Simplify $(4 - 5i) - (-2i - 8) + (-1 + 8i).$

The exact solutions of an quadratic equation, 9x² - 4 is equals to the values of x, i.e., x = 2/3, - 2/3.

In algebra, a quadratic equation is any equation that can be written in standard form as ax² + bx + c = 0, where x represents an unknown variable, and a, b, and c are known constants, where a ≠ 0. The solutions of a quadratic equation represent x values, where values stratified the equation . Quadratic formula is used to find the solution of standard equation and it can be written as, x = (- b ±√b² - 4ac)/2a .

We have, an quadratic equation,9x²- 4=0

Comparing it with standard equation ax² + bx + c = 0, we get, a = 9 , b = 0 , c = - 4

Using the quadratic formula to determine the solution of it , x = (- b ±√b² - 4ac)/2a

=> x = { -0 ±√0 - 4×9×(-4)}/2×9

=> x = ±(√144/18)

=> x = ± 12/18 = ± 2/3

Hence, the required solution are x = ± 2/3.

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The perimeter of the isosceles triangle is 128.8/(√35 +2) cm.

What is an isosceles triangle?

A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that are the same length.

We are given that the base of an isosceles triangle is equal to 1/3 of the lateral side.

Also, the height of the base together with the height is 9.2 cm.

Let the lateral side be 'x' and the height be 'h'

So, the base is x/3

Since the height of the triangle, divides it into two right angled triangles, therefore,

x^2= h^2 + (x/6)^2

⇒h^2 = x^2 - (x/6)^2

⇒h^2 = √[x^2 - (x/6)^2]

We are given h+b=9.2 cm

So,

⇒√[x^2 - (x/6)^2] + x/3 = 9.2

⇒x√35/6 + x/3 = 9.2

⇒(x√35 +2x)/6 = 9.2

⇒x√35 +2x = 55.2

⇒x(√35 +2) = 55.2

⇒x = 55.2/(√35 +2)

So, the base is 1/3*55.2/(√35 +2) = 18.4/(√35 +2)

Perimeter = 2*55.2/(√35 +2) + 18.4/(√35 +2)

= (110.4 + 18.4)/(√35 +2)

= 128.8/(√35 +2) cm

Hence, the perimeter of the isosceles triangle is 128.8/(√35 +2) cm.

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Answer:

  y = 250(0.96^n)

Step-by-step explanation:

You want an equation for the number of students in the senior class after n years, when it has 250 students now and decreases at 4% per year. You also want to know the number of years until the class is 100 students.

The exponential equation will have the form ...

  y = a·b^x

where 'a' is the initial value, 'b' is the growth factor, and x is the independent variable.

You have an initial value of 250, a growth factor of (1+(-4%)) = 0.96, and an independent variable of 'n', representing the number of years the population has been declining. The equation is ...

  y = 250(0.96^n)

The population will reach 100 students when n has the value that satisfies ...

  100 = 250·0.96^n

  0.4 = 0.96^n . . . . . . . . . divide by 250

  log(0.4) = n·log(0.96) . . . . . take logarithms

  n = log(0.4)/log(0.96) ≈ 22.45

The senior class will have about 100 students in 22.45 years.

__

Additional comment

The growth factor used in these exponential equations is (1 + growth rate), where the growth rate is the fractional change in the period of interest. The independent variable (x or n) is the number of such periods. Here, the fractional change is given as -4%, a 4% per year decrease. This tells us a period is 1 year. Of course -4% is the decimal fraction -0.04.

[tex] \bold{(x-6)(x+6)}[/tex]

To simplify this equation, quadratic factoring patterns should be used. These patterns are the following:

[tex] \bold{a^2-b^2=(a-b)(a+b)}[/tex]

This pattern works because if one distributes the terms in the parentheses by multiplying each term in one of the parentheses by each term in the other, the result is the original equation:

[tex]\bold{36=6^2}[/tex] so it can be applied to the given equation:

[tex]\begin{gathered} \bold{x^2-36}\end{gathered}[/tex]

[tex]\bold{(x-6)(x+6)}[/tex]

∴ The factored form of the expression is (x - 6) (x + 6).

Answer:

A

Step-by-step explanation:

The side-length of square C as required in the task content is; 5 ft.

It follows from the task content that the side length of square C is to be determined according to the given diameter.

Recall that the Area, A of a square in terms of its side length, s is; A = s².

Therefore, s = √A.

On this note, for each of the given squares their side lengths are as follows;

For square A; side length is; √9 = 3ft.

For square B; side length is; √16 = 4ft.

Hence, since sides A, B and C form a right triangle;

C² = A² + B²

C² = 3² + 4²

C² = 9 + 16

C² = 25

C = 5.

