Synthetic Division to Find Zeros

if f(x)=x^3−3x^2+16x+20 and x+1 is a factor of f(x), then find all of the zeros of f(x) algebraically.

Answers

Answer 1

Answer:

Step-by-step explanation:

Since we know that x + 1 is a factor of f(x), we can use synthetic division to find the other factor and then solve for the remaining zeros.

We set up synthetic division as follows:

-1 | 1 -3 16 20

| -1 4 -20

|_____________

1 -4 20 0

The last row of the synthetic division gives us the coefficients of the quadratic factor, which is x^2 - 4x + 20. We can use the quadratic formula to find its roots:

x = (-(-4) ± sqrt((-4)^2 - 4(1)(20))) / (2(1))

= (4 ± sqrt(-64)) / 2

= 2 ± 2i√2

Therefore, the three zeros of f(x) are -1, 2 + 2i√2, and 2 - 2i√2.


Related Questions

- The table shows the number of
miles Michael ran each day over
the past four days. How many
more miles did he run on day 3
than on day 2? Determine if there
is extra or missing information.

Answers

By conducting subtraction we know that Michael ran 5 miles more on day 3 than on day 2.

What is subtraction?

The four arithmetic operations are addition, multiplication, division, and subtraction.

Removal of items from a collection is represented by the operation of subtraction.

For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches.

The number that the other number is deducted from is known as a minuend.

Subtrahend: The amount that needs to be deducted from the minuend is known as a subtrahend.

Difference: A difference is an outcome obtained by deducting a subtractor from a minimum.

So, more miles Michael ran on day 3 than on day 2:

= 7 - 2

= 5 miles

Therefore, by conducting subtraction we know that Michael ran 5 miles more on day 3 than on day 2.

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select a random integer from -200 to 200. which of the following pairs of events re mutualyle exclusive

Answers

The pairs of events of random integers are pairs of events are,

even and odd , negative and positive integers, zero and non-zero integers.

Two events are mutually exclusive if they cannot occur at the same time.

Selecting a random integer from -200 to 200,

Any two events that involve selecting a specific integer are mutually exclusive.

For example,

The events selecting the integer -100

And selecting the integer 50 are mutually exclusive

As they cannot both occur at the same time.

Any pair of events that involve selecting a specific integer are mutually exclusive.

Here are a few examples,

Selecting an even integer and selecting an odd integer.

Selecting a negative integer and selecting a positive integer

Selecting the integer 0 and selecting an integer that is not 0.

But,

Events such as selecting an even integer and selecting an integer between -100 and 100 are not mutually exclusive.

As there are even integers between -100 and 100.

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Find the Z score that has 48.4% of the distributions area to its left.

Answers

Answer:

To find the Z-score that has 48.4% of the distribution's area to its left, we can use a standard normal distribution table or a calculator.

Using a standard normal distribution table, we can look for the closest probability value to 0.484. In the table, we find that the closest probability value is 0.4838, which corresponds to a Z-score of approximately 1.96.

Alternatively, we can use a calculator with a built-in normal distribution function. Using the inverse normal distribution function, also known as the quantile function, we can find the Z-score that corresponds to a given probability. For a probability of 0.484, we get:

To find the Z-score that has 48.4% of the distribution's area to its left, we can use a standard normal distribution table or a calculator.

Using a standard normal distribution table, we can look for the closest probability value to 0.484. In the table, we find that the closest probability value is 0.4838, which corresponds to a Z-score of approximately 1.96.

Alternatively, we can use a calculator with a built-in normal distribution function. Using the inverse normal distribution function, also known as the quantile function, we can find the Z-score that corresponds to a given probability. For a probability of 0.484, we get:

To find the Z-score that has 48.4% of the distribution's area to its left, we can use a standard normal distribution table or a calculator.

Using a standard normal distribution table, we can look for the closest probability value to 0.484. In the table, we find that the closest probability value is 0.4838, which corresponds to a Z-score of approximately 1.96.

Alternatively, we can use a calculator with a built-in normal distribution function. Using the inverse normal distribution function, also known as the quantile function, we can find the Z-score that corresponds to a given probability. For a probability of 0.484, we get:

invNorm(0.484)= 1.96

Therefore, the Z-score that has 48.4% of the distribution's area to its left is approximately 1.96.

