[50 POINTS] According to the Fundamental Theorem of Algebra, how many zeros does the function f(x) = 5x^6+2x^3−4x + 1
There are ________ Zeros

Answer:

4

Step-by-step explanation:

the distance around the field is the perimeter, which is 2(length) + 2(width)

2(150) + 2(100) = 500

2 kilometres = 2000 metres, and 2000/500 = 4

Answer: 4 times

Step-by-step explanation:

Step 1: find the Perimeter

Perimeter = 2L + 2W

= 2(150 meters) + 2(100 meters)

= 500 meters.

Step 2: find how many times the runner would have to run around the perimeter.

2 kilometers = 2000 meters

2000/500=4

The runner would need to go around the field 4 times to run 2km.

We can use the distance formula to find the distance between two points in a coordinate plane. The distance formula is:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.

Using this formula, we can find the distance between (16, 0) and (0, 12) as:

d = sqrt((0 - 16)^2 + (12 - 0)^2)

d = sqrt((-16)^2 + 12^2)

d = sqrt(256 + 144)

d = sqrt(400)

d = 20

Therefore, the distance between (16, 0) and (0, 12) is 20 units.

To accumulate $100,000 over 20 years at a 10% annual interest rate compound annually, you would need to make annual payments of $8,218.64.

You can use the formula for the future value of an annuity to accumulate $100,000 over 20 years at a 10% annual interest rate compound on a yearly basis:

[tex]FV = Pmt * [(1 + r)^n - 1] / r[/tex]

Where:

FV is future value, which is $100,000 in that case

Pmt: annual payment

r: annual interest rate, which is 10%

n: number of payment periods, which is 20

By plugging in values:

[tex]$100,000 = Pmt * [(1 + 0.1)^(20) - 1] / 0.1[/tex]

Solving for Pmt, we get:

[tex]Pmt = $100,000 / [(1 + 0.1)^(20) - 1] / 0.1\\Pmt = $100,000 / 12.167\\Pmt = $8,218.64[/tex]

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The horizontal distance covered by Viola is approximately 1282.6 meters.

The height of the plane is approximately 461.7 meters

The height of the pole is approximately 159.8 feet.

The perimeter is 44.2.

The horizontal distance covered by Viola can be calculated by using trigonometry. The angle of inclination is 9°, and the distance traveled up the hill is 200 meters.

Let x be the horizontal distance covered. Then we have:

tan(9°) = 200/x

x = 200/tan(9°) ≈ 1282.6 meters

Therefore, the horizontal distance covered by Viola is approximately 1282.6 meters.

We can use trigonometry to find the height of the plane. Let h be the height of the plane above the atoll, and let d be the horizontal distance from the airplane to the atoll. Then we have:

tan(7°) = h/d

h = d * tan(7°) ≈ 461.7 meters

Therefore, the height of the plane is approximately 461.7 meters.

We can use trigonometry to find the height of the pole. Let h be the height of the pole, and let d be the distance from the surveyor to the base of the pole. Then we have:

tan(44°) = h/(d + 4)

h = (d + 4) * tan(44°)

h = (140 + 4) * tan(44°) ≈ 159.8 feet

Therefore, the height of the pole is approximately 159.8 feet.

In a 30°-60°-90° triangle, the hypotenuse is twice as long as the shorter leg and √3 times as long as the longer leg. Therefore, the shorter leg has length 18/2 = 9, and the longer leg has length 18√3/2 = 9√3.

The perimeter of the triangle is the sum of the lengths of the three sides, which are 9, 9√3, and 18. Therefore, the perimeter is:

9 + 9√3 + 18 = 27 + 9√3 ≈ 44.2

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Answer:

6. closed

7. open

8. open

Step-by-step explanation:

im so sorry if its wrong im not entirely sure

The relative frequency is 8/25.

