Solve the problem below:

(-10)+13-2=?

The explicit formula for the sequence is an = 14-6(n-1).Each word in an arithmetic sequence increases by adding or subtracting a certain constant, k.

Arithmetic sequence.This are sequence that has. a common difference that is the difference between the preceding and sthe explicit formula for the sequence is an = 14-6(n-1) is equal.Each word in an arithmetic sequence increases by adding or subtracting a certain constant, k.

As opposed to a geometric sequence, where each term is increased by dividing or multiplying a certain constant k, this one does not.

A series of numbers in the following format is an arithmetic sequence: a, a + d, a + 2 d, a + 3 d, a + 4 d,...

The common difference between the terms in the series is d, and number an is the first term.

An = a + (n - 1)d gives the nth term of an arithmetic series.

Given the following

a1 = 14

an = an-1 - 6

The nth term of the sequence is expressed as:

An = a+(n-1)d

an = 14+(n-1)(-6)

an = 14 -6n + 6

an = 14-6(n-1)

Hence the explicit formula for the sequence is an = 14-6(n-1).

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Answer:

x=13

Base=25

Leg=21

Step-by-step explanation:

Firstly, since the triangle is an isosceles triangle, both legs measure the same. So we can write:
[tex]3x-18=21\\3x=39\\x=13[/tex]

With x being solved, we can substitute it into the leg and the base:

Base:

[tex]2(13)-1\\26-1\\25[/tex]

Leg (Since the other leg is 21, we can just conclude this leg to also be 21):

[tex]3(13)-18\\39-18\\21[/tex]

If it has any units, don't forget to put the correct unit measures.

The expressions  15x − 45 and –3 (15 − 5x)  are always equivalent.

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Therefore, let's check of the expressions are equivalent by simplifying the expressions.

Hence, the first expression is 15x - 45.

Let's simplify the expression -3(15 - 5x) to know if it's equivalent to the expression 15x - 45.

Therefore,

-3(15 - 5x)

open the brackets

-3(15 - 5x)  = -45 + 15x = 15x - 45

Therefore, the expression are always equivalents.

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The algebraic expression of the word expression are as follows:

a.5 + x

b. 12y

c. z - 5

d. 2b + 4

An algebraic expression is an expression which is made up of variables and constants, along with algebraic operations such as addition, subtraction, multiplication, division etc.

Therefore, let's convert the word expression to algebraic expressions.

a.

Sum of 5 and x

5 + x

b.

Product of 12 and y

12 × y = 12y

c.

5 less than of z

z - 5

d.

4 more than double b​

2b + 4

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Answer: The coordinate points are: -6, -7

Step-by-step explanation:

When you reflect a point over the y-axis, the y -coordinate stays the same, but the x -coordinate changes signs.

The length of y to the nearest inch is 4 inches.

Length is a measure of distance. It is the linear dimension of an object, the longest side of an object, or the measurement of something from end to end. Length can be measured in many different units, including feet, yards, meters, miles, centimeters, and millimeters. Length is a fundamental concept in mathematics and science and is used to calculate the area, volume, and speed of an object.

Using the trigonometric law of sines, we can find the length of y: y = x*sin(θ) = 7*sin(37∘) ≈ 4.14 inches. Therefore, the length of y to the nearest inch is 4 inches.

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Fraction times 7, the length of RTS is 84/7.

Length is a measure of how long an object is, or the distance between two points. It is a fundamental concept in physics, mathematics, and engineering. Length can be measured in a variety of ways, including inches, centimeters, feet, and meters. Length is an important factor when designing objects, as it can affect their usability, strength, and overall performance.

The shaded sector of the circle has an area of 27, which is equal to one-fourth of the entire circle. Therefore, the sector angle, RTS, is equal to one-fourth of the entire angle of the circle, which is 360 degrees. Therefore, the angle RTS is 90 degrees.

The ratio of the radius to the arc length for the sector is 1:2, which means the arc length of RTS is equal to twice the radius, or QR*. Therefore, the length of RTS is equal to 2 * QR = 12. Expressing this answer as a fraction times 7, the length of RTS is 84/7.

