Suppose that a particle moves along a straight line with velocity defined by v(t) = t2 − 3t − 18, where 0 ≤ t ≤ 6 (in meters per second). Find the displacement at time t and the total distance traveled up to t = 6.

Answer:

1.) A prime factor is any prime number that can be multiplied to give the original number.

For example, the prime factor of 24 is:

1, 2, 3, 4, 6, 8, 12, and 24.

2.) A prime factor is a natural number, other than 1, whose only factors are 1 and itself. The first few prime numbers are actually 2, 3, 5, 7, 11, and so on.

Step-by-step explanation:

You're welcome.

i³³ simplified is i.

What is the Complex Number?

A complex number is a number in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.

When raising a complex number to a power, we can use the property [tex](a + bi)^n = a^n + (na^{(n-1)})bi + (n(n-1)/2!)a^{(n-2)(bi)^2} + .... + (n(n-1)...21)(a*bi)^n[/tex]

It is also possible to simplify the powers of complex numbers using De Moivre's Theorem:

[tex](a + bi)^n = a^n + (na^{(n-1)})bi + (n(n-1)/2!)a^{(n-2)(bi)^2} + .... + (n(n-1)...21)(a*bi)^n[/tex]

Where [tex](a + bi)^n = r^n * (cos(n\theta) + i*sin(n\theta))[/tex]

Where r is the magnitude, θ is the argument, and n is an integer.

For example, if we raise i to the power of 3, we can use De Moivre's Theorem:

i³ = (cos(90) + isin(90))³ = cos(270) + isin(270) = -i

So, i³ = -i

When raising complex numbers to powers, the magnitude will be raised to the power of n while the argument will be multiplied by n.

i² = -1, so i³³ can be written as (i²)¹⁶ * i = (-1)¹⁶ * i = i

Therefore,  i³³ simplified is i.

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Answer:

y = 7

Step-by-step explanation:

12-5=7

7+5=12

Answer:

y = 7

Step-by-step explanation:

12 - y = 5

Subtract 12 from both sides.

-y = -7

Multiply both sides by -1.

y = 7

The  greatest common factor of the polynomial 20x^3-14x is D. 2x.

The concept that will be sued here is common factor. A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. The largest factor that splits both numbers is said to be the greatest common factor. List the prime factors of each integer before calculating the greatest common factor.

For instance, the numbers 12, 20, and 24 share the components 2 and 4. The GCF of 12, 20, and 24 is 4 because it is the largest.

The common factor that ca be gotten from 20x² : are:  1, 2, 4, 5, 10, 20, x

The  common factor that ca be gotten from 14x are : 1, 2, 7, 14, x

Then greatest common factor of the polynomial is 2x.

Hence,  2x(10x² - 7)

Therefore, option D is correct.

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Answer: -5y

Step-by-step explanation:

2.5+-5y-2.5

=-5y

or 0+-5y

From the provided value of the paid price of the car and sales tax percentages, The answer is $564.

Percentages are a way to express a number as a part of 100. The symbol for percentage is %. For example, 25% means 25 out of 100, or one quarter. To convert a percentage to a decimal, divide it by 100. For example, 25% = 25/100 = 0.25. To convert a decimal to a percentage, multiply it by 100. For example, 0.25 = 0.25 * 100 = 25%. You can also calculate percentage by multiplying the number with the percentage rate. For example, if you want to find out what 25% of 50 is, you can calculate it by multiplying 50 by 0.25 (since 25% is the same as 0.25 as a decimal).

Tax is a financial charge imposed by a government on individuals, businesses, and other entities. The revenue generated by taxes is used to fund government programs and services such as infrastructure, education, healthcare, and defense. There are many types of taxes, including income tax, sales tax, property tax, and capital gains tax. The specific tax that a person or entity is required to pay depends on the jurisdiction and the type of activity or transaction involved. Tax laws and rates can vary widely between countries and even within a country.

Griffith paid 6% of $9400 in sales tax. To find out how much that is, you can multiply $9400 by 0.06 (since 6% is the same as 0.06 as a decimal).

$9400 * 0.06 = $564

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The value of function f(x) ⋅ g(x) is,

⇒ x³ + 3x² + 16x - 20

A relation between a set of inputs having one output each is called a function.

