Which expression is equivalent to 3 x 5 x 5 x5 x 5 x 5 x5 ?

The quadratic equation with roots 5 + i√2 and 5 - i√2 is:

x^2 - 10x + 27 = 0

To write a quadratic equation with roots 5 + i√2 and 5 - i√2, we can use the fact that complex roots occur in conjugate pairs. Therefore, the equation will have the form:

(x - root1)(x - root2) = 0

Substituting the given roots:

(x - (5 + i√2))(x - (5 - i√2)) = 0

Now, we expand the equation:

(x - 5 - i√2)(x - 5 + i√2) = 0

Using the difference of squares formula:

((x - 5)^2 - (i√2)^2) = 0

Simplifying the equation:

(x - 5)^2 + 2 = 0

Expanding the square:

x^2 - 10x + 25 + 2 = 0

Combining like terms:

x^2 - 10x + 27 = 0

Therefore, the quadratic equation with roots 5 + i√2 and 5 - i√2 is:

x^2 - 10x + 27 = 0

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Answer:

Step-by-step explanation:

z=6

The number in the green box is 31.78° .

Given,

Triangle with sides 11 , 12 , 20.

From Cosine Law.

Let △ABC have sides a, b,  c.

Here,

a = 11

b = 20

c = 12

Length of the side opposite vertex A is called a.

Length of the side opposite vertex B is called c.

Length of the side opposite vertex C is called c.

Let θ = ∠C

Then, the Cosine Law says that

c²=a²+b²−2abcosθ.

Substitute the values of a , b , c .

12²  = 11² + 20² - 2 × 11× 20 cosθ

θ = 31.78°

Hence the angle can be found out from cosine law.

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The simplified exponential expression in the context of this problem is given as follows:

[tex](6m^5g^5)^2 = 32m^{10}g^{10}[/tex]

The exponential expression in the context of the problem is defined as follows:

[tex](6m^5g^5)^2[/tex]

The power of a power rule is used when a single base is elevated to multiple exponents, and states that simplified expression is obtained keeping the base, while the exponents are multiplied.

Applying the exponent of 2, we have that:

Hence the simplified exponential expression in the context of this problem is given as follows:

[tex](6m^5g^5)^2 = 32m^{10}g^{10}[/tex]

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Answer:

(a) x-intercept = -2

(b) y-intercept = 4

By using the table of values, a graph of the exponential function is shown in the image below.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

Based on the information provided above, we can logically deduce the following exponential function;

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

Next, we would create a table of values based on the exponential function;

when x = 0, the y-value is given by;

y = 2⁰

y = 1

when x = 1, the y-value is given by;

y = 2¹

y = 2

x                     y____

-2                 0.25

-1                  0.5

0                   1

1                    2

2                   4

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Answer:

B. 108 ft³

Step-by-step explanation:

solution given:

We have Volume of solid = Area of base * length

over here

base : 9ft

height : 6 ft

length : 4ft

Now

Area of base : Area of traingle:½*base*height=½*9*6=27 ft²

Now

Volume : Area of base*length

Volume: 27ft²*4ft

Therefore Volume of the solid=108 ft³

Step-by-step explanation:

prism

v=1/2 X 12cm X 8cm

V= 48

rectangular prism

v=80cm+48cm

v=128cm

The test statistic and critical value needed to test the claim that the success is independent of the type of treatment are 9.750 and critical value is 6.635.

The expected value for each cell is calculated as follows:

E = row total * column total / grand total

The grand total is 150.

The row totals are 83 and 67.

The column totals are 86 and 64.

The expected values are as follows:

Successful: 60 * 86 / 150 = 36.4

Unsuccessful: 60 * 64 / 150 = 29.6

Surgery treatment

Successful: 67 * 86 / 150 = 49.6

Unsuccessful: 67 * 64 / 150 = 27.4

The test statistic is calculated as 9.750

The critical value is calculated as follows:

α = 0.01

df = (r-1)(c-1) = (2-1)(2-1) = 1

x²(α, df) = 6.635

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The area of triangle ABC is 19 square units.

To find the area of a triangle, we can use different formulas depending on the information available. Since we have the coordinates of the vertices A(-9, -8), B(-2, -9), and C(-8, -5), we can use the Shoelace Formula (also known as the Gauss's area formula) to calculate the area of the triangle.

The Shoelace Formula states that if the coordinates of the vertices of a triangle are (x1, y1), (x2, y2), and (x3, y3), then the area (A) of the triangle can be calculated as:

Area = 0.5 * |(x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2))|

Using the coordinates of the vertices A(-9, -8), B(-2, -9), and C(-8, -5), we can substitute these values into the formula to calculate the area.

