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the sum of each infinite geometric series sum is 36

If the ratio between any two consecutive terms in a series of numbers is always the same, the progression is said to be geometric. The ratio of any two successive terms in the sequence (common difference) must be the same for the sequence 2, 4, 8, or 16 to be a general prime.

S = a/1-r is a general formula for calculating the sum of an infinite geometric series, where s stands for the sum, a1 is the series first term, and r is the common ratio.

a = first term = 18

r = common ratio = 1/2

sum of Geometric progression

r< 1

S∞ = a/(1-r)

S∞ = 18/(1-1/2) =36

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The distance from the town to the North Pole is approximately 2290 miles.

To find the distance in miles from the town to the North Pole, we need to calculate the length of the meridian arc from the town to the North Pole. The meridian arc is a portion of a great circle passing through the town and the North Pole.

The length of the meridian arc can be calculated using the formula:

Length = (π/180) x radius of the Earth x angle in degrees

where π is approximately 3.14159, and the radius of the Earth is 3960 miles.

Since the town is located at latitude 32°N, the angle between the town and the North Pole is 90° - 32° = 58°.

Plugging in these values into the formula, we get:

Length = (π/180) x 3960 miles x 58°

Length = (3.14159/180) x 3960 miles x 58

Length ≈ 2290 miles

Therefore, the distance from the town to the North Pole is approximately 2290 miles.

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If Benjamin invests $400 in a savings account that earns 5% interest each year, the expression that shows the correct balance is  A = 400(1 + 0.05)(1 + 0.05)(1 + 0.05)

The principal amount = $400

interest rate = 5%

The equation of the simple interest

A = P (1+ rt)

Where A is the final amount

P is the principal amount

r is the interest rate

t is the time period

The final amount after one year

= 400( 1 + 0.05×1)

= 400(1 + 0.05)

The final amount after two year

= 400(1 + 0.05)(1 + 0.05)

The final amount after three year

= 400(1 + 0.05)(1 + 0.05)(1 + 0.05)

Therefore, the balance amount after three years is A = 400(1 + 0.05)(1 + 0.05)(1 + 0.05)

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Answer: Width = 45 feet; Length = 15 feet;

Step-by-step explanation: Start by substituting 3w for the length because it says that in the problem. We know that 2(L+W) equals the perimeter. Since we substituted 3w for length we get 8w for the perimeter. Divide 120 by 8 to find that the width is 15 feet and plug it into 3w to get the length of 45 feet.

Answer:

45 feet and 15 feet are the length and width

Step-by-step explanation:

P = 120 feet

a (length) = 3 * b (width)

P = 2 * (a + b)

P = 2 * (3b + b)

P = 2 * 4b

P = 8 * b

                           => 8b = 120 feet

P = 120 feet

b = 120 / 8

b = 15 feet

a = 3 * b

a = 3 * 15

a = 45 feet

Answer:

18 cm

Step-by-step explanation:

Let's assume that the length of the stick is x cm.

Then, the lengths of pieces A, B and C would be 2x/10 cm, 3x/10 cm, and 5x/10 cm respectively.

Since C is longer than B by 8 cm, the length of C is 3x/10 + 8 cm, and the length of B is 3x/10 cm.

Therefore, the total length of the stick would be:

x = 2x/10 + 3x/10 + (3x/10 + 8)

x = 10x/10 + 8

x = 10 + 8

x = 18 cm

So, the length of the stick is 18 cm.

Answer: 20 cm

Step-by-step explanation:

create an equation.

2x : 3x : 5x

We are also told C is longer than B by 8 cm. So,

A : x : x+8

If 5x = x+8, solve for this: 4x = 8 so x =2.

Now, we can plug back in the original values.

2(2) + 3(2) + 5(2) = 20.

the stick is 20 centimeters long.

After solving for the line with slope as -2 and point (3,-2) , the y intercept is  (0,4)  .

We use the Point Slope form of a linear equation to write the equation of a line given its slope and a point on the line.

So , the point slope form is ⇒ y - y₁ = m(x - x₁)  ;

Where m = slope , and (x₁, y₁) = point on line .

So , by using the slope (m = -2) and point (x₁, y₁) = (3, -2),

Substituting  these values and simplifying further ,

We get ; ⇒ y -(-2) = (-2)×(x - 3)  ;

⇒ y + 2 = (-2)×(x) + (-2)×(-3) ;

Subtracting 2 from both sides,

we have ;

⇒ y = -2x + 4

The y intercept of line is value of "y" when x = 0.