A line passes through points (5,3) and (-5,-2). Another line passes through points (-6,4) and (2,-4). Find the coordinates (ordered pairs) of the intersection of the two lines.

Step 1: Find the slope of each line
Step 2: Find the y-intercept of each line
Step 3: Write each line in slope-intercept form (y = mx + b)

Step 4: Solve for the system. Find the point of intersection for the system

Please help I will mark brainliest!!!

Answers

The point of intersection of the two lines is (-3.4, -1.2).

How to find the slope of each line?

Step 1: The slope of a line passing through two points (x1,y1) and (x2,y2) can be found using the formula:

m = (y2-y1)/(x2-x1)

Using this formula, we can find the slope of the first line:

m1 = (−2−3)/(-5 -5) = −5/(-10) = 1/2

And the slope of the second line:

m2 = (−4−4)/(2 -(-6)) = -8/4 = -2

Step 2: Find the y-intercept of each line

The y-intercept of a line in slope-intercept form (y = mx + b) is the value of y when x=0. We can use one of the two given points on each line to find the y-intercept:

For the first line passing through points (5,3) and (−5,−2):

y = mx + b

3 = (1/2)(5) + b

b = 3 - 5/2

b = 1/2

So the first line can be written as y = 1/2x + 1/2

For the second line passing through points (−6,4) and (2,−4):

y = mx + b

4 = (-2)(−6) + b

b = 4 - 12

b = -8

So the second line can be written as y = -2x - 8

Step 3: Each line in slope-intercept form (y = mx + b):

First line: y = 1/2x + 1/2

Second line: y = -2x - 8

Step 4: To find the point of intersection of the two lines, we need to solve the system of equations. We can solve for x by setting the two right-hand sides equal to each other:

1/2x + 1/2 = -2x - 8

(x + 1)/2 = -2x - 8

x + 1 = -4x - 16

5x = -16 - 1

5x = -17

x = -17/5

x = -3.4

Now that we know x, we can find y by substituting x=10 into one of the two equations:

y = -2x - 8

y = -2(-3.4) - 8

y = - 1.2

Thus, the point of intersection of the two lines is (-3.4, -1.2).

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Mr. Brown's Thrift Shop
Quarter of 2012 Profit (in dollars)
1 $9,841.28
2 $8,957.67
3 $7,429.84
4 $11,095.67




How much total profit did Mr. Brown's store earn in the third and fourth quarters?

A.
$17,298.45
B.
$17,548.65
C.
$18,124.78
D.
$18,525.51

Answers

The correct option is D. $18,525.51. is the total profit made in the third as well as fourth quarters by Mr. Brown's store.

Explain about addition?

In math, addition is the process of adding two or more integers together. The numbers having added are known as addends, while the outcome of the addition process, or the final response, is known as the sum. It is among the most fundamental mathematical operations we employ on a daily basis.

Quarterly profit for Mr. Brown's Goodwill Store in 2012 (in dollars)

1 $9,841.28

2 $8,957.67

3 $7,429.84

4 $11,095.67

Total profit = profit of 3rd quarter + profit of 4th quarter

Total profit = $7,429.84 + $11,095.67

Total profit =  $18,525.51.

Thus, $18,525.51. is the total profit made in the third as well as fourth quarters by Mr. Brown's store.

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What is the code to this I need help asap.

Answers

Based on the information in the image, the values of the symbols in order would be: 5, 9.86, 9.93, 7.91. 10.56.

How to find the equivalent value of each symbol?

To find the equivalent value of each symbol we must apply the Pythagorean theorem and find the value of the hopotenuse of all triangles as shown below:

Triangle 1:

4² + 3² = c²16 + 9 = c²c = 5

Triangle 2:

5² + 8.5² = c²25 + 72.25 = c²c = 9.86

Triangle 3:

9.86² + b² = 14²b² = 14² - 9.86²b² = 98.78b = 9.93

Triangle 4:

a² + 6² = 9.93²a² = 9.93² - 6²a² = 62.60a = 7.91

Triangle 5:

7.91² + 7² = c²62.56 + 49 = c²111.56 = c²10.56 = c

According to the above, the values of the symbols in order would be:

5, 9.86, 9.93, 7.91. 10.56.

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What is the meaning of "Euclidean geometry"?

Answers

The concept of Euclidean geometry is the study of geometrical shapes (plane and solid) and figures based on different theorems and axioms.

What is the concept of Euclidean geometry?

