Define the geometric sequence as a recursive function of the following five numbers.

The equation that will produce the given graph is; 6x² + 6y² = 144

The standard equation of a circle can be expressed as:

(x + a)² + (y - b)² = r²

where;

(a, b) is the center of the circle

r is the radius of the circle.

From the diagram, we can see that the radius of the circle is between 4 and 5.  Thus, the correct equation must have a radius between these values.

From the option, we can see that the only equation that will have a radius between 4 and 5 is;

6x² + 6y² = 144

Divide through by 6 to get;

x² + y² = 24

x² + y² = √24

Thus r = √24 which is greater than 5

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The theorem that would be included in the proof is: CPCTC theorem.

CPCTC stands for, "corresponding parts of the congruent triangles are congruent". The theorem states that, if two triangles can be proven to be congruent, then all the corresponding parts of the two triangles are equal to each other.

To prove that DB ≅ FC, given regular triangle DAF in the image attached below, we would have the following statements followed by their reasons in the bracket:

1. angle D ≅ angle F [given]

2. angle DBE ≅ angle ECF [given]

3. side DE ≅ side EF [given]

4. ΔDBE ≅ ΔECF [by the AAS congruence theorem]

5. DB ≅ FC [by the CPCTC theorem]

With the given proof, we can state that side DB is congruent to side FC.

Therefore, to prove that DB ≅ FC, the theorem that would be included in the proof is: CPCTC theorem.

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The value of m based on the given equation -7 + 4m + 10 = 15 - 2m is 2

-7 + 4m + 10 = 15 - 2m

4m + 2m = 15 + 7 - 10

6m = 12

m = 12/6

m = 2

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Answer:

C

Step-by-step explanation:

Please refer to the attached photo for step by step solutions.

Note: Square roots and squares will always cancel out each other.

The tiles to match the descriptions are;

Hull house - Neighbourhood assistance.

Muckrakers - Investigative journalists.

Protestants - Temperance movement.

Women's suffrage - Nineteenth amendment.

The Progressive Era, which encompassed the years between the 1890s and the 1920s in US history, was one of intense social and political reform with the goal of advancing the creation of a better society.

Case 1: The settlement home that welcomed newly arrived European immigrants to the United States in 1889 is known as Hull House. There were also social, educational, and artistic initiatives for immigrants in this building.

Case 2: Muckrakers A name used to describe a group of North American journalists in the early 20th century who made public criticisms of: government corruption, abuse of labor is destructive to society and is committed by influential people or institutions of the time.

Case 3: Third, the term "Protestantism" is used to describe a variety of 16th-century religious movements. Because the Catholic Church had a different understanding of the Bible's holy texts, this movement was distinguished by its break with it.

Case 4: The 19th Amendment to the United States Constitution, which was adopted in June 1919, guaranteed every American woman the right to vote.

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The complete question is-

Think about what you learned about the events during the Progressive time period. Drag and drop the tiles to match the

descriptions                        

Tiles;

Hull House

Muckrakers

Protestants

Women's Suffrage

Pairs;

Investigative journalists

Temperance Movement

Neighbourhood assistance

Nineteenth Amendment

x² ( 4x - 3)

Apply the multiplicative law of distribution.

Multiply the monomial

Multiply the monomial

Therefore, the correct option is "C".

The new statement will be:

Nuclear energy is known to be one that produce a lot of radioactive waste and this tends to pose a threat to  human health and the environment.

Hence, The new statement will be:

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The dimension of the box should be 1.7×1.7×3.58 in inches, applying minimization of surface area.

Dimensions to Minimize the Surface Area of the Box

It is given that the box is square based with an open top.

⇒ The box has one square and 4 rectangles

Thus, the total surface area of the box is given as,

S= a²+ab+ab+ab+ab  

S= a²+4ab ______________ (1)

Here, a is the side of the squared base and length of the rectangular sides of the box, b is the breath of the rectangular sides of the box.

This equation is later used for minimization of the surface area.

Also, the volume, V = a²b

It is also given that volume of the box is 184 in³.

⇒ 184 = a²b _____________ (2)

Forming a One-Variable Equation

From equation (2), b=184/a²

Now, substitute this value of b in equation (1) to get,

S = a² + 4a(184/a²)

S = a² + 4(184/a)

S = a² + 736/a

Minimization of Surface Area to find the Dimension

We require a dimension that will minimize the surface area of the box. Hence, applying minimization surface area, dS/da = 0

dS/da = 2a -736/a²

0 = 2a -736/a²

⇒ 0 = 2a³- 736

2a³ = 736

a³ = 736/2

a³ = 368

a = ∛368

a= 7.17 in

∵V = a²b

184 = (7.17)²b

b = 184/7.17²

b = 184/51.4089

b = 3.58 in

Therefore, 1.7×1.7×3.58 in inches is the required dimension for the box, using minimization of surface area..