Ultimately, the side-length of square C is; 5 ft.

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There are major two formulas in arithmetic progression which is related to the nth term of A.P.

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence. For instance, the natural number sequence 1, 2, 3, 4, 5, 6,... is an example of an arithmetic progression. It has a common difference of 1 between two succeeding terms (let's say 1 and 2). (2 -1). We can see that the common difference between two subsequent words will be equal to 2 in both the case of odd and even numbers.

Definition 1: An acronym for a mathematical sequence where the difference between any two consecutive terms is always a constant.

Definition 2: An arithmetic sequence or progression is a series of numbers in which the second number in each pair of consecutive terms is obtained by adding a predetermined number to the first.

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Answer:

Step-by-step explanation:

Hello! You know that the price of a new car is $29,990 and the sales tax rate is 6.5%.  To calculate the tax you will have to pay, you have to multiply 0.065 by 29,990.  You have to move the decimal space two spaces to the left to get rid of the percentage.  29,990 x 0.065 = 1949.35.  The sales tax being charged for the car is $1949.35.  The total cost of the car including tax is $29,990 + $1949.35, which equals $31939.35. Hope this helps!

To calculate std deviation in R you can create a list of values or import a CSV file to find the standard deviation.

It is simple to compute an average and standard deviation in R. The mean() and sd() functions compute the average and standard deviation, respectively.

The positive square root of the variance is the standard deviation. One of the fundamental techniques used in statistical analysis is standard deviation. Standard deviation, also known as SD or indicated by the symbol "," indicates how far a value deviates from the mean value.

A low standard deviation indicates that the values are often within a few standard deviations of the mean, whereas a large standard deviation indicates that the values are much outside of the mean. Learn how to determine a random variable's standard deviation as well as the standard deviation of data that has been grouped and ungrouped.

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Yes, it is possible to find the HCF (highest common factor) of 7 and 9 without using the prime factorization method.

One way to find the HCF of two numbers without using prime factorization is to use the Euclidean algorithm.

The Euclidean algorithm for finding the HCF of two numbers is as follows:

Divide the larger number by the smaller number and get the remainder.

Divide the smaller number by the remainder obtained in step 1 and get the remainder.

Repeat step 2 until the remainder is 0.

The last non-zero remainder obtained is the HCF of the two numbers.

Using the Euclidean algorithm for 7 and 9:

9/7 = 1 remainder 2

7/2 = 3 remainder 1

2/1 = 2 remainder 0

So the last non-zero remainder obtained is 1.

Therefore, the HCF of 7 and 9 is 1.

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The simplified exponential expression for this problem is given as follows:

-9h^7g^5.

The exponential expression for this problem is defined as follows:

2h²g^4h^5g - 7hg²h^6g³ - 4g²h³h^4g³.

When two terms with the same base and different exponents are multiplied, the bases are kept while the exponents are added.

Hence the terms are simplified as follows:

Hence the simplified expression is given as follows:

2h^7g^5 - 7h^7g^5 - 4h^7g^5.

(2 - 7 - 4)h^7g^5.

-9h^7g^5.

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Step-by-step explanation:

DISCUSSION QUESTIONS (DQ's).

1. Is division always a negative in a religious faith? Why or why not?

Four red cells and eight blue cells make up the body. Then, C is the right answer.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional. A ratio that connects a part to a whole is a percentage. For instance, there are 100 students in the class with 20 men and 80 women. The percentage of men is 20/100, or 20%. 80 out of 100, or 80%, are women.

There are 12 square boxes in the grids.

Let R stand for red and B for blue.

R + B = 12                                    ...1

R / B = 1/2                                    ...2

We have by resolving equations 1 and 2

R + 2R = 12

3R = 12

R = 4

Then

4 + B = 12

B = 8

Then, C is the right answer.

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Complete Question -

The angle of the refracted ray is 15°.

When an incident light ray strikes the surface of the water at an angle of 20 degrees, it will be refracted, or bent, as it enters the water. The refracted ray will continue to travel through the water at a different angle than the incident ray.

In order to determine the angle of the refracted ray, we may apply Snell's law, which states that the ratio of the sines of the angles of incidence and refraction is constant for a given wave when it passes through two different media. Mathematically, this is:

n₁sin(θ₁) = n₂sin(θ₂)

Where n is the refractive index. Substituting the values given into the equation:

1.0003 * sin(20°) = 1.33 * sin(θ)

θ = 14.91

The angle of the refracted ray is 15°.

