What do you call the pairs of roots of quadratic
equation with complex solutions?
Math

Answer:

$ 30

$ 20

Step-by-step explanation:

Sea el costo fijo xy el costo por km sea y suponiendo que es el mismo para ambos taxis.

De la pregunta obtenemos las dos ecuaciones

\(x+8y=190\quad ...(i)\)

\(x+5y=130\quad ...(ii)\)

Aplicando \((i)-(ii)\)

\(8y-5y=190-130\\\Rightarrow 3y=60\\\Rightarrow y=\dfrac{60}{3}\\\Rightarrow y=20\)

Sustituyendo en \((ii)\)

\(x+5y=130\\\Rightarrow x+5\times 20=130\\\Rightarrow x=130-100\\\Rightarrow x=30\)

Entonces, el costo fijo es de $ 30 y el costo por km es de $ 20.

Let X be the number of fixed points of a random permutation of n elements. A fixed point is an element that remains in the same position after the permutation. Thus, the probability that an element is fixed is 1/n, and the probability that it is not fixed is (n-1)/n.

Using the linearity of the expected value, we can calculate the expected value of X as:

E(X) = E(X1 + X2 + ... + Xn) = E(X1) + E(X2) + ... + E(Xn)

where Xi is the indicator random variable that is equal to 1 if the i-th element is fixed and 0 otherwise. Since the probability of an element being fixed is 1/n, we have E(Xi) = 1/n. Therefore,

E(X) = n * (1/n) = 1

To find the variance of X, we need to compute E(X^2) - E(X)^2. We can use the fact that X^2 = X1 + X2 + ... + Xn, where Xi is the indicator random variable that is equal to 1 if the i-th and j-th elements are both fixed and 0 otherwise. Then,

E(X^2) = E(X1 + X2 + ... + Xn)^2 = E(X1^2 + X2^2 + ... + Xn^2) + 2 E(X1X2 + X1X3 + ... + X(n-1)n)

Since there is only one way to fix two elements out of n, we have E(XiXj) = 1/(n(n-1)). Therefore,

E(X^2) = n * (1/n) + n(n-1) * (1/(n(n-1))) = 1 + 1/n

Finally, the variance of X is

Var(X) = E(X^2) - E(X)^2 = 1 + 1/n - 1^2 = 1/n

Therefore, the variance of the number of fixed elements of a randomly selected permutation of n elements is 1/n.

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Answer: x = 20

Step-by-step explanation:

Step-by-step explanation:

the answer is in the above image

Answer:

\(-12^{2}\) + 9a - 5

Step-by-step explanation:

combine like terms :

-7\(a^{2}\) - 5\(a^{2}\) = -12\(a^{2}\)  

+3a - (-6a) = 9a    

-9 - (-4) = -5          

Using system of linear equations he will require 20kg of 15% copper and 30kg of 70% copper to produce an alloy of 48% in 50kg

The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables.

To solve this problem, we need to write a system of linear equations and find the equivalent amount of the metal required to make the desired amount of the alloy.

0.15x + 0.7y = 0.48(50) ..eq(i)

0.15x + 0.7y = 24 ...eq(i)

x + y = 50 ...eq(ii)

solving equation (i) and (ii)

x = 20, y = 30

He needs 20kg of 15% copper and 30kg of 70% copper to get 48% of 50kg of alloy.

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Answer:

\(\boxed{\pink{\tt \leadsto Sum \ of \ first \ five \ terms \ is \ 50 . }}\)

Step-by-step explanation:

Given that , the sum of the first nine terms of an arithmetic series is 162 and the sum of the first 12 terms is 288.

\(\boxed{\red{\bf \bigg\lgroup For \ answer \ refer \ to \ attachment \bigg\rgroup }}\)

• The sum of n terms of an AP is

\(\boxed{\orange{\sf S_n = \dfrac{n}{2}[2a+(n-1)d] }}\)

• nth term of an AP is given by ,

\(\boxed{\blue{\sf T_n = a+(n-1)d }}\)

The radical form of the given exponential form of a number 11x^(1/4) is written as ( 11 ) × \(\sqrt[4]{x}\).

