Find the next three terms of the geometric sequence -8, 12, -18,27

Answer:

[tex]\displaystyle x=\frac{5}{2}, x=\frac{2}{5}[/tex]

Step-by-step explanation:

Quadratic Equations

The quadratic equation has the following general form

[tex]ax^2+bx+c=0[/tex]

It can be solved by several methods, including the well-known quadratic formula

[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

The question requires us to find a number that added with its reciprocal results 2 9/10. If x is the required number

[tex]\displaystyle x+\frac{1}{x}=2\ \frac{9}{10}=\frac{29}{10}[/tex]

Operating

[tex]\displaystyle \frac{x^2+1}{x}=\frac{29}{10}[/tex]

Rearranging

[tex]10(x^2+1)=29x[/tex]

[tex]10x^2-29x+10=0[/tex]

Comparing with the general quadratic equation, we have

[tex]a=10,\ b=-29,\ c=10[/tex]

Using the formula

[tex]\displaystyle x=\frac{29\pm \sqrt{(-29)^2-4(10)(10)}}{2(10)}[/tex]

[tex]\displaystyle x=\frac{29\pm \sqrt{441}}{20}=\frac{29\pm 21}{20}[/tex]

It gives us two possible solutions

[tex]\displaystyle \boxed{x=\frac{5}{2}, x=\frac{2}{5}}[/tex]

Both are valid solutions since

[tex]\displaystyle \frac{5}{2}+\frac{2}{5}=\frac{29}{10}[/tex]

Step-by-step explanation:

The sum of first n odd positive integer is n^2. The nth odd number is 2n-1.

                          i.e. 1 + 3 + ........+ (2n-1) = n^2.  

                                1 + 3 +..........+ (2n-1) = 64

                                                                n^2 = 64

                                                                    n = 8.

The positive integers between 100 and 200 which are divisible by 14 are 112, 126, 140, 154, 168, 182, 196. It is obtained by the multiples of 14 between 100 and 200.

100 = 7 * 14 + 2

200 = 14 * 14 + 4. The answer is 14 - 7 = 7

The seven numbers are

                        14 * 8 = 112

                        14 * 9 = 126

                        14 * 10 = 140

                        14 * 11 = 154

                        14 * 12 = 168

                        14 * 13 = 182

                        14 * 14 = 196

Answer: 7+3=4+6

Step-by-step explanation: 7+3=10 and so does 4+6

After 28 years, there will be approximately $48,505.29 in the account.

To calculate the amount of money that will be in the account after 28 years with an annual interest rate of 8.25%, we can use the formula for compound interest:

[tex]\[ A = P \times (1 + r)^n \][/tex]

Where:

- A  is the amount of money accumulated after  n years, including interest.

- P  is the principal amount (the initial amount of money), which is $6700 in this case.

- r  is the annual interest rate (in decimal form), which is 8.25% or 0.0825.

- n is the number of years, which is 28 in this case.

Plugging in the values into the formula:

[tex]\[ A = 6700 \times (1 + 0.0825)^{28} \][/tex]

Calculating the value:

[tex]\[ A = 6700 \times (1.0825)^{28} \][/tex]

[tex]\[ A \approx 6700 \times 7.2417 \][/tex]

[tex]\[ A \approx 48,505.29 \][/tex]

Answer:

 n (A'  U  B )  = 75

Step-by-step explanation:

Here, given :  n(U)=120, n(A)=45, and n(B)=50

As we know:

n (A ' U B)  =  n(A) − n (A∩B)   ... (1)

Here, n(A) = 45

So, n( A')  = n(U) - n(A)  = 120 - 45  = 75

⇒ n(A')  = 75

Now, as given A and B are disjoint sets.

⇒   n (A ∩ B)   = Ф

So, (A'  U  B )  = A'

So, n (A'  U  B )  =n( A') = 75

⇒  n (A'  U  B )  = 75

Answer:

Mean, median, and mode are three kinds of "averages".

