( - 8 - 3 )^{2} }[/tex]

                                               = [tex]\sqrt{(5)^{2} + ( - 11 )^{2} }[/tex]

                                               = [tex]\sqrt{25 + 121}[/tex]

                                               = √146

Perimeter of triangle = AB + BC + CA

                                  = √212 +  √306  +  √146

                                 = √664

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After conducting some mathematical operations, we know that the cost of 13 packages of pencils of $16.77.

So, the cost of 13 packages of pencils:

Then, obtain the cost of 13 packages of pencils as follows:

Therefore, after conducting some mathematical operations, we know that the cost of 13 packages of pencils of $16.77.

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The absolute value functions graphed are given as follows:

1. y = |x + 1|.

3. y = |x + 1| - 4.

4. y = 0.5(|x - 1| + 1)

An absolute value function of vertex (h,k) is defined by the following rule:

y = |x - h| + k.

For item 1, the vertex of the function is at point (-1,0), hence h = -1 and k = 0, and the rule is:

y = |x + 1|.

For item 3, the vertex of the function is at point (-1, -4), hence the coefficients are h = -1 and k = -4, and the rule is:

y = |x + 1| - 4.

For item 4, the vertex of the function is at point (1,1), and the function is also vertically compressed by a factor of 0.5, as when x changes by 2, y changes by 1, hence the rule is:

y = 0.5(|x - 1| + 1)

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In the standard conversion unit, 24 m/s equals 54 mph in mph

The conversion equation is given as

8 km/h = 5 mph

Convert 8 km to meters

So, we have the following equation

8 x 1000 m/h = 5 mph

Evaluate the products

So, we have the following equation

8000 m/h = 5 mph

Convert 1 hour to seconds

So, we have the following equation

8000 m/3600 s = 5 mph

Evaluate the quotient

So, we have the following equation

20/9 m/s = 5 mph

Multiply both sides by 9/20

1 m/s = 9/20 * 5 mph

Multiply both sides by 24

24 * 1 m/s = 24 * 9/20 * 5 mph

Evaluate the products

24 m/s = 54 mph

Hence, the equivalent of 24 m/s in mph is 54 mph

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First we have to calculate 20% of 240

Let's multiply 240 by 20/100, therefore the result is 48

Then we subtract 48 from 240, the result is 192

The answer is $192.

Answer:

the last one so it would be

0.890

Step-by-step explanation:

Answer: ..

Step-by-step explanation:

Wed: 0%

Thu: 30%

Fri: 50%

Sat: 80%

Sun: 100%

I got these answers by taking 100, and subtracting the rain percentage from it. For instance, if it was a 45% to rain, and a unknown amount for it to not rain, I would take 100 and subtract 45 from it, resulting in a 55% chance of it not raining.

Answer:

9 bases were stolen by elena

Step-by-step explanation:

Let n = number of bases stolen by Natasha

    e = number of bases stolen by Elena

So, n = 2e -3

So, if n=15,   15 = 2e-3   >>

e=9 bases stolen by Elena

If Natasha stole three fewer bases than twice the number Elena stole. If Natasha stole 15 bases, Then 9 bases did Elena steal

Two or more expressions with an Equal sign is called as Equation.

Given,

Natasha stole three fewer bases than twice the number Elena stole. If Natasha stole 15 bases, we need to find bases stolen by Elena.

Let N be the number of bases stolen by Natasha

E be the number of bases stolen by Elena

Natasha stole three fewer bases than twice the number Elena stole.

We can write this sentence as expression.

So, N= 2E -3

When Natasha stole 15 bases, then we need to find E

15=2E-3

Add 3 on both sides

18=2E

Divide both sides by 2

9=E

Hence 9 bases were Elena steal when Natasha steals 15.

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The most appropriate choice for expansion will be given by -

9 is needed to complete the square.

What is expansion?

Expansion is used when there is a product of factors in an algebraic expression and multiplication of algebraic expansion is needed by removing the brackets. Two most important formulas in expansion are

[tex](a+b)^2 = a^2+2ab+b^2\\(a-b)^2 = a^2-2ab + b^2[/tex]

Here,

[tex]x^2 - 6x +\\x^2 - 2\times x \times 3+[/tex]

To complete the square, [tex]3^2 = 9[/tex] is needed

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60 liters of 50% and 20 liters of 90% solution should be used.

By mixture and allegation

90                 50

          60

10                  30

10:30 = 1:3

We must mix the acid solution in a 1:3 ratio.