As given in the question ,

Given exponential form is equal to :

11x^(1/4)

Using th formula to convert exponential form into radical form in standard form we have :

( y )^ ( a / b ) = \(\sqrt[b]{y^{a} }\)

Here y is equal to x

a is equal to 1

b is equal to 4

Substitute the value of the given expressions in the formula we have,

11x^(1/4)

= ( 11 ) ×  [x^(1/4) ]

= ( 11 ) × \(\sqrt[4]{x^{1} }\)

Any thing raise to one is the number or variable itself the required radical form is equal to:

=  ( 11 ) × \(\sqrt[4]{x}\)

Therefore, the radical form of the given expression 11x^(1/4) is given by :

( 11 ) × \(\sqrt[4]{x}\).

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Can you please show the triangle?

Step-by-step explanation:

let the amount that Krutika gets be x, therefore, gets him the amount that jim get will be x +40

therefore 3/1=x+40/x

hence 3x=x+40

therefore x=40/2

x=20

Step-by-step explanation:

let the amount that Krutika gets be x, therefore, gets him the amount that jim get will be x +40

therefore 3/1=x+40/x

hence 3x=x+40

therefore x=40/2

x=20

Answer:

Answer:

37.7 ft

Step-by-step explanation:

formula: C = πd

so circumference = π x 12 = 37.6991118

to nearest tenth = 37.7 ft

Please note this is if you take pi as π on the calculator. If it is simplified to 3.14 or 3.142, the answer will be slightly different.

Answer:

37.7

Step-by-step explanation:

C = d  x π

C = 12 x 3.14

C = 37.68

rounded to 37.7

Answer:

Step-by-step explanation:

A) 12x² y⁵z = 2² * 3 * x² * y⁵ * z

150x⁶y⁵z    = 5² * 2 * 3 * x⁶ * y⁵ * z

66y⁹z   =   2 * 3 * 11 * y⁹ * z

GCF =  2 * 3 * y⁵ * z = 6y⁵z

B) 4x² - 40x + 100 = (2x)² - 2 * 2x * 10 + 10²

                             = (2x - 10)²

C) 81x² - 64 = (9x)² - 8²             {a² - b² = (a + b)(a - b)}

                   = (9x + 8)(9x - 8)

D) (a + b)² = a²+ 2ab + b²

E) a² - b² = (a + b)(a - b)

Answer:

Simplifying 4x2y + 12xy2 + 9y3 Reorder the terms: 12xy2 + 4x2y + 9y3 Factor out the Greatest Common Factor (GCF), 'y'. y(12xy + 4x2 + 9y2) Factor a trinomial.

Step-by-step explanation:

Subtracting Perfect Squares · (a+b)(a-b)=a2-b · Example · 4x2-9= · Subtracting Perfect Cubes · a3-b3=(a-b)( · Adding Perfect Cubes · x3+27=(x+3)(x2-3x+9).

π/4 [2 + 1/5x] is the equation that expresses the cross-sectional area of the bar as a function of the position, x, along the length. The area of a circle is given by A=πr2.

Let us now consider a uniformly tapering circular bar having length,

L = 10 inches

and having diameter,

d₁ = 2 inches

at one end and

d₂ = 4 inches

at the other end, therefore we know that d₂ > d₁

let us consider a very short section xx of length kx and diameter dx, situated at a distance x from end A

now diameter, dx = d₁ + (d₂ - d₁)x

= d₁ + kx

where k = d₂ - d₁/ L

= 4-2/10 = 2/10 = 1/5

cross section area of the given circular bar 1

π/4 d₁²

π/4(d₁+Kx)

π/4 [2 + 1/5x]

here the cross section over 1x function of the given position of x, along the length.

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Answer:

R theta 1 = 20 x

R theta 2 = 11 x  - 6

R ( theta 1 + theta 2) = 31 x - 6     adding equations

R pi = 31 x - 6       since theta 1 + theta 2 = 180 deg

x = (R pi + 6)  / 31

This equation depends only R

If one lets R be one then   x = (pi + 6) / 31

This would give x = .29489 rad for the value of pi is deg

The numerical value of x appears to depend on the value of R

Answer:

y = x - 2

Step-by-step explanation:

points: (3, 1) and (0, -2)

slope = m = (-2 - 1)/(0 - 3) = 1

y-intercept = b = -2

y = x - 2

Answer:

True

Step-by-step explanation:

If a quadrilateral (with one set of parallel sides) is an isosceles trapezoid, its legs are congruent.

Answer:

the correct answer is true

Step-by-step explanation:

An isosceles trapezoid is a trapezoid with congruent legs.=true

hope this helps you!!!!!!!!!!

