2. 19 x - x = + 1, what is the value of x?

[tex] \Large{\boxed{\sf \dfrac{1 + 2i}{3 - 4i} + \dfrac{2 - i}{5i } = - \dfrac{2}{5}}} [/tex]

[tex] \\ [/tex]

Given sum:

[tex] \sf \: \dfrac{1+2i}{3-4i} + \dfrac{2-i}{5i}[/tex]

[tex] \\ [/tex]

We can simplify the sum only if the denominators of the two fractions are the same. Since they are different, we have to multiply the numerator and the denominator of each fraction by the denominator of the other one.

[tex] \sf \: \dfrac{1+2i}{3-4i} + \dfrac{2-i}{5i} = \dfrac{5i(1 + 2i)}{5i(3 - 4i)} + \dfrac{(3 - 4i)(2 - i)}{(3 - 4i)5i} \\ \\ \\ \sf \: = \dfrac{5i + 10 {i}^{2} }{15i - 20 {i}^{2} } + \dfrac{6 - 3i - 8i + 4 {i}^{2} }{15i - 20 {i}^{2} } [/tex]

[tex] \\ [/tex]

Replace i² with -1:

[tex] \sf \dfrac{5i + 10 {i}^{2} }{15i - 20 {i}^{2} } + \dfrac{6 - 3i - 8i + 4 {i}^{2} }{15i - 20 {i}^{2} } \: \\ \\ \\ \\ \sf \: = \dfrac{5i + 10( - 1)}{15i - 20( - 1)} + \dfrac{ 6 - 11i + 4( - 1)}{15i - 20( - 1)} \\ \\ \\ \\ \sf = \dfrac{5i - 10}{20 + 15i} + \dfrac{2 - 11i}{20 + 15i} [/tex]

[tex] \\ [/tex]

Simplify the expression:

[tex] \sf = \dfrac{5i - 10}{20 + 15i} + \dfrac{2 - 11i}{20 + 15i} \\ \\ \\ \\ \sf \: = \dfrac{5i - 10 + 2 - 11i}{ 20 + 15i} = \sf \dfrac{ - 8 - 6i}{20 + 15i}[/tex]

[tex] \\ [/tex]

To write our solution in the x + iy form, also known as the algebraic form, we have to understand what the conjugate of a complex number is.

[tex] \textsf{Let z be our complex number, and} \: \overline{\sf z} \: \textsf{its conjugate.} [/tex]

[tex] \\ [/tex]

The conjugate of z, [tex] \overline{ \sf z}, [/tex] is the complex number formed of the same real part as z but of the opposite imaginary part.

Since x is the real part of z, and y is its imaginary part, this can be expressed as:

[tex] \sf If \: z = x + iy \:, then \: \overline{ \sf z} = x - iy [/tex]

[tex] \\ [/tex]

Now, we have to multiple both the denominator and the numerator of our fraction by the conjugate of its denominator:

[tex]\sf \dfrac{ - 8 - 6i}{20 + 15i} = \dfrac{( - 8 - 6i)( \overbrace{20 - 15i}^{ \overline{z}}) }{ (20 + 15i)( \underbrace{20 - 15i}_{ \overline{z}}) } \\ \\ \\ \sf = \dfrac{ - 160 + 120i - 120i + 90 {i}^{2} }{400 - 300i + 300i - 225 {i}^{2} } \\ \\ \\ \sf = \dfrac{ - 160 + 90 {i}^{2} }{400 - 225 {i}^{2} }[/tex]

[tex] \\ [/tex]

One more time, substitute -1 for i²:

[tex] \sf \: \dfrac{ - 160+ 90 {i}^{2} }{400 - 225 {i}^{2} } \: = \dfrac{ - 160 + 90( - 1)}{400 - 225( - 1)} \\ \\ \\ \sf = \boxed{\sf - \dfrac{ 250}{625}} [/tex]

[tex] \\ [/tex]

Finally, let's simplify our result:

[tex] \sf - \dfrac{250}{625} = - \dfrac{2 \times 125}{5 \times 125} = \boxed{ \boxed{ \sf - \dfrac{2}{5}}}[/tex]

[tex] \\ \\ [/tex]

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We have proved that the ray FE is parallel to the ray GC.

What is meant by parallel lines?

In geometry, parallel lines are coplanar straight lines that do not intersect at any point. Parallel planes are planes in the same three-dimensional space that never meet. Parallel curves are curves that do not touch each other or intersect and keep a fixed minimum distance.

