The third term and the sixth term of A geomatric sequence are 2 and 16 respectively. Find the first term and the common ratio

Answers

Answer 1

The first term of the geometric sequence is 1/2 and the common ratio is 2.

What is the geometric sequence?

A geometric sequence is a sequence of numbers in which each term after the first is obtained by multiplying the previous term by a fixed number called the common ratio. The general form of a geometric sequence is:

a, ar, ar², ar³, ar⁴, ...

where 'a' is the first term, 'r' is the common ratio, and the subscripts represent the position of the term in the sequence.

Let's denote the first term of the geometric sequence by "a" and the common ratio by "r".

We know that the third term of the sequence is 2, which means that:

a * r² = 2 (1)

We also know that the sixth term of the sequence is 16, which means that:

a * r⁵ = 16 (2)

Now we can solve for "a" and "r" by dividing equation (2) by equation (1):

(a * r⁵)/(a * r²) = 16/2

Simplifying, we get:

r³ = 8

Taking the cube root of both sides, we get:

r = 2

Now we can use equation (1) to solve for "a":

a * 2² = 2

Simplifying, we get:

4a = 2

a = 1/2

Therefore, the first term of the geometric sequence is 1/2 and the common ratio is 2.

To learn more about the geometric sequence visit:

https://brainly.com/question/24643676

#SPJ1


Related Questions

Only numbers 20 and 22

Answers

1. The transformation of f is a reflection across the y-axis, followed by a shift of 8 units along the y-axis.

2. stretching by a factor of 2 along the y-axis

3. reflection

4. shift

5. reflection

6. stretch

7. stretch

8. reflection

What is modifying function?

The transformation of a function f represented by g is the process of modifying the function f to create a new function g. This can be done in a number of ways, such as shifting the graph, stretching it, or reflecting it in some way.

1. f(x) = √x, g(x) = √(x+1)+8, the transformation of f is a reflection across the y-axis, followed by a shift of 8 units along the y-axis.

2. f(x) = √x, g(x) = 2√(x - 1), the transformation of f is a stretching by a factor of 2 along the y-axis, followed by a shift by -1 along the x-axis.

3. f(x) = ³√x, g(x) = −³√x-1, the transformation of f is a reflection across the x-axis, followed by a shift of -1 along the x-axis.

4. f(x) = ³√x, g(x) = ³√(x +4)-5, the transformation of f is a shift of 4 units along the x-axis, followed by a shift of -5 units along the y-axis.

5. f(x) = x^½, g(x) =1/4(-x)^½, the transformation of f is a reflection across the y-axis, followed by a stretching by a factor of 1/4 along the y-axis.

6. f(x) = x^⅓, g(x) =1/3x^⅓+6, the transformation of f is a stretching by a factor of 1/3 along the y-axis, followed by a shift of 6 units along the y-axis.

7. f(x)= ⁴√x, g(x) =2 ⁴√(x+5)-4, the transformation of f is a stretching by a factor of 2 along the y-axis, followed by a shift of 5 units along the x-axis, followed by a shift of -4 units along the y-axis.

8. f(x)= ⁵√x, g(x) =⁵√(-32x)+3, the transformation of f is a reflection across the x-axis, followed by a stretching by a factor of 32 along the x-axis, followed by a shift of 3 units along the y-axis.

For more questions related to transformation

https://brainly.com/question/10904859

#SPJ1

19. The transformation of f is a reflection across the y-axis, followed by a shift of 8 units along the y-axis.

20. The transformation of f is a stretching by a factor of 2 along the y-axis

21. The transformation of f is a reflection across the x-axis.

22. The transformation of f is a shift of 4 units along the x-axis, followed by a shift of -5 units along the y-axis.

23. The transformation of f is a reflection across the y-axis.

24. The transformation of f is a stretching by a factor of 1/3 along the y-axis.

25. The transformation of f is a stretching by a factor of 2 along the y-axis.

26. The transformation of f is a reflection across the x-axis, followed by a stretching by a factor of 32 along the x-axis

Define function modification?

The transformation of a function f represented by g is the process of modifying the function f to create a new function g. This can be done in a number of ways, such as shifting the graph, stretching it, or reflecting it in some way.

