Find the 15th term of the sequence: 1, 3, 9, 27. ...​

The regular pentagon can be rotated through at angles of 72, 144°, 216°, and 288° to map it onto itself.

A polygon is a two-dimensional geometric shape having a finite number of sides. Single-direction segments are connected end to end to make a closed shape on the sides or edges of polygons. The locations where two line segments converge to construct an angle are referred to as vertices or corners.

It is given that:

The pentagon has five sides.

As we know, the standard pentagon has five vertices and internal angles that are each 72 degrees. A regular pentagon also possesses rotational symmetry.

The angles are 72°.144°,216°, and 288°.

Thus, the regular pentagon can be rotated through at angles of 72, 144°, 216°, and 288° to map it onto itself.

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A is either 45° or 135°.

To prove the given statement, let's assume that the points B and C lie on a coordinate plane, with the origin (0, 0) as the common vertex of the right angles at points B, C, and A. Let the coordinates of points B and C be (x₁, y₁) and (x₂, y₂) respectively.

Using the distance formula, we have:

AB² = x₁² + y₁²

AC² = x₂² + y₂²

According to the given equation, +b4+c4 = 20² (b²+c²), we can rewrite it as:

(x₁² + y₁²) + (x₂² + y₂²) = 20² [(x₁² + y₁²) + (x₂² + y₂²)]

Expanding and simplifying the equation, we get:

x₁² + y₁² + x₂² + y₂² = 20² (x₁² + y₁² + x₂² + y₂²)

This equation can be further simplified to:

(x₁² + y₁²) + (x₂² + y₂²) = (20² - 1) (x₁² + y₁² + x₂² + y₂²)

Since the left side represents the sum of the squares of the distances from the origin to points B and C, and the right side is a constant multiplied by the same sum, we can conclude that the points B and C must lie on a circle centered at the origin.

In a circle, the sum of angles subtended by two perpendicular chords at the center is either 180° or 360°. Since the given problem involves right angles, we consider the sum of angles to be 180°.

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Answer:

these are real solutions

9514 1404 393

Answer:

  4 acres of each

Step-by-step explanation:

Let s and c represent the number of acres of soybeans and corn, respectively. The problem statement gives rise to several constraints. There is also an objective function to maximize. The linear programming problem can be described by ...

  maximize 500s +300c subject to ...

  s ≥ 2

  200s +100s ≤ 1200 . . . . cost to plant

  s + 2c ≤ 12 . . . . . . . . . . . . hours to plant

__

The attached graph shows the objective function is maximized at (s, c) = (4, 4).

The farmer should plant 4 acres each of soybeans and corn.

__

For the solution here, the constraint that s ≥ 2 is irrelevant. If the graph included it, the vertices of the feasible solution space would be (2,5), (4, 4), (6, 0) and (2, 0). The solution that maximizes profit is (4, 4).

GIVEN:

We are told that Jina had an opening balance of $240 in her toll road account.

Also, we are told that the amount left in the toll road account is given by the function;

Required;

(a) To find how much money she has left in her acount after 11 trips.

(b) To find out how many trips she can take until her account is empty.

Step-by-step solution;

We first take note of the variable t, which represent the number of trips taken. Also, the function shows how many trips multiplied by 16 would be subtracted from the opening balance. The result would be how much amount (variable A) would be left in her account.

Therefore;

(a) After 11 trips, Jina would have;

For the (A) part, the answer is $64.

(b) For her account to be empty, then the function given would be equal to zero. That is, after an unknown number of trips, the balance would be zero. We can now re-write the function as follows;

Add 16t to both sides of the equation;

This means after 15 trips she would have emptied her toll road account.

ANSWER:

Answer:

2 and 4

Step-by-step explanation:

Using the rule for a rotation 90º counterclockwise, the triangles are sketch on the graph given at the end of the answer.

Transformations on the graph of a function are classified as follows:

All these transformations are defined by rules, and the rule for a rotation 90º counterclockwise is given by:

(x,y) -> (-y, x).

Hence, applying the rule, the vertices of triangle A'B'C' are given as follows:

Both triangles are sketched in the graph given at the end of the answer, with the original triangle in black and the rotated triangle in blue.

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Answer:

I don't know sorry:(((

Step-by-step explanation:

÷::&":;,';

Answer:

257.

Step-by-step explanation:

seperate the shapes. we know that the side on the left upper corner is 7 because 29 - 22. The we find the other missing side, which is 26 - 21, 5. then we multiplt the first "box" to find the area, 21 x 7 = 147. Then the second box 5 x 21 = 110. Add the two, and you find your answer. 257

Ordered pair for the equation 4x-y=5 which is a solution of a given equation is (0,-5).

An ordered pair refers to a pair of two numbers or variables written inside the bracket and separated by comma.