Relative frequency is a statistical concept that refers to the proportion of times that an event occurs in a given sample or population. It is calculated by dividing the number of times the event occurs by the total number of observations in the sample or population.

Relative frequency is an important concept in probability theory and statistics because it provides a way to estimate the probability of an event occurring based on the observed data. As the sample size increases, the relative frequency becomes a more accurate estimate of the true probability of the event.

Relative frequency is also used in hypothesis testing, where it is used to test whether a particular hypothesis is supported by the data. In this case, the observed relative frequency is compared to the expected relative frequency under the null hypothesis to determine whether the difference between the two is statistically significant.

The total number of spins is 75 and the number of times the spinner landed on 3 is 24.

Therefore, the relative frequency for the event "spin a 3" is:

24/75 = 8/25

So, the relative frequency is 8/25.

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The total number of spins is 75 and the number of times the spinner landed on 3 is 24.

The "spin a 3" occurrence has a relative frequency of [tex]\frac{8}{25}[/tex].

A statistical concept known as "relative frequency" describes the percentage of times an event happens in a given sample or population. It is calculated by dividing the total number of observations in the sample or group by the frequency of the event.

Because it offers a method to calculate the probability of an event occurring based on the observed data, relative frequency is a crucial concept in probability theory and statistics. The relative frequency becomes a more precise indicator of the actual probability of the event as sample size rises.

In order to determine whether a specific hypothesis is backed by the data, relative frequency is also used in hypothesis testing. To determine

whether the difference between the two is statistically significant, the observed relative frequency is in this instance compared to the expected relative frequency under the null hypothesis.

There were 75 total spins, and 3 appeared 24 times during those rotations.

As a consequence, the proportional frequency of "spin a 3" is as follows:

[tex]\frac{24}{75} =\frac{8}{25}[/tex]

So, the relative frequency is [tex]\frac{8}{25}[/tex].

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Concept: "Logos" has had a significant impact on Western thought. Importance: its recognition of the interplay between rational thought and empirical observation Acknowledgement: role of language and discourse in shaping our understanding of the world.

Topic: The concept of "Logos" in Greek philosophy and its significance in modern scientific fields.

The concept of "Logos" is central to Greek philosophy and has been interpreted in various ways throughout history. In its most basic sense, "Logos" refers to rational thought, speech, and language. It is often associated with the divine or the cosmic principle that governs the universe, as well as human reasoning and discourse.

The significance of "Logos" can be seen in its influence on modern scientific fields, including biology, psychology, and technology, among others. The term "biology," for example, comes from the Greek words "bios" (life) and "logos" (word or reason), reflecting the idea that the study of life requires both empirical observation and rational analysis.

Similarly, the field of psychology, which deals with the workings of the human mind and behavior, derives its name from the Greek word "psyche," meaning "soul," and "logos," meaning "reason." This reflects the idea that the study of the mind and behavior requires both empirical research and theoretical analysis.

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Translation: The Greek word "logos" is typically interpreted as the pinnacle of Western rationalist civilization, having been established by the first schools of classical philosophy. In reality, he is responsible for the names of many scientific fields, including biology, philology, psychology, technology, and others. Since it requires both mind and action, internal and external, the mental notion and pronouncing the word, the concept of "logos" does not have such an abstract meaning. Topic:____________________________________________________ Principal Concept:

Hence, Y = 8X represents the equation for the quantity of parts generated by machine R.

Variables, numbers, and mathematical operations like addition, subtraction, multiplication, and division are frequently included. Equations are used in many disciplines, including physics, engineering, economics, and finance, to describe connections between quantities and to solve problems. For instance, the formula "2x + 5 = 11" states that the number 11 is equal to the sum of the two variables x and 5. We can determine that x equals 3 by finding a solution for x. On the basis of mathematical relationships, equations enable us to locate unknown values and create predictions.

given

We must evaluate the supplied data and search for trends to ascertain which machine generates parts at a steady rate. Calculating the ratio of parts produced for each machine over time and checking to see if the ratios are stable are two methods for achieving this.