We have to given that;

The functions are,

⇒ f (x) = x² + 3x − 4 and g(x) = x + 5.

Hence, The value of function f(x) ⋅ g(x) is,

⇒ f(x) ⋅ g(x) = (x² + 3x − 4) × (x + 5)

                 = x³ + 5x + 3x² + 15x - 4x - 20

                 = x³ + 3x² + 16x - 20

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The mantissa of scientific notation or standard form is between 1 and 10 in absolute value, or 1 ≤ |a| < 10.  It can be 1, hence, it does not have to be greater than 1.

Standard form is also called scientific notation and has the form:

a x 10ᵇ

Where b is an integer and is called exponent.

a is a real number between 1 and 10 (in absolute value), it includes 1 but not 10, or we can write a should satisfy 1 ≤ |a| < 10.

Usually, a is called mantissa.

Example:

2467 can be written in standard form as:

2467 = 2.467 x 10³

0.0095 can be written in standard form  as:

0.0095  = 9.5 x 10⁻³

150 x 10² can be written in standard form  as:

150 x 10² =1.5 x 10⁴

-0.062 can be written instandard form  as:

-0.062 = -6.2 x 10⁻²

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So the strength of a man who is 200 pounds is approximately 2649.2 newton, rounded to the nearest tenth.

Weight is a measure of the force exerted on an object due to gravity. It is measured in units of force such as pounds, kilograms, or newtons. The weight of an object is equal to the force of gravity acting on it and is equal to the mass of the object multiplied by the acceleration due to gravity.

Newton (N) is the unit of force in the International System of Units (SI). It is named after Sir Isaac Newton, the famous English physicist, mathematician, and astronomer. It is defined as the force that is required to accelerate an object with a mass of one kilogram at a rate of one meter per second squared.

f = 500 ln(200 + 1)

f = 500 ln(201)

then we can calculate the value of ln(201) using a calculator, and the result is 5.298317366548036

then we can substitute the result into the original equation and get

f = 500 * 5.298317366548036 = 2649.15868

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To find the endpoint with the midpoint and one endpoint formula, use the following steps:

Step 1: Identify the midpoint of the line segment. The midpoint is the point that is exactly halfway between the two endpoints.

Step 2: Identify one endpoint of the line segment. This is the point that you already know.

Step 3: Use the midpoint and one endpoint to find the other endpoint. To do this, add or subtract the difference between the x-coordinates of the midpoint and one endpoint from the x-coordinate of the midpoint to find the x-coordinate of the other endpoint. Then, add or subtract the difference between the y-coordinates of the midpoint and one endpoint from the y-coordinate of the midpoint to find the y-coordinate of the other endpoint.

Step 4: Write the coordinates of the other endpoint. The point (x,y) represents the other endpoint of the line segment.

Note: The x-coordinate of the other endpoint is the x-coordinate of the midpoint + or - the difference of x-coordinate of the midpoint and one endpoint, and the y-coordinate of the other endpoint is the y-coordinate of the midpoint + or - the difference of y-coordinate of the midpoint and one endpoint.

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Answer:

No they do not

Step-by-step explanation:

Sides 5 cm and 12cm can form a right angled triangle because 5 + 12 = 17 which is a greater number than 13 meaning it cannot

Answer:

The only even prime number is 2.

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The required equation is:

1. d = 81t

2. f(t) = 81t

Now, According to the question:

Given that a car moving at a constant speed passed a timing device at t=0.

In other words, at t = 0 second, d = 0 ft.

We know that

distance = rate × t

After 7 ​seconds, the car has traveled 567 ft.

In other words, at t = 7 seconds, d = 567 ft

Thus, there are two points

(0, 0)

(7, 567)

Finding the slope between (0, 0) and (7, 567)

Using the formula

Slope = Rate of change = [y₂-y₁] / [x₂-x₁]

                                       = [567 - 0] / [7-0]

                                       = 567 / 7

                                       = 81 ft./second

Given that the car is moving at constant speed. So, we don't have any other factor or term to consider

Thus, the required equation is:

distance = rate × t

d = 81 × t

d = 81t

or

f(t) = 81t

VERIFICATION

Given the equation

d = 81 × t

Put t = 0 to find the distance in 1 sec

d = 81 × (0) = 0 ft.

