Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Simplify the complex numbers using de Moivre's Theorem and match them with their solutions 2(3+1) 2. cos(20°) + sin(20°)] 2[ coo(4)+isin(7)]* (-1+i) -41 (1+1) -16 4+4731 Reset Next

The nature of roots of quadratic equation 5x² = 4x - 1 is imaginary roots.

The standard form of a quadratic equation is:

ax² + bx + c = 0

The discriminant is defined as:

D = b² - 4ac

Using  the value of discriminant, we can determine the nature of roots of a quadratic equation.

If:

D > 0, the quadratic equation has two distinct real roots or the roots are real and distinct.

D = 0, the quadratic equation has 1 real equal roots or the roots are unique

D < 0, the quadratic equation has complex conjugate roots or the roots are imaginary.

In this case, the quadratic equation is:

5x² = 4x - 1

transform it into the standard form:

5x² - 4x + 1 = 0

Calculate the discriminant:

D = (-4)²  - 4 (5)(1)

  = 16 - 20 = -4

Since D < 0, the roots are imaginary.

Your question is incomplete, but most probably your question was:

What is the nature of roots of quadratic equation 5x² = 4x - 1?

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Answer: To find the total cost of the candy including the sales tax, we first need to calculate the amount of tax by multiplying the cost of the candy by the tax rate.

The cost of the candy is 10.00.

The tax rate is 5%, which can be written as 0.05.

The total cost of the candy would be

10 + (10*0.05) = 10+0.5 = 10.50

So the correct answer is $10.50.

Step-by-step explanation:

Answer:

64(ab÷c²)

step by step:

(when you multiply two similar bases you can add their exponents but when dividing similar bases you subtract their exponents)

for example

a³x a= a⁴

a²÷ a= a²-¹= a

so

4a³x 16a⁰b¹÷ 1ac²=

64a³b÷ac²

64a²b/c²

The number of hours that the team trians per week is 17 hours.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since the the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. The number of hours will be:

( 1 1/4 + 1/2 + 2 1/2) × 4

= 4.25 × 4

= 17 hours.

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Answer: 125

Step-by-step explanation:

The first term is 1³. The second term is 2³. The third term is 3³. And the Fourth term is 4³.

So the pattern is n term = n³

plug in 5

= 5³

= 125

-7 is the opposite of 7.

Simply adding a negative sign yields the negative number 7, which is the opposite of the positive number 7. 7 and 7 are the opposites of one another since they are both seven units apart from 0 on the number line.

The inverse of a number is the number on the other side of the 0 number line and at the same distance from 0. Oppositely positioned numbers on the number line. The opposite of an integer is its additive inverse. As a result, on a number line, the opposite of a number is the number that is located in the other direction from 0 but at the same distance from it.

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The measure of the exterior angle for Object 1 - a decagon is 36°, while th measure of the exterior angle for Object 2  - a dodecagon is 30°.

n object with 12 sides is called a dodecagon while an object with 10 sides is called a decagon.

Note that the exterior angles of all shapes, regular or irregular is 360°. In this case, the shapes are regular, which means that the sides are equal, hence their angles will be equal.

To derive the exterior angle of a regular geometric shape, the formula is given as:

Exterior angle measure = 360 / number of sides

Hence for A (the decagon), we have:

EAM = 360/10

= 36°

For B (the dodecagon) we have:

EAM = 360/12

= 30°

Thus the exterior angle for both shapes are 36° and 30° respectively.

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The margin of error is $148.89. The upper limit is $2215 and lower limit is $1914.

In statistics, confidence is another word for probability. If you create a confidence interval, for instance, with a 95% level of confidence, you can be sure that 95 out of 100 times, the estimate will fall between the upper and lower values indicated by the confidence interval.

First we need to name some of the variables we are given:

n = 38 the sample size

x = 6.88 the sample mean

= 1.86 the population standard deviation

We need to find a 90% confidence interval for the mean price per 100 lbs of watermelon:

= 1-.90 = .10

/2 = .05

z(/2) = -1.64

-z(/2) = 1.64

This can give us a probability expression:

P(-1.645 < z < 1.645) = .90

The margin of error is calculated with the formula: E = z(/2)(/√n)

E = 1.645(1.86/√38) = $.4963(300) = $148.89  

Then to calculate the upper and lower limit we add and subtract E from x:

lower limit = 6.88 - .4963 = $7.38(300) = $2214

upper limit = 6.88 + .4963 = $6.38(300) = $1914

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Answer: Spent $120 originally, profited by $36

Step-by-step explanation:

The total cost Stefan earned from selling the helmet and the bicycle is $139 + $17 = $156.

130% can be rewritten as [tex]\frac{130}{100}[/tex] which is simplified to 1.3.

Set up and this equation to find 130% of this price.

[tex]1.3x = 156\\x = 120[/tex]

Stefan spent $120 on these items.