19. f(x) = √x, g(x) = √(x+1)+8, the transformation of f is a reflection across the y-axis, followed by a shift of 8 units along the y-axis.

20. f(x) = √x, g(x) = 2√(x - 1), the transformation of f is a stretching by a factor of 2 along the y-axis, followed by a shift by -1 along the x-axis.

21. f(x) = ³√x, g(x) = −³√x-1, the transformation of f is a reflection across the x-axis, followed by a shift of -1 along the x-axis.

22. f(x) = ³√x, g(x) = ³√(x +4)-5, the transformation of f is a shift of 4 units along the x-axis, followed by a shift of -5 units along the y-axis.

23. f(x) = x½, g(x) =1/4(-x½, the transformation of f is a reflection across the y-axis, followed by a stretching by a factor of 1/4 along the y-axis.

24. f(x) = x⅓, g(x) =1/3x⅓+6, the transformation of f is a stretching by a factor of 1/3 along the y-axis, followed by a shift of 6 units along the y-axis.

25. f(x)= ⁴√x, g(x) =2 ⁴√(x+5)-4, the transformation of f is a stretching by a factor of 2 along the y-axis, followed by a shift of 5 units along the x-axis, followed by a shift of -4 units along the y-axis.

26. f(x)= ⁵√x, g(x) =⁵√(-32x)+3, the transformation of f is a reflection across the x-axis, followed by a stretching by a factor of 32 along the x-axis, followed by a shift of 3 units along the y-axis.

For more questions related to transformation

https://brainly.com/question/10904859

#SPJ1

E I D 27° A I C m DC = 40° F B What is the mZAFB? |​

Answers

let's keep in mind that arc's get their angle value from the central angle they cover, so in this case whatever angle value the arcAFB has, will also be the same for the ∡AFB.

Check the picture below.

Work out the value of 2^6

Answers

Answer:

2^6 = 64

Step-by-step explanation:

2^6 = 2⁶ = 2*2*2*2*2*2

= 64

Identify the segment bisector of XY

XM= 3x+1
MY= 8x-24
The length of XY is

Answers

Answer:

The length of XY is 32.

Step-by-step explanation:

3x + 1 = 8x - 24

1 = 5x - 24

5x = 25

x = 5

3(5)+1 = 16

16*2 = 32

The length of XY is 32.

Use graphing technology to find the range of the function f ( x) = − ∣ x∣ + 7. f(x)=−∣x∣+7.

Answers

Using graphing technology, we have came to know that the range οf the given functiοn is f(x )≤ 7.

What is range οf a functiοn?

The set οf all resulting values οf a functiοn is called the range οf a functiοn.

Fοr example if the functiοn is f(x)= 2x.

Fοr the given set οf values x={ 1,2,3 and sο οn} the range will be {2,4,6 and sο οn}

Given functiοn is f(x)= -|x|+7

The range οf an absοlute function οf the fοrm -c| [tex]ax+b[/tex]| is f(x) ≤ k

here k=7

sο the range will be f(x) ≤ 7

Hence range οf the given functiοn  will be f(x) ≤ 7.

To know mοre about range

https://brainly.com/question/2709928   from the link.

#SPJ1

A house blueprint has a scale of 1 in. : 4 ft. The length and width of each room in the actual house are shown in the table. Complete the table by finding the length and width of each room on the blueprint. Living room Kitchen Office Bedroom Bedroom Bathroom Actual l w (ft.) 12 8 16 16 8 16 16 8 20 20 10 20 Blueprint l w (in.)

Answers

To find the length and width of each room on the blueprint, we need to use the given scale of 1 in. : 4 ft. This means that every 1 inch on the blueprint represents 4 feet in the actual house.

To find the length and width of each room on the blueprint, we can multiply the actual length and width of each room by 1/4 (or divide by 4). This gives us:

Living room: Length = 12 ft. ÷ 4 = 3 in., Width = 8 ft. ÷ 4 = 2 in.

Kitchen: Length = 16 ft. ÷ 4 = 4 in., Width = 16 ft. ÷ 4 = 4 in.

Office: Length = 16 ft. ÷ 4 = 4 in., Width = 8 ft. ÷ 4 = 2 in.

