Given: 3x+12=8x−18 algebraic proofs


Step Reason
3x+12=8x−18
12=5x−18
30=5x
6=x
x=6

The expression of the weight carried by x hikers is x (3.4 + 4.6 + 2.2).

The weight carried by each hiker is 10.2 lb.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Three items are given.

The weight of each items are 3.4 lb, 4.6 lb, and 2.2 lb.

Now,

The total weight of all the items.

= 3.4 + 4.6 + 2.2

= 10.2 lb

The weight carried by x hikers.

= x (3.4 + 4.6 + 2.2)

= 10.2x lb

The weight carried by each hikers.

= 3.4 + 4.6 + 2.2

= 10.2 lb

Thus,

Weight carried by x hikers is 10.2x lb.

Weight carried by each hiker is 10.2 lb.

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Answer:

4) 100

5) 120

Step-by-step explanation:

4) Number of sides in the polygon = n = 6

Sum of all the angles of n-sided polygon = (n -2)* 180

                                                                    = (6 - 2) *180

                                                                    = 4 * 180

                                                                    = 720

x + x + 9 + 90 + 120 +156 + 145 = 720

Combine like terms,

                             2x + 520  = 720

Subtract 520 from both sides,

                                           2x = 720 - 520

                                           2x = 200

Divide both sides by 2,

                                             x = 200÷2

                                             [tex]\sf \boxed{x = 100^\circ}[/tex]

5)    Sum of all the angles of 5 sided polygon = ( 5 - 2)*180

                                                                           = 3 * 180

                                                                            = 540

    x + x + x + x + 60 = 540

                    4x + 60 = 540

                            4x = 540 - 60

                             4x = 480

                               x = 480 ÷ 4

                               [tex]\sf \boxed{x = 120^\circ}[/tex]

Answer:

4.) You need 720 degrees sum for 6 sided polygon.

5.) You need 540 degrees for a 5 sided polygon.

Step-by-step explanation:

4.) -

120 + 156 + 145 + 90= 511

720 - 511 = 209.

209 - 9 = 200

200 / 2 = 100

X is equivalent to 100 Degrees

-

5.) -

Since X is the same for all sides we'll take 60 from 540 = 480

480 / 4 = 120

X = 120

The requried ratio of boys in the club to girls is given as 7/9 or 7:9. Option A is correct.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
The conservation club has 32 members. There are 18 girls in the club.
Number of boys = 32 - 18 = 14
Ratio of boys to girls = number of boys / number of girls
                                = 14 / 18 = 7/9

Thus, the requried ratio of boys in the club to girls is given as 7/9 or 7:9. Option A is correct.

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Explanation:

The shorter side lengths 3 and 3 add to 3+3 = 6, which is not larger than the remaining side 9. This is why a triangle is not possible.

For a triangle to be possible, we need the sum of any two sides to be larger than the third side. Refer to the triangle inequality theorem.

I recommend making slips of paper that are 3 inches, 3 inches, and 9 inches long (or replace "inches" with "centimeters"). Then try to make a triangle with those slips of paper. You should find such a task is impossible: as mentioned, the 3 inch sides come up short when trying to attach to the 9 inch side.

The statement "It's not possible to build a triangle with side lengths of 3, 3, and 9" is true.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

A triangle cannot be formed with side lengths of 3, 3, and 9.

To form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

However, in this case, the sum of the lengths of any two sides is 3+3=6, which is less than the length of the third side, 9.

Therefore, it is not possible to form a triangle with side lengths of 3, 3, and 9.

Thus,

The statement "It's not possible to build a triangle with side lengths of 3, 3, and 9" is true.

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For the given system of equations −x+4y = 8 & 2x+3y = −5

he proceed to the solution in following way,

Step 1:   Inv. of [tex]\left[\begin{array}{ccc}-1&4&\\2&3&\\&\end{array}\right][/tex] × [tex]\left[\begin{array}{ccc}8\\-5\\\end{array}\right][/tex]

Step 2:  -1/11 [tex]\left[\begin{array}{ccc}3&-4&\\-2&-1&\\\end{array}\right][/tex]

Step 3:  -1/11 [tex]\left[\begin{array}{ccc}-44\\11\\\end{array}\right][/tex]

Step 4:  [tex]\left[\begin{array}{ccc}-4\\1\\\end{array}\right][/tex]

Inverse matrix is a type of matrix which we get by taking the transpose of an adjoint matrix.