Angle DEF intersects at B

which results in angle DEF corresponding to the angle  ACG.

As DEF = 45 so angle ACG = 45

So by the above discussion, we can say that the ray FE is parallel to the ray GC.

Hence, we have proved that the ray FE is parallel to the ray GC.

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The slant height of the cone c² = 5² + (1)² or c ≅ 5.1.

Option (A) is correct option.

A cone is a three-dimensional geometric structure with a smooth transition from a flat, usually circular base to the apex or vertex, a point that creates an axis to the base's center.

Given that,

The radius of the cone = 1 inch,

And the height of the cone = 5 inch.

Let the slant height of the cone is c,

To find the slant height of the cone, use Pythagorean theorem,

c² = 5² + (1)²

c² = 25 + 1

c² = 26

c= 5.09

c ≅ 5.1

The slant height of the cone is 5.1 inch.

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The answer, based on the information provided, fractional exponents will be 3.

A product in which the same integer is used repeatedly as a factor is represented by a number elevated to a power. The exponent provides the power, and the integer is referred to as the base. The exponent indicates the number of factors, while the base is the repeating factor (the multiplied number).

That number will be the outcome! One of the simplest exponent laws is this one. You'll see that this rule doesn't merely apply to numerical data. We might, for example, elevate a statistic to the initial power.

[tex]=3^{\frac{1}{4} }\times3^{\frac{1}{4} }\times3^{\frac{1}{4} }\times3^{\frac{1}{4} }\\=3^{\frac{1}{4}+{\frac{1}{4}+{\frac{1}{4}+{\frac{1}{4}\\\\=3^{1} \\=3[/tex]

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Answer:

Step-by-step explanation:

Let's call the side lengths of the first quadrilateral a, b, c, and d, and the side lengths of the second quadrilateral A, B, C, and D. We are given that the perimeter of the second quadrilateral is 20 cm, and that the quadrilaterals are similar. This means that the ratio of the side lengths of the two quadrilaterals is the same for all four sides. Let's call this ratio r. Then we have:

A + B + C + D = 20 cm

and

A/a = B/b = C/c = D/d = r

We can find the value of r by taking the ratio of any two sides of the quadrilaterals. For example, we can take the ratio of A to a:

A/a = r

Substituting the expressions for A and a in terms of r, we get:

(ra)/a = r

Solving for r, we get:

r = a/a = 1

This means that the ratio of the side lengths of the two quadrilaterals is 1. Therefore, the side lengths of the second quadrilateral are equal to the side lengths of the first quadrilateral. Substituting the given values for the side lengths of the first quadrilateral, we get:

A = 6 cm

B = 5 cm

C = 8 cm

D = 11 cm

Therefore, the side lengths of the second quadrilateral are A = 6 cm, B = 5 cm, C = 8 cm, and D = 11 cm.

Answer:

2

Step-by-step explanation:

1+1=2
XD

Answer:

2

Step-by-step explanation:

I know this is a joke but I don't care

Answer:

[tex]\dfrac{8}{12}[/tex]

Step-by-step explanation:

Let the unknown fraction be:

If the sum of the numerator and denominator is 20 then:

[tex]\implies a+b=20[/tex]

Rewrite the equation to isolate b:

[tex]\implies b=20-a[/tex]

If the fraction is equal to 2/3 then:

[tex]\implies \dfrac{a}{b}=\dfrac{2}{3}[/tex]

Cross multiply:

[tex]\implies 3a=2b[/tex]

Substitute the expression for b into the cross-multiplied equation and solve for a:

[tex]\implies 3a=2(20-a)[/tex]

[tex]\implies 3a=40-2a[/tex]

[tex]\implies 5a=40[/tex]

[tex]\implies a=8[/tex]

Substitute the found value of a into the equation for b and solve for b:

[tex]\implies b=20-8[/tex]

[tex]\implies b=12[/tex]

Therefore, the fraction for which the sum of the numerator and denominator is 20, and the value of the fraction is equal to 2/3 is:

-2(-3)+18=24

6+18 = 24

24 = 24

6(-3) +9=-13

-18+9 = -13

-9 ≠ - 13

4(-3)-9=-21

-12 -9 =-21

-21 = -21

Answer:

Translation: 4 to the right and 8 up.

Scale factor: 3

Step-by-step explanation:

If you move CDE 4 spaces to the right and 8 spaces up C and C' will match up. If you dilate (make bigger) CDE 3 times it will perfectly be C'D'E'.