The ratios for machine Q are:

9/1 = 9

18/3 = 6

72/9 = 8

Machine Q doesn't create parts at a constant rate since the ratios are inconsistent.

The ratios for machine R are:

8/1 = 8

24/3 = 8

72/9 = 8

As a result of the constant ratios, machine R consistently produces parts.

The ratios for machine S are:

6/1 = 6

18/3 = 6

52/9 ≈ 5.78

Machine S does not generate parts at a constant rate because the ratios are inconsistent.

As a result, we may formulate the following equation to represent the components made by machine R:

Y = kX

where k represents the machine R's constant rate of production and Y represents the quantity of components produced in minutes. Any of the ratios calculated above can be used to determine the value of k:

8 pieces per minute equals k.

Hence, Y = 8X represents the equation for the quantity of parts generated by machine R.

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Answer:

The area of the figure is 286 cm^2

Area of upper triangle = (1/2) base X height

= (1/2) 12 X 10

= 60

The middle portion is square so

area = l^2

= 100

the base of bottom triangle = 4 + 10 + 4 = 18

height of bottom triangle = 14

so area = (1/2) base X height

= 126

total area = area of upper triangle + area of square +area of bottom triangle

= 60 + 100 + 126

= 286 cm^2

The term used for discovery sampling is statistical random sampling.

What is statistical random sampling?

A simple random sample is a subset of individuals chosen at random, all with the same probability, from a larger set of individuals. It is a method of choosing a sample at random.

Here,

We have to find another term for discovery sampling.

We concluded that another term that is used for discovery sampling is statistical random sampling.

Hence, the term used for discovery sampling is statistical random sampling.

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The probability that no more than 3 of them weigh 65 lb or more is 0.0165 (approximately).

The Australian Sheep Dog is a breed renowned for its intelligence and work ethic. It is estimated that 45% of adult Australian Sheep Dogs weigh 65 pounds or more. A sample of 16 adult dogs is studied. We need to determine the probability that no more than 3 of them weigh 65 pounds or more. Solution:Step 1The number of trials (n) is 16. The probability of success in one trial is p = 0.45. The probability of failure is q = 1 - p = 1 - 0.45 = 0.55.Step 2We need to find the probability that no more than 3 of them weigh 65 lb or more.P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X distribution with parameters n = 16 and p = 0.45.Using the binomial probability formula,P(X = k) = nCk * pk * q(n - k)P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)= 16C0 * 0.45^0 * 0.55^16 + 16C1 * 0.45^1 * 0.55^15 + 16C2 * 0.45^2 * 0.55^14 + 16C3 * 0.45^3 * 0.55^13≈ 0.0165 (rounded to 4 decimal places)Therefore, the probability that no more than 3 of them weigh 65 lb or more is 0.0165 (approximately).

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Step-by-step explanation:

The three internal angles of a triangle sum to 180 °

x + 23      +      4x+17     +   80    = 180

5x + 120 = 180

5x = 60

x = 12 °

The given series converges only when x = 0

To determine the values of x for which the series n!x⁵ⁿ converges, we can use the ratio test, which states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges, and if the limit is greater than 1, the series diverges.

Applying the ratio test to the series, we obtain |aₙ ₊ ₁ /aₙ| = |(n+1)! x⁵(n+1)/(n! x⁵)| = |(n+1)x⁵|. We simplify this expression to obtain |(n+1)x⁵|.

We then take the limit as n approaches infinity of |(n+1)x⁵|. If x is not equal to zero, this limit will approach infinity, since n+1 grows without bound as n approaches infinity, and x⁵ is a constant factor that does not affect the growth rate. In this case, the limit will be greater than 1, indicating that the series diverges.

However, if x is equal to zero, then the limit of |(n+1)x⁵| is zero, indicating that the series converges.