Step-by-step explanation:

Find the mean, median, mode, and range for the following list of values:

13, 18, 13, 14, 13, 16, 14, 21, 13

The mean is the usual average, so I'll add and then divide:

(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15

Note that the mean, in this case, isn't a value from the original list. This is a common result. You should not assume that your mean will be one of your original numbers.

The median is the middle value, so first I'll have to rewrite the list in numerical order:

13, 13, 13, 13, 14, 14, 16, 18, 21

There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number:

13, 13, 13, 13, 14, 14, 16, 18, 21

So the median is 14.

The mode is the number that is repeated more often than any other, so 13 is the mode.

The largest value in the list is 21, and the smallest is 13, so the range is 21 – 13 = 8.

mean: 15

median: 14

mode: 13

range: 8

Final answer:

Mean, median, and mode are basic statistical measures used to find the center of a data set. Mean finds the average, median identifies the middle value when data is ordered, and mode determines the most frequently occurring value.

Explanation:

Mean, median, and mode are measures of central tendency that describe the way in which different values cluster around a central point in a set of data.

The mean is the average of all the numbers in the data set. You calculate the mean by adding up all the numbers and dividing by the total number of values.

The median is the middle value of an ordered data set. If the data set has an odd number of values, the median is the exact middle number. If there is an even number of values, the median is the average of the two central numbers.

The mode is the value that appears most frequently in the data set. If no number repeats, the data set has no mode; if two or more numbers occur with equal frequency and more often than any other number, the dataset is multimodal, having several modes.

Each of these measures provides a different perspective on the typical value or center of a dataset, and is useful in various statistical analyses.

Answer:

8 and 5

Step-by-step explanation:

The sum of 8 and 5 implies

8 + 5 = 13

The difference between 8 and 5 implies:

8 - 5 = 3

Therefore, the sum of two numbers that gives 13 and their difference being 3 are 8 and 5.

The area of the rectangle is 300 square inches, calculated by multiplying the length (20 inches) by the width (15 inches).

To find the area of the rectangle, we can use the formula for the area of a rectangle, which is [tex]\( \text{length} \times \text{width} \).[/tex] However, we need to find the length of the rectangle first.

We are given that the width of the rectangle is 15 inches. Let's denote the length of the rectangle as [tex]\( l \).[/tex]

We know that the diagonal of a rectangle forms a right triangle with the length and width of the rectangle. Therefore, we can use the Pythagorean theorem to find the length of the rectangle.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the lengths of the other two sides (the length and the width).

So, we have:

[tex]\[ l^2 + 15^2 = 25^2 \][/tex]

Solving for[tex]\( l \):\[ l^2 = 25^2 - 15^2 \]\[ l^2 = 625 - 225 \]\[ l^2 = 400 \][/tex]

Taking the square root of both sides:

[tex]\[ l = \sqrt{400} \]\[ l = 20 \][/tex]

Now that we have found the length of the rectangle to be 20 inches, we can calculate the area:

[tex]\[ \text{Area} = \text{length} \times \text{width} \]\[ \text{Area} = 20 \times 15 \]\[ \text{Area} = 300 \, \text{square inches} \][/tex]

So, the area of the rectangle is 300 square inches.

Option 2: A and B only

Step-by-step explanation:

A: [tex]\{(0,9),(3,12),(-5,10),(5,10)\}[/tex]

The function can be represented in ordered pairs. Also, the x-values are not repeated and each has only one y-value. Hence, in this given ordered pair the values of x are not repeated and each has only one y-value.

Thus, A is a function.

B: [tex]y=x^{2} +10[/tex]

This is the general way of representing a function in which the input value (x-value) exactly related to one output value (y-value). Hence, in this given function the x-value has only one y-value.

Thus, B is a function.

C: The function can also be represented using tables in which each x-value is not repeated and has only one y-value. But, in this given table, the values of x (x=10) are repeated twice.