Let's calculate step by step:

x1 = -9

y1 = -8

x2 = -2

y2 = -9

x3 = -8

y3 = -5

Area = 0.5 * |(-9 * (-9 - (-5)) + (-2) * (-5 - (-8)) + (-8) * ((-8) - (-9)))|

Area = 0.5 * |(-9 * (-4) + (-2) * (3) + (-8) * (-1))|

Area = 0.5 * |(36 + (-6) + 8)|

Area = 0.5 * |(38)|

Area = 0.5 * 38

Area = 19

Therefore, the area of triangle ABC is 19 square units.

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Answer:

28 meters Aprox

Step-by-step explanation:

To find the width of the rectangular park, we can use the Pythagorean theorem. The diagonal running from one corner to the opposite corner forms a right triangle with the length and width of the park.

Given:

Length of the park (L) = 45 meters

Diagonal distance (d) = 53 meters

Using the Pythagorean theorem:

d² = L² + W²

(53 meters)² = (45 meters)² + W²

2809 = 2025 + W²

W² = 2809 - 2025

W² = 784

Taking the square root of both sides:

W ≈ √784

W ≈ 28

Therefore, the width of the rectangular park is approximately 28 meters.

The y-intercept of f(x + 4) + 8 is given as follows:

10.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function for this problem is given as follows:

[tex]f(x) = \log_2{x}[/tex]

The translated function is then given as follows:

[tex]g(x) = \log_2{x + 4} + 8[/tex]

The y-intercept of the function is the numeric value at x = 0, hence:

[tex]g(0) = \log_2{0 + 4} + 8[/tex]

g(0) = 2 + 8 = 10.

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The correct classification for this triangle is an acute triangle.

The angle measures given are 51, 89, and 40 degrees.

There are no angles that are either equal to or greater than 90 degrees among those mentioned. Consequently, the triangle does not contain any angles that are either right or obtuse.

To categorize a triangle according to its angles, the total of the angles within the triangle, which is invariably 180 degrees, is taken into account.

51 + 89 + 40 = 180

Given that the total of the angles is 180 degrees, we can deduce that this particular triangle is acute in nature. An acute-angled triangle is a type of triangle that has three angles which are each smaller than 90 degrees.

Therefore, the correct classification for this triangle is an acute triangle.

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The rule used to determine the term value from its position in the sequence is often referred to as the "nth term" rule.

The nth-term rule involves identifying a pattern or relationship between the position (n) of a term in the sequence and the value of that term.

By analyzing the pattern, such as the common difference or common ratio, the nth-term rule allows us to express the value of any term in the sequence based on its position.

This rule provides a formula or equation that relates the position of a term to its corresponding value in the sequence.

Mathematically, the rule is:

T(n) = a + (n - 1) * d

where:

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The total number of possible outcomes is the number of rows in the table, which depends on the size of the table.

To determine the experimental probability of correctly guessing exactly one correct answer out of five choices, we can utilize the random number table provided, where 0's represent incorrect answers and 1's represent correct answers.

Since we have five choices for each answer, we will focus on a single row of the random number table, considering five consecutive values.

Let's assume we have randomly selected a row from the table, and the numbers in that row are as follows:

0 1 0 1 0

In this case, the second and fourth answers are correct (represented by 1's), while the remaining three choices are incorrect (represented by 0's).

To calculate the experimental probability of exactly one correct answer, we need to determine the number of favorable outcomes (i.e., rows with exactly one 1) and divide it by the total number of possible outcomes (which is equal to the number of rows in the table).

Looking at the table, we can see that there are several possible rows with exactly one 1, such as:

0 1 0 0 0

0 0 0 1 0

0 0 0 0 1

Let's assume there are 'n' favorable outcomes. In this case, 'n' is equal to 3.

The total number of possible outcomes is the number of rows in the table, which depends on the size of the table. Without the specific size of the table, we cannot provide an accurate value.

To calculate the experimental probability, we divide the number of favorable outcomes by the total number of possible outcomes:

Experimental probability = n / Total number of possible outcomes

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Answer:

The answer would lie within 31 degrees of MP and also as in PM.

Answer:

central m arc MP=118°

Step-by-step explanation:

here

central m arc MN=2* inscribed m arc MN=2*31=62°

again

central m arc MN+ central m arc MP=180° being linear pair

substituting value

62°+central m arc MP=180°

central m arc MP=180°-62°

central m arc MP=118°

Answer:

Step-by-step explanation:

Answer:

For month 1, the current balance is $2750.00, the interest is $45.38, and the payment is $75.00. The amount applied to principal is $29.62.

For the remaining months, the interest and payment amount will stay the same, but the current balance and amount applied to principal will change based on the previous month's numbers.