For 1 liter of 60% acid solution, we must use 1l 90% acid solution and 3l  50% acid solutions.

Then for 20 l of 60% acid solution, 1*20 = 20 l of 90% acid solution and 3 * 20 = 60 l of 50% acid solution should be used.

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The difference in the birth rate and death rate of the herd of buffalo as indicated in the task content is; 6% net death rate.

The population is in a state of decay.

The exponential equation which models the population is; P = 125,000 (0.94)^n.

The population of the herd after 10 years would be; P = 67,327.

It follows from the task content that the average birth rate is 31% per year, but the death rate is 37% per year.

Hence, the difference between the birth rate and death rate is; 6% net death rate per year.

It therefore follows from the statement above that the population is in a state of decay as it reduces after each successive year due to.higher death rate than birth rate.

Also, since the difference between death and birth rate is a 6% net death rate.

It follows that the model is such that we have;

P = 125,000 (100% - 6%)^n

P = 125,000 (0.94)^n

where, P = current population and n = number of years after.

Finally, the population of the herd after 10 years would be;

P = 125,000 (0.94)¹⁰

P = 67,327.

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Answer:

1. n + 7 ≤ 9

2. 3w < 18

3. 3 < s + 4

4. 4 ≥ x/2.1

The statement that is true about the function f(x)=4[tex]x^{5}[/tex] is that the function is odd because f(-x)=-f(x).

Given that the function is f(x)=4[tex]x^{5}[/tex].

We are required to choose which statement is true for the given function.

Function is basically the relationship between two or more variables that are expressed in equal to form. The values that enter in the function are known as part of domain of the function and the values that we get from the function are known as part of range of the function.

f(x)=4[tex]x^{5}[/tex]

f(-x)=4[tex](-x)^{5}[/tex]

Since the power of negative x is odd so the result which we will get will be negative. So,

f(-x)=-4[tex]x^{5}[/tex]

f(-x)=-f(x)

So, the function is odd.

Hence the statement that is true about the function f(x)=4[tex]x^{5}[/tex] is that the function is odd because f(-x)=-f(x).

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The equation of the line is x-y=0

What is point of intersection?

A point of intersection is a point where two lines intersect.

We are given the two equations as x-y=0 and x+y=0

The point of intersection can be given by finding the coordinates of which will satisfy both the equation

Now the equation can be solved by

The point of intersection is (0,0)

We have to find the equation of the line passing through the point (0,0),(2,2)

This can be done by

[tex]\frac{y-0}{0-2}=\frac{x-0}{0-2}[/tex]

[tex]\frac{-y}{2}=\frac{-x}{2}[/tex]

[tex]x-y=0[/tex]

Hence the equation of the line passing through the point of intersection of x-y=0 and x+ y=0 and (2,2) The equation of the line is x-y=0

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Answer: It would be $5.00

I hope you have a nice day!

The algebraic representation of the given figure is y = y₁ + 14, for B (x, y) and C (x ,y₁)

A module for an associative algebra is that algebraic representation in abstract algebra. In this case, an associative algebra is a ring, which need not be unitary.

If the algebra is not unitary, it can be made to be so using a standard method (see the adjoint functors page); there is no fundamental difference between the algebraic representations and the modules for the resulting unitary ring, in which the identity acts through the identity mapping.

Point A in both triangles are same

For Point B(-2,8) and Point C(-2, -6)

we can see Point B y = Point C y+14

So the algebraic representation is Point B(x, y) =  Point C (x ,y+14)

As x is same we get

y = y₁ + 14

Where y is point B y and y₁ is point C y,

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Answer:

The side length, s, of a cube is 4x^2 + 3. If V = s^3, what is the volume of the cube? The volume of the cube is 64 x^6 + 144x^4 + 108x^2 + 27.

Step-by-step explanation:

Hope this helps you

Answer:

X > -5

if the bubble were shaded in, it would be >

Part a: There are 4735 ways in which the event planner can choose 9 dishes if the number of hot dishes must be greater than or equal to 7

Part b: There are 91963 ways in which the event planner chooses 9 dishes if the number of hot dishes must be less than 7

Number of cold dishes = 9

Number of hot dishes = 10

Total number of dishes = 19

Part a:

The number of ways 9 dishes can be chosen, given the number of hot dishes, must be greater than or equal to 7:

= (¹⁰C₇*⁹C₂) + (¹⁰C₈*⁹C₁) + ¹⁰C₉

= 4320 + 405 + 10

= 4735 ways

Part b:

Choosing 9 dishes, when the number of hot dishes must be less than 7

= (¹⁰C₇*⁹C₂) + (¹⁰C₆*⁹C₃) + (¹⁰C₅*⁹C₄) + (¹⁰C₄*⁹C₅) + (¹⁰C₃*⁹C₆) + (¹⁰C₂*⁹C₇) + (¹⁰C₁*⁹C₈) + (¹⁰C₀*⁹C₉)

= 4320 + 17640 + 31752 + 26460 + 10080 + 1620 + 90 +1

= 91963 ways

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Check the picture below.