Therefore, the series n!x⁵n converges only when x is equal to zero.

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Answer & Step-by-step explanation:

We can make y the subject first

y = [tex]\frac{1}{5}[/tex](x + 8) - 7

Substitute values of x into the equation to find their corresponding y value

For example, when x is 0

[tex]\frac{1}{5}[/tex](0 + 6) - 7 = -5.8

When x is 1, y = -5.6

Repeat for other values of x

Here is an example of me plotting the points for x from -2 to 2:

Answer:

see attachment.

Step-by-step explanation:

To find:-

Answer:-

We need to find out the graph of the following line,

[tex]:\sf\implies y + 7 = \dfrac{1}{5}(x+6)\\[/tex]

For graphing this line we need to find at least two coordinates through which the graph passes . We can find out the third point to check if the other coordinates are correct.If all the three points do not come in a straight line , then there is some mistake .

Now solve out for any of the variables , i am solving out for "y" .

For that subtract 7 on both the sides,

[tex]:\sf\implies y =\dfrac{1}{5}(x+6)-7 \\[/tex]

Substitute x = 4 :-

[tex]:\sf\implies y =\dfrac{1}{5}(4+6)-7 \\[/tex]

[tex]:\sf\implies y = \dfrac{10}{5}-7 = 2-7 \\[/tex]

[tex]:\sf\implies \pink{ y =-5} \\[/tex]

Therefore one of the coordinate to mark on the graph is (4,-5) .

Again, substitute x = -6 ,

[tex]:\sf\implies y =\dfrac{1}{5}(-6+6)-7\\[/tex]

[tex]:\sf\implies y = 0 - 7 \\[/tex]

[tex]:\sf\implies \pink{ y = -7} \\[/tex]

Therefore the second coordinate to mark on the graph is (-6,-7) .

After marking these two points join the points by drawing a line. The line will represent the graph of the given equation.

You can see attachment for the graph for the same .

The area of the shape given above which is the addition of area of semi circle and the area of the triangle prism =660.48 ft²

To calculate the area of a triangular prism the formula given below is used:

Area of a triangular prism = ab+ 3bh

where;

a = side = 20ft

b= base = 10 ft

h = height = 12 ft

Area = 20×10 + 3×10×12

= 200 + 360

= 560ft²

The area is semi circle = πr²/2

π = 3.14

R = 16/2 = 8ft

area = 3.14× 8²/2

= 200.96/2

= 100.48 ft²

Area of the shape = 560+100.48 = 660.48 ft²

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The given ratio of 0.42 to 1 means that for every 1 active subscription, there are 0.42 expired subscriptions.

What is a ratio?

The ratio is a comparison of two quantities that is expressed as a fraction. It is used to compare two values in mathematics. It is possible to write the ratio between a and b as:

a : b or a/b.

What does a ratio of 0.42 to 1 mean? The ratio of 0.42 to 1 means that there are 0.42 expired subscriptions for every 1 active subscription. It is worth noting that the ratio is less than 1, indicating that there are fewer expired subscriptions than active subscriptions.

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Answer:

Let the fraction be represented by "a/b".

According to the problem statement, we can create two equations:

Equation 1: (a-1)/(b+2) = 1/2

Equation 2: (a+3)/(b-2) = 1 1/4 = 5/4

We can simplify Equation 1 by cross-multiplying to get:

2(a-1) = b+2

2a - 4 = b + 2

2a = b + 6 --- (Equation A)

Similarly, we can simplify Equation 2 by converting 1 1/4 to an improper fraction:

5/4 = 1 + 1/4 = 4/4 + 1/4 = (4+1)/4 = 5/4

So, Equation 2 becomes:

5(a+3) = 4(b-2)

5a + 15 = 4b - 8

5a = 4b - 23 --- (Equation B)

Now, we have two equations (Equation A and B) with two unknowns (a and b). We can solve for one variable in terms of the other and substitute in either equation to find the value of the other variable. Here, we will solve for 'b' in Equation A:

2a = b + 6

b = 2a - 6

Substitute this value of 'b' in Equation B:

5a = 4b - 23

5a = 4(2a - 6) - 23

5a = 8a - 47

3a = 47

a = 47/3

Substitute this value of 'a' in Equation A to find 'b':

2a = b + 6

2(47/3) = b + 6

94/3 - 6 = b

b = 76/3

Therefore, the fraction is (a/b) = 47/76.