Point of view:

Here's your answer but I prefer you to focus and study hard because school isn't that easy. But i'm glad I could help you!

:)

The volume of the largest piece is 10, 597. 5 cm³

The largest part of the cone takes the shape of a cylinder.

Now, the formula for calculating the volume of a cylinder is expressed as;

V = πr²h

The parameters of the formula are enumerated as;

Now, substitute the values, we get;

Diameter = 2 radius

Radius = 30/2

Radius = 15cm

Height = 15cm

Now, substitute the values, we get;

Volume = 3.14 × 15² ×15

Find the square value and substitute, we have;

Volume = 10, 597. 5 cm³

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Applying the tangent ratio, the value of x in the image, rounded to the nearest thousandth is: 15.824.

The tangent ratio, commonly referred to as "tangent," is a trigonometric function that relates the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle in a right triangle. It is expressed as:

tan (∅) = opposite/adjacent

We have the following:

Reference angle (∅) = 53 degrees

Length of opposite side = 21

Length of adjacent side = x

Plug in the values:

tan 53 = 21/x

x * tan 53 = 21

x = 21 / tan 53

x = 15.824

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The volume of the sphere, given that the sphere has a diameter of 14.6 mm is 1628.7 mm³

The following data were obtained from the question:

The volume of a sphere is giving by the following formula

Volume of sphere = 4/3πr³

Inputting the given parameters, we can obtain the volume of the sphere as follow:

Volume of sphere = (4/3) × 3.14 × 7.3³

Volume of sphere = (4/3) × 3.14 × 389.017

Volume of sphere = 1628.7 mm³

Thus, we can conclude from the above calculation that the volume of the sphere is 1628.7 mm³

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Answer: There are several expressions that are equivalent to the given expression 3x^2 - 5a^3 + 2y^4. Here are a few examples:

These expressions have the same terms but may differ in the order in which the terms are written. It's important to note that the coefficients and exponents of the variables remain unchanged in each expression.

Answer:

Refer to the step-by-step, follow along carefully.

Step-by-step explanation:

Verify the given identity.

[tex]\frac{\sin(x)}{1-\cos(x)} -\frac{\sin(x)\cos(x)}{1+\cos(x)} =\csc(x)(1+\cos^2(x))[/tex]

Pick the more complicated side to manipulate, so the L.H.S.

(1) - Combine the fractions with a common denominator

[tex]\frac{\sin(x)}{1-\cos(x)} -\frac{\sin(x)\cos(x)}{1+\cos(x)}\\\\\Longrightarrow \frac{\sin(x)(1+\cos(x))}{(1-\cos(x))(1+\cos(x))} -\frac{\sin(x)\cos(x)(1-\cos(x))}{(1+\cos(x))(1-\cos(x))} \\\\\Longrightarrow \frac{\sin(x)+\sin(x)\cos(x)-\sin(x)\cos(x)+\sin(x)\cos^2(x)}{(1+\cos(x))(1-\cos(x))} \\\\\Longrightarrow \boxed{\frac{\sin(x)+\sin(x)\cos^2(x)}{(1+\cos(x))(1-\cos(x))}} \\\\[/tex]

(2) - Simplify the denominator

[tex]\frac{\sin(x)+\sin(x)\cos^2(x)}{(1+\cos(x))(1-\cos(x))}\\\\\Longrightarrow \frac{\sin(x)+\sin(x)\cos^2(x)}{1-\cos(x)+\cos(x)-\cos^2(x)}\\\\\Longrightarrow \boxed{\frac{\sin(x)+\sin(x)\cos^2(x)}{1-\cos^2(x)}}[/tex]

(3) - Apply the following Pythagorean identity to the denominator

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Pythagorean Identity:}}\\\\1-\cos^2(\theta)=\sin^2(\theta)\end{array}\right}[/tex]

[tex]\frac{\sin(x)+\sin(x)\cos^2(x)}{1-\cos^2(x)}\\\\\Longrightarrow \boxed{\frac{\sin(x)+\sin(x)\cos^2(x)}{\sin^2(x)}}[/tex]

(4) - Simplify the fraction and split it up

[tex]\frac{\sin(x)+\sin(x)\cos^2(x)}{\sin^2(x)}\\\\\Longrightarrow \frac{1+\cos^2(x)}{\sin(x)}\\\\\Longrightarrow \boxed{\frac{1}{\sin(x)}+\frac{\cos^2(x)}{\sin(x)}}[/tex]

(5) - Apply the following reciprocal identity

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Reciprocal Identitiy:}}\\\\\csc(\theta)=\frac{1}{\sin(\theta)} \end{array}\right}[/tex]

[tex]\frac{1}{\sin(x)}+\frac{\cos^2(x)}{\sin(x)}\\\\\Longrightarrow \csc(x)+\frac{1}{\sin(x)}\cos^2(x) \\\\\Longrightarrow \csc(x)+\csc(x)\cos^2(x) \\\\\therefore \boxed{\boxed{\csc(x)(1+\cos^2(x))}}[/tex]

Thus, the identity is verified.