The concept of Euclidean geometry as required to be discussed is basically introduced for flat surfaces or plane surfaces. The postulates of the Euclidean geometry are as follows!

1 : A straight line may be drawn from any one point to any other point.

2 :A terminated line can be produced indefinitely.

3 : A circle can be drawn with any centre and any radius.

4 : All right angles are equal to one another (Congruent).

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Tara bought 12 yards of fabric to make tote bags. Each bag requires 1.25 yards of fabric. Write an equation that shows how the number of yards or fabric remaining, depends on the number of tote bags Tara sews, x.

Answers

Answer: y = 12 - 1.25x

Step-by-step explanation:

Let y be the number of yards of fabric remaining after Tara sews x tote bags.

Initially, Tara has 12 yards of fabric. For every tote bag she sews, she uses 1.25 yards of fabric. Therefore, the total amount of fabric used after sewing x tote bags is 1.25x yards.

The number of yards of fabric remaining is the difference between the initial amount of fabric and the total amount of fabric used:

y = 12 - 1.25x

This equation shows how the number of yards of fabric remaining depends on the number of tote bags Tara sews, x. As she sews more tote bags, the amount of fabric remaining decreases.

Answer:

5.75 yds left

1.25 yards each bag multiplied by 5 bags is 6.25 yards utilized

Tara's yardage was 12-6.25 = 5.75.

She has 5.75 yards to go.

Step-by-step explanation:

brainliest pls

Question 11 (1 point)

(06.03 LC)


What is the product of the expression, 5x(x2)?


a

25x2


b

10x


c

5x3


d

5x2

Answers

The expressiοn 5x(x²) is equal tο 5 * x¹ * x² (5 * x³ = 5x³). Thus, οptiοn (c) 5x3 is the cοrrect respοnse.

Hοw are prοducts οf expressiοn determined?

The cοefficients (the numbers in frοnt οf the variables) οf the expressiοn 5x(x²) can be multiplied, and the expοnents οf the variables can be added, tο determine the prοduct.

The first cοefficient we have is 5 times 1, giving us 5. Sο, using the secοnd x², we have x tο the pοwer οf 2 multiplied by x tο the pοwer οf 1 (frοm the first x). Expοnents are added when variables with the same base are multiplied. Sο, x¹ multiplied by x² results in x³.

Cοmbining all οf the parts, the phrase becοmes:

5x(x²) is equal tο 5 * x¹ * x² (5 * x³ = 5x³).

Thus, οptiοn (c) 5x³ is the cοrrect respοnse.

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se spherical coordinates to evaluate the triple integral where is the region bounded by the spheres and .

Answers

The value of the triple integral[tex]\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}[/tex] by using spherical coordinates [tex]2\pi(e^{-1}-e^{-9})[/tex].

Given that the triple integral is-

[tex]\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}[/tex]

E is the region bounded by the spheres which are,

[tex]x^2+y^2+z^2=1\\\\x^2+y^2+z^2=9[/tex]

In spherical coordinates we have,

x = r cosθ sin ∅

y = r sinθ sin∅

z = r cos∅

dV = r²sin∅ dr dθ d∅

E contains two spheres of radius 1 and 3 () respectively, the bounds will be like this,

1 ≤ r ≤ 3

0 ≤ θ ≤ 2π

0 ≤ ∅ ≤ π

Then

[tex]\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}[/tex]

[tex]\int\int\int _{E} \frac{e^{-r^2}}{r}r^2Sin\phi drd\phi d\theta\\\\2\pi \int_{0}^{\pi} \int_1^3 re^{-r^2} dr d\phi\\\\2\pi \int_1^3 re^{-r^2} dr\\\\2\pi(e^{-1}-e^{-9})[/tex]

The complete question is-

Use spherical coordinates to evaluate the triple integral ∭ee−(x2 y2 z2)x2 y2 z2−−−−−−−−−−√dv, where e is the region bounded by the spheres x2 y2 z2=1 and x2 y2 z2=9.

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What was your recommended intake of carbohydrates (grams), and how far were you from it? Show the mathActual Intake Recommended Intake Percentage159.00 115-166 100%

Answers

The actual intake of carbohydrates is 138% as compare to recommended intake.

Recommended intake of carbohydrates or any other nutrient are,

Based on the information provided,

Consumed 159 grams of carbohydrates,

Recommended intake is between 115 and 166 grams.

