If α and β are the zero of the quadratic polynomial p(x)=4x 2 −5x−1, find the value of α 2 ββ2 α

Answer:

x + 5 = 8

Step-by-step explanation:

x + 5 = 8

Subtract 5 from both sides.

x + 5 - 5 = 8 - 3

x = 3

Answer: x+5=8

Step-by-step explanation:

The similarity between solving a compound inequality in a compact form and solving a simple inequality is that the same basic ways of resolving an algebra are followed in both cases. The difference is that any manipulation on one side of the equation must be repeated on all three sides of the compound inequality.

The similarity between solving a compound inequality and a simple one is that they both follow the same basic principles of solving an algebra.

However, there is a slight difference because any change that is applied in one part of the expression must be spread to other parts of the expression.  If we are dividing or multiplying in compound inequalities, the same must apply to all sides.

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The given system is :

a) Linear

b) Time-invariant

c) Casual

d) Impulse response function is h(n) = 2δ(n-1) + δ(n-2).

a) Linear: A system is considered linear if it satisfies the superposition principle, meaning that if the inputs x1(n) and x2(n) produce outputs y1(n) and y2(n), respectively, then the output of the system to a weighted sum of inputs is equal to the weighted sum of the outputs. In this system, 2x(n-1) and x(2n) are both linear operations, and the sum of two linear operations is also a linear operation. Therefore, this system is linear.

b) Time-invariant: A system is considered time-invariant if the output is not dependent on the current time, but only on the input and its previous values. In this system, the coefficients 2 and 1 do not change with time, and the system does not depend on the current time. Therefore, this system is time-invariant.

c) Causal: A system is considered causal if the output only depends on the present and past inputs, and not on future inputs. In this system, x(2n) only depends on the past and present inputs, and x(n-1) only depends on past inputs. Therefore, this system is causal.

d) Impulse response function: The impulse response function of the system can be found by taking the unit impulse as the input, solving for the output and normalizing it.

h(n) = 2δ(n-1) + δ(n-2)

where δ(n) is the unit impulse function and h(n) is the impulse response function of the system.

Correct Question :

y(n) = 2x(n-1) + x(2n). is the system linear or non-linear? you need to justify your answer. b) is the system time-varying or time-invariant? you need to justify your answer. c) is the system causal or not causal? you need to justify your answer. d) find the impulse response function of the system

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Answer: Keith on top, Patricia below Keith, Jim below Patricia, and Sara at the bottom.

The domain of function is ( 2 , -4 ) and range of function is ( 4 , -8 ) . The term "range" refers to the set of numbers that the function assumes.

The term "parameters" refers to the set of values that can be entered into the domain of a function. This collection (x) contains the x values for a function like f. The term "range" refers to the set of numbers that the function assumes.

The collection of all y-coordinates with values of 2, 3, and so on is called the range. There are two parts to functions: their range and their domain. A function's domain is the collection of all its input values, while its range is its potential output.

A domain function is range. If f is a function: There is a state known as A B in which each element in A is mapped to one in B. A is the domain, and B is the co-domain. The set of photos is the range of the function if (a,b) R, and then "b" provides the image of element "a" within relation "R."

The following are the domain and range of a function in this general notation: Range(f) = f(x) and domain(f) = x R: domain(x) (f). The domain and range of this function are denoted by D = x N and R = (y): y and x are the same.

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The integral of the magnitude of a given vector is 0.

What is vector ?

Vector can be defined as the object  in which it has both magnitude and direction.

Given

vector ,  V=4t i-6t j

we have to find the Integral of the magnitude over the bounds [-2,2]

So, Lets integrate the given vector

we get,

-[tex]\int\limits^2_2 { v dt } \, dx[/tex]    =

|v| =   √4t^2 + (-6t)^2

=  √16t^2 + 36t^2

= √52t^2

=  2√13 t

-[tex]\int\limits^2_2 {2\sqrt{13}t } \, dt[/tex]  =   2√13 t^2 / 2

when we integrate t , we get t = t^2 / 2

= √13 t^2  

=√13 (2^2 - (-2)^2 )

=√13 (4 - 4 )

= 0

Hence, The integral of the magnitude of a given vector is 0.

