The net below is for a number cube. What are the three sums of the numbers on opposite surfaces of the cube?

A linear system in three variables has infinitely many solutions when the equations are dependent on each other and represent the same line or plane. To determine if a system has infinitely many solutions, we can solve the system and check if any of the equations can be derived from the others or if they represent the same line or plane.

When a linear system in three variables has infinitely many solutions, it means that the three equations are dependent on each other and represent the same line or plane. This happens when the coefficients of the variables in the equations are proportional to each other. To determine if a system has infinitely many solutions, we can solve the system and check if any of the equations can be derived from the others or if they represent the same line or plane.

Let's take the system of equations given in the question:

We can start by solving equations (1) and (2) for y:

Simplifying equation (2), we get:

y = 2

Substituting y = 2 into equation (1), we have:

7(2) = 6x + 8

14 = 6x + 8

6x = 14 - 8

6x = 6

x = 1

Now, let's substitute the values of x and y into equation (3):

y + 7 = 3x

2 + 7 = 3(1)

9 = 3

This equation is not true. Therefore, the system of equations is inconsistent and does not have infinitely many solutions. The system does not represent the same line or plane.

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Final answer:

To solve the inequality -38d-57 ≥ -19d+76, we isolate d, resulting in d ≤ -7, meaning d is any number less than or equal to -7.

Explanation:

The question asks us to solve an inequality: -38d - 57 ≥ -19d + 76. This requires us to isolate the variable d on one side of the inequality.

Add 19d to both sides: -38d + 19d - 57 ≥ 76.

Simplify: -19d - 57 ≥ 76.

Add 57 to both sides: -19d - 57 + 57 ≥ 76 + 57.

Simplify: -19d ≥ 133.

Divide both sides by -19, and remember to reverse the inequality sign when dividing by a negative number: d ≤ -7.

The solution to the inequality is d ≤ -7. This means that d can be any number less than or equal to -7.

Final answer:

To find the lengths of the two pieces, set up an equation using the given information. Solve for x and find the lengths of the two pieces.

Explanation:

To solve this problem, let's assume the length of one piece is x inches. Since the other piece is two times the length of the first piece, its length is 2x inches. According to the given information, the total length of the board is 90 inches. Therefore, setting up the equation x + 2x = 90, we can solve for x and find the lengths of the two pieces.

Combining like terms, we have 3x = 90. Dividing both sides of the equation by 3, we get x = 30. Therefore, the length of one piece is 30 inches, and the length of the other piece is 2(30) = 60 inches.

Lenny used the Associative property of addition to show that rearranging the grouping of numbers being added does not change the outcome of the equation.

While solving an equation, Lenny used the Associative property of addition which guarantees that the second equation (2x + (1+5) = 9) is equivalent to the first ((2x + 1) + 5 = 9). This property states that the grouping of numbers being added does not change the sum, as shown:

(A + B) + C = A + (B + C).

In the context of the provided equations, Lenny grouped the 1 and 5 together without changing the sum, illustrating that it doesn't matter how the numbers are grouped in addition.

Answer:

Never true

Step-by-step explanation:

Given inequality,

[tex]4x - 8 > 1 + 4(x+3)[/tex]

[tex]4x-8 > 1 + 4x + 12[/tex]

[tex]4x-8 > 4x + 13[/tex]

[tex]-8 > 13[/tex] ( false )

Since, when after solving an equation or inequality we get a true statement then the equation or inequality has infinitely many solution or true for all numbers while if we get a false statement then the equation of inequality has no solution or not true.

Hence, the given inequality is never true.

NMO = LMO = x+34

LMO = 1/2 of LMN

so 2(x+34) = 6x-28

2x+68 = 6x-28

2x +96 = 6x

96 = 4x

x =96/4 = 24

x = 24

 LMO = x+34 = 24+34 = 58

 since NMO = LMO, NMO = 58

The response explains which statements are substantiated facts and why. It clarifies the concept by using examples from the question.

Substantiated facts are statements supported by evidence or proof. In the given examples:

The equation that represents the function B(a) as the length of the side parallel to the base is B(a) = a/6 - 9, as per the area of a trapezoid.

If the length of two parallel sides of a trapezoid is 'a', 'b' and the height of that trapezoid is 'h', then the area of a trapezoid can be represented as

= [(a + b)h]/2

Given, the base of the trapezoid is 9 and the height of the trapezoid is 12.

Therefore, 'b' is the parallel side of the base.

The given function that represents the area of the trapezoid is:

A(b) = [12(b + 9)]/2

Let, A(b) = a.

Therefore, a =  [12(b + 9)]/2

⇒ 2a = 12(b + 9)

⇒ a = 6(b + 9)

⇒ a = 6b + 54

⇒ 6b = a - 54

⇒ b = (a - 54)/6

⇒ b = a/6 - 9

If we assume the length of the side parallel to the base 'b' = B(a), therefore, the equation will be:

B(a) = a/6 - 9

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Inga lives 2b + 3 miles from school, where b is the distance Brent lives from school in miles.

Therefore, the distance that Inga lives from school, in terms of b, is 2b + 3 miles.

The problem states that Inga lives 3 miles more than twice the distance that Brent lives from school. If the distance Brent lives from school is b miles, this can be expressed algebraically as 2*b (twice the distance of Brent) + 3 (the extra 3 miles that Inga lives). Therefore, the distance that Inga lives from school, in terms of b, is 2b + 3 miles.

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Answer:

The correct answer is A) 15, 19, 26, 51, 18, 21

Step-by-step explanation:

So let me start by explaining what an outlier is: An outlier is any data that falls outside of the given points, The reason the answer is A) is because 51 is included in the points, While most of the points in A) Are anywhere from 15-26 51 is an outlier because its outside of that standard range. The other ones don't have an outlier.