Calculate the percentage of actual intake compared to the recommended intake, use the following formula,

Percentage = (Actual Intake / Recommended Intake) x 100%

Substituting the values in the formula we have,

⇒Percentage = (159 / 115) x 100%

⇒Percentage ≈ 138.3%

Therefore,  the actual intake of carbohydrates is about 138% of the recommended intake, indicating that consumption of more carbohydrates than recommended.

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Consider g(x) = {a sin x + b, if x 2pi .
A. Find the values of a and b such that g(x) is a differentiable function.
B. Write the equation of the tangent line to g(x) at x = 2pi.
C. Use the tangent line equation from part B to write an approximation for the value of g(6).
Do not simplify

Answers

Answer:

A. For g(x) to be differentiable, the derivative of g(x) must exist at every point in its domain. The derivative of a sin x + b is a cos x, which exists for all values of x. Therefore, any values of a and b will make g(x) a differentiable function.

B. To find the equation of the tangent line to g(x) at x = 2π, we need to find the slope of the tangent line, which is the derivative of g(x) evaluated at x = 2π.

g'(x) = a cos x, so g'(2π) = a cos(2π) = a

Therefore, the slope of the tangent line at x = 2π is a. To find the y-intercept of the tangent line, we can plug in x = 2π into g(x) and subtract a times 2π:

y = g(2π) - a(2π)

= (a sin 2π + b) - a(2π)

= b - 2aπ

So the equation of the tangent line is:

y = ax + (b - 2aπ)

C. We can use the tangent line equation to approximate g(6) by plugging in x = 6 and using the equation of the tangent line at x = 2π.

First, we need to find the value of a. Since g'(2π) = a, we can use the derivative of g(x) to find a:

g'(x) = a cos x

g'(2π) = a cos (2π) = a

g'(x) = a = 2

Now, we can plug in a = 2, b = any value, and x = 2π into the tangent line equation:

y = ax + (b - 2aπ)

g(2π) = 2πa + (b - 2aπ)

a sin 6 + b ≈ 12π + (b - 4π)

Since we don't know the value of b, we can't find the exact value of g(6), but we can use the approximation:

g(6) ≈ 12π + (b - 4π)

Jenny took the car, the bus, and the train to get home in time.
What form of punctuation is missing?
O A. No punctuation is missing.
OB.
A period
OC.
A comma
OD. A semicolon

Last three times I have tried to take a picture of my question. Nothing comes up that resembles any of it. I don’t know what’s wrong with this app but it’s not helping.

Answers

According to the question. A. No punctuation is missing.

What is punctuation ?

Punctuation is the use of symbols to indicate the structure and organization of written language. It is used to help make the meaning of sentences clearer and to make them easier to read and understand. Punctuation marks can also be used to indicate pauses in speech, to create emphasis, and to indicate the speaker’s attitude. There are many different types of punctuation marks, each with its own purpose. The most commonly used punctuation marks are the period, comma, question mark, exclamation mark, quotation marks, and the apostrophe.

Quotation marks are used to enclose quoted material, while the apostrophe is used to indicate possession or to replace missing letters in a word or phrase. By using punctuation correctly, writers can ensure that their messages are correctly understood by their readers.

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Help i need this question solved

Answers

Answer: D. Square

Step-by-step explanation:

The shape created by the cross section of the cut through a square pyramid is a square.

To see why, imagine the pyramid sitting on a table with its square base flat against the surface. The cut goes through the vertex, which is the point at the top of the pyramid. Since the cut is perpendicular to the base, it divides the pyramid into two smaller pyramids with congruent, but not identical, bases. Each of these smaller pyramids has a triangular base that is an isosceles right triangle. The two triangles share a common hypotenuse, which is the line of the cut.

The cross section of the cut is the shape formed where the two triangles meet along the hypotenuse. Since both triangles are congruent and the hypotenuse is the same for both, the cross section is a square. The sides of the square are equal to the base of the original pyramid, which is one of the legs of the isosceles right triangles formed by the cut. Therefore, the answer is D, a square.

it’s D square !!!!!!

it looks as if the graphofr ~ tan 0, -'1r/2 < 0 < '1r/2, could be asymptotic to the lines x ~ i and x ~ -i. is it? give reasons for your answer.

Answers

No, the graph of tan 0, -1r/2 < 0 < 1r/2, is not asymptotic to the lines x = i and x = -i.