Thus, C is not a function.

Option 1: A only

Reason: A and B are the correct representations of the function.

This option 1 is not the correct answer.

Option 2: A and B only

Reason: A and B are the correct representations of the function.

This option 2 is the correct answer.

Option 3: A and C only

Reason: C is not a function. Only A and B are the correct representations of the function.

This option 3 is not the correct answer.

Option 4: A, B and C

Reason: Only A and B are the correct representations of the function and C is not a function.

This option 4 is not the correct answer.

Answer:

$47

Step-by-step explanation:

Andy's initial amount was $28.

The question is on subtraction. It is meant to understand your capacity on worded form of subtraction.

After Andy cashed the cheque, his amoussou rose from $28 to $75.

Therefore, to know the amount on the cheque we subtract the initial amount from the total amount.

$75 - $28 = $47

Answer: -425

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

John has 16 cups of apples and 15 cups of flour..

A pie needs 4 cups of apples and 3 cups of flour.

Apples: 16/4 = 4     he has enough apples to make 4 pies.

Flour: 15/3 = 5      he has enough flour to make 5 pies.

He can only make 4 pies, because of the amount of apples he has.

By making 4 pies, he uses all his apples, and he can make no cobblers.

x = 4 pies; y = 0 cobblers

Plot (4, 0).

A pie needs 2 cups of apples and 3 cups of flour.

Apples: 16/2 = 8     he has enough apples to make 8 cobblers.

Flour: 15/3 = 5        he has enough flour to make 5 cobblers.

He can only make 5 cobblers, because of the amount of flour he has.

By making 5 cobblers, he uses all the flour, and he can make no pies.

x = 0 pies; y = 5 cobblers

Plot (0, 5).

Now we calculate the amount of money.

At point (4, 0), 4 * $3 = $12

At point (0, 5), 5 * $2 = $10

Point (4, 0) shows a profit of $12 which is the most profit he can make.

Answer:

21

Step-by-step explanation:

You know the length of JK 12

you also know the length of GF 2.5*12=30

HL is a mid segment because it cuts both legs it intersects in half.

Using the rule saying that the mid segment is half the bases added up we can figure out that HL = (12+30)/2 = 21

Answer:

21

Step-by-step explanation:

Find attached the solution

Answer:

8.33

Step-by-step explanation:

Answer:

The domain of the function (cd)(x) will be all real values of x except x = 2.

Step-by-step explanation:

The two functions are [tex]c(x) = \frac{5}{x - 2}[/tex] and d(x) = x + 3

So, (cd)(x) = [tex](\frac{5}{x - 2})(x + 3) = \frac{5(x + 3)}{x - 2}[/tex]

Then, for x = 2 the function (cd)(x) will be undefined as zero in the denominator will make the function (cd)(x) undefined.

Therefore, the domain of the function (cd)(x) will be all real values of x except x = 2. (Answer)

Answer:

the answer is b on edg2020

Step-by-step explanation:

c = cost of food/med for cats

d = cost of food/med for dog

y = total cost/spent

What you know:

y = 6c + d              [has 6 cats and 1 dog]  

c = 2/3d - 5        [cost for cat is 5 less than 2/3 cost for dog]

y = $195

y = 6c + d    

Substitute/plug in what you know, plug in (2/3d - 5) for c and 195 for y

195 = 6(2/3d - 5) + d        Distribute/multiply 6 into (2/3d - 5)

195 = 4d - 30 + d        Combine like terms

195 = 5d - 30      Add 30 on both sides of the equation

225 = 5d        Divide 5 on both sides

$45 = d            

Answer:

See explanation

Step-by-step explanation:

Use formula

[tex]I=P\cdot r\cdot t,[/tex]

where

I = interest,

P = principal,

r = rate (as decimal),

t = time

In your case,

[tex]P=\$1,539\\ \\r=0.01[/tex]