To find an ordered pair of a equation we just need to find the values of x and y which will satisfy the given equation.

Here given equation is 4x-y=5

So we will put x=0 and y=-5

⇒ 4(0)-(-5)=5

Therefore (0.-5) satisfy given equation.

Hence (0.-5) is an ordered pair of 4x-y=5.

Note:- There are many ordered pairs that satisfy the given equation.

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Answer:

938 feet

Step-by-step explanation:

264^2+ 900^2= c^2

879696= c^2

938= c

Based on the information we can infer that the equation shown in the image is 1.23 - 0.35 = 0.88 (option B).

To identify the correct equation we must look at the graph and identify the information it provides. In this case we have two squares divided into 100 squares each. Additionally, the square on the left has 88 squares painted in red and 12 squares with an X inside. In the case of the square on the right, it has 23 squares colored in red with an X inside.

In total we have 123 squares painted in red, which in decimal number is equivalent to 1.23. On the other hand, the number of squares painted red and with an X inside is 35, this value would be 0.35.

On the other hand, the squares painted only in red are 88, so the equivalent in decimal numbers would be 0.88. Therefore, the correct way to express this relationship through an equation would be:

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Answer:

Answer:

94.6ft

step by step explanation :

sine(52) = x/120

multiply both sides by 120

120 sine(52°) = x

put it in a calculator

X=94.56129043

round to nearest tenth

X = 94.56ft

Answer: Choice 1

3(MC) = SC

=====================================================

Explanation:

The three medians intersect at the centroid, which is point M in this case. The intersecting medians subdivide themselves in the ratio 2:1

This means that SM is twice as long as MC. We can say SM = 2MC

Then by the segment addition postulate, we know that:

SC = SM + MC

SC = 2MC + MC

SC = 3MC

3(MC) = SC

So having three copies of MC glued together will form segment SC.

The same idea applies for the other medians also (EK = 3EM and RL = 3ML).

Answer:

KKRNF.EWBVERUVHUYLERBVHJDBREVVVLEKVOEUFJOE

Step-by-step explanation:NWEKFK.EWBFEWHBV.KWEUF67OFVD.KFERLUGVK34UGILBEFLIUBYETRNTYM6

Answer:

x intercept- (8,0)

y intercept-(0,-4)

Step-by-step explanation:

hope this helps!

Answer:

36=4*9

Step-by-step explanation:

Answer:

The p-value of the test is 0.0301 > 0.02, which means that there is not sufficient evidence at the 0.02 level to support the company's claim.

Step-by-step explanation:

The company's promotional literature claimed that under 64% fail in the first 1000 hours of their use.

At the null hypothesis, we test if the proportion is of at least 64%, that is:

\(H_0: p \geq 0.64\)

At the alternative hypothesis, we test if the proportion is of less than 64%, that is:

\(H_1: p < 0.64\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

64% is tested at the null hypothesis:

This means that \(\mu = 0.64, \sigma = \sqrt{0.64*0.36}\)

A sample of 900 computer chips revealed that 61% of the chips fail in the first 1000 hours of their use.

This means that \(n = 900, X = 0.61\)

Value of the test statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{0.61 - 0.64}{\frac{\sqrt{0.64*0.36}}{\sqrt{900}}}\)

\(z = -1.88\)

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion below 0.61, which is the p-value of z = -1.88.

Looking at the z-table, z = -1.88 has a p-value of 0.0301.

The p-value of the test is 0.0301 > 0.02, which means that there is not sufficient evidence at the 0.02 level to support the company's claim.

Answer:

sin(100°) = 0.985

sin(-100°) = -0.985

Step-by-step explanation:

In a unit circle, each point (x, y) on the circumference corresponds to the coordinates (cos θ, sin θ), where θ represents the angle formed between the positive x-axis and the line segment connecting the origin to the point (x, y).

Therefore, sin(100°) equals the y-coordinate of the point (-0.174, 0.985), so:

\(\boxed{\sin(100^{\circ}) = 0.985}\)

Similarly, sin(-100°) equals the y-coordinate of the point (-0.174, -0.985), so:

\(\boxed{\sin(-100^{\circ}) = -0.985}\)

In the unit circle the value of sin (100) = 0.985 and the value of sin (-100) = -0.985, in three decimal places.

The value of the sine of the angles is calculated by applying the following formula as follows;

The value of sin (100) is calculated as follows;

sin(100°) corresponds to the y-coordinate of the point (-0.174, 0.985) as given on the coordinates of the unit circle.

sin (100) = 0.985

The value of sin (-100) is calculated as follows;

sin(100°) corresponds to the y-coordinate of the point (-0.174, -0.985), as given on the coordinates of the circle.

sin (-100) = -0.985

Thus, in the unit circle the value of sin (100) = 0.985 and the value of sin (-100) = -0.985, in three decimal places.