D__ is 7.5<x

C is x<10

Step-by-step explanation:

just do the inequality and graph

The Fourier transforms of the given functions can be expressed as mathematical equations involving the Fourier transform X of x.

The Fourier transforms of the given functions are as follows:

(a) y(t) = x(at - b)

  Y(f) = (1/|a|) X(f/a) * exp(-j2πfb)

(b) y(t) = ∫[0 to t] x(τ) dτ

  Y(f) = (1/j2πf) X(f) + (1/2)δ(f)

(c) y(t) = ∫[-∞ to t] x(τ) dτ

  Y(f) = X(f)/j2πf + (1/2)X(0)δ(f)

(d) y(t) = D(x * x)(t)

  Y(f) = (j2πf)²X(f)

(e) y(t) = t * x(2t - 1)

  Y(f) = j(1/4π²) d²X(f) / df² * (f/2 - 1/2δ(f/2))

(f) y(t) = e\(^(j2πt)\) * x(t - 1)

  Y(f) = X(f - 1 - j2πδ(f - 1))

(g) y(t) = (t * e\(^(-j5t)\) * x(t))*

  Y(f) = (1/2)[X(f + j5) - X(f - j5)]*

(h) y(t) = (Dx) * x₁(t), where x₁(t) = e\(^(-jt)\) * x(t)

  Y(f) = (j2πf - 1)X(f - 1)

Please note that these are the general forms of the Fourier transforms, and they may vary depending on the specific properties and constraints of the signals involved.

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As per the side splitter theorem, the segment length would complete the proportion is GJ

In math, the side splitter theorem states that "if a line is parallel to a side of a triangle and the line intersects the other two sides, then this line divides those two sides proportionally".

Here we have to find the segment length that would complete the proportion by using the side splitter theorem.

According to this theorem and by using the following diagram, we can elaborate the following proportion

=> GH/HE = GJ/JF

Here we have identifies that the segment that completes the proportion is GJ, because it must be used according to the theorem.

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The problem is to find two numbers that satisfy two conditions: their sum is 23, and their product is maximized. In other words, we need to determine two numbers that maximize their product while their sum remains constant.

To solve this problem, we can use algebraic reasoning. Let's assume the two numbers are x and y. We know that their sum is 23, so we have the equation x + y = 23. To maximize their product, we can express one variable in terms of the other. Solving the equation for y, we have y = 23 - x. Substituting this value of y in terms of x into the equation for the product, we get P = x(23 - x). This is a quadratic equation in terms of x. To find the maximum product, we can determine the vertex of the parabola represented by the quadratic equation. The x-coordinate of the vertex represents the value of x that maximizes the product. By solving for x, we can then find the corresponding value of y.

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42.827  seconds do passengers experience weightlessness on such a flight

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The height h (in feet) of a plane after t seconds in a parabolic flight path can be modeled by h=−11t²+700t+21,000.

The passengers experience a weightless environment when the height of the plane is greater than or equal to 30,800 feet.

h=30800

30800=−11t²+700t+21,000.

−11t²+700t+21,000-30800=0

−11t²+700t−9800=0

11t²-700t+9800=0

a=11

b=-700

c=9800

Apply in quadratic formula

t=-(-700)±√(-700)²-4.11.9800/2.11

t=350±70√3/11

t=350+70×1.73/11

t=42.827

Hence, 42.827  seconds do passengers experience weightlessness on such a flight

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Answer:

114 sq ft

Step-by-step explanation:

Find out the area of the end triangle;

2x3=6

6x0.5 (1/2) = 12

Find the perimeter of the end triangle;

3+3+3=9

Find the area of the rectangle;

9x10=90

Find the total surface area;

2x12=24

24+90=114 sq ft

Answer:

3

Step-by-step explanation:

the surface area is the base

you will know what the base is based on the name

since it's a triangular prism, the base is a triangle

the triangle in the picture is 2 in hight and and 3 on the ground

2 x 3/2

6/2

3

Answer:

d(5) = 5

Step-by-step explanation:

The nth term is given by :

\(d(n)=\dfrac{5}{16}\times 2^{n-1}\) ...(1)

We need to find the 5th term of the above sequence. For this, put n = 5 in the above formula.

\(d(5)=\dfrac{5}{16}\times 2^{5-1}\\\\=\dfrac{5}{16}\times 2^4\\\\=\dfrac{5}{16}\times 16\\\\=5\)

So, the 5th term in the above sequence is 5.

Answer:

5

Step-by-step explanation

The dimensions of the field should be 125m by 100m to enclose the maximum area.