An asymptote is a line that a graph approaches but never crosses. The graph of tan 0, -1r/2 < 0 < 1r/2, has a period of π, meaning it repeats after every π, and will never cross the lines x = i and x = -i. This can be seen in the equation y = tan 0, where the x-values of -1r/2 and 1r/2 are replaced with the x-values of i and -i. The equation would be y = tan(i) and y = tan(-i), and the graphs of these equations would not be asymptotic to the lines x = i and x = -i.No, the graph of tan 0, -1r/2 < 0 < 1r/2, is not asymptotic to the lines x = i and x = -i.

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The dot plots below show the number of students in attendance each day in Mr. Wilson's class and Mr. Watson's class in April. What is the difference of the medians as a multiple of the interquartile range? A. B. C. D.

Answers

The difference of the medians as a multiple of the interquartile range is 0.5,So the correct answer is option (A) 0.5.

What is median?

The median is a measure of central tendency that represents the middle value in a data set when the values are arranged in numerical order.

For example, consider the data set {3, 5, 2, 6, 1, 4}. When the values are ordered from smallest to largest, we get {1, 2, 3, 4, 5, 6}. The median in this case is the middle value, which is 3.

We can first find the medians and interquartile ranges of the two dot plots.

For Mr. Wilson's class:

Median = 12

Q1 = 10

Q3 = 14

IQR = Q3 - Q1 = 14 - 10 = 4

For Mr. Watson's class:

Median = 10

Q1 = 8

Q3 = 12

IQR = Q3 - Q1 = 12 - 8 = 4

The difference of the medians is |12 - 10| = 2. Therefore, the difference of the medians as a multiple of the interquartile range is:

$$\frac{2}{4} = \boxed{0.5}$$

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Mr. Nkalle invested an amount of N$20,900 divided in two different schemes A and B at the simple interest
rate of 9% p.a. and 8% p.a, respectively. If the total amount of simple interest earned in 2 years is N$3508,
what was the amount invested in Scheme B?

Answers

Answer:

Let's assume that Mr. Nkalle invested an amount of x in Scheme A and (20900 - x) in Scheme B.

The simple interest earned on Scheme A in 2 years would be:

SI(A) = (x * 9 * 2)/100 = 0.18x

The simple interest earned on Scheme B in 2 years would be:

SI(B) = [(20900 - x) * 8 * 2]/100 = (3344 - 0.16x)

The total simple interest earned in 2 years is given as N$3508:

SI(A) + SI(B) = 0.18x + (3344 - 0.16x) = 3508

0.02x = 164

x = 8200

Therefore, Mr. Nkalle invested N$8200 in Scheme A and N$12700 (20900 - 8200) in Scheme B. So the amount invested in Scheme B was N$12700.

Find the closed formula for each of the following sequences by relating them to a well known sequence. Assume the first term given is a1.
(a) 2, 5, 10, 17, 26, . . .
(b) 0, 2, 5, 9, 14, 20, . . .
(c) 8, 12, 17, 23, 30, . . .
(d) 1, 5, 23, 119, 719, . . .

Answers

The final closed formula answers for each part,

(a) an = n^2 + 1

(b) an = n(n + 1)(n + 2)/6

(c) an = 2n + 6

(d) an = n! + (n-1)! + ... + 2! + 1!

(a) The given sequence can be seen as the sequence of partial sums of the sequence of odd numbers: 1, 3, 5, 7, 9, . . . . That is, the nth term of the given sequence is the sum of the first n odd numbers, which is n^2. Therefore, the closed formula for the given sequence is an = n^2 + 1.

(b) The given sequence can be seen as the sequence of partial sums of the sequence of triangular numbers: 1, 3, 6, 10, 15, . . . . That is, the nth term of the given sequence is the sum of the first n triangular numbers, which is n(n + 1)(n + 2)/6. Therefore, the closed formula for the given sequence is an = n(n + 1)(n + 2)/6.

(c) The given sequence can be seen as the sequence of differences between consecutive squares: 1, 5, 9, 16, 21, . . . . That is, the nth term of the given sequence is the difference between the (n+1)th square and the nth square, which is (n + 1)^2 - n^2 = 2n + 1. Therefore, the closed formula for the given sequence is an = 2n + 6.