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It is noticed that the factors then the x-intercepts are the same value as that of factors.

Given that, the quadratic equation represented on the graph in factored form is y=(x-3)(x+2).

From the graph, x-intercepts are x=-2 and x=3.

The vertex of the given quadratic graph is (0.5, -6)

Therefore, it is noticed that the factors then the x-intercepts are the same value as that of factors.

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so what was the question again?

Answer:

Step-by-step explanation:

(a) To meet the desired 20g protein and 80g carbohydrate intake, prepare 4 servings of Pork & Beans and combine with 15 slices of "lite" rye bread.

(b) Bread: A/4 slices, Beans: B/21 - (A/4) * (12/21) servings.

(a) To prepare a meal of "beans-on-toast" that supplies 20 grams of protein and 80 grams of carbohydrates, you can use the following combination:

- Servings of Campbell's Pork & Beans: 4 servings.

- Slices of "lite" rye bread: 15 slices.

By using 4 servings of Campbell's Pork & Beans, you will obtain a total of 20 grams of protein (5 grams per serving) and 84 grams of carbohydrates (21 grams per serving).

Combining this with 15 slices of "lite" rye bread will contribute an additional 60 grams of carbohydrates (12 grams per slice) and 4 grams of protein (4 grams per slice). Thus, your meal will meet the desired nutritional requirements of 20 grams of protein and 80 grams of carbohydrates.

(b) The formula to determine the number of slices of bread and servings of Pork & Beans needed to meet specific protein and carbohydrate requirements is as follows:

- Number of slices of bread (Bread): A divided by 4.

- Number of servings of Pork & Beans (Beans): (B divided by 21) minus ((A divided by 4) multiplied by (12 divided by 21)).

Using this formula, you can calculate the appropriate quantities of bread and beans based on the desired protein (A) and carbohydrate (B) values.

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The factored expression of 4x³ - 2x² + 8x - 4 is (2x² + 4)(2x - 1) by grouping

From the question, we have the following parameters that can be used in our computation:

4x³ - 2x² + 8x - 4

Group the expression in 2's

So, we have

(4x³ - 2x²) + (8x - 4)

Factorize each group

2x²(2x - 1) + 4(2x - 1)

So, we have

(2x² + 4)(2x - 1)

Hence, the factored expression is (2x² + 4)(2x - 1)

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Answer:

D. 54

Step-by-step explanation:

Remember that for geometric series, it's a progression by multiplication. From the first term, you multiply by your common ratio to get each successive term.

\(a_{n}\) = \(ar^{n-1}\)

In which \(a_{n}\) is the nth term in a sequence.

A is the first term.

And R is the common ratio.

The common ratio is 1.5. Which was found by dividing 24 by 16.

Our equation would now be : \(16*1.5^{n-1}\)

By replacing n with 4, you will get 54.

Or, if we multiply each term by 1.5, you will end up with 54 by the time you reach the fourth term.

Hope this helps mate.

Answer:

greater to

Step-by-step explanation:

one is greater then the other

4 patio pavers = 63.2 inches

1 patio pavers = 15.8 inches.

The length of one patio paver is 15.8 inches.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

The total length of the side of the rectangle that has four patio pavers is sixty-three and two-tenths inches.

This means,

Length of the side with 4 patio pavers.

= 63(2/10) inches

= 632/10

= 63.2 inches

Now,

The length of one patio paver.

4 patio pavers = 63.2 inches

Divide both sides by 4.

1 patio pavers = 63.2/4

1 patio pavers = 15.8 inches.

Thus,

The length of one patio paver is 15.8 inches.

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Answer:

All of them

Step-by-step explanation:

All we have to do is replace the x and y with their following coordinates

A.(5, -5/6) - - > 5(5) + 12(-5/6) = 25 + (-10) = 15

15 = 15

Yes

B. ( -3, 5/2) - - > 5(-3) + 12(5/2) = -15 + 30 = 15

15 = 15

Yes

C. (-6, 15/4) - - > 5(-6) + 12(15/4) = -30 + 45 = 15

15 = 15

Yes

D. (-5, 10/3) - - > 5(-5) + 12(10/3) = -25 + 40 = 15

15 = 15

Yes

Answer:

Step-by-step explanation:

Typically yes you need to know

Mean

Median

Mode

and Range

Mean = average, add all numbers then divide by how many

Median = midpoint, middle number.  Be sure to list numbers from small to large if there are 2 middle numbers (this happens when there are an even amount), take the average of the 2 middle numbers

Mode = numbers that occurs the most in the list of numbers

Range = This is the largest number minus the smallest number.