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Answer:

h = 11cm

Step-by-step explanation:

Rectangular pyramid formula:

[tex] \frac{lwh}{3} [/tex]

therefore

[tex]\frac{7 \times 9 \times h}{3} = 231[/tex]

simplify 7x9=63, then multiply the equation by 3

[tex]63h = 693[/tex]

now divide by 63

[tex]h = 11cm[/tex]

h=11cm

The perimeter of a 500-square-foot square is roughly 89.44 feet.

To calculate the perimeter, we must assume the room is square. We take the square root of the area to calculate the length of one side of a square:

√500 = 22.36 feet

As a result, each side of the square is roughly 22.36 feet long. 

To get the perimeter, multiply the length by four: 

22.36 feet × 4 = 89.44 feet.

This dimension is critical for establishing the quantity of baseboard and flooring required. To make the computation procedure easier, round the measurements to the closest foot. Cindy will be able to evaluate the cost and make an informed buying decision with the aid of this information.

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The question is -

Solve the following multiplying polynomials question: Cindy wants to buy flooring and baseboards for her office. She needs to know how much to buy. What is the perimeter of 500 square feet?

Workers in an office of 40 staff were asked their favourite type of take- away.1/9 bit of a person is one degree.

What's Fraction?

An element of a total is a bit. The number is represented mathematically as a quotient, where the numerator and denominator are resolve. Both are integers in a simple bit. A bit appears in the numerator or denominator of a complex bit. The numerator of a proper bit is lower than the denominator.

The magnitude of an angle is measured using a unit of dimension. In magnitude, 1 degree is original to1/360 of a full gyration.

Degree 1 – direct.

Degree 2 – quadratic.

Degree 3 – boxy.

Degree 4 – quartic( or, if all terms have indeed degree, biquadratic)

Given that;

total workers = 40

Bit of a person = 1 degree

we know that 360 ° = 40 person

so for 1 degree = 40/360 = 1/9

Hence,1/9 bit of a person is one degree.

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Answer:

24

Step-by-step explanation:

12*8*5 =480 current surface

double = 960

so make the 12 into 24 height.

done

The initial height of the ball is the y-intercept of the function. The initial height she threw the ball from was 35.

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient, and 'c' is called the absolute term of f (x).

The function is as follows:

h(x) = -16x² + 3x + 35

Substitute the value of x = 0.

So, we have:

h(0) = -16(0)² + 3(0) + 35

Evaluate the exponent

h(0) = -16(0) + 3(0) + 35

Evaluate the products

h(0) = 0 + 0 + 35

Evaluate the sum

h(0) = 35

Hence, the initial height she threw the ball from was 35.

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The final number is 176

Suppose a number is 'a'

Suppose another number is 'b'

We want to know how much percent of 'b' is 'a'.

Then, it is calculated as:

[tex]\dfrac{a}{b} \times 100[/tex]

(in percentage)

7.Given;

Original price = $275

Resell price = $660

660-275=385

Percent markup= 385*100/275

=140%

9.Given;

The number 200 is increased by 20%

The result is then decreased by 20%

So, 20% increase of 200= 220

Now,20% less of 220=220-44

=176

Therefore, 20 percent decreased number will be 176

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A graph of the solution of this inequality w ≤ 200 is shown in the image attached below.

In this exercise, we would solve the given inequality by making w the subject of formula as follows;

w/-10 ≤ -20

By multiplying both sides of the inequality by -10, we have the following:

-10 × w/-10 ≤ -20 × -10

w ≤ 200

Next, we would use an online graphing calculator to plot the inequality as shown in the graph attached below. Additionally, the circle on the number line (graph) is closed because of the less than or equal to (≤) symbol.

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The quotient of the expression 76 ÷ 6 is, 4

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

⇒ 76 ÷ 6

Now, By using division calculation, we get;

   | 10     | 2   |

   |         |       |  4

6  | 60   | 16   |

   _________

Thus, We get;

The quotient of the expression 76 ÷ 6 is, 4

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Answer:

The slope of the line is -2.