Answer:

No.

Step-by-step explanation:

An integer is defined as a whole number.

The number given, "1.765", is not a whole number, as it includes the decimal .765. 1.765, as implied by decimal point, is a decimal number.

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Answer:

After factorization the result is: (7x + 4)(x - 1).

Step-by-step explanation:

To factor 7x² + 3x - 4, we can use the following steps:

Look for two numbers that multiply to give the constant term (-4) and add to give the coefficient of the linear term (3). These two numbers are -4 and 1.

Use these numbers to create two binomials, one with a positive sign and one with a negative sign: (7x + 4) and (7x - 1).

Factor the quadratic expression by grouping:

(7x + 4)(x - 1)

We can check that this is the correct answer by multiplying the two binomials:

(7x + 4)(x - 1) = 7x² + 3x - 4

This is the original expression, so we have successfully factored it.

Note: Depending on the specific problem, there may be more than one way to factor the expression. This is just one possible solution.

Answer:

[tex]y' = \dfrac{1 + x \sin x - x \cos x + \sin x + \cos x}{(\cos x - x)^2}[/tex]

Step-by-step explanation:

[tex] y = \dfrac{x + \sin x}{\cos x - x} [/tex]

Derivative of a quotient:

[tex] \dfrac{d}{dx} \dfrac{f(x)}{g(x)} = \dfrac{g'h - h'g}{h^2} [/tex]

Recall:

[tex] \dfrac{d}{dx} \sin x = \cos x [/tex]

[tex] \dfrac{d}{dx} \cos x = - \sin x [/tex]

[tex] y = \dfrac{x + \sin x}{\cos x - x} [/tex]

[tex] y' = \dfrac{dy}{dx} = \dfrac{(1 + \cos x)(\cos x - x) - [(- \sin x - 1)(x + \sin x)]}{(\cos x - x)^2} [/tex]

[tex]y' = \dfrac{\cos x - x + \cos^2 x - x \cos x - (-x \sin x - \sin^2 x - x - \sin x}{(\cos x - x)^2}[/tex]

[tex]y' = \dfrac{\cos x - x + \cos^2 x - x \cos x + x \sin x + \sin^2 x + x + \sin x}{(\cos x - x)^2}[/tex]

[tex]y' = \dfrac{\sin^2 x + \cos^2 x + x - x - x \cos x + x \sin x + \sin x + \cos x}{(\cos x - x)^2}[/tex]

[tex]y' = \dfrac{1 + x \sin x - x \cos x + \sin x + \cos x}{(\cos x - x)^2}[/tex]

Answer:

Step-by-step explanation:

Let, the Speed of the water be 'x'

and the Radius be 'r'

Now, the speed of Water Varies inversely with the Radius

So, x ∝ 1/r

      x = k/r   -----------(i)

Here, k is the proportionality constant

Now,

Given that, x = 2.5 ft per sec

then, 30 ft,

So, from eq. (i)

               2.5 = k/30

          So, k = 75

Again From eq. (i)

                    x = 75/r

          Now, if r = 3ft

           then, x = 75/3

                     x = 25

Hence, Speed of the water (x) = 25 ft per sec.

Answer:

Step-by-step explanation:

There is a scale factor of 2 so since the trapezoid is 9 we can divide by 2 so AD is 4.5 and CB is 4.5

YZ is the same as ZW so 8

Using the scale factor we can divide 8 by 2 to get 4

Perimeters can be found from the sums so

ABCD would be 19 and WXYZ would be 38

By dividing the length of bacteria cell to length of amoeba cell we find option (D) i.e 6.67x102 is the correct answer.

Division is an arithmetic operation that involves dividing one number (the dividend) by another number (the divisor) to find the quotient.

Arithmetic operators are symbols that represent mathematical operations that can be performed on one or more operands. The most common arithmetic operators are:

Addition (+): Adds two operands and produces the sum.

Subtraction (-): Subtracts one operand from another and produces the difference.

Multiplication (*): Multiplies two operands and produces the product.

Division (/): Divides one operand by another and produces the quotient.

Modulo (%) : Divides one operand by another and produces the remainder.

Exponentiation (**): Raises one operand to the power of the other and produces the result.

To compare the sizes of the two cells, we need to divide the length of the bacterial cell by the length of the amoeba cell. The result is 3 x 10^−6 m / 4.5 x 10^−4 m = 0.67 x 10^−2.

So, the bacterial cell is approximately 0.67 x 10^−2 times smaller than the amoeba cell.