So , we substitute x = 0 in the equation of line y = -2x + 4  ;

that means ⇒  y = -2(0) + 4 ;

⇒  y = 4 .

Therefore, the y intercept of the line with slope "-2" and passing through the point (3, -2) is (0, 4).

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The total surface area of the rectangular prism is 24 * 2 + 36 * 2 + 6 * 2 = 72 + 72 + 12 = 156 square yards.

The surface area of a rectangular prism is given by the sum of the areas of its six faces. To find the surface area of a rectangular prism that is 3 yards long, 2 yards wide, and 12 yards high, we need to find the area of each of its four rectangular faces and then add these areas together.

First, we find the area of the two faces that are 2 yards wide and 12 yards high. Each of these faces has an area of 2 * 12 = 24 square yards.

Next, we find the area of the two faces that are 3 yards long and 12 yards high. Each of these faces has an area of 3 * 12 = 36 square yards.

Finally, we find the area of the two faces that are 3 yards long and 2 yards wide. Each of these faces has an area of 3 * 2 = 6 square yards.

So, the total surface area of the rectangular prism is 24 * 2 + 36 * 2 + 6 * 2 = 72 + 72 + 12 = 156 square yards.

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ANSWER is one- incher=1 while two inch binder=2.By using simultaneous equation.

The solution to this system of equations is (10, 50).

A graph of this system of equations is shown in the image attached below.

Based on the information provided above, one of the plan includes a membership fee of $10 and charges $4 for every DVD borrowed. Therefore, the total cost, y, can be represented by this equation:

y = 4x + 10    .......equation 1.

where:

x represents the number of DVDs borrowed in a month.

For the second plan, it costs $50 per month for unlimited DVD rentals. Therefore, the total cost, y, can be represented by this equation:

y = 50    ....equation 1.

By equating equation 1 and equation 2, we have the following:

4x + 10 = 50

4x = 50 - 10

4x = 40

x = 40/4

x = 10 DVDs.

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Answer:

Y < (1/3) x - 5

The height of the tree before it got broken  is given as 72.43 feet

we have

the angle made at 45 degrees

The top touched the ground from 30 feet

we have tan 45 = x / 30

1 = x /30

x = 30

cos 45 = 1 / √2

1 / √2 = 30 / y

y = 30√2

the height = x + y

= 30 + 42.43

= 72.43

The height of the tree before it was broken is 72.43 ft

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Two paintings in an art display have shapes that are similar figures. the similarity ratio is 9:7 and the perimeter of the smaller painting is 6 meters therefore the perimeter of the larger painting to the nearest tenth is 7.7 meters.

This is referred to as the total distance around a two-dimensional shape.

Perimeter of the smaller painting is 6 meters and similarity ratio is 9:7

9 = x

7 = 6

7x = 54

x = 54/7 = 7.7 meters.

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The number when divided by 15, 20, and 30 and the remainder is always 8 will be 68.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The number which is divisible by 15, 20, or 30 will be given as,

LCM of the numbers 15, 20, and 30 will be given as,

2  |    15,       20,       30

2  |    15,        10,       15

3  |    15,         5,       15

5  |     5,          1,        5

          1,          1,         1

LCM = 2 x 2 x 3 x 5

LCM = 60

The number whose remainder is always 8 is given as,

⇒ 60 + 8

⇒ 68

The number when divided by 15, 20, and 30 and the remainder is always 8 will be 68.

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The relations that are functions are 2, 3, 4, 5, 6, and 7.

The ones that aren't functions are 1 and 8.

A relationship maps elements from one set (the domain) into elements from another set (the range), and a relation is a function only if each element of the domain is mapped into only one value of tha range.

For example, if you look at the relation 8, you can see that the input x = 1 is mapped into two different outputs, then this is not a function.

With that in mind, the options that are functions are:

2, 3, 4, 5, 6, and 7.

The ones that aren't functions are 1 and 2.