P⁻¹ = adj(P)/ |P|

|P| = Determinant of P

Property of inverse matrix,

P⁻¹×P = I

Given that,

system of equations

−x+4y = 8 & 2x+3y = −5

He multiplies the left side of the coefficient matrix by the inverse matrix

 Inv. of [tex]\left[\begin{array}{ccc}-1&4&\\2&3&\\&\end{array}\right][/tex]× [tex]\left[\begin{array}{ccc}-1&4&\\2&3&\\&\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right][/tex] = Inv. of [tex]\left[\begin{array}{ccc}-1&4&\\2&3&\\&\end{array}\right][/tex]× [tex]\left[\begin{array}{ccc}8\\-5\\\end{array}\right][/tex]

By using property of inverse matrix

[tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right][/tex] =  -1/11 [tex]\left[\begin{array}{ccc}3&-4&\\-2&-1&\\\end{array}\right][/tex]× [tex]\left[\begin{array}{ccc}8\\-5\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right][/tex] =   -1/11 [tex]\left[\begin{array}{ccc}-44\\11\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right][/tex] =   [tex]\left[\begin{array}{ccc}-4\\1\\\end{array}\right][/tex]

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Answer:

Not a lot of information given but if you are looking for the difference in price it is 31 CHF

It is 31 more CHF in Manchester than in Switzerland.

Step-by-step explanation:

1.55(145) = 224.75

224.75-193.75 = 31

Answer: 4 1/3

Step-by-step explanation:

(12 + 1) 3 = 12 3 + 1 3 = 4 + 1 3 = 4 1 3 13 3 = 4 1 3 Hence, 13/3 as a mixed number is 4 1/3

If you cannot vote, then you are under 18. If the next month is not March, then this month is not February. If you cannot afford a new laptop computer, then you do not have $400.

What is Inverse, Converse and Contrapositive Statement?

Inverse Statement: The inverse statement, denoted pq, assumes the inverse of each of the original statements (if not p, then not q).

Converse Statement: The converse statement is notated as q→p (if q, then p).In the original "if-then" statement, the original statements trade places.

Contrapositive Statement: The conditional statement's inverse is "If not Q, then not P."

1) The inverse statement would be,

If you cannot vote, then you are under 18.

2) The converse statement would be,

If the next month is not March, then this month is not February.

3)The Contrapositive statement would be,

If you cannot afford a new laptop computer, then you do not have $400.

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Answer: 4.5

Step-by-step explanation: Those bars are absolute value. Hope it helps, please mark brainliest and give your thanks.

Answer:

Oreos is a better deal by lower unit price But i like Nutter Butters

Step-by-step explanation:

A package of Oreos is a better deal because it has a lower unit price per ounce. Oreos have a unit price of $0.19 per ounce, while Nutter Butters have a unit price of $0.21 per ounce.

The expression that is different from "Add −4.5 and 3.5" will be "What is the distance between negative 4 point 5 and 3 point 5?"

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator

In this case, the expression that is different from "Add −4.5 and 3.5" will be "What is the distance between negative 4 point 5 and 3 point 5?" This is because finding the distance simply means:

= -4.5 - 3.5

= -8.0

This is different from the initial value.

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The value of x for the given expression -2(4x+5.5) = 3/4x +27.6+5/4x is, 3.86

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given expression,

-2(4x+5.5) = 3/4x +27.6+5/4x

-8x -11  =  3/4x + 27.6 + 5/4x

-8x-2x = 27.6 + 11

-10x =  38.6

x  = -3.86

Hence, the value of x is -3.86

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Answer:sThe symbol of the standard deviation of a random variable is "σ“, the symbol for a sample is "s". The standard deviation is always represented by the same unit of measurement as the variable in question. This makes its interpretation easier, compared to the variance.

Step-by-step explanation:

For solving the equation we are using

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.

The equation is 2x = 13 - 5

here by subtracting 5 from 13 we get 8

so 2x = 8

or x = 4 (proved)

for solving the equation we are using

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Answer:

3(1-3x)

Step-by-step explanation:

factor out 3 from the expression

Mary and Jane have multiple ways to choose their subset of figurines for the comic book convention.

We know that Mary must include every figurine that Jane brings, so Mary must choose a subset of her collection that is at least x+1 figurines.

Since Mary must also choose at least one additional figurine, the total number of figurines that Mary can choose from is n-(x+1) + 1 = n-x

The total number of ways that Mary and Jane can choose their subsets is the product of the number of ways each can choose their subsets.

So, the number of ways is

(choose x out of n) * (choose x+1 out of n)

This is also known as binomial coefficient, which can be represented as nCx or (n x)

Hence the number of ways is

nCx * (n-(x))C(x+1)

Mary and Jane have multiple ways to choose.

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Answer:  The ocean liner is approximately 5.2 miles from the fishing boat.

The equation to find the number of leaves which Aidan has now, n is given by 8 × 12 - 7 = n.

In Mathematics, an equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.

Next, we would write the equation that gives n, the number of leaves Aidan would have after collecting leaves for an art project as follows:

The number of leaves that Aidan collected from 8 different trees is equal to 8 leaves. Additionally, Aidan picks 12 leaves from each tree to have a total of 96;

n = 8 × 12 = 96.