Bedroom: Length = 20 ft. ÷ 4 = 5 in., Width = 20 ft. ÷ 4 = 5 in.

Bedroom: Length = 10 ft. ÷ 4 = 2.5 in., Width = 20 ft. ÷ 4 = 5 in.

Bathroom: Length = 16 ft. ÷ 4 = 4 in., Width = 8 ft. ÷ 4 = 2 in.

Therefore, the length and width of each room on the blueprint are:

Living room: 3 in. x 2 in.

Kitchen: 4 in. x 4 in.

Office: 4 in. x 2 in.

Bedroom: 5 in. x 5 in.

Bedroom: 2.5 in. x 5 in.

Bathroom: 4 in. x 2 in.

Learn more about width here brainly.com/question/30282058

#SPJ1

The figure is made up of 2 rectangles and 2 right triangles.

What is the area of the figure?

Responses

173 units2


253 units2


277 units2


325 units2

Answers

173 units2 is the area of the figure.

What are angles?

A point where two lines meet produces an angle.

The breadth of the "opening" between these two rays is referred to as a "angle". It is depicted by the figure.

Radians, a unit of circularity or rotation, and degrees are two common units used to describe angles.

By connecting two rays at their ends, one can make an angle in geometry. The sides or limbs of the angle are what are meant by these rays.

The limbs and the vertex are the two main parts of an angle.

The common terminal of the two beams is the shared vertex.

Hence, 173 units2 is the area of the figure.

Learn more on angles here click here:

brainly.com/question/2046046

#SPJ1

The number of students in the tutoring center was recorded for 40 randomly selected times. The data is summarized in the frequency table below. Number of Students Frequency 0 – 1 15 2 – 3 1 4 – 5 14 6 – 7 2 8 – 9 8 What is the class width for this Frequency Distribution Table?

Answers

After answering the presented question, we can conclude that As a range result, the class breadth in this frequency distribution table is one.

What is range?

The variable's range is calculated by taking its maximum observed value and subtracting its minimum observed value (minimum). Possible range or variational bounds: a variety of steel costs; a variety of styles; The scope or magnitude of a method or action: perception. The maximum or anticipated range of a weapon's projectile. A list or set's range is the number between the lowest and maximum. Align all of the numbers before identifying the region. Next, subtract (reduce) the lowest number from the highest number. The solution includes the range of the list. The solution specifies the range of the list.

To calculate the class width, we must first determine the range of values within each class interval.

The class intervals are as follows:

[tex]0-1\s2-3\s4-5\s6-7[/tex]

8-9

0-1 interval range: 1-0 = 1

2-3 interval range: 3-2 = 1

5-4 = 1 interval range of 4-5

7-6 = 1 interval range of 6-7

8-9 interval range: 9-8 = 1

The intervals all have the same range of one.

To calculate the class width, subtract the upper limit of the first interval from the lower limit of the first interval.

Higher limit of first interval - Lower limit of first interval = class width

1 - 0 class width

1 class width

As a result, the class breadth in this frequency distribution table is one.

To know more about range visit:

https://brainly.com/question/28135761

#SPJ9

A teacher assigns a score from 1 to 4 to each student project. The table below shows the probability distribution of the scores for a randomly selected student. Which score is most likely?Probability DistributionScore: XProbability: P(X)10.0620.2030.4840.261234

Answers

Based on the probability distribution, the score that is most likely is 3, since it has the highest probability of 0.48.

7. Reasoning Hilary walked 654 feet in 3
minutes. She says she walked 218 feet
per minute. Is Hilary's answer reasonable?
Explain.

Answers

653/3 = 218

So it is reasonable that she walked 218 ft in 1 minute


what is the domain of the function?

Answers

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited

Indicate whether each statement is the converse, inverse, or contrapositive of the given statement.
The diagonals of a parallelogram bisect each other.

Answers

Answer:

first box, first box, second box

Step-by-step explanation:

At a speed of 22 revolutions per minute, how long will it take a wheel with radius 10",
rolling on its edge to travel 10 feet?

