For the following geometric sequence, find the recursive formula.
{-80, 20, -5, ...}

To find each interior angle of a decagon given as expressions with x, we sum the expressions and set equal to 1440 degrees, the total sum of interior angles. Solving for x, we find x=100 and then substitute to find each angle.

To find the measure of each interior angle of a decagon where the angles are given as expressions involving x, we must use the fact that the sum of interior angles in a polygon is (n-2)180 degrees, where n is the number of sides in the polygon. For a decagon, which has 10 sides, the sum would be (10-2)180 = 1440 degrees.

x + 5 + x + 10 + x + 20 + x + 30 + x + 35 + x + 40 + x + 60 + x + 70 + x + 80 + x + 90 = 1440

Combining like terms, we find that:

10x + 5 + 10 + 20 + 30 + 35 + 40 + 60 + 70 + 80 + 90 = 1440

10x + 440 = 1440

10x = 1440 - 440

10x = 1000

x = 100

Once x is found, we substitute back into each angle expression to find the measure of each interior angle:

x + 5 = 105 degrees

x + 10 = 110 degrees

x + 20 = 120 degrees

x + 30 = 130 degrees

x + 35 = 135 degrees

x + 40 = 140 degrees

x + 60 = 160 degrees

x + 70 = 170 degrees

x + 80 = 180 degrees

x + 90 = 190 degrees

The slope of the line that contains the given point is the rise/run, which is: 1/8.

The slope of a line = rise / run = change in y / change in x.

Given the points on a line as (9, –4) and (1, –5):

Change in y = (-4 -(-5) = 1

Change in x = (9 - 1) = 8

Slope of the line = change in y/change in x = 1/8.

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The cost of one ounce of peanuts is $ 0.15 and the cost of one ounce of cashews is $ 0.40. Then the correct option is B.

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

A store is selling two mixtures of nuts in 20-ounce bags.

The first mixture has 15 ounces of peanuts combined with five ounces of cashews and costs $4.25.

The second mixture has five ounces of peanuts and 15 ounces of cashews and costs $6.75.

Let the cost of one ounce of peanuts be x and one ounce of cashews cost be y. Then we have

15x + 5y = 4.25 ...1

5x + 15y = 6.75 ...2

By solving equations 1 and 2, Then we have

x = $ 0.15 and y = $ 0.40

Then the cost of one ounce of peanuts is $ 0.15 and the cost of one ounce of cashews is $ 0.40.

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The value stored at x will be 0.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ x = 3 / static_cast(4.5 + 6.4)

Now,

Since, The expression is,

⇒ x = 3 / static_cast(4.5 + 6.4)

Hence, The value of x is find as;

The operands 4.5 and 6.4 are added as;

⇒ 4.5 + 6.4 = 10.9

So, When this value is cast to int datatype, it becomes 10.

So, We get;

⇒ x = 3/10

       = 0.3

Since,  x in a variable of type int.

So, when a value of 0.3 is assigned to x, it is stored as 0.

Thus, The value stored at x = 0.

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Answer:

The answer is B = 1

Step-by-step explanation:

The exponent zero rule states that any  number raised to the power of zero equals to 1 or mathematically:

x^0 = 1 for any real number x

So applying this rule

153^0 = 1 with x =153

The answers is D.)7.15 × 10-8

Answer:

7.15 × 10-8 0 or 7.15 * 10^-8

Step-by-step explanation:

(6!(49 - 6)!)/49!

720/10068347520

= 7.15 * 10^-8

I hope this answer gives you an idea of the process used to find the answer.

14/112 =0.125

2600*0.125 = 325

 c) 325

To find the area of a segment formed by a square inscribed in a circle, calculate the circle's radius from the square's diagonal, then find the circle's area and divide by 4. The area of one segment is approximately 14.14 square inches.

Finding the Area of a Segment in an Inscribed Circle

To find the area of one segment formed by a square with sides of 6 inches inscribed in a circle, we first need to determine the radius of the circle. The given ratio of 1:1:square root of 2 is key here. In a right-angled triangle with sides of equal length (1:1), the hypotenuse will be the square root of 2, according to the Pythagorean theorem. Since the diagonal of the square is the diameter of the circle, and the square has sides of 6 inches, we can calculate the diameter (d) of the circle as:

d = 6 inches × square root of 2

Therefore, the radius (r) is half of that:

r = (6 inches × square root of 2) / 2 = 4.24 inches (approximately)

With the radius, we can calculate the area (A) of the circle:

A = πr² = 3.1415927… × (4.24 inches)²

A ≈ 56.55 square inches (to two significant figures)

Now, the area of one segment is the area of the circle divided by the number of segments, with this particular scenario having 4 equal segments:

Area of one segment = Total area / 4

Area of one segment ≈ 56.55 square inches / 4 = 14.14 square inches (approximately)

The area of one segment formed by the inscribed square in the circle is approximately 14.14 square inches.