Subtract this value from the selling price and solve.

[tex]156-120 = 36[/tex]

Stefan made $36 from selling the helmet and bicycle.

Therefore , the solution of the given problem of expression comes out to be 794.0481.

combinations of numbers, symbols, and operations (such + and) that show how much something is worth. Examples: • 2 + 3 is the formula.

• 3 x/2 variable  is another formula.There is no equals sign in the expression. A mathematical expression is a sentence made up of variables, numbers, or both. There is never an equal symbol in an expression. These expressions are examples. An equation is a mathematical statement proving the equality of two expressions.

Here,

Given : 5 + [tex](5.3)^{4}[/tex]

=> 5 + (5.3)*(5.3)*(5.3)*(5.3)

=> 789.0481 + 5

=> 794.0481

Therefore , the solution of the given problem of expression comes out to be 794.0481.

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Answer:

3.6 miles

Step-by-step explanation:

Given information from the question,

[tex]\frac{1}{6} \ hour = \frac{3}{5} \ miles\\ 1 \ hour = \frac{3}{5} / \frac{1}{6} \ miles\\1 \ hour = \frac{18}{5} \ or\ 3\frac{3}{5} \ or \ 3.6 miles[/tex]

Answer:

Velocity is the term to illustrate speed

Step-by-step explanation:

velocity = distance ÷ time

velocity = 3/5 ÷ 1/6

= 18/5 m/h

Answer:

17 + x + 3 + 17

X is 3

Therefore , the solution of the given problem of circle comes out to be PQ length is 20.5 units.

A moving point on a plane is followed so that its distance from a specific point remains constant to produce the circular form known as a circle. The English term circle derives from the Greek word kirkos, which meaning hoop or ring. Area of circle= πr²

Here,

For each secant, the sum of the lengths from R to the circle's intersection points is the same:

=>RS*RT = RQ*RP

=>40(40 +31) = (44)(PQ +44)

=>40(71)/44 = PQ +44

=>PQ = 2840/44 -44 = 64 6/11 -44 = 20 6/11

=>PQ ≈ 20.5

Therefore , the solution of the given problem of circle comes out to be PQ length is 20.5 units.

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The equation of the line passing through (3, 6) and (6, 0) is 2x + y = 12

An equation shows how two or more numbers and variables are related to each other.

The standard linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

The line passes through (3, 6) and (6, 0). Hence:

y - 6 = [(0 - 6)/(6 - 3)](x - 3)

y - 6 = -2(x - 3)

y = -2x + 12

2x + y = 12

The equation of the line is 2x + y = 12

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FG stands for Function Generator, which is a device that produces electrical signals with a function of frequencies and amplitudes. It is commonly used in scientific laboratories to generate signals for testing and research purposes.

A function generator is an electrical device used to generate electrical signals with a range of frequencies and amplitudes. It is commonly used in scientific laboratories to generate test signals for testing and research purposes. Function generators typically consist of an oscillator, amplifier, and waveform selector. The oscillator generates a signal of a given frequency and amplitude, while the amplifier adjusts the output voltage. The waveform selector allows the user to choose from a variety of waveforms, such as sine, square, triangle, and sawtooth. Function generators can be used to simulate various types of electrical signals, such as AC and DC signals, as well as a variety of noise signals. They are also used to test various types of electronic components, such as transistors and capacitors, and to conduct research in fields such as telecommunications and signal processing. The acronym FG stands for Function Generator.

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The value of p is 12.322

In mathematics, the logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as: For x > 0 , a > 0, and a ≠1, y= logₐ x if and only if x = a^y Then the function is given by f(x) = logₐ x The base of the logarithm is a. This can be read it as log base a of x.

Given here p=-log(2.1×10¹²)

                  p= - ( log(2.1) +12 log10)

                  p= -(0.322+12)

                  p=12.322

Hence, the value of p is 12.322

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Real value numbers are both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc are all real numbers.

The real number that consist of different types of numbers for example prime numbers, odd numbers, even numbers, rational numbers, whole numbers, etc. These numbers can be expressed in the form of figures.Any number that we can think except complex numbers is a real number.

Real numbers encompass three classifications of numbers.Whole numbers, rational numbers, and irrational numbers are all real numbers.Even counting and natural number are all real numbers.

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Answer:

[tex]\frac{2t-4}{3}[/tex]

Step-by-step explanation:

[tex]\frac{2}{3}[/tex][tex](t-2)\\[/tex]
=> [tex](\frac{2}{3} * t ) + (\frac{2}{3} * -2)[/tex]
=> [tex]\frac{2t}{3} + (-\frac{4}{3})[/tex]
=> [tex]\frac{2t-4}{3}[/tex]

Hope you understood!!