After 2013 "changesums", the list {20, 1, 3} becomes {x, x, x}. The maximum difference between two numbers is 0 since all numbers are equal.

We can start by applying the "changesum" procedure to the list {20, 1, 3} repeatedly, until we have done it 2013 times.

After the first application, we get the list {4, 23, 21}. After the second application, we get {44, 25, 27}. We can continue applying the procedure to get the following list of values:

{44, 25, 27}

{69, 71, 52}

{142, 120, 140}

{262, 282, 262}

{524, 524, 544}

{1048, 1068, 1048}

{2116, 2096, 2116}

{4212, 4232, 4212}

After 2013 consecutive "changesums", the list will have the form {x, x, x} for some value x. The maximum difference between two numbers in the list will be 0 in this case, since all the numbers are equal.

Therefore, the maximum difference between two numbers of the list after 2013 consecutive "changesums" is 0.

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The value of the given integral by converting it into polar coordinates is [a⁴ / 4] (1 - (-1)) = [a⁴ / 2].Hence, the correct option is (d) [a⁴ / 2].

To evaluate the iterated integral by converting to polar coordinates,

we need to change the limits of the integral into polar coordinates.

So the given integral in polar form is ∫(from θ = 0 to θ = π/2) ∫(from r = a to r = 0)[tex]4r^3cos(θ)sin(θ)dr dθ.[/tex]

The polar coordinate conversion is given by x = r cos(θ) and y = r sin(θ).Given integral ∫a0∫0−√a2−y24x2y dx dy can be expressed in the form of polar coordinates as follows:

∫(from θ = 0 to θ = π/2) ∫(from r = a to r = 0) 4r³cos(θ)sin(θ) dr dθ

Where, x = r cos(θ) and y = r sin(θ)

Now, we can evaluate this integral using the polar coordinate conversion.

∫(from θ = 0 to θ = π/2)

∫(from r = a to r = 0) 4r³cos(θ)sin(θ) dr

dθ=∫(from θ = 0 to θ = π/2) [cos(θ)sin(θ) ∫(from r = a to r = 0) 4r³ dr ]

dθ= ∫(from θ = 0 to θ = π/2) [ cos(θ) sin(θ) (r⁴) / 4] (from r = a to r = 0)

dθ=∫(from θ = 0 to θ = π/2) [cos(θ) sin(θ) (a⁴) / 4]

dθ= [a⁴ / 4] ∫(from θ = 0 to θ = π/2) sin(2θ)

dθ= [a⁴ / 4] ([- cos(2θ)] from θ = 0 to θ = π/2)

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Here's a visual representation of the lines connecting each value to 10.56:

In geometry, a line intersect is a point where two or more lines cross or meet. When two lines intersect, they share a single point in common, which is called the point of intersection. This point of intersection is the solution to the system of equations formed by the two lines.

by the question.

sure, I can help you with that!

To join 10.56 to all the equivalent values, you can draw lines connecting each value to 10.56. Here's how:

105 tenths and 6 hundredths:

To convert 105 tenths and 6 hundredths to a decimal, you can add the two values together: 105/10 + 6/100 = 10.56.

Draw a line connecting "105 tenths and 6 hundredths" to "10.56".

10 ones and 56 tenths:

To convert 10 ones and 56 tenths to a decimal, you can add the two values together: 10 + 56/10 = 10.56.

Draw a line connecting "10 ones and 56 tenths" to "10.56".