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Answer:

m∠m = 130

m∠n = 105

Step-by-step explanation:

Break the shape into 2 isosceles triangles.  Base angles of isosceles triangles are congruent.

m∠m = 130       sum of interior angles of a triangle = 180; 180 - 25 - 25 = 130

m∠n = 130 - 25 = 105

Answer:

the answer is in the picture

Answer:

y=6.4 and x=16.25

Step-by-step explanation:

angle b is the same as e

5y-3=29

   +3  +3

5y=32

/5   /5

y=6.4

line AC is equal to line DF.

8x-11=119

   +11  +11

8x=130

/8   /8

x=16.25

Given system of linear equations has No solutions i.e. D.

What are linear equations ?

A linear equation is one in which the variable's maximum power is always 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. In this equation, x is a variable, A is a coefficient, and B is constant. A linear equation in two variables has the conventional form Ax + By = C. The variables x and y are variables, the coefficients A and B are coefficients, and the constant C is a constant.

As given

y=-3x-4

y=-3x  

      when we make a graph of these equations we can see that these are parallel lines and as parallel lines have no solution because they do not intersect at any point.

Hence, these equations have no solution.

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By using the rule  a^m/a^n = a^m-a^n , x^10y^14/729 is the equivalent expression of the provided expression.

Math allows for addition, subtraction, multiplication, and division. Following is the structure of an expression: Calculator, number or variable, and expression The components of a mathematical expression include numbers, variables, and operations (such as addition, subtraction, multiplication or division etc.) You can contrast phrases and expressions.

given

(27x^3y^-15/x^8y^-8) ^-2

[ 27x^3-8 y ^-15-(-8)]^-2...... a^m/a^n = a^m-n

= 1/(27)^2 * (x^10y^11) = x^10y^14/729 .

By using the rule  a^m/a^n = a^m-a^n , x^10y^14/729 is the equivalent expression of the provided expression.

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The total money paid if 4 snacks are bought is $61

The total money paid if x snacks are bought is $45 + $4x

The form of the equation that represents the total money that Peyton would pay is:

Total money paid = total cost of the tickets + total cost of snacks

= (cost of one ticket x total ticket bought) + (cost of one snack x total number of snacks bought)

Total money paid if 4 snacks are bought = ($15 x 3) + (4 x 4)

= $45 + $16 = $61

Total money paid if x snacks are bought = ($15 x 3) + (4 x x)

= $45 + $4x

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the slope of the line is 1/2.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

here, we have,

from the graph,

we get,

the equation of the line is , y= 0.5x

hence, the slope of the line is 1/2.

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The set of the expression (A ∪ B) ∩ (B ∩ C') is {2, 3, 6}.

What is set?

Sets in mathematics, are simply a collection of distinct objects forming a group. A set can have any group of items, be it a collection of numbers, days of a week, types of vehicles, and so on. Every item in the set is called an element of the set.

Given that, U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {6, 8, 2}, B = {3, 2, 5, 6}, and C = {5, 1, 7}.

If U is a universal set and A be any subset of U then the complement of A is the set of all members of the universal set U which are not the elements of A.

So, complement of set C is C'={2, 3, 4, 6, 8}

Now, (A ∪ B) ∩ (B ∩ C')

= ({6, 8, 2}∪{3, 2, 5, 6}) ∩ ({3, 2, 5, 6}∩{2, 3, 4, 6, 8})

= {2, 3, 5, 6, 8} ∩ {2, 3, 6}

= {2, 3, 6}

Therefore, the set of the expression (A ∪ B) ∩ (B ∩ C') is {2, 3, 6}.

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"Your question is incomplete, probably the complete question/missing part is:"

Let U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {6, 8, 2}, B = {3, 2, 5, 6}, and C = {5, 1, 7}. Find the following.

(A ∪ B) ∩ (B ∩ C').

By using the 68-95-99.7 Rule, the percent of scores in the data set that are expected to be below a score of 120 is 84.1%.

In Mathematics, the 68-95-99.7 Rule is sometimes referred to as the  Empirical Rule and it can be defined as a statistical rule which states that:

The middle 68% of a normal distribution would be within one (1) standard deviation of its mean i.e between μ - σ and μ + σ.

The middle 95% of a normal distribution would be within two (2) standard deviations of its mean i.e between μ - 2σ and μ + 2σ.