The area of one segment of a circle formed by an inscribed square with sides of 6 inches is approximately 14.14 square inches, calculated by first finding the radius of the circle using the 1:1:√2 ratio and then using the area formula A = πr².

To find the area of one segment formed by a square with sides of 6 inches inscribed in a circle, we first need to calculate the radius of the circle using the given ratio of 1:1:√2. In an inscribed square, the diagonal is equal to the diameter of the circle. The diagonal of the square can be found using the Pythagorean theorem (a² + b² = c²) where a and b are the sides of the square and c is the diagonal. In this case, the diagonal is √(6² + 6²) = √(36 + 36) = √72 = 6√2 inches, which is also the diameter of the circle.

Thus, the radius (r) of the circle is half of the diameter, r = 6√2 / 2 = 3√2 inches. Now we can compute the area (A) of the circle using the formula A = πr². Plugging our radius into this formula gives us A = π(3√2)² = π(18) ≈ 56.55 square inches.

The circle is divided into four equal segments by the square, so the area of one segment is one-fourth of the total area of the circle. Therefore, the area of one segment is approximately 56.55 / 4 = 14.14 square inches.

The radian measure of the angle is 1.5 radians.

To find the radian measure of the angle, we need to determine the length of the arc intercepted by the angle. We know that the diameter of the circle is 8 centimeters, so the radius is half of that, which is 4 centimeters. The circumference of the circle is given by the formula C = 2πr, where r is the radius.

In this case, the arc length intercepted by the angle is 12 centimeters. We can use the formula for the circumference to find the radian measure of the angle.

C = 2πr

12 = 2π(4)

12 = 8π

Dividing both sides of the equation by 8, we get:

π = 1.5 radians

The correct answer is 180° about the center.

To map the given figure onto itself, we need to find the rotational symmetry. Let’s analyze the “X” shape:

A 90° rotation would not work because it would overlap the arms of the “X.”

Similarly, a 270° rotation would also result in overlapping arms.

A 45° rotation would not preserve the original shape due to the asymmetry of the “X.”

However, a 180° rotation about its center will bring each arm of the “X” back to a position occupied by another arm, effectively mapping it onto itself. An “X” has rotational symmetry at 180°; every half turn gives us an identical view.

The correct answer is 180° about the center. This specific degree of rotation is required due to the symmetrical nature of an “X” shape where each arm aligns with another after being rotated by this angle.

Allow ABC to be an equilateral triangle so AB = AC = BC. Let X be the midpoint of BC, AX is the median of BC, and BX = CX. Look at triangles BAX and CAX. Obviously, AX = AX since AB = AC and BX = CX, subsequently by SSS Congruence Test, we have that triangles BAX and CAX are congruent. Therefore, corresponding angles are congruent so <ABX = <ACX. Because <ABX and <ABC are the same angle, they are obviously congruent, and then <ABX = <ABC. Likewise, <ACX and <ACB are the same angles so <ACX = <ACB. Then, <ABC = <ACB. Please note that <ABC = <B and <ACB = <C. Therefore, <B = <C. 

At present, disregard AX and let Y be the midpoint of AC. Then BY is the median of AC. Then AY = CY. Evidently, BY = BY.  Because AB = BC, we see that triangles ABY and CBY are congruent by SSS. Then corresponding sames are congruent so <BAY = <BCY. Since <BAY and <BAC are the same angles then <BAY = <BAC. Similarly, <BCY = <BCA since they are the same angles. Then <BAC = <BCA. Note that <BAC = <A and <BCA = <C. Therefore, <A = <C. 

Thus, <A = <C = <B. So all the angles are congruent.

Final answer:

The measure of angle 1 can be found by using the fact that angle 1 and angle 2 form a linear pair. By setting up an equation and solving, we find that angle 1 measures 113 degrees.

Explanation:

To find the measure of angle 1, we need to understand that angle 1 and angle 2 form a linear pair. A linear pair of angles is formed when two adjacent angles are supplementary, meaning they add up to 180 degrees. So, angle 1 + angle 2 = 180 degrees. Given that angle 2 measures 67 degrees, we can substitute this value into the equation to find angle 1: angle 1 + 67 degrees = 180 degrees. Solving for angle 1, we get angle 1 = 180 degrees - 67 degrees = 113 degrees.