Put t = 7 to find the distance in 7 seconds

d = 81 × (7) = 567 ft.

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The complete question is this:

A car moving at a constant speed passed a timing device at t=0. After 7 ​seconds, the car has traveled 567 ft. Write a linear function rule to model the distance in feet d the car has traveled any number of seconds t after passing the timing device.

Answer:

24 cups

Step-by-step explanation:

16/8 = 2

[tex]\frac{2}{1}[/tex] = [tex]\frac{x}{12}[/tex]

Since 1 x 12 = 12, then 2 x 12 = 24

Answer:

100

Step-by-step explanation:

week 7 = 110

week 8 = 100

week 9 = 90

week 10 = 110

........

The function in terms of balance of the savings account is B(a) = 200 - 5a.

A formula known as an equation uses the equals sign to express how two expressions are equal. The variables for which the equation must be solved are also known as the unknowns, and the unknowns' values that fulfil the equality are known as the equation's solutions.

Let the number of months be represented as a.

The fee that would be deducted ever month can thus be represented as 5a.

The initial deposit in the bank is $200, and if we include the deduction the equation is as follows:

B(a) = 200 - 5a

Hence the function in terms of balance of the savings account is B(a) = 200 - 5a.

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The 10th term round to the nearest thousandth of the geometric progression is found as 0.001.

For the stated sequence:

5, 2,4/5,...

Check for AP:

a₂ - a₁ = 5 - 2 = 3

a₃ - a₂ = 4/5 - 2 = -6/10 = -3/10

As the common difference is not same, it is not an AP.

Check for GP:

a₁  = 5

a₂ = a₁ q²⁻¹

a₂ = 5q = 2

a₃ = a₁q³⁻¹

    =  a₁q²

a₃ = 5q² = 4/5

As,

a₂/ a₁ = 2/5

a₃/a₂ = 2/5, it is an GP

Thus,

a₁₀ = a₁qⁿ⁻¹

    = 5*(2/5)⁹

    = 0.001

Thus, the 10th term round to the nearest thousandth of the geometric progression is found as 0.001.

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We have to reflect over x- axis to transform parallelogram ABCD to create A'B'C'D'.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

The Coordinates of ABCD are:

A( -4, 1), B(-3, 2), C(-1, 2) and D(-2, 1)

and,  Coordinates of A'B'C'D' are:

A'( 4, -1), B'(3, -2), C'(1, -2) and D'(2, -1)

Now, Reflection over the x-axis.

A"(-4, 1)- 2(0, 1) ---> A"( -4, -1)

B"(-3, 2) - 2(0, 2)----> B"(-3, -4)

C"(-1, 2)-2(0, 2)--->C"(-1, -2)

D"(-2, 1)- 2(0,1)--->D"(-2, -1)

and,  Reflection over the y-axis.

A"(-4, 1)- 2(-4, 0) ---> A"( 4, 1)

B"(-3, -4) - 2(-3, 0)----> B"(-3, -4)

C"(-1, -2)-2(-1, 0)--->C"(1, -2)

D"(-2, 1)- 2(-2, 0)--->D"(2, -1)

So, we must reflect over the x-axis and then reflect over the y-axis to map parallelogram ABCD onto parallelogram A'B'C'D'.

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All values of z are negative numbers less than -5, which are -6, -7 and -8 so on.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that, the opposite of z is greater than 5.

So, we have the following absolute value inequality.

|z|>5

This can be written as z>5 or z<-5

5 is a positive number.

So, we make use of the inequality z<-5.

From the above inequality, the possible values of z are -6 and -7

Note that there are other values of z

The values that z cannot be

We have: z>5 or z<-5

The values that z cannot be, are represented with the inequality z>5.

From the above inequality, z cannot be 6 and 7

The true statement about the values of z are, they are all negative numbers less than -5.

Therefore, all values of z are negative numbers less than -5, which are -6, -7 and -8 so on.

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The given inequality 6 > x + 1 > 3 is an "and" inequality.