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Answer:

D. y = 5x

Step-by-step explanation:

This graph shows a linear relationship between the number of sandwiches bought (x) and their cost (y). In this question, we are asked to define the relationship between x and y using an equation. Since this relationship is linear and thus has a constant of proportionality, we can represent it in the form: y = mx, where m is the ratio of the cost of sandwiches to the number of sandwiches. We can solve for m with the formula:

m = rise / run

So, the value m of the given line is:

m = 10 / 2

m = 5

Hence, the equation that displays the proportional relationship between the number of sandwiches bought (x) and their cost (y) is D. y = 5x.

Answer:

x = 111°

Step-by-step explanation:

Sum of interior angle

(n - 2) 180°

=(7 - 2) 180

=(5) 180°

=900°.

The value of x

=139° + 141° + 120° + x + 136° + 118° + 135° = 900°

=400° + x + 389° = 900°

=789° + x = 900°

x = 900° - 789°

x = 111°.

Answer:

Below in bold.

Step-by-step explanation:

To do this we keep dividing by successive primes, using the lowest prime that divides exactly.

2) 12600

2) 6300

2) 3150

3) 1575

3) 525

5) 175

5) 35

7        <---we end up with a prime number so tha's the end of the process

So, 12,600 = 2*2*2*3*3*5*5*7 or 2^3*3^2*5^2*7.

Answer:

2 weeks

Step-by-step explanation:

The next week Mr Blair’s class will have written 5 letters because his class wrote one more letter, while Ms Stevenson’s class will have written 4 letters because her class wrote 2 more letters. This next week Mr Blair’s class will write another letter leaving them at 6 letters, and Ms Stevenson’s class will write 2 more letters leaving them at 6 letters also. So all in all, in 2 weeks, the two classes will be at equal amounts and caught up to each other.

Answer:

A = 42

Step-by-step explanation:

If 6 / 7 = A / 49, then:
(multiply both sides of the equation by 49)
A = 49 * 6 / 7
A = 42

You can also solve by the rule of proportions (see picture):
7 * A = 6 * 49
A = 6 * 49 / 7
A = 6 * 7 = 42

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30 : 15 : 15, cookies in total, we say that y is directly proportional to x when two variables, x and y, are such that the ratio yx remains constant.

We say that y is directly proportional to x when two variables, x and y, are such that the ratio yx remains constant. If k is used to denote the constant, we can obtain the equations y = kx or y = k, where k 0.

When added to your sugar cookie batter, a teaspoon or two of extracts will significantly enhance flavor. The obvious option is vanilla. Add both vanilla and almond extracts for a more interesting flavor. Other wonderful options to think about are rum, maple, and anise.

1/30 : 2/30 : 2/30.

30 : 15 : 15.

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Answer:

1.

-x² + 2x

Step-by-step explanation:

x² + x - 2.

=x³ - x² + 2x - 2.

1

=-x² + 2x.

note: x³ cancel x² and x, and -2 cancel -2.

Answer:

Etymology

Step-by-step explanation:

The pizza pie cost  $16.50.

We have the following information. An equation is a mathematical statement that asserts the equality of two expressions. It is written in the form of "left-hand side = right-hand side," where both sides are expressions that are made up of numbers, variables, and mathematical operations.

Gentiana spent $10 on her entrance fee, so she has $40 - $10 = $30 left.

25% of $30 is $30 x 0.25 = $7.50.

She spent $7.50 on a Movie.

20% of $30 is $30 x 0.20 = $6.

She spent $6 on popcorn.

So, the total amount spent on Movie and popcorn is $7.50 + $6 = $13.50.

Therefore, the pizza pie cost $30 - $13.50 = $16.50

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25% of $30 is $30 x 0.25 = $7.50.

She spent $7.50 on a Movie.

20% of $30 is $30 x 0.20 = $6.

She spent $6 on popcorn.

So, the total amount spent on Movie and popcorn is $7.50 + $6 = $13.50.

Therefore, the pizza pie cost $30 - $13.50 = $16.50

The measure of length PQ will be 22 units.

A triangle's third side is stated to be parallel to the line segment uniting its two midpoints, and it is also half as long as the third side.

Given:

PQ = 5x + 62, and MN = 6x-4

Now, using Mid- Point Theorem

PQ= 1/2 MN

-5x+ 62 = 1/2( 6x - 4)

-5x+ 62 = 3x - 2

-5x- 3x = -2 - 62

-8x = -64

x= 8

PQ= 5x+ 62 = -5(8) + 62 = -40 + 62 = 22

Hence, the measure of PQ is 22 units.

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Answer: 183sr3, 370sr3

Step-by-step explanation:

Different quadrilaterals have different properties to get proven.

what are quadrilaterals?

A quadrilateral is a polygon with four sides, four vertices, and four angles.

