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Answer:

the answer is in the picture

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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a. The bill when Cameron and Cadena go out to eat for lunch is $24.525

b. The percentage of the cost of their food and beverages that they give as tip will be 18%.

From the information, Cameron and Cadena go out to eat for lunch. If their food and beverages cost $22.50 and there is a 9% meals tax, the bill will be:

= $22.50 + (9% × $22.50)

= $22.50 + $2.025

= $24.525

The percentage of the cost of their food and beverages that they give as tip will be:

= (28.95 - 24.525) / 24.525 × 100

= 18%

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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.

Answer:

The regular falsi method, also known as the false position method, is a numerical method for finding the root of an equation. It is a variant of the bisection method and is used when the function is not continuous or when the bisection method is too slow.

To find the real root of the equation x tan x + 1 = 0 using the regular falsi method, you will need to:

Choose two initial guesses for the root, x0 and x1.

Evaluate the function at each of the guesses and note their signs.

Use the following formula to calculate the next guess for the root, x2:

x2 = x1 - f(x1) * (x1 - x0) / (f(x1) - f(x0))

Evaluate the function at the new guess and note its sign.

If the sign of the function at x2 is the same as the sign at x0, update x0 to x2 and repeat the process from step 3.

If the sign of the function at x2 is the same as the sign at x1, update x1 to x2 and repeat the process from step 3.

Repeat the process until x2 is close enough to the root or until a maximum number of iterations is reached.

It's important to note that this method is not as efficient as other method like newton-raphson, bisection and secant method.

Answer:

m<G is 60 degrees

Step-by-step explanation:

the sides are congruent so you can split it down the middle into 2 triangles. 150÷2=75 90÷2=45 add 45 and 75 to get 120. Subtract 120 from 180 and you get 60.

Answer:

m∠G = 60°

Step-by-step explanation:

From inspection of the given quadrilateral EFGH:

The interior angles of a quadrilateral sum to 360°:

⇒ m∠E + m∠F + m∠G + m∠H = 360°

⇒ m∠E + 150° + m∠G + 90° = 360°

⇒ m∠E + m∠G + 240° = 360°

⇒ m∠E + m∠G = 120°

As EFGH has two pairs of adjacent sides that are equal in length, it is a kite.

A kite has one pair of equal angles.

As m∠F and m∠H are not equal, then m∠E must be equal to m∠G.

⇒ m∠E = m∠G = 120° ÷ 2 = 60°

The value of x in the triangle is 10

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted by triangle ABC.

The sum of the three angles in a triangle is 180°.

Therefore

(5x - 5)° + 8x + (6x - 5) =180

5x-5+8x+6x-5 = 180

collect like terms

5x+8x+6x-5-5 = 180

19x = 180+10

19x = 190

divide both sides by 19

x = 190/19

x= 10

therefore the value of x is 10

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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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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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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

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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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 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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Answer:

The headteacher is wrong because exactly 89% of 80 would be 71.2, and there cannot be decimals or fractions of teachers.

Explanation:

To find 89% of 80, we first need to divide 80 by 100 to find 1% of the number.

Doing so gives us 0.8.

Next, we multiply 0.8 by 89, to find 89%.

We get 71.2, and we know that humans cannot be split into fractions or decimals.

That is why the headteacher is wrong.

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The value of x from the figure is 5±√138

A triangle is a three-sided polygon that consists of three edges and three vertices.

From the given figure we can write a proportionality formula

35/x-3=x-7/4

Now apply cross multiplication

35×4=(x-3)(x-7)

140=x²-7x-3x+27

140=x²-10x+27

Subtract 140 on both sides

x²-10x-113=0

When we apply quadratic formula by taking a is 1, b=-10 and c as -113

we get x as 5±√138

Hence, the value of x is from the figure is 5±√138

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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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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 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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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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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').

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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Answer: 43

Step-by-step explanation: calculator...i named it jaden

Answer:

Four times two is less that 10. It equals 8

Answer:

x>123

Step-by-step explanation:

subtract 23.40 from both sides

2.40x>295.20

divide both sides by 2.40

x>123

Answer:

x>123

Step-by-step explanation:

To solve this you first need to get the x alone to figure out what number it has to be. We do this by subtracting 23.40 from each side:

2.40x+23.40>318.60 turns into

2.40x>295.20

Now we have to divide both sides by 2.40 to get x alone and we get

x>123

So we know that x must be greater than 123

(If you set x=123 you will get 0, so x must be greater than 123)

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

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 average speed on Wednesday is 63 mph.

Given data :

Tuesday

time= 5.4 hours

rate = x

Wednesday

time= 6 hours

rate = 7 mph slower than on Tuesday = x - 7

We know that distance= (rate)(time)

So the distance on Tuesday is 5.4 x and the distance on

Wednesday is 6 (x-7)

As we know she drove the same distance so we have that

5.4 x = 6(x-7)

5.4x= 6x - 42

5.4x-6x =  -42

-.06x = -42

x = 70

Hence 70 - 7 = 63 mph

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