(d) The given sequence can be seen as the sequence of partial sums of the sequence defined recursively by a1 = 1 and an+1 = an(n + 1) for n ≥ 1. That is, the nth term of the given sequence is the sum of the first n terms of the recursive sequence. It can be shown that the nth term of the recursive sequence is n! (n factorial), and therefore the nth term of the given sequence is the sum of the first n factorials. That is, an = 1 + 1! + 2! + ... + (n-1)! + n!. Therefore, the closed formula for the given sequence is an = n! + (n-1)! + ... + 2! + 1!.

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Samir bought three pounds of strawberries for $12.00. What is the price, in dollars
per ounce of strawberries?
1 pound = 16 ounces
Before you try that problem, answer the question below.
How many ounces of strawberries did Samir buy?

Answers

Samir bought 48 ounces of strawberries (3 pounds x 16 ounces per pound = 48 ounces).
To find the price per ounce, we can divide the total cost by the number of ounces:
$12.00 ÷ 48 ounces = $0.25 per ounce.
Therefore, Samir paid $0.25 for each ounce of strawberries he bought.

Write a sine function that has a midline of, y=5, an amplitude of 4 and a period of 2.

Answers

Answer:

y = 4 sin(π x) + 5

Step-by-step explanation:

A sine function with a midline of y=5, an amplitude of 4, and a period of 2 can be written in the following form:

y = A sin(2π/ x) +

where A is the amplitude, is the period, is the vertical shift (midline), and x is the independent variable (usually time).

Substituting the given values, we get:

y = 4 sin(2π/2 x) + 5

Simplifying this expression, we get:

y = 4 sin(π x) + 5

Therefore, the sine function with the desired characteristics is:

y = 4 sin(π x) + 5

are the ratios 2:1 and 20:10 equivalent

Answers

Yes, there is an analogous ratio between 2:1 and 20:10.

What ratio is similar to 2 to 1?

We just cancel by a common factor. So 4:2=2:1 . The simplest representation of the ratio 4 to 2 is the ratio 2 to 1. Also, since each pair of numbers has the same relationship to one another, the ratios are equivalent.

By dividing the terms of each ratio by their greatest common factor, we may simplify both ratios to explain why.

As the greatest common factor for the ratio 2:1 is 1, additional simplification is not necessary.

The greatest common factor for the ratio 20:10 is 10. When we multiply both terms by 10, we get:

20 ÷ 10 : 10 ÷ 10

= 2 : 1

As a result, both ratios have the same reduced form, 2:1, making them equal.

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For the functions f(x)=−7x+3 and g(x)=3x2−4x−1, find (f⋅g)(x) and (f⋅g)(1).

Answers

Answer:

Find f(g(x)) f(x)=7x-8 , g(x)=3x-2. f(x)=7x−8 f ( x ) = 7 x - 8 , g(x)=3x−2 g ( x ) = 3 x - 2. Step 1. Set up the composite result function. f(g(x)) f ( g ...

please mark me as a brainalist

.2 In the diagram below, given that XY = 3cm, XZY = 30° and YZ = x, is it possible to solve for x using the theorem of Pythagoras? Motivate your answer. Show Calculations ​

Answers

Sin 30 =3/x

1/2=3/x

x=6

the zeros of f(x)=20x^2 - 19x + 3

Answers

The quadratic function's zeros are therefore  [tex]x = 1[/tex] and [tex]x = 0.2[/tex] . A degree two polynomial in one or so more variables that is a quadratic function.

What ways in which quadratic function be recognized?

Three points are used to determine a quadratic function, which has the form [tex]f(x) = ax2 Plus bx + c.[/tex]

[tex]Sqrt(b2 - 4ac) = [-b sqrt(b)][/tex] Where the quadratic function's coefficients are a, b, and c.

Here,  [tex]a = 20[/tex] , [tex]b = -19[/tex] , & [tex]c = 3[/tex]  . We obtain the quadratic formula by substituting these values: [tex]x = [-(-19) sqrt((-19)2 - 4(20)(3)] / 2(20) (20)[/tex]

When we condense this phrase, we get:

[tex]x = [19 +/- sqrt(361 - 240)] / 40 x = [19 +/- sqrt(121)] / 40\sx = [19 ± 11] / 40[/tex]

Therefore, The zeros of a quadratic equation   [tex]f(x) = 20x2 - 19x + 3[/tex] are as follows: [tex]x = (19 Plus 11) / 40 = 1 and x = (19 − 11) / 40 = 0.2.[/tex]

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A, B, and C are mutually exclusive.
P(A) = .2, P(B) = .2, P(C) = .3. Find P(A ∪ B ∪ C).
P(A ∪ B ∪ C) =

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The probability of the union of events A, B, and C is 0.7 where P(A)=0.2, P(B)=0.2 and P(C)=0.3.