Prove of the expression sin x / (1 - cos x) - [sin x cos x ] / (1 + cos x) by using trigonometry formula is shown below.

We have to given that,

Expression to verify is,

⇒ sin x / (1 - cos x) - [sin x cos x ] / (1 + cos x)

Now, We can simplify as,

⇒ sin x / (1 - cos x) - [sin x cos x ] / (1 + cos x)

⇒ sin x [ 1 / (1 - cos x) - cos x / (1 + cos x)]

⇒ sin x [1 + cos x - cos x (1 - cos x )] / (1 - cos²x)

⇒ sin x [1 + cos x - cos x + cos²x] / sin²x

⇒ (1 + cos²x) / sin x

⇒ cosec x (1 + cos²x)

Thus, Prove of the expression sin x / (1 - cos x) - [sin x cos x ] / (1 + cos x) by using trigonometry formula is shown above.

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Answer:  if the length of the second rectangular field is 200 meters, the width should be 35 meters to have the same perimeter but a larger area.

Step-by-step explanation:

STEP1:- Let's denote the length of the second rectangular field as L2 and the width as W2.

The perimeter of a rectangle is given by the formula:

Perimeter = 2(length + width).

For the first rectangular field with length L1 = 135 meters and width W1 = 100 meters, the perimeter is:

Perimeter1 = 2(135 + 100) = 470 meters.

STEP 2:- To find the length and width of the second rectangular field with the same perimeter but a larger area, we need to consider that the perimeters of both rectangles are equal.

Perimeter1 = Perimeter2

470 = 2(L2 + W2)

STEP 3 :- To determine the larger area, we need to find the corresponding length and width. However, there are multiple solutions for this problem. We can set an arbitrary value for one of the dimensions and calculate the other.

For example, let's assume the length of the second rectangular field as L2 = 200 meters:

470 = 2(200 + W2)

470 = 400 + 2W2

2W2 = 470 - 400

2W2 = 70

W2 = 35 meters

HENCE L2 = 200 meters and W2 = 35 meters

The simplified expression in the context of this problem is given as follows:

[tex]5\sqrt{5}(\sqrt{10} - 3) = 25\sqrt{2} - 15\sqrt{5}[/tex]

The expression in the context of this problem is given as follows:

[tex]5\sqrt{5}(\sqrt{10} - 3)[/tex]

Applying the distributive property, we multiply the outer term by each of the inner terms, hence:

[tex]5\sqrt{50} - 15\sqrt{5}[/tex]

The number 50 can be written as follows:

50 = 2 x 25.

Hence the square root is simplified as follows:

[tex]\sqrt{50} = \sqrt{2 \times 25} = 5\sqrt{2}[/tex]

Hence the simplified expression is given as follows:

[tex]25\sqrt{2} - 15\sqrt{5}[/tex]

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The area of the rhombus is 100 mm². The Option D.

To get area of a rhombus, we will use the formula: Area = (d₁ * d₂) / 2 where d₁ and d₂ are the lengths of the diagonals.

Given that the horizontal diagonal length is 25 millimeters (d₁ = 25 mm) and the vertical diagonal length is 8 millimeters (d₂ = 8 mm.

We will substitute values into the formula:

Area = (25 mm * 8 mm) / 2

Area = 200 mm² / 2

Area = 100 mm².

Full question:

A rhombus with horizontal diagonal length 25 millimeters and vertical diagonal length 8 millimeters. what is the area of the rhombus? 25 mm2 33 mm2 50 mm2 100 mm2

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The marked price (M.P.) is 1,72,000 when the selling price is 1,61,680 with discount of 6%.

To find the marked price (M.P.), we can use the formula:

M.P. = S.P. / (1 - D%)

Given:

S.P. = 1,61,680

D% = 6%

First, we need to convert the discount percentage to decimal form by dividing it by 100:

D% = 6/100 = 0.06

Now, we can substitute the values into the formula:

M.P. = 1,61,680 / (1 - 0.06)

M.P. = 1,61,680 / 0.94

M.P. = 1,72,000

Therefore, the marked price (M.P.) is approximately 1,72,000.

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The integer number that represents the change in Lily's account balance is given as follows:

-25.

Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.

For the balance of the bank account, we have that:

Lily withdrew $25 from her savings account to buy a birthday gift for her grandfather, hence the integer number is given as follows:

-25.

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Hello!:

24/12 - 8

= 2 - 8

= -6