Answers

Answer:

0.4 seconds or

0.00667 minutes

Step-by-step explanation:

https://brainly.com/question/517612

pi times radius times 2 = circumference

pi times 10 inches times 2 = 62.83 inches = circumference

In one revolution, the wheel covers a distance equal to its circumference. So, at a speed of 22 revolutions per minute, the wheel covers a distance of:

22 x 62.83 inches inches per minute

1382.26 revolutions per minute

The wheel travels 1383.8 ft. in 60 seconds.

The wheel travels 1 ft. in (60 /  1383.8) seconds.

The wheel travels 10 ft. in (60 /  1383.8) * 10 seconds = 0.4 seconds

= 0.4 seconds divided by 60 = 0.00667 minutes

4. The value of (1+2+3+...+20) is 210. What is the value of (3+6+9+...+57)?
B) 630
A) 627
C) 570
D) 573
E) 580

Answers

By using sum of sequence the value of (3+6+9+...+57) is 570, which is option C).

What is sum of the sequence ?

The sum of a sequence is the total result of adding up all the numbers in the sequence. The method for finding the sum of a sequence depends on whether the sequence is arithmetic or geometric.

For an arithmetic sequence, in which each term is obtained by adding a fixed number (called the common difference) to the previous term, the sum of the first n terms can be found using the formula:

[tex]Sn = n/2(2a + (n-1)d)[/tex]

where a is the first term, d is the common difference, and n is the number of terms.

For a geometric sequence, in which each term is obtained by multiplying the previous term by a fixed number (called the common ratio), the sum of the first n terms can be found using the formula:

[tex]Sn = a(1-r^n) / (1-r)[/tex]

where a is the first term, r is the common ratio, and n is the number of terms.


According to the question:
We can notice that each number in the sequence 3, 6, 9, ..., 57 is 3 times the corresponding number in the sequence 1, 2, 3, ..., 19.

So, we can find the sum of the sequence 3, 6, 9, ..., 57 by finding the sum of the sequence 1, 2, 3, ..., 19 and then multiplying by 3.

The sum of the sequence 1, 2, 3, ..., 19 is:

1 + 2 + 3 + ... + 19 = (19/2)(1 + 19)/2 = 190

Multiplying by 3, we get:

3 + 6 + 9 + ... + 57 = 3(1 + 2 + 3 + ... + 19) = 3(190) = 570

Therefore, the value of (3+6+9+...+57) is 570, which is option C).

To know more about sum of sequence visit:
https://brainly.com/question/28812249
#SPJ1

how long does it take for a population that is growing with a constant relative growth rate of 10% per year to triple

Answers

It would take approximately 7.2 years for a population that is growing with a constant relative growth rate of 10% per year to triple.

At the end of the spring semester, the dean of students sent a survey to the entire freshman class. One question asked the students how much weight they had gained or lost since the beginning of the school year.
The average was a gain of µ = 15 pounds with a standard deviation of
σ = 6. The distribution of scores was approximately normal.
A sample of n = 4 students is selected, and the average weight change is computed for the sample.
What is the probability that the sample mean will be greater than M = 10 pounds? In symbols, what is p (M > 10) (four decimals)

Answers

The probability that the sample mean will be greater than M = 10 pounds is 0.9525.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating the event is impossible and 1 indicating it is certain. Probability is used in many fields, including mathematics, statistics, science, and finance.

To solve this problem, we need to use the central limit theorem (CLT), which states that the distribution of sample means will be approximately normal, regardless of the shape of the population distribution, as long as the sample size is large enough.

Since the sample size is small (n = 4), we need to use the t-distribution instead of the normal distribution. However, since the population standard deviation is known, we can use the standard normal distribution with a z-score.

First, we need to calculate the standard error of the mean:

SE = σ / sqrt(n) = 6 / sqrt(4) = 3

Next, we can calculate the z-score:

z = (M - µ) / SE = (10 - 15) / 3 = -1.67

Finally, we can use a standard normal distribution table or calculator to find the probability of a z-score greater than -1.67:

p(M > 10) = P(z > -1.67) = 0.9525 (rounded to four decimals)

Therefore, the probability that the sample mean will be greater than M = 10 pounds is 0.9525.