The correct answer is therefore (D) 6.67 x 10

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Answer: LCD = 60

Step-by-step explanation:

Rewriting input as fractions if necessary:

1/30, 9/20

For the denominators (30, 20) the least common multiple (LCM) is 60.

Therefore, the least common denominator (LCD) is 60.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

1/30 = 1/30 × 2/2 = 2/60

9/20 = 9/20 × 3/3 = 27/60

The number 'n' is equal to 14

In the question, we have been given that the number n is equal to 7 more than half of the number 'n'.

So in these linear equation-solving types of problems, first of all, we convert the written sentence into an equation.

So the equation for the following problem statement is -

n = 7 + n/2  

{since we have been given the number equals 7 more than half of the number }

Solving the equation we have,

n = 14.

We can easily see that 14 is the number which is 7 more than half of itself.

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The numerical expression to represent the rate of temperature change in degrees Fahrenheit per foot is 0.14 degrees Celsius per foot.

What do you mean by numerical expression?

A group of numbers that have been written together using the arithmetic operations addition, subtraction, multiplication, and division is known as a numerical expression in mathematics. The number can be stated in a variety of ways, including verbally and numerically.

According to the given question,

To calculate the rate of temperature change in degrees Fahrenheit per foot,

We need to first convert degrees Fahrenheit to degrees Celsius.

To do this, we divide 100 by 5.9.

This yields a result of 0.14 degrees Celsius per foot.

Therefore, the numerical expression to represent the rate of temperature change in degrees Fahrenheit per foot is 0.14 degrees Celsius per foot.

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The statements that apply to the given random sample situation are:

(A) Despite the idea that the sample must be random, we are unsure of this.

(C) It is underreported how many pupils don't drive to school.

(D) n(1p) is not greater than 10.

A simple random sample, also known as an SRS, is a smaller group of individuals (also known as a sample) chosen randomly and with equal probability from a larger population.

This technique involves picking a sample at random.

The probability of being chosen from any subset of k persons in SRS is the same as that of being chosen from any other subset of k people.

A simple random sample is an objective sampling approach.

A basic sampling method that can be used in conjunction with other, more advanced sampling techniques is simple random sampling.

So, statements that apply in the given situation are:

- We don't know if the sample is random, despite the fact that it must be.

- The number of students who don't drive to school is undercounted.

- n(1−^p) does not exceed 10.

Therefore, the statements that apply to the given random sample situation are:

(A) Despite the idea that the sample must be random, we are unsure of this.

(C) It is underreported how many pupils don't drive to school.

(D) n(1p) is not greater than 10.

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Correct question:
The administration at GSU wants to estimate the number of parking spaces they will need next year. They survey 80 students; 75 of the students in the sample drive to campus by themselves each day. Which of the following is a reason the administration should not calculate a confidence interval for the proportion of all students who drive to campus? Check all that apply.

a. The sample needs to be random but we don’t know if it is.

b. The actual count of drivers is too small.

c. The actual count of those who does not drive to campus is too small.

d. n ^ p is not greater than 10. n ( 1 − ^ p ) is not greater than 10.

Answer:

see explanation

Step-by-step explanation:

(a)

given y is inversely proportional to x² then the equation relating them is

y = [tex]\frac{k}{x^2}[/tex]

to find k use any ordered pair from the table

using (1, 4 ) and substituting into equation

4 = [tex]\frac{k}{1^2}[/tex] = [tex]\frac{k}{1}[/tex] , thus

k = 4

y = [tex]\frac{4}{x^2}[/tex] ← equation of proportion

(b)

when y = 25 , then

25 = [tex]\frac{4}{x^2}[/tex] ( multiply both sides by x² )

25x² = 4 ( divide both sides by 25 )

x² = [tex]\frac{4}{25}[/tex] ( take square root of both sides )

x = ± [tex]\sqrt{\frac{4}{25} }[/tex] = ± [tex]\frac{2}{5}[/tex]

then

positive value of x when y = 25 is x = [tex]\frac{2}{5}[/tex]

Answer: 10w

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let total mass be x

(3/4)*x=15

on solving

x=20

now,

mass of 2/5 of piece of metal is-

=> (2/5)*20

=> 8

Ans- 8kg

Answer: -10,-8.7, -9.1, 8, 8.7, 8.06, 9

Step-by-step explanation:

77 squared rooted equals 8.7

-83 square rooted equals -9.1

-76 square rooted equals -8.7 ( remember negative numbers are greater than positive numbers)

65 square rooted equals 8.06

The different combinations of groups for the group project is (b) 560

From the question, we have the following parameters that can be used in our computation:

Total number of people, n = 16

Numbers to selection, r = 3 people

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 16 and r = 3

Substitute the known values in the above equation

Total = ¹⁶C₃

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 16!/(13! * 3!)