The middle 99.7% of a normal distribution would be within three (3) standard deviations of its mean i.e between μ - 3σ and μ + 3σ.

At the middle 68% of the normal distribution, we would apply the 68-95-99.7 Rule to the given data as follows;

μ - σ = 108 - 12 = 96.

μ - σ = 108 + 12 = 120.

Where:

Now, we can determine the percent of scores (P) in the data set that are expected to be below a score (x) of 120 by using the probabilities and standard distribution table;

P(x < 120) = P((x - μ)/σ < (120 - 108)/12)

P(x < 120) = P((x - μ)/σ < 12/12)

P(x < 120) = P(z < 1)

P(x < 120) = 0.841

P(x < 120) = 84.1%

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The true statement exists

2. <1 + <3 = 180 because form a straight angle.

3.  ∠3 ≅ ∠6 because they are alternate interior angles.

4. ∠1 and ∠6 are supplementary because ∠3 ≅ ∠6 and m∠1 + m∠3 = 180°.

If two lines in a plane can be stretched indefinitely in both directions without coming to an intersection, they are said to be parallel.

If the equivalent angles generated when two lines are intersected by a transversal line are equal, the lines are parallel. Typically, the comparable angles are situated side by side and on the same transversal side.

If the alternate internal angles so created are equivalent, two lines sliced by a transversal line are considered parallel. The pairs of the alternate interior are often located on the inner side but are located on the opposing sides of the transversal.

1. <3 = <2 because of vertically opposite angle.

Therefore, it is false

2. <1 + <3 = 180 because form a straight angle.

Therefore, it exists true.

3.  ∠3 ≅ ∠6 because they are alternate interior angles.

Therefore, it exists true.

4. ∠1 and ∠6 are supplementary because ∠3 ≅ ∠6 and m∠1 + m∠3 = 180°.

Therefore, it exists true.

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A pair of or more monomials' GCF (greatest common factor) is the sum of all their prime factors that are shared.

Following are the steps we use to factor the GCF out of a polynomial:

The polynomial's GCF for each of its terms.

The GCF and another factor should be used to express each word.

To factor the GCF out, use the distributive property.

Let's factor the GCF using 2 x ³ - 6 x² cubed, and negative 6, x, squared.

First, locate the GCF.

2x³ = 2 . x . x . x

6x² = 2. x . x . x

So the GCF of 2x³ - 6x² is 2.x.x =2x²

Step 2: Summarize each term as the product of two.

2x³ = ( 2x² ) (x )

6x² = (2x ² ) ( 3 )

2x³ - 6x² = (2x²) (x) - (2x²) (3)

Take the GCF into account.

2x² (x) - 2x²(3) = 2x²(x - 3).

The Complete Question.

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The area of a square is equal to (side) × (side) square units. The area of a square when the diagonal, d, is given is d2÷2 square units.

What is the formula for calculating the area of a rectangle?

Rectangle surface area. A = l × b. Once the length and breadth of a rectangle are determined, the area is computed. The area of a rectangle may be calculated by multiplying its length and width. The area of a form is the measurement of its surface. To calculate the area of a rectangle or square, multiply the length and breadth of the rectangle or square. A is equal to x times y.

The area of a square with each side 8 feet long, for example, is 8 8 or 64 square feet (ft2).

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Answer:

A circle centered at the origin (0,0) can be represented by the equation (x-0)^2 + (y-0)^2 = r^2, where r is the radius of the circle.

Given that the circle is passing through the point (6,0), we can use this point to find the radius of the circle. The distance between the center of the circle (0,0) and a point on the circle (6,0) is the radius of the circle.

We can use the distance formula to find the radius:

r = √((x2-x1)^2 + (y2-y1)^2)

where (x1,y1) is the center of the circle and (x2,y2) is a point on the circle.

Plugging in the values:

r = √((6-0)^2 + (0-0)^2) = √(6^2) = √36 = 6

Therefore, the equation of the circle centered at the origin and passing through the point (6,0) is (x-0)^2 + (y-0)^2 = r^2, where r is 6.

So the equation of the circle is: x^2 + y^2 = 36.