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The total surface area of the trapezoidal prism is 180m². Option C

The formula for the total surface area of a trapezoidal prism is;

Total surface area = h (b + d) + l (a + b + c + d)

Where

b and d are parallel sides = 3, 9

h is the distance = 8

l is the length of the trapezoidal prism. = 12

Substitute into the formula

Total surface area = [tex]8(3 + 6) + 12(3 + 6)[/tex]

Total surface area = 72 + 108

Total surface area = 180 m²

Thus, the total surface area of the trapezoidal prism is 180m². Option C

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Answer:

-7, 8.

Step-by-step explanation:

x^2 - x - 56 = 0

Let's see if we can factor this function:

We need 2 numbers whose product is -56 and whose sum is -1 ( which is the coefficient of x).

They are  -8 and 7 , so the factors are:

(x - 8)(x + 7) = 0

x - 8 = 0 giving x =  8 and

x + 7 = 0 giving x = -7.

The zeros are -7, 8

Answer:

7.55

Step-by-step explanation:

A midpoint can be found by doing 7.2 + 7.9 then dividing by the number of points (in this case 2).

Answer:

1025.76

Step-by-step explanation:

Formula for a right rectangular pyramid is (l*w*h)/3

The length and width are both 18.7, so we can plug that in. The height is 8.8.

It becomes:

(18.7*18.7*8.8)/3, which equals the answer above.

Answer: A

Step-by-step explanation:

[tex]m\angle ABC=59^{\circ}[/tex] by the inscribed angle theorem.

The solution to the expression x/3 - 3/4 = 5/12 is given as x = 7/2

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the equation:

x/3 - 3/4 = 5/12

Hence:

x/3 = 5/12 + 3/4

x/3 = 7/6

x = 7/2

The solution to the expression x/3 - 3/4 = 5/12 is given as x = 7/2

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Answer: 80 square units

Step-by-step explanation:

[tex]A=(8)(10)=80[/tex]

There is a 0.02275 to 0.0968 chance that a random family's bill will be between $350 and $400.

Provided that,

Mean of the population = 500

The standard deviation(S.D) of the population = 75

Assume,the variable in normal distribution = X

Z= (x- mean)/ S.D

Provided , x = $350 - $400

Z= 350-500/75 = -2(when x=$350)

Z= 400-500/75 = -1.3 (taken x= $400)

The probability that a household will spend between $350 and $400 monthly

P(350>X<400) = P( -2>Z<-1.3)

                        = 0.02275 to 0.0968 (from probability table)

Therefore, the final answer is 0.02275 to 0.0968.

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The equations which gave the same solution as; 2.3p – 10.1 = 6.5p – 4 – 0.01p are;

It follows from the answer choices that the equation; 2.3p – 10.1 = 6.49p – 4 is equivalent to the given equation as the algebraic sum of p variables is evaluated on the right hand side.

The second equation; 230p – 1010 = 650p – 400 – p also is equivalent to the given equation, when multiplied through by 100.

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Answer:

B & C

Step-by-step explanation:

edge 2023

The cost of the Baseball is $5.

Lets take football cost as "x"

And taking baseball cost as "y"

According to given conditions,

2y + 3x = 67

x= 3y + 4

Lets put the values of x in equation (1):

2y + 3 (3y+4) = 67

=> 2y + 9y + 12 = 67

=> 11y = 55

y = 5

x = 3(5) + 4

x = 19

Hence the cost of the Baseball is $5.

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Based on definition of unit circle and angle properties on Cartesian plane, we find the following results: A: π/5, B: 3π/7, C: 4π/3.

Units circles are commonly used to understand angles and trigonometric functions in a simple way. Vectors in a unit circle are ordered pairs of polar form: (x, y) = (cos θ, sin θ).

To solve this problem, we must take these tips into account:

Then, we have the following results: A: π/5, B: 3π/7, C: 4π/3.

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The next step Juan will take is to multiply the second fraction by (x-2)/(x-2).

Given that Juan needs to rewrite this difference as one expression (3x/(x²-7x+10))-(2x/(3x-15)) and factor the denominator as (3x/(x-2)(x-5))-(2x/3(x-5)).

An algebraic expression in mathematics is an expression composed of variables and constants and algebraic operations (addition, subtraction, etc.). Expressions are made up of concepts.

The given expression is (3x/(x²-7x+10))-(2x/(3x-15))

Firstly, we will factored the denominator as

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

Now, we will multiply and divide the second fraction by (x-2), we get

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

Hence, the next step when subtracting these expressions (3x/(x-2)(x-5))-(2x/3(x-5)) is multiply the second fraction by (x-2)/(x-2).