It is formed by joining four non-collinear points. The sum of the interior angles of quadrilaterals is always equal to 360 degrees. The word quadrilateral is derived from the Latin words ‘Quadra’ which means four and ‘Latus’ means ‘sides’. Not all the four sides of a quadrilateral need to be equal in length. Hence, we can have different types of quadrilaterals based on sides and angles.

Now,

Five special quadrilaterals are shown below in the image, along with their definitions and pictures, and points for them to get proven.

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The area of the right triangle is equal to 1.5√187 square meters.

Right triangles are triangles with a right angle, whose side relationship is described by Pythagorean relationship:

r = √(x² + y²)

Where:

And the area of the triangle (A), in square meters, is determined by the following formula:

A = 0.5 · x · y

First, determine the length of the missing leg by Pythagorean theorem:

x = √(14² - 3²)

x = √187

Second, calculate the area of the triangle:

A = 0.5 · (3 m) · (√187 m)

A = 1.5√187 m²

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1: Convert the mixed number into an improper fraction.

2: Rewrite the whole number as a fraction with the denominator 1.

3: Multiply two fractions by multiplying the numerators and denominators separately.

4: Convert it into simplified form if required.

Now, According to the question:

A mixed number is a whole number and a proper fraction represented together.  It generally represents a number between any two whole numbers.

To multiply a mixed number with a fraction, first, convert the mixed number to a fraction and then multiply the two fractions. Two fractions can be multiplied by multiplying the numerators and denominators separately to get a fraction as an answer. The fraction can be written in its simplest form by removing any common factors between the numerator and denominator.

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Answer:

Step-by-step explanation:

Simplify the following:

(sqrt(48))/(sqrt(42))

Rationalize the denominator. (sqrt(48))/(sqrt(42)) = (sqrt(48))/(sqrt(42))×(42^(1 - 1/2))/(42^(1 - 1/2)) = (sqrt(48)×42^(1 - 1/2))/42:

(sqrt(48)×42^(1 - 1/2))/42

Combine powers. (sqrt(48)×42^(1 - 1/2))/42 = sqrt(48)×42^((1 - 1/2) - 1):

sqrt(48)×42^((1 - 1/2) - 1)

Put 1 - 1/2 over the common denominator 2. 1 - 1/2 = 2/2 - 1/2:

sqrt(48)×42^((2/2 - 1/2) - 1)

2/2 - 1/2 = (2 - 1)/2:

sqrt(48)×42^(((2 - 1)/2) - 1)

2 - 1 = 1:

sqrt(48)×42^(1/2 - 1)

Put 1/2 - 1 over the common denominator 2. 1/2 - 1 = 1/2 - 2/2:

sqrt(48)×42^(1/2 - 2/2)

1/2 - 2/2 = (1 - 2)/2:

sqrt(48)×42^((1 - 2)/2)

1 - 2 = -1:

sqrt(48)×42^((-1)/2)

sqrt(48) = sqrt(2^4×3) = 2^2 sqrt(3):

2^2 sqrt(3) 1/sqrt(42)

2^2 = 4:

4 sqrt(3) 1/sqrt(42)

Rationalize the denominator. (4 sqrt(3))/(sqrt(42)) = (4 sqrt(3))/(sqrt(42))×(sqrt(42))/(sqrt(42)) = (4 sqrt(3) sqrt(42))/42:

(4 sqrt(3) sqrt(42))/42

The gcd of 4 and 42 is 2, so (4 sqrt(3) sqrt(42))/42 = ((2×2) sqrt(3) sqrt(42))/(2×21) = 2/2×(2 sqrt(3) sqrt(42))/21 = (2 sqrt(3) sqrt(42))/21:

(2 sqrt(3) sqrt(42))/21

sqrt(3) sqrt(42) = sqrt(3×42):

2/21 sqrt(3×42)

3×42 = 126:

(2 sqrt(126))/21

sqrt(126) = sqrt(3^2×14) = 3 sqrt(14):

2/21 3 sqrt(14)

3/21 = 3/(3×7) = 1/7:

Answer: (2 sqrt(14))/7

Answer:

7

Step-by-step explanation:

v is is and e is 5

2v is 20 and e is 5 and plus 3

20 divided by 5 plus 3 will equal to 7

Answer:

[tex] \sf \: 2v ÷ e + 3 = 7[/tex]

Step-by-step explanation:

Given expression,

→ 2v ÷ e + 3

Now we have to use,

→ v = 10

→ e = 5

Let's solve the expression,

→ 2v ÷ e + 3

→ 2(10) ÷ (5) + 3

→ 20 ÷ 5 + 3

→ 4 + 3

→ 7 => final value

Therefore, the answer is 7.