Compound inequalities are kind of inequality expressions which consists of two or more simple inequalities.

"And" inequality represents that both the inequalities are true.

"Or" inequality represents that either of the statement is true.

Given inequality is,

6 > x + 1 > 3

Subtracting 1 from throughout the inequality,

6 - 1 > x > 3 - 1

5 > x > 2

This implies that x is less than  and x is greater than 2, for which the value of x are 3 and 4.

Hence the given inequality is an "and" inequality.

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Answer:

jejejdhudsjhshsiwvvjsjsjd

The angles are a pair of linear angles. They complement one another and are close by. They intersect at a right angle. x = 33,

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

Additional angles add up to 180.

(x-17)+(5x-1) = 180

x-17+5x-1 = 180

(x+5x)+(-17-1) = 180

6x-18 = 180

6x = 180+18

6x = 198

x = 198/6

x = 33

Additional information

x = 33, therefore if

x-17 = 33-17 = 16

5x-1 = 5*33-1 = 165-1 = 164

Angles added together result in 16+164 = 180

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Complete question -

Answer:

<B = 83* and x = 5

Step-by-step explanation:

<D = 83*
<CAD = 50* = <BCA
<ACD = 180 - (50+83) = 47* = <CAB

<B = 180 (sum of interior angles of triangle ABC) - <BCA - <CAB

<B = 180 - 50 - 47 = 83*

AD = BC

5x = 25

x = 5

Hope this helps!

The seven types of triangles based on side length are equilateral triangle, isosceles triangle, scalene triangle and based on angles are acute triangle, right triangle, obtuse triangle and oblique triangles.

Equilateral triangle: A triangle with all three sides of equal length and all angles of 60 degrees.

Isosceles triangle: A triangle with two sides of equal length and two angles of equal measure.

Scalene triangle: A triangle with all three sides of different lengths and all angles of different measures.

Right triangle: A triangle with one angle measuring exactly 90 degrees.

Acute triangle: A triangle with all angles measuring less than 90 degrees.

Obtuse triangle: A triangle with one angle measuring greater than 90 degrees.

Oblique triangle: A triangle that is not a right triangle, which means all angles are not 90 degrees.

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Answer: x = 25

Step-by-step explanation:
2x-10 = x+15
x = 15+10

x=25

The required value of x in the given triangle is 25, evaluated by following the definition of angle bisectors.

Given that, MNO is a triangle, where OP is the angle bisector, in the given scenario we have to determine the value of the x.

Following the definition of an angle bisector, the angle bisector for any angle bisects the angle into two equal halves, So,
Angle PNO = Angle PMO
2x-10=x+15

Simplify the above expression to evaluate x.
2x-10=x+15
2x-x=15+10
x=25

Thus, the required value of x in the given triangle is 25, by following the definition of angle bisectors.

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To dilate a triangle with center points we multiply the coordinates of the points in the preimage by the scale factor to determine the points in the image.

What is a scale factor?

A scale factor is a numerical value that is used to represent an object's larger or shrunk shape. It is a number that can be used to alter the size of any geometric figure or shape in relation to its initial size. It aids in altering the figure's size but not its shape.

Here,

we have to determine how we dilate a triangle with center points.

We concluded that

The origin is often used as the center of dilation. If you are dilating a figure centered at the origin, you can multiply the coordinates of the points in the preimage by the scale factor to determine the points in the image.

Hence, to dilate a triangle with center points we multiply the coordinates of the points in the preimage by the scale factor to determine the points in the image.

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Answer:

84 divided by 7 - 5x

Step-by-step explanation:

The graph of the player two's function g(t)=16(t-5)²+290 is given in the attachment. The baseball's maximum height is 290 ft. At 5 seconds the baseball was at its maximum height. After 9.25 second the baseball hit the ground.

A function is a mathematical device that converts one value to another in a predictable manner. We can think of it as a machine. You give the machine an input, it performs some calculations on it, and then returns another value - the result of the calculations.

The function's name is f. We can call it anything we want, but single letters are common. The input* value is referred to as x. Again, we could use anything, but x is common. What the function does with the input is shown to the right of the equals sign.

In this case, the function takes the input x, multiplies it by three, and returns the result.

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