Lastly, Aidan lost 7 leaves on his way home. Therefore, we would subtract 7 leaves from the total number of leaves that Aidan collected from 8 different trees;

n = 96 - 7 = 89 leaves.

In conclusion, the complete equation is represented by 8 × 12 - 7 = n.

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The volume of the baseball to the nearest cubic inch is 9 cubic inches.

A sphere is a three dimensional figure which consists of set of all the points which are at an equal distance from a point called the center of the sphere.

Volume is the space occupied by a three dimensional object.

Given that,

Radius of a baseball = 1 3/10 inches = (1 × 10 + 3) / 10 = 13/10 inches.

Also we know that,

Volume of a sphere = 4/3 π r³, where r is the radius.

Volume of the baseball = 4/3 π (13/10)³

                                       = 4/3 π (1.3)³

                                       = 4/3 π × 2.197

                                       = 2.9293 π

                                       = 2.9293 × 3.14

                                       = 9.198 cubic inches.

                                       ≈ 9 inches³

Hence the volume of the baseball is 9 cubic inches.

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Answer:

6p + 3s = 500

p + s = 120

Step-by-step explanation:

p represents the parents and s represents the students

the total amount of tickets should be p and s, hence why they equal 120

The total cost should be 500, and each parent ticket is $6 while each student ticket is $3 hence the 6p and 3s

Answer:

Tabitha's commission would be 6% of the total sales from the three cars

Step-by-step explanation:

which is $(23,000 + 13,800 + 25,760) * 0.06 = $3,638.40

Answer:

27 cm^2

Step-by-step explanation:

The formula for finding area of trapezoid:

[tex] \frac{a + b}{2} \times h[/tex]

[tex] \frac{6 + 12}{2} \times 3 = 27[/tex]

So the answer is 27 cm^2

The actual length of the train is calculated to be 18.33 feet

Scale factors are used to increase or decrease image. The situation of increment is usually called enlargement, and it is case for the problem.

solving for the factor, assuming the factor is k, using the ratio 1 : 40.  the scale factor is 40 / 1 = 40

Solving for the actual length

actual length =  scale facto * model length

actual length = k * 5.5 in

actual length = 40 * 5.5 in

actual length = 220 in

converting to feet

12 in = 1 foot

220 in = ?

cross multiplying

12 * ? = 220

? = 220 / 12

? = 18.33 feet

the actual length of the train is 18.33 feet

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The inequality h ≤ 8 represents the number of hours, Carmen works on the job.  

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

On Saturday, Carmen works no more than 8 hours at her job.

Let h be the number of hours, he works on the job.

According to the question,

h ≤ 8.

That means,

Carmen works less than or equals to 8 hours.

Therefore, the inequality is h ≤ 8.

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Answer:

the growth factor of the initial amount is correct

The proof of the given question is given in the solution as follows

A technique for factoring a number or a polynomial is called factorisation. The polynomials are divided into the sums of their component parts. As an illustration, x2 + 2x may be factored as x(x + 2), where x and x+2 are the factors that can be multiplied to obtain the original polynomial.

The six types of factoring are: greatest common factor, difference in two squares, grouping, sum or difference in two cubes, trinomials, and general trinomials.

In the given equation

we separate m2-1/n2 to (a+b)(a-b) form

and hence we get the answer as

(n+1/m)^m-n/(m-1/n)^m-n

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Answer: yes

Step-by-step explanation: a square is always a rectangle but a rectangle is only a square when all sides are equal

Answer:

Absolutely!

Step-by-step explanation:

Since a square has 4 right angles, it can also be classified as a rectangle.

Answer:I don’t onos

Step-by-step explanation:I don’t know

Step-by-step explanation:

last week = 15

this week 2o%

therefore =. last WK + this WK = 15×20÷100/1

= 300÷100/1=. 3

Diana scored 3point this week

The solution is x minus 2 divided by 6 open parentheses x + 12 close parentheses.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The product of 8 and 3 equals 11. 8 + 3 is an expression.

Here,

=quantity x squared minus 100 over quantity x squared plus 2 x minus 120 divided quantity 6 x plus 60 over quantity x minus 2

=((x²-100)/(x²+2x-120))/((6x+60)/(x-2))

Let's simplify some of the factors:

x² - 100 = x² - 10²

= (x - 10)(x + 10)            

6x + 60 = 6 * x + 6 * 10

= 6 * (x+10)

x² + 2x - 120 =  x² + 12x - 10x - 12 * 10

= (x * x - 10 * x) + (12 * x - 12 * 10)

= x(x - 10) + 12(x - 10)

= (x - 10)(x + 12)

The solution is amount x minus 2 over 6 open parentheses x + 12 close parentheses.

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