What is union?

In set theory, the union of two or more sets is a set that contains all the distinct elements of the sets being considered. Formally, the union of sets A and B, denoted as A ∪ B, is the set of all elements that are in either set A or set B, or in both.

According to question:

When A, B, and C are mutually exclusive events, it means that they cannot happen at the same time. Therefore, the probability of the union of these events is equal to the sum of their individual probabilities.

In this case, we are given that:

P(A) = 0.2

P(B) = 0.2

P(C) = 0.3

To find the probability of the union of these events, we need to add their probabilities:

P(A ∪ B ∪ C) = P(A) + P(B) + P(C)

Substituting the given probabilities, we get:

P(A ∪ B ∪ C) = 0.2 + 0.2 + 0.3

P(A ∪ B ∪ C) = 0.7

Therefore, the probability of the union of events A, B, and C is 0.7.

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The question is A, B, and C are mutually exclusive. P(A) = 0.2, P(B) = 0.2, P(C) = 0.3. Find P(A ∪ B ∪ C).

P(A ∪ B ∪ C) = ?

Find the volume of the solid generated by revolving the region enclosed by the following curves: a. y=4-2x², y = 0, x = 0, y = 2 through 360° about the y-axis. b. x = √y+9, x = 0, y =1 through 360° about the y-axis.​

Answers

The volume of the solid generated by revolving the region enclosed by the curves y = 4 - 2x², y = 0, x = 0, and y = 2 through 360° about the y-axis is (16/3)π cubic units.

How to find the volume?

To find the volume of the solid generated by revolving the region enclosed by the curves y = 4 - 2x², y = 0, x = 0, and y = 2 through 360° about the y-axis, we use the formula:

V = ∫[a,b] πr²dy

where a and b are the limits of integration in the y-direction, r is the radius of the circular cross-sections perpendicular to the y-axis, and V is the volume of the solid.

First, we need to find the equation of the curve that is generated when we rotate y = 4 - 2x² around the y-axis. To do this, we use the formula for the equation of a curve generated by revolving y = f(x) around the y-axis, which is:

x² + y² = r²

where r is the distance from the y-axis to the curve at any point (x, y).

Substituting y = 4 - 2x² into this formula, we get:

x² + (4 - 2x²) = r²

Simplifying, we get:

r² = 4 - x²

Therefore, the radius of the circular cross-sections perpendicular to the y-axis is given by:

r = √(4 - x²)

Now, we can integrate πr²dy from y = 0 to y = 2:

V = ∫[0,2] π(√(4 - x²))²dy

V = ∫[0,2] π(4 - x²)dy

V = π∫[0,2] (4y - y²)dy

V = π(2y² - (1/3)y³)∣[0,2]

V = π(8 - (8/3))

V = (16/3)π

Therefore, the volume of the solid generated by revolving the region enclosed by the curves y = 4 - 2x², y = 0, x = 0, and y = 2 through 360° about the y-axis is (16/3)π cubic units.

b. To find the volume of the solid generated by revolving the region enclosed by the curves x = √y+9, x = 0, and y = 1 through 360° about the y-axis, we use the same formula as in part (a):

V = ∫[a,b] πr²dy

where a and b are the limits of integration in the y-direction, r is the radius of the circular cross-sections perpendicular to the y-axis, and V is the volume of the solid.

First, we need to solve the equation x = √y+9 for y in terms of x:

x = √y+9

x² = y + 9

y = x² - 9

Next, we need to find the equation of the curve that is generated when we rotate y = x² - 9 around the y-axis. Using the same formula as in part (a), we get:

r = x

Now, we can integrate πr²dy from y = 1 to y = 10 (since x = 0 when y = 1 and x = 3 when y = 10):

V = ∫[1,10] π(x²)²dy

V = π∫[1,10] x⁴dy

V = π(1/5)x⁵∣[0,3]

V = π(243/5)

Therefore, the volume of the solid generated by revolving the region.

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Create a trigonometric function that models the ocean tide..
Explain why you chose your function type. Show work for any values not already outlined above.