To know more about Average visit :-

https://brainly.com/question/130657

#SPJ1

Of the following , which measurement is in the base units 5mg, 10kL, 2.5g, 100mm

Answers

For the given measurements of 5mg, 10kL, 2.5g, 100mm, the base unit is 10kL as per the metric system.

Explain about the standard measurement units?

The most widely used measurement unit is a standard unit. As the units used are standardised, everyone can understand an object's size, weight, and perhaps other characteristics.

The values of Standard Units of Measurement are constant and cannot be altered. To ensure that everyone uses the same measurements and has the same understanding of measurement, measurements must be consistent between users.The identity of a quantity is described using standard units of measurement. It is simpler to identify the type of data we are working with when there are units of measurement available.

The Metric System is currently used in the majority of nations. The Imperial Units of Measuring, often known as the US Standard Measurement System, are used in the US.

Given units :

5mg, 10kL, 2.5g, 100mm

In this, standard measurement units or base units if 10 kilo litres or 10 KL.

Know more about the standard measurement units

https://brainly.com/question/13321281

#SPJ1

A BICYCLE WHEEL HAS AN INSIDE RADIUS OF 12 CM. WHAT IS THE WIDTH OF THE TYRE IF THE OUTSIDE CIRCUMFERENCE IS 32П СМ?​

Answers

Answer:

Your answer is 4cm.

Step-by-step explanation:

simple calculation

x (12+x) π = 32 π

x = 4cm

which expression is equivalent to g^2/3h

Answers

The given expression [tex]g^2/3h[/tex] is equivalent to the option (c) [tex]8g^2/24h[/tex]as we have multiplied 8 in both numerator and denominator.

The given expression is [tex]g^2/3h[/tex].

Now, to further simplify the expression, we can multiply both numerator and denominator by 8. This gives us:

[tex](g^2/3h) * (8/8)[/tex]

Simplifying further, we get:

[tex](8g^2)/(24h)[/tex]

Therefore, the expression equivalent to [tex]g^2/3h[/tex] is [tex](8g^2)/(24h)[/tex].

Thus, the given expression [tex]g^2/3h[/tex] is equivalent to the option (c) [tex]8g^2/24h[/tex] as we have multiplied 8 in both numerator and denominator.

The numerator is the top part of a fraction, which represents the number of equal parts being considered. It is the value that is above the fraction bar and represents the quantity being divided into equal parts.

Learn more about denominator :

https://brainly.com/question/7067665

#SPJ1

The complete question is :

Which expression is equivalent to [tex]g^2/3h[/tex]?

Click on the correct answer.

(A) [tex]g^2+5/3h+5[/tex]

(B) [tex]6g^2/15h[/tex]

(C) [tex]8g^2/24h[/tex]

Find the set of the solutions of each of the following absolute value inequalities. Check your answers. |(x+1)/2 - x/2|<1/2

Answers

Thus, the solution set of the given absolute value inequalities is found as: 0 ≥ x ≥ -1

Explain about the absolute value inequalities:

The comparison of the connection here between variable and its value is a compound inequality. In a compound inequality, a variable is compared across two ranges which may provide the variable's range by satisfying either one or both of the limitations .

The given absolute value inequalities :

|(x+1)/2 - x/2| < 1/2

Removing the modulus sign will for 2 equations:

(x+1)/2 - x/2 < 1/2  and  (x+1)/2 - x/2 < - 1/2

Simplifying each:

(x+1)/2 - x/2 < 1/2  

x/2 + 1/2 - x/2 < 1/2

Both values will get cancelled:

0 < 0

But 0 = 0

and  (x+1)/2 - x/2 > - 1/2

x/2 + 1/2 - x/2 > -1/2

0 > -1 (correct)

here also the terms are getting completely cancelled to

Thus, the solution set of the given absolute value inequalities is found as: 0 ≥ x ≥ -1

Know more about the absolute value inequalities

https://brainly.com/question/27307313

#SPJ1

Complete question:

Find the set of the solutions of the following absolute value inequalities.

|(x+1)/2 - x/2| < 1/2

If 2x2 + 8x – 14 = 0, find the sum and the product of its roots.
a. sum = 4; product = 7 c. sum = -4; product = -7
b. sum = -4; product = 7 d. sum = 4; product = -7