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

well, keeping all that in mind, the equation is already in standard form.

PAGE 1

1.) 5 x 7 + 5 x 3 = 50

2.) 3 x 3 + 3 x 4 = 21

3.) 2 x 8 + 2 x 8 = 32

4.) 6 x 8  - 6 x 5  = 18

5.) -3 x 9 - (-3) x 2 = (-21)

6.) -2 x 8 - (-2) x 4 = (-8)

PAGE 2

1.) 2 x 3 + X

2.) 5 x 6 + Y

3.) 7 x 8 + Y

4.) 9 x 2 - M

5.) 15 x 3 - S

6.) -15 x 6 - A

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We are given the following system of equations:

we are asked to determine if the point (0, 3) is a solution of the equation. To do that, we will replace the points x = 0 and y = 3 in each of the equations to see if they are both satisfied:

Replacing in equation (1):

Since equation (1) is not satisfied by the point this means that this is not a solution.

Answer:

28

Step-by-step explanation:

1 0/4 = 8

2 0/4 = 16, so 3 0/4 = 24.

2/4 = 1/2, and 2/4 has 4 grams.

24 + 4 = 28.

Answer: b

Step-by-step explanation: because if u see the numbers and they match

Answer:

f(x) is -1 and g(x) is 2 this is because f(x) intersect at -1 which is x axis and g(x) intersect 2 which is y axis

Answer

The triangle might be an equilateral triangle.

False

The triangle must be a right triangle.

False

The triangle might be an acute triangle.

True

Explanation

First of, we will explain the different types of triangles that exist based on side lengths and angle measures respectively,

Based on side lengths,

- Scalene triangle has none of its three sides having the same length as another. All the three sides have different lengths. To use angle to know this, all the three angles of a Scalene triangle have different values.

- Isoscelles triangle has two of its sides with the same lengths. In terms of angles, an Isoscelles triangle has two of its angles equal to each other.

- Equilateral triangle has all of its sides equal to one another. In terms of angles, all of the angles of an Equilateral triangle are equal to one another. Each of the angle is equal to 60°.

Based on angle measures,

- Acute triangle has all of the angles in the triangle being less than 90 degrees.

- Right angle triangle has one of the angles in the triangles being equal to 90 degrees.

- Obtuse triangle has one of the angles in the triangle being greater than 90 degrees but obviously less than 180 degrees.

So, a sketch of the triangle described would look like

So, we can see that the triangle has two sides equal, hence, the two base angles will be equal to.

If we call those base angles, x,

x + x + 45° = 180°

2x = 180° - 45°

2x = 135°

Divide both sides by 2

(2x/2) = (135°/2)

x = 67.5°

Three angles of the triangle are 45°, 67.5° and 67.5°

So, taking the statements one at a time now

The triangle might be an equilateral triangle.

This statement is False since it is evident that all the angles of this triangle are not equal to one another, hence, the sides cannot all be equal too.

The triangle must be a right triangle.

This statement too, is False. None of the angles of the triangle is equal to 90°.

The triangle might be an acute triangle.

This statement is True. All of the angles of the triangle are less than 90°.

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A. The function that models the inverse variation is y = 144/x

b. The value of x when y = 36 is 4

An inverse variation simply shows the relationship between two variables whereby when one value increases, the other value will decrease

1. In this case, x and y vary inversely and that x=48 when y=3. The inverse relationship will be:

y = k/x

3 = k/48

Cross multiply

k = 48 × 3

k = 144

Therefore, y = 144/x

2. When y is 36, x will be:.

y = 144/x

36 = 144/x

Cross multiply

36x = 144

Divide

x = 144 / 36

x = 4

The value of x is 4.

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Answer:  The correct answer is y= -8

Step-by-step explanation:  A line with a slope of zero is a horizontal line. In this case, the horizontal line intersects the y-axis at -8 and includes all values of x.