question 1 a number increases by 10%, and then decreases by 10%. will the result be greater than, less than, or equal to the original number

A) One of the factors of the given function would be (x + 2).

B) The factored form of the function would be f(x) = (x+2)(x+1)(x-1).

C) The zeroes are -2, -1, and 1.

What is the cubic function?

A cubic function is a type of polynomial function with the highest degree of 3, meaning the highest power of the variable in the equation is 3. The general form of a cubic function is f(x) = ax³ + bx² + cx + d, where a, b, c, and d are real numbers and a is not equal to 0.

The given function f(x) = x³ + 9x² + 14x - 24
x     -2       -1       0      1       2
f(x)  -24     -30   -24   0     48

A) One factor of f(x) without using a calculator is (x+2) because, when x = -2, f(-2) = (-2)³ + 9(-2)² + 14(-2) - 24 = -24 and it's the same result as the table of values.

B) To completely factor f(x) without using a calculator we can use the rational root theorem. The rational root theorem states that if a polynomial function has rational roots, they must be of the form a/b, where a is a factor of the constant term (in this case -24) and b is a factor of the leading coefficient (in this case 1).

The factors of -24 are: -24, -12, -8, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6, 8, 12, 24

The factors of 1 are: 1,-1

So, using the rational root theorem, we can test the values of x that are in the form of a/b where a is a factor of -24 and b is a factor of 1.

By testing x=-2, x=-1, x=1, we find that f(x) = (x+2)(x+1)(x-1)

C) To determine the zeros of f(x) without using a calculator, we can use the fact that a zero of a polynomial function is a value of x that makes the function equal to zero. Since we already factorized the polynomial, we know that the zeros are -2, -1, and 1.

Hence,

A) One of the factors of the given function would be (x + 2).

B) The factored form of the function would be f(x) = (x+2)(x+1)(x-1).

C) The zeroes are -2, -1, and 1.

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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:

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

Answer:  P= mgh

Step-by-step explanation: Gravitational potential energy is the energy possessed or acquired by an object due to a change in its position when it is present in a gravitational field. It can be said that gravitational potential energy is an energy that is related to gravitational force or to gravity.

Therefore P= mgh

where m is the mass of an object

g is the acceleration due to gravity

h is the height of an object

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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:

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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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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Answer: -7

Step-by-step explanation:

Use this equation to help your answer

April lost 5 pounds. -5
She lost 3 pounds -3
She gained 2 pounds +2
She lost 1 pound

Now in a formula, this is -5-3+2-1 = x
To find x we have to simplify
X = -7
Make sure to include the negative since she lost weight

I hope this helps you :D

Answer:Over the fur weeks April lost 7 pounds

Step-by-step explanation:5+3-2+1=7

Answer:

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

Step-by-step explanation:

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

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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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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(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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Answer: To find the direction and magnitude of the resultant of these three forces, we will use the law of cosines and law of sines.

First, we will find the horizontal and vertical components of each force using trigonometry:

F1x = 80 * cos(30) = 69.28 pounds

F1y = 80 * sin(30) = 40 pounds

F2x = 95 * cos(45) = 67.08 pounds

F2y = 95 * sin(45) = 67.08 pounds

F3x = 125 * cos(120) = -62.5 pounds

F3y = 125 * sin(120) = -106.57 pounds

Next, we will add the horizontal and vertical components of each force together to find the overall horizontal and vertical components of the resultant force:

Rx = F1x + F2x + F3x = 69.28 + 67.08 + (-62.5) = 72.86 pounds

Ry = F1y + F2y + F3y = 40 + 67.08 + (-106.57) = 0.51 pounds

Finally, we can use the law of cosines to find the magnitude of the resultant force, and the law of sines to find the direction of the resultant force:

R = sqrt(Rx^2 + Ry^2) = sqrt(72.86^2 + 0.51^2) ≈ 114.66 pounds

theta = atan(Ry/Rx) = atan(0.51/72.86) = 0.0068 radians ≈ 0.39 degrees

So, the direction of the resultant force is 0.39 degrees counter-clockwise from the positive x-axis, and the magnitude of the resultant force is 114.66 pounds.

Note: Keep in mind that angle given in the question is in degree and the trigonometric functions in most programming languages accept the angle in radians, so you have to convert the angle to radians before using the trigonometric functions.

Step-by-step explanation:

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 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 greatest integer is ten.

An integer is a number that does not contain a decimal or fractional element and can be positive or negative, including zero.

Let’s call the three integers a,b, and c.

Because the sums of each distinct pair of numbers are 6, 8, and 18,

A + b = 6 (1) (1)

B + c = 8 (2) (2)

C + a = 18 (3) (3)

Subtraction of equation (1) and equation (2):

C – a = 2

Add the preceding equation to equation (3):

2c = 20

C = 10

In equation (3), substitute c = 10:

10 + a = 18

A = 8

In equation (1), substitute a = 8:

8 + b = 6

B = -2

As a result, the three integers are 8, -2, and 10.

As a result, the greatest integer is 10.

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The height of 14 uch notebook placed one over the other is 420mm

Given that

Thickness of one notebook is 30 mm

To find the height of 14 such placed one over the other

For each  notebook's thickness is 30mm.

stacked notebooks equals fourteen

•°• 30×14=420mm

42 cm or 420 mm.

After placing 14 such notbooks one over the other we get the final Thickness  as 420 mm

This can we converted into 42 centimeters or 0.42 meters

So Therefore the final answer for the height of 14 such notebook placed one over the other is 420 mm or 42 cm

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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 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?

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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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]

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

Answer:

767 mph

Step-by-step explanation:

At 20 °C (68 °F), the speed of sound in air is about 343 metres per second (1,125 ft/s; 1,235 km/h; 767 mph; 667 kn), or one kilometre in 2.91 s or one mile in 4.69 s. It depends strongly on temperature as well as the medium through which a sound wave is propagating.

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

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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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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