1 ten and 56 hundredths:

To convert 1 ten and 56 hundredths to a decimal, you can add the two values together: 10 + 56/100 = 10.56.

Draw a line connecting "1 ten and 56 hundredths" to "10.56".

156 hundredths:

To convert 156 hundredths to a decimal, you can divide the value by 100: 156/100 = 1.56.

Add 1 to the whole number part to get 10.56: 1 + 0.56 = 10.56.

Draw a line connecting "156 hundredths" to "10.56".

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The coordinates of the final image for S' are (0, -7). The solution has been obtained by using the concept of transformation.

What is transformation?

Transformations allow for the rotation, reflection, and translation of forms on a coordinate plane. Any line can be reflected, any point can be rotated, and every vector can be translated.

We are given a triangle QRS whose vertices are Q(-6, 6), R(-6, 0),and S(0, 0). The triangle is translated 7 units right, then rotated 90° clockwise about the origin.

So, from this we get the another triangle as Q'R'S' whose vertices become as follows after translation:

Q' = (-6 + 7, 6) = (1, 6)

R' = (-6 + 7, 0) = (1, 0)

S' = (0 + 7, 0) = (7, 0)

Now, we know that the rule for 90° clockwise rotation is that (x, y) becomes (y, -x).

So, we get the coordinates as:

Q' = (6, -1)

R' = (0, -1)

S' = (0, -7)

Hence, the coordinates of the final image for S' are (0, -7).

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Answer:

Step-by-step explanation:

You want to know if the binomial 2x³ -10x can be factored further than 2x(x² -5) and how you can tell.

Usually, when we say "factor p(x)", where p(x) is a polynomial, we mean we want it factored to factors that have integer coefficients. In many cases, the result will be a product of linear and/or quadratic factors. Here, ...

  2x³ -10x = 2x(x² -5) . . . . . is factored to integers

When we want the polynomial "factored completely", or "factored to linear factors" the restriction that coefficients be integers or real numbers is removed. The difference of squares can be factored further, but irrational values are required:

  = 2x(x -√5)(x +√5) . . . . . factored completely to linear factors

You can tell if further factoring is possible by looking at the roots of the non-linear factors in question. If those roots are rational, you can continue factoring. If they are irrational or complex, then the problem statement will tell you whether further factoring is desired.

__

Additional comment

Of course, you need to be familiar with methods of factoring and of determining the possible rational roots of a polynomial. (A good graphing calculator can help.)

The minimum value is 16 , the maximum value is 50, the first quartile is 20, the third quartile is 38 and the median is 24.

The box plot that represents the dataset is the second box plot.

The numbers would first be rearranged in ascending order. The numbers arranged in ascending order is:

16, 18, 22, 23, 25, 32, 43, 50

The five number summary are the median, minimum, first quartile, third quartile and maximum.

Median = (n + 1) / 2 = (8 + 1) / 2 = 4.5th term = (23 + 25) / 2 = 24

Minimum = 16

Maximum = 50

First quartile = (n + 1) / 4 = (8 + 1) / 4 = 2.25 term = 20

Third quartile = 3/4 x (n + 1) = 3/4 x (9/4) = 6.75th term = 38

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Answer: 55 min

Step-by-step explanation:

10:40 + 1 hr = 11:40

11:40 - 5min= 11:35

1hr - 5min= 55min

Answer:

[tex]\large\boxed{\mathtt{x=8}}[/tex]

Step-by-step explanation:

[tex]\textsf{For this problem, we are asked to solve for x.}[/tex]

[tex]\textsf{Note that our equation is in word form, let's change it into numerical form.}[/tex]

[tex]\large \tt { {4 \ plus \ 3 \ eighths \ x \ equals \ seven. } \atop {4+ \frac{3}{8} x = 7. } }[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\textsf{Our goal is to find x. We should isolate x where its alone on the left side.}[/tex]