If [tex]t_1=5[/tex] years, then

[tex]I_1=1,539\cdot 0.01\cdot 5=76.95[/tex] and the whole sum is [tex]\$1,539+\$76.95=\$1,615.95[/tex]

If [tex]t_2=10[/tex] years, then

[tex]I_2=1,539\cdot 0.01\cdot 10=153.9[/tex] and the whole sum is [tex]\$1,539+\$153.9=\$1,692.9[/tex]

If [tex]t_3=15[/tex] years, then

[tex]I_3=1,539\cdot 0.01\cdot 15=230.85[/tex] and the whole sum is [tex]\$1,539+\$230.85=\$1,769.85[/tex]

Answer:

The number of persons surveyed leaving a movie theater is 150.

Step-by-step explanation:

Science fiction 18% or 0.18 = 27 persons surveyed.

Total of persons surveyed = 2,700/18

Total of persons surveyed = 150

The number of persons surveyed leaving a movie theater is 150.

Answer:

150 people were surveyed.

Final answer:

The equivalent expression to 5(3x+4-x) is obtained by combining like terms and distributing the 5, which results in 10x + 20.

Explanation:

To find an expression equivalent to 5(3x+4-x), we must first simplify the expression inside the parentheses. We combine like terms 3x and -x, which gives us 2x. Then, we distribute the 5 across the simplified expression within the parentheses:

5(3x+4-x) = 5(2x+4) = 5*2x + 5*4 = 10x + 20.

So the expression equivalent to 5(3x+4-x) is 10x + 20. This process involves simplifying expressions step by step, ensuring clarity and accuracy in mathematical computations. By systematically combining like terms and distributing constants, we obtain a concise and equivalent expression that represents the original expression's value.

Answer:

A

Step-by-step explanation:

An inscribed angle of circle T has a measure of 36°.

The cantral angle subtended on the same arc as this inscribed angle has the measure twice greater than inscribed angle, so the measure of the central angle is

[tex]36^{\circ}\cdot 2=72^{\circ}[/tex]

The measure of the intercepted arc (at which angles are subtended) is the same as the measure of the central angle, so correct option is option A

Answer:

a is the answer

Step-by-step explanation:

Answer:2

Step-by-step explanation:

For 57 to be a prime number, it would have been required that 57 has only two divisors, i.e., itself and 1. However, 57 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 57 = 3 x 19, where 3 and 19 are both prime numbers.

Answer: No

Step-by-step explanation: For 57 to be a prime number, it would have been required that 57 has only 2 divisors, ie itself and 1. How ever 57 is a semiprime because it is the product of a two non- necessarily distinct prime numbers. inderd, 57= 3×19, where 3 and 19 are prime numbers.

Answer:

OkAy reeee

Step-by-step explanation:

BOOMER

The solution is x < 3.

Solution:

The given expression is 3x + 4 < 13.

To solve the given inequality.

3x + 4 < 13

Subtract 4 tiles on both sides of the inequality.

⇒ 3x + 4 – 4 < 13 – 4

⇒ 3x < 9

Divide by 3 tiles on both sides of the inequality.

⇒ [tex]\frac{3x}{3} =\frac{9}{3}[/tex]

⇒ x < 3

Hence the solution is x < 3.

Final answer:

To solve the inequality using algebra tiles, represent 3x+4 with tiles on one side and 13 units on the other, remove 4 units from both sides to get 3x < 9 and then divide the remaining 9 units into 3 groups to find x < 3.

Explanation:

To solve the inequality 3x+4<13 using algebra tiles, we follow these steps:

Start by representing the inequality with algebra tiles. Place 3 x-tiles (each representing 'x') and 4 unit tiles (each representing '1') on one side of a mat to model the expression 3x+4.

On the other side, place 13 unit tiles to represent the number 13.

To isolate the variable x, we need to remove the same number of unit tiles from each side. Remove 4 unit tiles from each side of the mat, which corresponds to Subtracting 4 from both sides of the inequality.