Step-by-step explanation:

Rise/Run

you have 2 points on the graph since this is a negative slope you start on the top point

you count straight down up to your next point and you should get 8.

then you count to the right to your next point and should get 4.

that would give you 8/4 as your slope.

8/4 simplified is 2.

The slope is 2

By Interception of a point f(x) = 3.75b + 25 and this we get the Value 3.75.

Examples :

f(x) = 3.75b + 25

Axis interception points of 3.75b + 25:

X intercepts:(-20 / 3,0),

Y intercepts : (0.25)

Slope of 3.75b + 25: 3.75.

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Answer: Undefined

Step-by-step explanation:

[tex]\displaystyle\\x=-3\ \ \ \ \Rightarrow\\\\f(x)=\frac{3x+9}{x^3+4x^2+x-6} \\\\\\f(-3)=\frac{3(-3)+9}{(-3)^3+4(-3)^2+(-3)-6}\\\\\\f(-3)=\frac{-9+9}{-27+4(9)-3-6} \\\\\\f(-3)=\frac{0}{-36+36} \\\\\\f(-3)=\frac{0}{0}\\\\\\\\[/tex]

f(x) = 4800 * 1.5^x is the equation to model the relationship between the number of weeks, x, and the number of site visits.

It is said that the number of visits increased by a factor of 1.5 each week, which means it multiplied by 1.5 every week.

So the equation can be modeled as:

f(x) = 4800 * 1.5^x

Where x is the number of weeks and f(x) is the number of site visits.

Note that this equation is only valid for the number of weeks after the new marketing plan has been launched, since before that the number of visits was 4,800.

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Within his budget, he can still purchase 6 tickets. The inequality is 40 < 5x + 10.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

In light of the query

With his $40, Jamal may get tickets for himself, his friends, and a show.

If he spends $10 to join a membership,

Money remaining = $40 - $10 = $30

Now he may purchase the ticket at $5 apiece.

Now, tickets that he may purchase while staying within his budget found using utilizing the unitary technique.

Tickets= $30 / $5

Tickets = 6

As a result, he may purchase the remaining 6 tickets for his budget.

A:

Number of tickets = x

Hence, the inequality is 40 < 5x + 10.

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Answer:

1/16 gallons per minute

Step-by-step explanation:

The water level drops from 8 gallons to 6 gallons in 32 minutes

The volume of water that has leaked is 8 - 6 = 2 gallons

Since this volume of water has leaked in 32 minutes, rate of leak

+ 2/32 = 1/16 gallons per minute

Answer:

x [tex]\geq[/tex] -2

Step-by-step explanation:

The domain is all the possible numbers that x can be.

(4, 7) is a solution to the system, will their hair ever be the same length.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

The equation represents length y of Ben and Jada's hair in inches after x months.

And we have equations,

Ben : y = 3/4(x) + 4

Jada : y = 1/4(x) + 6.

Substituting the values of ordered pair,

when x = 0 then y = 0

we get,

Ben : y =  4

Jada : y = 6.

But not equals to y = 0.

When x = 4 then y = 8

we get,

Ben : y =  7

Jada : y = 7.

But not equals to y = 8.

When x = 4 then y = 7

we get,

Ben : y =  7

Jada : y = 7.

This is required solution.

Therefore, (4,7) is a solution.

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The equation of line is calculated and the value of y = 2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line QR be represented as A

Let the equation of line ST be represented as B

Now , the lines QR is perpendicular to the line ST

And , the product of slopes of lines will be -1

Now , the coordinates of point Q ( 1 , -5 )

The coordinates of point R is R ( 4 , -6 )

The slope of the line QR m₁ = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope m₁ = ( -6 - ( -5 ) ) / ( 4 - 1 )

Slope m₁ = -1/3

Now , the coordinates of point S ( -6 , 5 )

The coordinates of point T is T ( -7 , y )

The slope of the line ST m₂ = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope m₂ = ( y - 5 ) / ( -7 - ( - 6 ) )

Slope m₂ = ( y - 5 ) / -1

Slope m₂ = ( 5 - y )

Now , the product of slopes = -1

m₁ x m₂ = -1

Substituting the values in the equation , we get

( -1/3 ) x ( 5 - y ) = -1

On simplifying the equation , we get

Multiply by 3 on both sides of the equation , we get

- ( 5 - y ) = -3

Multiply by -1 on both sides of the equation , we get

5 - y = 3

Adding y on both sides of the equation , we get

y + 3 = 5

Subtracting 3 on both sides of the equation , we get

y = 2

Hence , the value of y is 2

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The entropy produced by the heat source is 2.17 J/K per hour.