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The answers are given as follows:

2
a)

A = 8

b = 10

x = 118°

y = 62°

b)

a = 8

b = 15

y = 50

x = 100°

3)

(a)

∠2 = 25°

∠3 = 65°
∠4 = 65°
∠5 = 90°

(b)

since SL = 10,
i) LT  10
ii) TM = 10

iii) SM = 10

4)

a) Since m∠118
∠2 = 18°
∠3 = 72°
∠4 = 72°

If FA = 27, then LO = 13.5

The above are resolved using the properties of Parallelograms; Rhombus, and Rectangle

Since the above answers are justified by the qualities or properties of :

Parallelograms; Rhombus, and Rectangle, lets look at them one by one.

2
a)

A = 8 - opposite sides of a parallelogram are equal in length

b = 10 -opposite sides of a parallelogram are equal in length

y = 62° - opposite angles of a parallelogram are of equal measure.

x = 118° - Sum of angles of a parallelogram - 360°. x = (360 - (62*2))/2

= 118°

3)

(a) Here we have a Rhombus.

∠2 = 25° - Opposite angles of a rhombus are equal; Diagonals bisect the angles of a rhombus. Thus ∠1≅∠2

∠3 = 65° - Since diagonals bisect each other at right angles, ∠3 = 180 - (25+90) = 65°
∠4 = 65° - Diagonals bisect the angles of a rhombus. Thus, ∠3≅∠3
∠5 = 90° - [properties of a Rhombus]

(b)

since SL = 10,
i) LT  10 - All sides of a Rhombus are equal
ii) TM = 10 - All sides of a Rhombus are equal

iii) SM = 10 - All sides of a Rhombus are equal


4) Here we have a Rectangle.

a) Since m∠18
∠2 = 18° because The diagonals bisect each other; and both the diagonals have the same length. Thus, m∠2≅∠1 (AAS)
∠3 = 72° - Each interior angle is equal to 90 degrees. Thus, m∠ =  90-18 = ∠72°
∠4 = 72° - because The diagonals bisect each other; and both the diagonals have the same length. Thus, m∠4≅∠3(AAS)

If FA = 27, then LO = 13.5 - The diagonals bisect each other.Thus,

LO = FA/2

LO = 27/2

LO = 13.5

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Answer:

x = 4 twice.

Step-by-step explanation:

x^2-8x+ 16=0

Bring the constant to the other side.

x^2-8x=-16

Half the coefficient of x and square the result. Add to both sides.

x^2-8x+[-8/2]^2=-16+(-8/2)^2

x^2-8x+16= 16-16

x^2-8x+16=0

Now, whenever there's a perfect square constant, take the root of that constant. Since the coeff. of x is negative (-8),

(x-4)(x-4)=0  [-4^2=16 and -4+(-4)=-8]

Therefore, x-4=0 twice.

x=4 twice.

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The number of ways a dinner patron can select appetizers and vegetables will depend on the number of options available for each course.

Let's say there are "m" appetizer options and "n" vegetable options on the menu.

Then, the patron has m options for the appetizer course and n options for the vegetable course. To find the total number of ways the patron can select both courses, you would multiply the number of options for each course:

m x n ways

So, if the patron has 4 options for appetizers and 3 options for vegetables, the total number of ways the patron can select both courses would be 4 x 3 = 12.

Therefore, the number of ways a dinner patron can select appetizers and vegetables will depend on the specific number of options available for each course.

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The solution is, Option A. Line X

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

We have to identify the line which represents the function f(x) = 3x - 5

The given equation is y = 3x -5, in which slope of the line should be 3 and y- intercept is -5.

In these lines line x is having y-intercept as -5.

Line x passes through (1, 2) and (0, -5)

So slope of the given line will be = y2 - y1/ x2 - x1

= -5-2/ 0-1

= 3

Therefore, option A : Line X is the answer.

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The explicit formula and recursive formula of the geometric sequence is  Aₙ = 12(R)ⁿ⁻¹ where n is an integer.

It is given that in a geometric sequence, the second term and the common ratio are 6 and /2 respectively.

Now, we have to write the standard formula that can be further formulated as the explicit formula and recursive formula of the geometric sequence, The formula goes as,

Aₙ = A₁(R)ⁿ⁻¹

Here,

Aₙ is the nth term of the sequence. So, if we want the first term then will put n = 1, n= 2 for second term and so on.

Now, putting n = 2,

A₂ = A₁(R)²⁻¹

A₂ = A₁(R)

6 = A₁(1/2)

A₁ = 12

So, the explicit and recursive formula will be Aₙ = 12(R)ⁿ⁻¹.