Answers

Answer:

One possible function that models the ocean tide is:

h(t) = A sin(ωt + φ) + B

where:

h(t) represents the height of the tide (in meters) at time t (in hours)

A is the amplitude of the tide (in meters)

ω is the angular frequency of the tide (in radians per hour)

φ is the phase shift of the tide (in radians)

B is the mean sea level (in meters)

This function is a sinusoidal function, which is a common type of function used to model periodic phenomena. The sine function has a natural connection to circles and periodic motion, making it a good choice for modeling the regular rise and fall of ocean tides.

The amplitude A represents the maximum height of the tide above the mean sea level, while B represents the mean sea level. The angular frequency ω determines the rate at which the tide oscillates, with one full cycle (i.e., a high tide and a low tide) occurring every 12 hours. The phase shift φ determines the starting point of the tide cycle, with a value of zero indicating that the tide is at its highest point at time t=0.

To determine specific values for A, ω, φ, and B, we would need to gather data on the tide height at various times and locations. However, typical values for these parameters might be:

1. A = 2 meters (representing a relatively large tidal range)

2. ω = π/6 radians per hour (corresponding to a 12-hour period)

3. φ = 0 radians (assuming that high tide occurs at t=0)

4. B = 0 meters (assuming a mean sea level of zero)

Using these values, we can write the equation for the tide as:

h(t) = 2 sin(π/6 t)

We can evaluate this equation for various values of t to get the height of the tide at different times. For example, at t=0 (the start of the cycle), we have:

h(0) = 2 sin(0) = 0

indicating that the tide is at its lowest point. At t=6 (halfway through the cycle), we have:

h(6) = 2 sin(π/2) = 2

indicating that the tide is at its highest point. We can also graph the function to visualize the rise and fall of the tide over time:

Tide Graph

Overall, this function provides a simple and effective way to model the ocean tide using trigonometric functions.

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Values of the Born exponents for Rb+ and l-are 10 and 12, respectively. The Born exponent for Rbl is therefore: O A. 2 O B.22 C. 1/11 OD. 11

Answers

The Born exponent or interatomic potential energy for Rbl is 11 ( approximately). The correct option is D).

The Born exponent for RbI can be calculated using the relationship between the Born exponent and the interionic distance. The Born exponent is defined as the ratio of the repulsive to attractive contributions to the interatomic potential energy, and it depends on the charges and sizes of the ions.

For Rb+ and I-, the Born exponents are 10 and 12, respectively. This means that the repulsive interaction between Rb+ and I- is weaker than the attractive interaction, as the repulsion is proportional to Rb+^10 and the attraction is proportional to I^-12. Therefore, the attractive interaction dominates.

For RbI, we can use the relationship between the Born exponent and the interionic distance to calculate the Born exponent. This relationship is given by:

B = (1/d) * ln[(l1 + l2)/|l1 - l2|]

where B is the Born exponent, d is the interionic distance, and l1 and l2 are the ionic radii of the cation and anion, respectively.

Assuming the ionic radii of Rb+ and I- are additive, we have:

l1 + l2 = l(RbI) = l(Rb+) + l(I-) = 1.52 + 1.81 = 3.33 Å

|l1 - l2| = |l(Rb+) - l(I-)| = |1.52 - 1.81| = 0.29 Å

Substituting these values into the equation for B, we get:

B = (1/d) * ln[(l1 + l2)/|l1 - l2|] = (1/d) * ln[3.33/0.29] ≈ 11.02

Therefore, the Born exponent for RbI is approximately 11.02.

The correct answer is D).

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Which expressions are equivalent to 8(3/4y - 2) + 6(-1/2x + 4) + 1

Answers

Answer:

8(3/4y - 2) + 6(-1/2x + 4) + 1 can be simplified as:

6(-1/2x) = -3x

8(3/4y) = 6y

8(-2) = -16

6(4) = 24

1 remains as 1.

So the expression becomes:

6y - 3x - 16 + 24 + 1

which simplifies to:

6y - 3x + 9

Therefore, the expressions that are equivalent to 8(3/4y - 2) + 6(-1/2x + 4) + 1 are:

6y - 3x + 9

Solve please geometry, solve for x

Answers

Answer: The answer is D

Step-by-step explanation:

Pythagorean theorem: a²+b²=c²

x²+x²=14²

2x²=196

Evaluate...

x=7√2

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