Evaluate

Total = 560

Hence, the number of ways is 560

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The farthest drainage ditch​ is 39 feet away from the well.

The length of the line segment bridging two points on a plane is known as the distance between the points.

The formula to find the distance between the two points is usually given by d=√{(x₂-x₁)² + (y₂-y₁)²}

Given, an environmental engineer graphed the locations of a well and all the drainage ditches in the vicinity.

She positioned the well at (−6,7) and the farthest drainage ditch at (33,7).

To find the distance:

Let d be the distance.

d = √{(x₂-x₁)² + (y₂-y₁)²}

Here, x₂ = 33, x₁ = -6, y₂ = 7 and y₁ = 7

Substituting the value to the distance formula,

d = √{(33+6)² + (7-7)²}

d = √{(39)² + (0)²}

d = √{(39)²

d = 39

Therefore, the value of d is 39.

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The measure of the angle ∠MAR will be equal to 26°. The correct option is A.

In geometry, an angle bisector is a line that divides an angle into two equal angles. A bisector is something that divides a shape or object into two equal parts. An angle bisector is a ray that divides an angle into two equal parts of the same measurement.

Given that Ray AT bisects ∠MAR. If m∠MAT = (8x − 3)° and m∠RAT = (2x + 9)°,

The two angles ∠MAT and ∠RAT will be equal. Then calculate the value of x.

8x - 3 = 2x + 9

8x - 2x = 9 + 3

6x = 12

x = 2

The angle ∠MAR is calculated as,

∠MAR = 2 x ∠RAT

∠MAR = 2 x ( 2x + 9)

∠MAR = 2 x ( 2 x 2 + 9 )

∠MAR = 2 x ( 13 )

∠MAR  = 26°

Option A is correct for the angle ∠MAR.

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Answer:

A all the way

Step-by-step explanation:

Assume you are buying a bond with a par value of $1,000 which is listed in the Wall Street Journal at a price of 100.50. The bond price is: $1,005.

Using this formula to determine the bond price

Bond price = Bond par value × price/100

Where:

Bond par value = $1,000

Price = 100.50

Let plug in the formula

Bond price = $1,000 × 100.50 /100

Bond price = $100,500 /100

Bond price =$1,005

Therefore the bond price is $1,005.

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Answer:

x < 4

Step-by-step explanation:

4x - 6 < 10

4x < 16

x < 4

[tex]4x-6 < 10[/tex]

Add 6 to both sides:

[tex]4x-6+6 < 10+6[/tex]

[tex]4x < 16[/tex]

Divide both sides by 4:

[tex]\dfrac{4x}{4} < \dfrac{16}{4}[/tex]

[tex]\fbox{x} < \fbox{4}[/tex]

Using mathematical operations on the word problem, the amount he will receive as his change is $1.43

A word problem is a few words are presented in a form of problem and  needs to be solved by way of a mathematical calculation.

This problem can be solved using mathematical operation such as addition and subtraction.

The total amount he has with him = $15

The current bill = $8.33

The fruit salad = $2.99

Tip = $2.25

Total amount spent = 8.33 + 2.99 + 2.25

The total amount spent = 13.57

The amount of change = total amount he has with him - total amount spent

The amount of change = 15 - 13.57

The amount of change = 1.43

The change he is going to receive is $1.43

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Let x be the number of sliders in the combination meal and y be the number of chicken wings in the combination meal. We can write the first equation in the system by equating the total number of sliders and chicken wings in the combination meal with the sum of the number of sliders and the number of chicken wings. Since the combination meal has 10 sliders and chicken wings altogether, we can write the equation x + y = 10.

The second equation in the system can be written by equating the total number of calories in the combination meal with the sum of the number of calories in the sliders and the number of calories in the chicken wings. Since each slider has 225 calories and each chicken wing has 70 calories, the total number of calories in the sliders is 225x and the total number of calories in the chicken wings is 70y. And since the combination meal contains 1165 calories, we can write the equation 225x + 70y = 1165.

Therefore, the system of equations that could be used to determine the number of sliders and chicken wings in the combination meal is x + y = 10 and 225x + 70y = 1165.