Answers

Answer:

c

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0

then

sum of roots = - [tex]\frac{b}{a}[/tex]

product of roots = [tex]\frac{c}{a}[/tex]

2x² + 8x - 14 = 0 ← is in standard form

with a = 2 , b = 8 , c = - 14

sum of roots = - [tex]\frac{b}{a}[/tex] = - [tex]\frac{8}{2}[/tex] = - 4

product of roots = [tex]\frac{c}{a}[/tex] = [tex]\frac{-14}{2}[/tex] = - 7

4.1 Exponential Functions
189
Work these problems. (See Example 5.)
37. Finance If money loses value, then as time passes, it takes
more dollars to buy the same item. Use the results of Exercise
36(a) to answer the following questions.
(a) Suppose a house costs $105,000 today. Estimate the cost of
the same house in 10 years. (Hint: Solve the equation
.74t =
$105,000.)
(b) Estimate the cost of a $50 textbook in 8 years.

Answers

we can estimate the cost of a $50 textbook in 8 years to be approximately $32.78.

What is logarithms?

Logarithms are mathematical functions that are used to solve equations involving exponents. Specifically, a logarithm is the inverse operation of exponentiation. Just as exponentiation involves raising a base to a power, logarithms involve finding the power to which a base must be raised to produce a given value.

The logarithm of a number y with respect to a base b is written as logb y, and it is defined as the exponent to which the base b must be raised to produce the number y. In other words, if [tex]b^x = y[/tex], then logb y = x.

According to the question:
In Exercise 36(a), we found that the value of a dollar decreases by 26% over 5 years. We can use this information to answer the following questions:

(a) To estimate the cost of the same house in 10 years, we need to solve the equation:

0.74t = 105,000

where t is the time in years. Solving for t, we get:

[tex]t = log(105,000) / log(0.74) = 17.9[/tex]

So it will take approximately 17.9 years for the value of the dollar to decrease by 26% enough to make the $105,000 house cost the same as it does today. Therefore, we can estimate the cost of the same house in 10 years to be:

[tex]$105,000 * (1 / 0.74)^(10/17.9) = $211,775.22[/tex]

(b) To estimate the cost of a $50 textbook in 8 years, we need to find the value of k in the exponential function:

[tex]V(t) = V(0) * e^kt[/tex]

where V(0) is the initial value (in this case, $50), t is the time in years, and V(t) is the value after t years. We know that the value of a dollar decreases by 26% over 5 years, so we can use this information to find k:

[tex]0.74 = e^(k*5)[/tex]

Taking the natural logarithm of both sides, we get:

ln(0.74) = 5k

Solving for k, we get:

k ≈ -0.064

So the exponential function for the value of a dollar over time is:

[tex]V(t) = $50 * e^{-0.064t}[/tex]

To estimate the cost of the textbook in 8 years, we can plug in t = 8 into this function and solve:

[tex]V(8) = $50 * e^{-0.064*8} = $32.78[/tex]

Therefore, we can estimate the cost of a $50 textbook in 8 years to be approximately $32.78.


To know more about logarithms visit:
https://brainly.com/question/30226560
#SPJ1

A net for a three-dimensional figure is shown on grid paper. Each square of the grid paper represents​

Answers

Thus, the total area of the figure made by square grids paper in three-dimensional figure is found as: 48 in².

Explain about the three-dimensional figure?

Three-dimensional (3D) shapes have three dimensions, like length, breadth, and height. Prisms and spheres are two examples of 3D shapes. Multidimensional and physically holdable 3D forms.

The three - dimensional dimensions comprising width, height, and depth are referred to as three dimensions, or 3D. The physical world is three dimensional, as is everything that can be seen there.

For the given net of 3-D figure.

Each  square of grip represents 1 in².

Total area = rectangle area + 2*triangle area

Total area = length*breadth + 2*(1/2*base*height)

Total area = 12*3 + 3*4

Total area =  48 in².

Thus, the total area of the figure made by square grids paper in three-dimensional figure is found as: 48 in².