[tex]\underline{\textsf{How?}}[/tex]

[tex]\textsf{Simply subtract 4 from both sides to isolate x.}[/tex]

[tex]\large\underline{\textsf{Isolating x;}}[/tex]

[tex]\tt 4 - 4 + \frac{3}{8} x = 7 - 4[/tex]

[tex]\underline{\textsf{We should have;}}[/tex]

[tex]\tt \frac{3}{8} x = 3[/tex]

[tex]\textsf{We don't know the value of x yet. We only know 3/8 of x.}[/tex]

[tex]\textsf{For x to equal 1, multiply both sides of the equation by the \underline{reciprocal} of the fraction.}[/tex]

[tex]\large\underline{\textsf{What is a Reciprocal?}}[/tex]

[tex]\textsf{A Reciprocal is a \underline{fraction} where the Numerator and the Denominator \underline{flip}.}[/tex]

[tex]\underline{\textsf{For example;}}[/tex]

[tex]\large \tt {Flip \ the \ Numerator \ and \ the \ Denominator.} \atop {The \ Reciprocal \ of \ \frac{5}{4} \ is \ \frac{4}{5}.}[/tex]

[tex]\large\underline{\textsf{Find the Reciprocal of} \ \frac{3}{8};}[/tex]

[tex]\tt{ The \ Reciprocal \ of \ \frac{3}{8} \ is \ \frac{8}{3}.}[/tex]

[tex]\underline{\textsf{Multiply;}}[/tex]

[tex]\tt \frac{8}{3} \times \frac{3}{8} x = 3 \times \frac{8}{3}[/tex]

[tex]\large\boxed{\mathtt{x=8}}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question reads:}[/tex]

[tex]\large\textsf{Four plus three eighths x equals seven}[/tex]

[tex]\huge\textbf{Equation should look like:}[/tex]

[tex]\mathtt{4 + \dfrac{3}{8}x = 7}[/tex]

[tex]\huge\textbf{How will we solve for it?}[/tex]

[tex]\mathtt{4 + \dfrac{3}{8}x = 7}[/tex]

[tex]\mathtt{\dfrac{3}{8}x + 4= 7}[/tex]

[tex]\large\text{SUBTRACT 4 to BOTH SIDES:}[/tex]

[tex]\mathtt{\dfrac{3}{8}x + 4 - 4 = 7 - 4}[/tex]

[tex]\large\text{CANCEL out: 4 } \rm{-}\large\text{ 4 because it gives you 0.}[/tex]

[tex]\large\text{KEEP: 7 }\rm{-}\large\text{ 4 because it help us solve for the x}-\large\text{value.}[/tex]

[tex]\mathtt{\dfrac{3}{8}x = 7 - 4}[/tex]

[tex]\mathtt{\dfrac{3}{8}x = 3}[/tex]

[tex]\large\text{MULTIPLY }\rm{\dfrac{8}{3}\large\text{ to BOTH SIDES:}[/tex]

[tex]\mathtt{\dfrac{3}{8}x\times\dfrac{8}{3} = 3\times\dfrac{8}{3}}[/tex]

[tex]\large\text{CANCEL out: }\rm{\dfrac{3}{8}\times\dfrac{8}{3}\large\text{ because it gives you 1.}[/tex]

[tex]\large\text{KEEP: }\rm{3\times\dfrac{8}{3}\large\text{ because it gives the x}\rm{-}\large\text{value.}[/tex]

[tex]\mathtt{x= 3\times\dfrac{8}{3}}[/tex]

[tex]\mathtt{x= \dfrac{3}{1}\times\dfrac{8}{3}}[/tex]

[tex]\mathtt{x = \dfrac{3\times8}{1\times3}}[/tex]

[tex]\mathtt{x = \dfrac{24}{3}}[/tex]

[tex]\mathtt{x = 24\div3}[/tex]

[tex]\mathtt{x = 8}[/tex]

[tex]\huge\textbf{What is the overall answer?}[/tex]

[tex]\huge\boxed{\mathtt{x = 8}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The planet will travel a distance of 17.088 x 106 miles in 8 days.