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Answer:

8.4 meters tall   ( one decimal place)

Step-by-step explanation:

See diagram below:

find distance 'd'   as     tan 68 = opp / adj = d/6

   then   d = 6 tan 68       =  14.85 m

Then find   h   as   tan 9  = h / d

                               d tan 9 = h

                              14.85  tan 9 = h = 2.35 m tall

                                      add the 6 m height of the house    8.4  m tall

The width that Mason should set his compass when constructing segment FG is: A. The distance from B to E.

FG should be congruent to segment BE. Based on this Mason should set his compass to the width of segment BE when Mason is constructing segment FG.

Hence, the width that Mason should set his compass when constructing segment FG is the distance from B to E which is option is A.

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Answer:

b to e

Step-by-step explanation:

plato

If the marriage licenses  issued in 2001,2003,2006,2010 were 141000,133000,121000,141000 then by solving arithmetic progression we will get that the marriage licenses issued in 2008 were 113000.

Given that the marriage licenses issued in 2001,2003,2006,2010 were 141000,133000,121000,141000.

We are required to find how many marriage licenses were issued in 2008.

Average difference between licenses issued from 2001 to 2003=

=133000-141000)/2

=-4000

Average difference between licenses issued from 2003 to 2006=

=(121000-133000)/3

=-12000/3

=-4000

Average difference between licenses issued from 2006 to 2010=

=(105000-121000)/4

=-16000/4

=-4000

It is an arithmetic progression because the difference between marriage issued from one year to another is equal.

An arithmetic progression is a sequence in which each terms are having equal difference between them.

Nth term=a+(n-1)d

8th term=141000+(8-1)*(-4000)

=141000+7*(-4000)

=141000-28000

=113000

Hence the marriage licenses issued in 2008 were 113000 which is

option A.

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The Lena has no common ratio for the sequence 1.0 1.5 2.5 2.0

According to the question,

1.0  1.5  2.5  2.0

a = 1.0

r = 1.5/1 = 1.5

r = 2.5/1.5 = 1.6667

r = 2/2.5 = 0.8

common ratio is different, so given sequence is not geometric sequence.

Hence,  the Lena has no common ratio for the sequence 1.0 1.5 2.5 2.0.

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The area of the logo is 136. 14 cm²

First, let's find the area of the semicircle

Area of semicircle = 1/2(πr²)

radius = 8/2 = 4cm

Substitute into the formula

Area of semicircle = [tex]\frac{1}{2} * 3. 142 * 4 * 4[/tex] = 25. 135 cm²

Now, let's find area of trapezium

Area of trapezium = [tex]\frac{a + b}{2} * h[/tex]

Area =  [tex]\frac{12 + 10. 2}{2} * 10[/tex]

Area = [tex]11. 1 * 10[/tex]

Area = 111 cm²

Area of logo = Area of trapezium + area of semicircle

Area of logo = 111 +  25. 135

Area of logo = 136. 14 cm²

Thus, the area of the logo is 136. 14 cm²

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The relation in option B is a function.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given are 4 relations, A, B, C, D.

From the definition of function, it is clear that, no input value have more than one output value.

A : The value of x = -2 is mapping to 2, 1, 0, -1.

That is, an input value is having more than one output values.

So this is not a function.

B : Here the input values, 0, 1, 2 and 3 maps to -2.

Here the input values are distinct. No input values are mapping to more than one output value.

So this is a function.

C : Here 1 is mapping to -2 and 3. So not a function.

D : For x = 0, there are two y values, 3 and -3.

So this is not a function.

Hence option B is a function.

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Answer: I believe its 50 because you would have to see 3 x what equals 150

Step-by-step explanation:

The time taken to her to bag 150 bags is 50 minutes.

Grocery Items are any of the items listed that are offered only for off-premises consumption are as follows:-

(1) packaged or fresh fish, meat, or poultry.

(2) packaged or fresh plants or vegetables.

(3) packaged or fresh dairy goods (other than ice cream, frozen yogurt, or other confection/dessert items).

According to the given question, Three grocery bags are packed every minute. So, the time taken to 150 bag the time taken is computed as follows:-

Time Taken =  Total number of bags/Number of bags per minute

                   =  150 / 3

                   =  50 minutes

Therefore, it can be concluded that the time taken for her to bag 150 bags is 50 minutes.

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A data value is considered significantly low or significantly high  if its​ z-score is less than -2 or greater than 2.

What does it mean if z-score is 2?

What does a standard deviation of 2 mean?

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The correct question is -

A data value is considered​ _______ if its​ z-score is less than minus−2 or greater than 2.