The data set that contains one outlier is,

{15, 19, 26, 51, 18, 21}.

The correct option is A.

Sets are groups of well-defined objects or components in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.

Given:

We have data set:

15, 19, 26, 51, 18, 21

22, 33, 31, 20, 28, 19

18, 20, 16, 22, 28, 26

27, 21, 31, 18, 21, 29

From the given choices,

the first data set has an outlier 51.

Because it is nowhere from the range of the data set.

Therefore, the set is {15, 19, 26, 51, 18, 21}.

To learn more about the set;

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A. calculate the average of the x-coordinates

C. divide 12 by 2

D. take the average of the endpoint

Final answer:

To factor a quadratic expression in the form of x² + bx + c, find two numbers whose sum is equal to b and whose product is equal to c.

Explanation:

To factor a quadratic expression in the form of x² + bx + c, we look for two numbers whose sum is equal to b and whose product is equal to c. Let's illustrate with an example:

For the expression x² + 5x + 6, we need to find two numbers whose sum is 5 and whose product is 6. In this case, the numbers are 2 and 3.

Therefore, we can factor the expression as (x + 2)(x + 3).

The linear  expression 30 + 12h represents Michael's lawn care service charges, where '30' is the fixed fee and '12h' is the variable fee depending on the hours worked.

Michael's lawn care service uses an equation to calculate the charges for his customers: 30 + 12h dollars, where h represents the number of hours spent working on a lawn. In this expression, the number 30 represents a fixed fee, likely covering base expenses such as equipment, transportation, or administrative costs. The term 12h represents the variable fee, where 12 is the hourly rate in dollars Michael charges for his labor, and h is the number of hours he works on the lawn.

Thus, to determine the total cost to a customer, one would multiply the number of hours Michael works (h) by his hourly rate (12) and then add the fixed fee (30). For instance, if Michael works 5 hours on a lawn, the total cost would be calculated as follows: 30 + 12(5) = 30 + 60 = 90 dollars.

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Answer:

To find point [tex]\( P \)[/tex] on line segment [tex]\( GK \)[/tex] such that [tex]\( 3(GP) = 2(PK) \)[/tex], we're seeking a point dividing [tex]\( GK \)[/tex] into segments at a \( 3:2 \) ratio.

Explanation:

To find the point [tex]\( P \)[/tex] on the line segment [tex]\( GK \)[/tex] such that [tex]\( 3(GP) = 2(PK) \)[/tex], we're essentially looking for a point [tex]\( P \)[/tex] that divides the line segment [tex]\( GK \)[/tex] into two segments, where the ratio of the length of the segment from [tex]\( G \) to \( P \)[/tex]  to the length of the segment from [tex]\( P \) to \( K \) is \( 3:2 \).[/tex]

Here's how to approach it:

1. Calculate the distances [tex]\( GP \) and \( PK \)[/tex] using the distance formula (or Pythagorean theorem if it's a 2D coordinate plane).

2. Let [tex]\( x \)[/tex] be the distance from [tex]\( G \) to \( P \)[/tex] and [tex]\( y \)[/tex] be the distance from [tex]\( P \)[/tex] to [tex]\( K \).[/tex]

3. Set up the equation [tex]\( 3x = 2y \),[/tex] representing the ratio of the lengths.

4. Solve for [tex]\( x \) and \( y \)[/tex] to find the coordinates of point [tex]\( P \).[/tex]

This process ensures that the point [tex]\( P \)[/tex] divides the line segment [tex]\( GK \)[/tex] into two segments according to the given ratio.

From the question given above, we were told that y varies directly with x. This can be expressed mathematically as:

y ∝ x

Replacing the proportionality sign (∝), we have

y = Kx

K => constant of proportionality

Next, we shall determine the value of K. This can be obtained as follow:

y = –252

x = 84

y = Kx

–252 = K * 84

Divide both side by 84

[tex]K = \frac{-252 }{84}[/tex]

Finally, we shall determine the value of y when x = 74. This can be obtained as follow:

x = 74

K = –3

y = Kx

[tex]y = - 3 * 74[/tex]

Therefore, the value of y when x = 74 is –222

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Joel borrowed money at an interest rate of approximately 2.73%. This was determined by using the simple interest formula to calculate the interest paid over 6 years and then re-formulating to find the interest rate using the known principal amount and time period.

The subject of this question is simple interest which is a concept in Mathematics. The question is asking for the interest rate at which Joel borrowed money to purchase a vehicle. By knowing that Joel borrowed $18,000, repaid a total of $20,953.80 after 6 years, and by applying the simple interest formula I = PRT (where I is interest, P is principal amount, R is interest rate and T is time in years), we can find out the interest rate.

The first step is to calculate the simple interest itself, which can be found by subtracting the original principal amount from the total amount repaid. So, $20,953.80 - $18,000 = $2,953.80 is the interest paid over 6 years.

Then we rearrange the simple interest formula to solve for the rate: R = I / (PT). Substituting the known values, our equation is: R = $2,953.80 / ($18,000 * 6), which gives R = 0.027325, or approximately 2.73% when expressed as a percentage.

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The measure of m∠D is 10 degrees

In line geometry, vertical angles are always equal.

Given the following vertical angles

m∠C=−2x+90 and m∠D=x−30

Since m∠C= m∠, hence;

-2x + 90 = x - 30

-2x - x = -30 - 90

-3x = -120

x = 40

Get the measure of m∠D

m∠D = x - 30

m∠D = 40 - 30

m∠D = 10degree

Hence the measure of m∠D is 10 degrees

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