Distance is a numerical measurement of how far apart two or more objects, people, or locations are from one another. It is a fundamental concept in geometry, physics, and mathematics. Distance can be measured in a variety of ways, such as kilometers, miles, feet, inches, and light years. Distance can also refer to the physical separation between two points, such as the length of a line or the circumference of a circle. Distance can also refer to the emotional or psychological divide between two people. Distance can be both positive and negative, as it can bring people together or drive them apart.

To calculate how far the planet will travel in 8 days, we must first calculate the distance the planet will travel in one day. To do this, we must multiply the speed of the planet (8.9 x 104 mph) by 24 hours, which represents one day:

Distance in 1 day = 8.9 x 104 mph x 24 hours
Distance in 1 day = 2.136 x 106 miles

Now that we know the distance in one day, we can calculate the distance the planet will travel in 8 days. To do this, we must multiply the distance in one day (2.136 x 106 miles) by 8 days:

Distance in 8 days = 2.136 x 106 miles x 8 days
Distance in 8 days = 17.088 x 106 miles

Therefore, the planet will travel a distance of 17.088 x 106 miles in 8 days.

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Yes we can say that Liam's interpretation of the algebraic expression is correct because it has two variables, coefficients of 6 and 3, and two terms.

In Mathematics, an algebraic expression is defined as an expression that is normally made up of variables, constants, coefficients, and then arithmetic operations. These mentioned items are the different parts that make up the algebraic expression.

Let us consider an expression, 3x + 5y - 8

Here, the parts of the expression are:

Coefficients are 3 and 5

Constant is 8

Variables are x and y

Terms are 3x, 5y

Mathematical operators used are plus (+) and minus (-).

We are given the algebraic equation 6x + (-4) = 3y

Thus, it has:

Two coefficients which are 6 and 3

Two variables which are x and y

Two terms which are 6x and 3y

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A rectangular pyramid has a rectangular base and four triangular faces that meet at a common vertex.

To match each net with its name, we need to understand the basic properties of both rectangular prism and rectangular pyramid.

A rectangular prism is a 3D shape that has six faces, and each face is a rectangle. A rectangular pyramid is also a 3D shape, but it has a rectangular base and four triangular faces that meet at a single point.
It consists of six rectangles connected along their edges to form a box-like structure.

On the other hand, the net for a rectangular pyramid is also a flat pattern, but it consists of a rectangle and four triangles attached to the edges of the rectangle.
To match each net with its name, we need to compare the features of both nets with the basic properties of both shapes. If we observe the net for a rectangular prism, we can see that it has six rectangles, which represents the six faces of the rectangular prism.

Also,

The edges of each rectangle connect with other rectangles in such a way that it forms a box-like structure. Hence, the net with six rectangles is the net for the rectangular prism.
The net for a rectangular pyramid consists of a rectangular base and four triangles attached to the edges of the rectangle.

The rectangular base is one of the features of a rectangular pyramid, and it matches with the rectangle in the net. The other four triangles are attached to the edges of the rectangle, forming a pyramid-like structure.

Therefore,

The net with a rectangle and four triangles is the net for the rectangular pyramid.
The net with six rectangles is the net for the rectangular prism, and the net with a rectangle and four triangles is the net for the rectangular pyramid.

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The volume of the sphere is 1372 cubic cm for the given radius.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere. Many forms have various volumes. We have examined the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry. We will discover how to find the volume for each of these forms.

The volume of the sphere is given by the formula:

V = 4/3πr³

Substituting the value of π = 3 and r = 7 we have:

V = 4/3(3)(7)³

V = 1372 cubic cm.

Hence, the volume of the sphere is 1372 cubic cm for the given radius.

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