After removal, the inequality on the mat now shows 3x tiles on one side and 9 unit tiles on the other, representing the inequality 3x < 9.

Lastly, to find the value of one x-tile, divide the remaining unit tiles into 3 equal groups. Since there are 9 units left, each group will consist of 3 unit tiles, indicating that each x-tile is less than 3. This gives us the final inequality x < 3.

From this process, we've determined that for the original inequality 3x+4<13, the solution is x<3.

Answer:

  x = y^2 – 7

Step-by-step explanation:

The first step in finding the inverse of y = f(x) can be to write the equation x = f(y). The equation shown above is such an equation.

Answer:

[tex]x= y^2-7[/tex]

Step-by-step explanation:

We have been given an equation [tex]y=x^2-7[/tex]. We are asked to determine that which equation can be simplified to find the inverse of our given equation.

We know that to find inverse of an equation, the x and y-values are interchanged.

Let us interchange x and y values for our given equation.

[tex]x= y^2-7[/tex]

Therefore, the equation [tex]x= y^2-7[/tex] can be simplified to find the inverse of our given equation.

Answer:

Laura and Erica will both have made 16 blankets in one more day.

Step-by-step explanation:

i) Erica has made 10 blankets already.

ii) Erica can make 6 blankets more per day

iii) Laura has completed 6 blankets already

iv) Laura can complete 10 more blankets per day.

v) Let x be the number of days to the point when they will have completed the same number of blankets

vi) Therefore the number of blankets that Erica makes till x days is = to the number of blankets that Laura makes till x days

vi) therefore 10 + 6x  = 6 + 10x    ⇒   4x  = 4    ⇒ x = 1 day

vii) Therefore Laura and Erica will both have made 16 blankets in one more day.

Answer:

r = 7

Step-by-step explanation:

Given

r + 15  = 4r - 6 ( subtract 4r from both sides )

- 3r + 15 = - 6 ( subtract 15 from both sides )

- 3r = - 21 ( divide both sides by - 3 )

r = 7

Answer:

0.3 units

Step-by-step explanation:

The ratio of the length of the arc to the circumference of the circle is proportional to the ratio of the central angle to the sum of angle in a circle.

[tex]\frac{l}{6}=\frac{20}{360}[/tex]

This implies that:

[tex]l=\frac{20}{360}*6[/tex]

This simplifies to: [tex]l=\frac{20}{60}[/tex]

[tex]l=\frac{1}{3}=0.3 units[/tex]

Since the circumference of this circle is 6 units, the length of the arc formed is equal to 0.33 units

Given the following data:

Circumference = 6 units.

Central angle = 20°

Mathematically, if you want to determine the length of the arc formed by a circle, you will divide the angle subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle as follows:

20/360 × 6 = 0.33 units.

Read more on circumference here: brainly.com/question/14478195

Answer:

The following observation and calculations show that the iterative rule is correct.

Step-by-step explanation:

The second reason why these calculations are true is the fact these calculations represent geometric sequence.

Considering the data

200, 220, 242, 266.2, 292.82, 322.102,....

Any sequence is said to be the geometric sequence If the ratio between two consecutive terms remains constant - commonly known as common ration which is denoted by 'r'.

As the ratio between two consecutive terms remains constant. For example,

[tex]r=\frac{220}{200} =1.1, r=\frac{242}{220} =1.1, r=\frac{266.2}{242} =1.1[/tex]

So, the given sequence is a geometric sequence. In other words, in Geometric Sequence each term can be found in terms of multiplying the previous term by a constant factor which is 1.1.

So,

220 is obtained by multiplying 200 by 1.1.

i.e. 200×1.1 = 220

Also,

242 is obtained by multiplying 220 by 1.1.

i.e. 220×1.1 = 242

and so on...

Therefore, it is clear from the current observation and calculation that the iterative rule is correct.

Keywords: sequence, geometric sequence

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