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The equation with infinitely many solutions is given as follows:

7(2W + 3) = 14W + 21.

The system of equations for this problem is defined as follows:

7(2W + 3) = 14W + 20.

Applying the distributive property to the left side, we will have that:

14W + 21 = 14W + 20.

The two lines have the same slope but different intercepts, hence the system contains zero solutions.

To contain an infinite number of solutions, they must have the same slope and the same intercept, then the equation is given as follows:

7(2W + 3) = 14W + 21.

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Step-by-step explanation:

=

[tex]7(2w + 3) = 14w \\ 14w + 21 = 14w \\ 14w - 14w = - 21 \\ 0 = - 21 \\ = - 21[/tex]

Answer:

2673+$&$&#7635+62578

The length of BD in the triangle is 24 units.

The triangles are similar by angle bisector theorem. The angle bisector theorem states that the angle bisector of an angle of a triangle divides the opposite side into two parts that are proportional to the other two sides of the triangle.

Therefore, let's find BD.

Hence, using the proportion,

12  / 20 = x / x + 6

cross multiply

12(x + 6) = 20x

12x + 72 = 20x

72 = 20x - 12x

72 = 8x

divide both sides by 8

x = 72  /8

x = 9

Therefore,

BD = x + x + 6 = 2x + 6

BD = 2(9) + 6

BD = 18 + 6

BD = 24 units

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The graph showing the line of best fit for the function y = 3x + 1 is attached below

The line of best fit is a line that is used to represent the relationship between two variables in a scatterplot. It is a line that passes through the center of the data points in the scatterplot in such a way that the total distance between the line and the data points is minimized. The line of best fit can be used to make predictions about the value of one variable based on the value of another variable. There are several methods to obtain the line of best fit, including the method of least squares, which finds the line that minimizes the sum of the squares of the differences between the observed values and the values predicted by the line.

In the problem given, the line of best fit the line of best fit can be plotted on a graph using a graphing calculator.

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Answer:  NIKES

Step-by-step explanation:

BEFAUSE 5/2 IS THE WHG0LE D[IWJAEOIDHNC;SHCOWIADHJA[OISHWNIOD

Answer: the answer is nike

Step-by-step explanation: Because the shipping fee on callaway is more than the order.

The speed of the Atlas V Rocket was approximately 8,727.27 miles per hour, based on the given information that it could go one mile in 0.11 seconds.

To find the speed of the Atlas V Rocket, we need to use the formula:

speed = distance / time

In this case, the distance is 1 mile, which is equal to 1609.34 meters. The time is 110th of a second, which is equal to 0.1 seconds (since there are 10 tenths in a second).

So, plugging these values into the formula, we get:

speed = 1609.34 meters / 0.1 seconds

speed = 16093.4 meters per second

Therefore, the Atlas V Rocket traveled at a speed of 16093.4 meters per second.

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Answer: As the ratio of newts and toads, 3:4

Step-by-step explanation:

The equation in standard form is x - 9y = -45.

The equation of a line in standard form is Ax + By = C, where x and y are variables and A, B and C are integers.

Given equation is y = 1/9 x + 5.

Here 1/9 is not an integer.

So multiplying the equation throughout by 9, we get,

9y = x + (5 × 9)

9y = x + 45

Subtracting both sides by x,

9y - x = 45

-x + 9y = 45

Multiplying throughout by -1,

x - 9y = -45, which is in standard form.

Hence the equation is x - 9y = -45 in standard form.

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Step-by-step explanation:

45g = 0.045kg

0.045 + 26 = 26.045

Final answer is 26.045 kg

Turning 180° counterclockwise is essentially the same thing as a horizontal flip about the y axis.

That means C will find itself on the opposite side of the x axis, with negative inputs. However, it is still above the x axis, so it will have a positive y coordinate.

Your answer should be (-3,1)

answer:

if you multiply the 2 sides of the ratio by a number it will give you an equivalent ratio

5:8 = 10:16 multiplying by 2

5:8 = 15:24 multiplying by 3

5:8 = 20:32 multiplying by 4

5:8 = 25:40 multiplying by 5

5:8 = 30:48 multiplying by 6

5:8 = 35:56 multiplying by 7

and so on ...