Answer:

17%

Step-by-step explanation:

Firstly, we can establish that the tip is a percentage of the bill, excluding tips. This means that the $75.29 would be 100%, thus to find the percentage of tip received, we would take
$12.80/$75.29 × 100 = 17%

0.167 or 0.17 rounded to the nearest hundredth.

How do you round off decimal to the nearest hundredth?

When rounding to the nearest hundredth, you want to look at the third decimal place, the one to the right of the hundredth place. If the value in the third decimal place is less than 5, you truncate everything to the right of the hundredth place, leaving the number unchanged.

If the value in the third decimal place is greater than or equal to 5, you add one to the number in the hundredth place.

The total area of the rectangle is 15*5 = 75 square feet.

The area of the triangle inside the rectangle is (1/2)25 = 12.5 square feet.

The shaded region is the area of the triangle, so the probability that a randomly chosen point lies inside the shaded region is

12.5/75 = 0.167 or 0.17 rounded to the nearest hundredth.

Hence, 0.167 or 0.17 is rounded to the nearest hundredth.

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Answer:

m = 2

Step-by-step explanation:

Slope = rise / run or (y2 - y1) / ( x2 - x1)

Let's pick 2 points (0,0) (1,2)

We see the y increase by 2 and the x increase by 1, so the slope is

m = 2

The slope of the straight line connecting the break's ends to the function's diagram.

For 0 < x < 4 will be -60

For 4 < x < 8 will be -31

The mathematical formula f (x) = [tex]$$a^{x[/tex] denotes an exponential function. a constant known as the function's base and a variable called x are present. The transcendental number e, roughly equivalent to 2.71828, is the most frequent exponential-function base.

When a positive constant other than 1 is raised to a variable exponent, the function is said to be exponential. Solving at a certain input value yields the evaluation of a function. If you know the growth rate and the starting point, you can find an exponential model.

We have to use the knowledge of functions to describe the average rates of each one of them, so:

For 0 < x < 4 will be -60

For 4 < x < 8 will be -31

It is a measurement of how much the function changed for one person on average throughout that interval. It results from the slope of the straight line connecting the break's ends to the function's diagram.

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The comparison operator "≥" in logic means that the number is either greater than or equal to a number , the greater than equal to symbol is used to describe the relationship between two terms .

What is a Comparison Operator ?

The Comparison operator in logic is used to compare logic statements ,such as [tex]a > b[/tex] or [tex]a < b[/tex] , by using a , b as variables, the operator compares their values, returns true and false.

The Comparison Operator "≥" , in logic is read as " greater than equal to" , For Example : if the statement is [tex]a \geq b[/tex] , then if the variable is greater than or equal to b , then the operator will return TRUE and if not then it will return FALSE .

The given question is incomplete , the complete question is

What does the comparison  operator "≥"(greater than equal to) mean in logic ?

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Answer:

Step-by-step explanation:

Converting 0.632 to a fraction, Step-by-Step

Step 1:

The first step to converting 0.632 to a fraction is to re-write 0.632 in the form p/q where p and q are both positive integers. To start with, 0.632 can be written as simply 0.632/1 to technically be written as a fraction.

Step 2:

Next, we will count the number of fractional digits after the decimal point in 0.632, which in this case is 3. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 0.632/1 each by 10 to the power of that many digits. For instance, for 0.45, there are 2 fractional digits so we would multiply by 100; or for 0.324, since there are 3 fractional digits, we would multiply by 1000. So, in this case, we will multiply the numerator and denominator of 0.632/1 each by 1000:

\frac{0.632 × 1000}{1 × 1000} = \frac{632}{1000}

1×1000

0.632×1000

​

=

1000

632

​

Step 3:

Now the last step is to simplify the fraction (if possible) by finding similar factors and cancelling them out, which leads to the following answer:

\frac{632}{1000} = \frac{79}{125}

1000

632

​

=

125

79

​

Answer:

x=3 y=1

Step-by-step explanation:

-2/3x+3=2x-5

x=3

y=-2/3(3)+3

y=1

y=2(3)-5

y=1

The values of x and y, given the angles in the diagram, can be found to be :

The angles given above are called vertical angles and they are such that the two corresponding angles are equal to each other.

This means that ( 8 x + 7 ) ° is equal to ( 9 x - 4 )° and 5 y° is equal to  ( 7y - 34 )°.

The value of x is :

8 x + 7 = 9 x - 4

9x - 8x = 7 + 4

x = 11

The value of y is :

5 y = 7y - 34

7y - 5y = 34

2 y = 34

y = 34 / 2

y = 17

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[tex]2x = 25-3x[/tex]

Simplify:

[tex]2x=-3x+25[/tex]

Add 3x to both sides:

[tex]2x+3x=-3x+25+3x[/tex]

[tex]5x=25[/tex]

Divide both sides by 5:

[tex]\dfrac{5x}{5} =\dfrac{25}{5}[/tex]

[tex]\fbox{x = 5}[/tex]