Know more about the three-dimensional figure

https://brainly.com/question/3204708

#SPJ1

Help!! I guessed on this so I’m not sure if it’s right but if it isn’t please help me lol

Answers

Answer:

x + 4

Step-by-step explanation:

When factored x^2 -16 is (x + 4)(x - 4)

When factored x^2 + 2x - 8 is (x - 2)(x + 4)

The common expression is x + 4

The cookie-stacking competition is a tradition at Westhaven's annual summer festival, and Bert is helping to set it up this year. The first contestant who creates a single stack using all of their cookies wins a prize! After Bert split all the cookies he had evenly among 4 contestants, each contestant got 24 cookies.
Let c represent how many cookies Bert had to start. Which equation models the problem?
Solve this equation to find how many cookies Bert had to start.
cookies

Answers

The problem states that Bert split all his cookies evenly among 4 contestants, so the total number of cookies Bert had can be found by multiplying the number of cookies each contestant received by the number of contestants:

4 * 24 = 96

Therefore, Bert had a total of 96 cookies to start with.

We can also write an equation to represent the problem, where c represents the number of cookies Bert had to start with:

c / 4 = 24

This equation states that the number of cookies Bert had divided by the number of contestants (4) is equal to the number of cookies each contestant received (24).

To solve for c, we can multiply both sides of the equation by 4:

c = 4 * 24

c = 96

So the solution confirms that Bert had 96 cookies to start with.

C/4=24 so 4*24= 96.

Use the function f(x) = 2x²-3x - 5 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the
graph. (4 points)

Answers

Answer:

Step-by-step explanation:

a) (x-1)(2x-5)

b) x=-1 x=-2.5      x+1=0 x=-1        2x-5=0      2x=5     x=2.5

c) The degree is even so the ends of the graph will point in the same direction, the leading coefficient is positive so both ends will point up

d) First plot the x intercepts, then plug f(0) into the equation to get the y intercept. Plot the y intercept and then connect the points

e)

When her first baby was born, a mom started investing $200 each month into a college fund earning 6% compounded monthly, how much will be available when the child turns 18 years?

Answers

FV = $200 x [(1 + 0.06/12)^(12*18) - 1] / (0.06/12)
FV = $94,219.55

Therefore, when the child turns 18 years old, there will be approximately $94,219.55 available in the college fund

Is there anyone who would know how to write this recursive relationship? Also anyone who could write the equation for the second question

Answers

The recursive relationship that describes how the number of Marco's followers is changing each day is Pt = Pt-1 + 32.

It should be noted that after 5 days, Marco will have 597 followers.

How to explain the relationship

The relationship is Pt = Pt-1 + 32 where Pt is the number of followers on day t and Pt-1 is the number of followers on the previous day.

In this case, to calculate how many followers Marco will have after 5 days, we can use this recursive relationship starting with P0 = 437 (the initial number of followers):

P1 = P0 + 32 = 437 + 32 = 469

P2 = P1 + 32 = 469 + 32 = 501

P3 = P2 + 32 = 501 + 32 = 533

P4 = P3 + 32 = 533 + 32 = 565

P5 = P4 + 32 = 565 + 32 = 597

Therefore, after 5 days, Marco will have 597 followers.

Learn more about recursive relationship on;

https://brainly.com/question/29760068

#SPJ1

Choose the item that has measurable volume.

a dollar bill

newspaper page

a water bottle

a postage stamp

Answers

A water bottle

Step-by-step explanation:

It's a water bottle because you cannot measure volume with a dollr bill or postage stamp.

PLEASE HELP!!!!!!!!!

△STU is reflected across the y-axis

What are the signs of the coordinates of △S’T’U’?

PLEASE LOOK AT THE PICTURE!!!!!!!!!!!!!!!

Answers

The signs of the coordinates of ΔS'T'U' the x-coordinate is positive and the y-coordinate is negative.

What is coordinate?

Coordinates are a set of numbers or values that define the position of a point or object in space or on a surface. They are used to locate a point or object in a specific location relative to a reference point, axis, or plane.

According to question:

The coordinate system is divided into four quadrants, numbered from I to IV, which are separated by the x- and y-axes. The origin is located at the intersection of the x- and y-axes, and has coordinates (0, 0)

The ΔSTU lies in Q3 if it reflected then ΔS'T'U' lies in Q4, it means that the point is located in the fourth quadrant of the Cartesian coordinate system. In this quadrant, the x-coordinates are positive and the y-coordinates are negative.