In order to calculate the amount of entropy produced by a heat source, we need to use the formula for entropy change: ΔS = Q/T,

where Q is the amount of heat transferred and T is the temperature of the surroundings in kelvins.

To convert the temperature to Kelvin, we add 273.15 to the temperature in degrees Celsius.

In this case, the heat source generates 70.0 W of heat and the temperature of the surroundings is 28.5 °C.

So, to find the entropy change per hour, we need to multiply the power generated by the time:

ΔS = (70.0 W) * (3600 s/h) / (28.5+273.15)

This calculation results in approximately 2.17 J/K * h or 2.17 J/K per hour.

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The measure of the missing length in the figure, found using Pythagorean Theorem is; x = 37 mm

Pythagorean Theorem states the relationship between the lengths of the sides of a right triangle. According to Pythagorean Theorem, the sum of the squares of the leg lengths of a right triangle is equivalent to the square of the length of the hypotenuse side.

Please find attached a possible figure in the question, obtained from a similar question posted on the website.

The 13 mm side hypotenuse length of the right triangle on the left  indicates a other leg length of the right triangle can be found using Pythagorean Theorem as follows;

Square of the length of the hypotenuse side = Sum of the square of the length of the other two sides

13² = 5² + (second leg length)²

The second leg length of the right triangle on the left = √(13² - 5²) = 12

The 12 mm leg length of the right triangle on the left indicates that the leg length of the right triangle on the right which correspond with the 12 mm leg length on the left is 12 mm

The length of the hypotenuse of the right triangle on the right, which is the missing length, x is therefore;

x² = 12² + 35² = 1369

The measure of the missing length x is therefore;

x = √(1369) = 37

The missing length in the figure is; x = 37 mm

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The total area of the pyramid is (24√3 + 72) square units or 113.57 square units.

A hexagonal pyramid is a 3D design in which the base is hexagonal and the faces or sides are isosceles triangles, which come together to form the hexagonal pyramid at the summit of the pyramid. A hexagonal pyramid has six sides on the base and six isosceles triangles on the sides.

Given a hexagonal pyramid,

base length = 4

slant height = 6

area of pyramid = sum of the area of the base to the lateral area

area of pyramid = A(base) + A(lateral)

Area of base = 3√3/2*(a²)

a = base length = 4

Area of base = 3√3/2*(4²)

Area of base = 24√3 square units

now lateral area or area of triangular faces,

lateral area = 6*1/2*b*h

h = height of triangle = 6

b = base of triangle = 4

lateral area = 6*1/2*4*6

lateral area = 72 square units

total area =  A(base) + A(lateral)

total area = (24√3 + 72) square units

Total area = 113.57 square units.

Hence the area of the pyramid is (24√3 + 72) square units or 113.57 square units.

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The equation of the parabola with the given vertex and y-intercept is:

y = -(x - 3)² + 3

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

Where (h, k) is the vertex of the parabola, and a is a nonzero constant. To find the equation of the parabola that satisfies the given conditions, we can use the vertex and the y-intercept to find the values of a, h, and k.

The vertex of the parabola is (3, 3), so h = 3 and k = 3. The y-intercept of the parabola is (0, -6), which means that when x = 0, y = -6. Substituting these values into the equation of the parabola, we get:

y = a(x - 3)² + 3

When x = 0, y = -6. Plugging in the value of x and y, we get

-6 = a(0 - 3)² + 3

-6 = 9a + 3

-9 = 9a

a = -1

Therefore, the equation of the parabola that satisfies the given conditions is:

y = -(x - 3)² + 3

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