Answer: 5x - 3

Step-by-step explanation:

10x² - 6x = 2x(5x - 3)

2x(5x-3)/2x = 5x - 3

Cheers

Answer:24%

Step-by-step explanation:

Answer: Hopefully this helps you out!

Given:

   ABCD is a parallelogram, which means opposite sides are parallel and equal in length.

   E is the midpoint of BC, which means that BE = EC.

Prove:

   AFBE ADCE.

Proof:

   Since ABCD is a parallelogram, we know that AB // DC and AD = AB (opposite sides are equal in length)

   Since E is the midpoint of BC, we know that BE = EC (definition of midpoint)

   From the first step and second step, we know that AB = AD and BE = EC

   Therefore, we can say that AFBE and ADCE (by CPCTC)

Therefore, given that ABCD is a parallelogram and E is the midpoint of BC, we have been able to prove that AFBE ADCE.

Step-by-step explanation:

The given function  x^2 - 12x+36 can be written in vertex form as

y=(x-6)^2 .

What is Quadratic Equation?

Quadratic equation can be defined as the equation in which it is in the form of ax^2+bx+c = 0

where a,,b,c are constants.

Given,

to find the vertex form for each function,

Given function x^2 - 12x+36

(x^2 - 12x ) can be written as the (x-6)^2-36

so , let

y = x^2-12x+36 .

y =  (x-6)^2-36 + 36

y = (x-6) ^2+0

y-0 = (x-6)^2 .

So, in this way the completing the square method works.

Hence, The given function  x^2 - 12x+36 can be written in vertex form as

y=(x-6)^2 .

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Answer:

We know that 37% of all college students were enrolled part time. If 5.9 millions college students were enrolled part time that year, we can use this information to find the total number of college students.

We know that the part-time enrollment percentage is represented by the ratio:

part-time students / total students = 37%

We can set up the equation:

5.9 million / x = 37/100

Where x represents the total number of students

To find the total number of students, we can cross-multiply and divide:

5.9 million * 100 = 37 * x

x = 5.9 million * 100 / 37

The total number of college students that year was:

x = 16,081,081

So the total number of college students that year was 16,081,081

The parallelogram with vertices U(2,−2), V(9,−2), W(9,−6), and X(2,−6) is a rectangle, and square.

It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

The distance formula can be given as:

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

Here, We have given the vertices of the parallelogram are,

⇒ U(2,−2), V(9,−2), W(9,−6), and X(2,−6)

So, The distance between U and W from the distance formula is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ d = √ (9 - 2)² + (- 6 - (-2))²

⇒ d = √ 7² + (-4)²

⇒ d = √65

So, UW = √65

The distance between V and X from the distance formula:

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ d = √ (2 - 9)² + (- 6 - (-2))²

⇒ d = √ -7² + (-4)²

⇒ d = √65

So, VX = √65

Here, UW = VX (diagonals are equal in length).

As we know, in a rectangle and square the diagonals are equal in measure.

Thus, the parallelogram with vertices U(2,−2), V(9,−2), W(9,−6), and X(2,−6) is a rectangle, and square the choices are rectangle and square.

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Answer:

GCF is 14

Step-by-step explanation:

the list of factors are

14 : 1, 2, 7, 14

28 : 1, 2, 4, 7, 14, 28

the common factors are 1, 2, 7, 14

with GCF being 14

Using the high-low method, the cost formula for shipping expenses for Richer Company is 200 + 350x, where x is the number of units shipped.

The high-low method can help separate the total cost's fixed and variable elements.

In the high-low method, we take the highest and lowest levels of activity and compare the total costs and the total units at each level.  The difference in costs is divided by the difference in units to determine the variable element.

With the variable cost determined, the fixed cost can be worked out.

Month   Units Shipped   Total Shipping Expense

January          3                            $ 1,500

February        6                           $ 2,000

March             4                            $ 1,400

April               5                            $ 1,700

May                7                           $ 2,000

June               8                          $ 3,000

July                2                             $ 900

Highest:

June               8                          $ 3,000

Lowest:

July                2                             $ 900

Difference     6                           $2,100

Unit rate = $350 ($2,100/6)

Fixed cost, a = 350(8) + a = 3,000

2,800 + a = 3,000

a = 200

= $200

200 + 350x

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