More specifically, if we assume that the point ΔS'T'U' is represented by the coordinates (x, y), then we have:

x > 0 (because it lies to the right of the y-axis)

y < 0 (because it lies below the x-axis)

For example, if the point ΔS'T'U' has coordinates (3, -2), then it lies in Q4, since the x-coordinate is positive and the y-coordinate is negative.

Learn more about coordinates visit:

https://brainly.com/question/16634867

#SPJ1

Other Questions
How many grams of argon, Ar, are present in 2.35 x 1024 atoms of argon? What is an example of compulsive buying disorder? With evidence-based decision-making, managers are encouraged to rely on data and information rather than their intuition.T/F If the area under the standard normal curve between z = -1.46 and z = 0 is 0.4279, then what is the area under the standard normal curve between z = -1.46 and z = 1.46? 0.0721 0.4279 0.8558 0.9279 in this experiment you need to examine the idea of thermal energy transfer. Using a controlled experiment what might a good question about the variables that affect thermal energy transfer be? Therapist energy transfer depends on many properties, but limit your question to only two is arresting a suspect a primary goal of a criminal investigator or is that the job of the patrol officers? Giving a test to a group of students, the grades are summarized below. If one student is chosen at random, find the probability that the student was NOT a female that got a A. Having trouble with finding the answer to this question. Can someone PLEASE help me ASAP its due today!! I will give brainliest if its all done correctly. Answer part A, B, and C for brainliest!! A All the costs chargeable to the bu Depreciation on the building for 2014 Explanations are not required. 2 Report Garrett's Book Store's plant assets on the company's balance sheet at December 31, 2014 3. What will Garrett's income statement for the year ended December 31, 2014, report for this situation? E-33 (Learning Objective 3: Determine depreciation amounts by three methods) Royce's Pizza bughaused Honda delivery van on January 2, 2014, for $43,000. The van was expected to emain in service for four years (208,000 miles). At the end of its useful life, Royce's officials esti- mated that the van's residual value would be $3,500. The van traveled 65,000 miles the first year, 64,000 miles the second year, 42,000 miles the third year, and 37,000 miles in the fourth year. Requirements 1. Prepare a schedule of depreciation expense per year for the van under the three depreciation roduction and double-declining-balance, mund to the nearest two decimal places after each step of the calculation.) 2. Which method best tracks the wear and tear on the van? 1. Which method would Royce's prefer to use for income tax purposes? Explain in detail why Royce's prefers this method. 27-448 ( help me on this assignment youll get ten points The figures shown represent three hypothetical populations; each circle is an individual. Which figure depicts a pattern that illustrates a scenario in which individuals establish exclusive territories to secure access to resources?A.) diagram KB.) diagram HC.) diagram M Raphael bought 2/3 pound bag of sugar. He used 3/4 of it for baking. How many pounds of sugar did he use? the supreme court ruling in korematsu v. united states upheld the constitutionality of metrics that track progress in executing strategies to attain organizational objectives are also known as Name atleast one of Alexander the Greats bad military accomplishments is a response to the scientific method and attempts to accountfor a human's free will.A) BehavioralismB) SubjectivityC) OntologyD) Empiricism Describe the process of decomposition-HOW does it occur company x makes a loan in exchange for a two-year, $8,000 note. the stated interest rate is 6%. the market rate is 4%. what amount of premium does the company amortize at the end of the second year? please round to the nearest whole number. De qu trata el video?, Por qu debera importarme el tema?, Qu importancia tiene la microbiologa del suelo?, Qu funciones cumple la materia orgnica en el suelo? Write a program that creates a 2 dimensional integer array of movie ratings from the command line arguments and displays the index of the movie that has the highest sum of ratings. Ratings range from 1 to 5 (inclusive). The rows of the 2D array correspond to movie reviewers and the columns of the 2D array correspond to movies. The reviewer at index 2 gave movie at index 0 a rating of 4. Take a look at the following example for an explanation on the command line arguments sequence