To solve this problem, we can use the fact that the area of a rectangle is given by A = lw, where l and w are the length and width of the rectangle, respectively. Since the field is to be subdivided into four congruent plots, we can express the width in terms of the length as w = (1/4)(l).

We can then use the fact that the total length of fencing available is 6000m to set up an equation for the perimeter of the rectangle, which is given by P = 2l + 5w. Substituting w with (1/4)(l), we get P = 2l + 5((1/4)(l)) = (9/2)l.

Solving for l in terms of P, we get l = (2/9)P. Substituting this expression for l into the equation for the area, we get A = (1/4)(l)(w) = (1/4)(l)((1/4)(l)) = (1/16)l^2.

We can now express the area in terms of P as A = (1/16)((2/9)P)^2 = (4/81)(P^2). To find the maximum area, we can take the derivative of A with respect to P and set it equal to zero, which gives dA/dP = (8/81)P = 0. This implies that P = 0 or P = 81/8. Since P cannot be zero, we have P = 81/8.

Substituting this value of P back into the equation for l, we get l = (2/9)(81/8) = 18.75. Finally, substituting l and w = (1/4)(l) into the equation for A, we get A = (1/16)(18.75)(4.6875) = 117.1875. Therefore, the dimensions of the field should be 125m by 100m to enclose the maximum area.

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In the expression, the values are:

a) k = 2.4

b) c = -141.0625

We have the expression:

a√(b² − c) = 5k

a)For the value of ‘k’ when a = 3, b = 6 and c = 20, we have:

a√(b² − c) = 5k

3√(6² − 20) = 5k             (solve for k)

3√(36 − 20) = 5k

3√(16) = 5k  

3*4 = 5k  

12 = 5k

k = 12/5

k = 2.4

b) For the value of ‘c’ when a = 4, b = 7 and k = 11, we have:

a√(b² − c) = 5k

4√(7² − c) = 5*11          (solve for c)

4√(49 − c) = 55

√(49 − c) = 55/4

√(49 − c) = 13.75

49 − c = 13.75²

49 - c = 189.0625

c = 49 - 189.0625

c = -141.0625

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Answer:

Step-by-step explanation:

Factors of 36 = 1 2 3 4 6 9 12 18 36

the Prime Factors of 36 are: 2, 2, 3, 3.

This is the answer

Answer:

36 = 2*2*3*3

or

2^2 * 3^2

Step-by-step explanation:

Break 36 into prime factors

36 = 6*6  

Since 6 isn't a prime number, factor 6

36 = 2*3   * 2*3

2 and 3 are prime numbers

In order from smallest to largest

36 = 2*2*3*3

or as exponents

36 = 2^2 * 3^2

Answer:

b = 10

b = 17

Step-by-step explanation:

Hello!

Usually, when you want two different integer solutions, you probably want the quadratic to be factorable.

So what we want to know is that b should be the sum of the factors in 16.

Factors of 16: 1, 2, 4, 8, 16

Factor pairs:

Factor Sums:

These are our possible b-values.

Check:

Let's try 17 first:

Now 10:

And finally, 8:

Since x = 4 is a repetitive integer, we cannot use 8 as a value for b.

The answers are b = 10, and b = 17.

Answer:

Step-by-step explanation:

\(A=P(1+r/4)^{(4t)}\\ \\ A=P(1+.02/4)^{(4t)}\\ \\ A=59000(1.005)^{4(20)}\\ \\ A=\$ 87929.98\)

Answer:

4.2 gallons

67.2 cups

Step-by-step explanation:

He had 3 gallons of punch.

He added another 1.2 gallons.

The number of gallons of punch he has now is:

3 + 1.2 = 4.2 gallons

1 gallon = 16 cups

=> 4.2 gallons = 4.2 * 16 = 67.2 cups

He has 67.2 cups

The value of the vector VU is <44, 40>

Vector:

in math vector consist an object that has both a magnitude and a direction.

Given:-

Here we have the vector v and u with the value of v = <11, 5> and the value of u = <4, 8>.

Now, we have to find the value of VU.

In order to find the value of VU, we have to perform the multiplication operation on the given vector,

In order to perform the multiplication on it, we have to arrange them in the following order,

=> VU = <11, 5> x <4,8>

Now, we have to combine the values like the following,

=> <(11 x 4) , (5 x 8)>

Now, do the multiplication then we get,

=> <44, 40>

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