find the length and breadth of the rectangle whose area is 6x^2-29x+30. Also find its perimeter.​

The units of a and b are m/sec³ and m/sec⁴

Given :v = at² + bt³

The dimension of velocity v = [L] [T]⁻¹

According to the Principle of Homogeneity of Dimension, "the terms combining the equation must have the same dimensions for the equation to have any physical meaning."

So, Dimensiona of v = Dimensions of at²

                       [L][T]⁻¹ = a[T]²

                 a = [L][T]⁻³ = m/sec³

Similarly, we can say

Dimension of v = Dimension of bt³

              [L][T]⁻¹ = b[T]³

       b = [L][T]⁻⁴ = m/sec⁴

Hence, the unit of a is m/sec³ and the unit of b is m/sec⁴

The question is incomplete, the complete question is

"During a short interval of time, the speed v in m/s of an automobile is given by v = at² + bt³ where the time t is in seconds the units of a and b are respectively:"

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The probability of winning the game with at least one Ace among the four draws is 0.736.

The probability of winning in this game is calculated as,

There are 4 Aces in a standard deck of 52 cards, so the probability of drawing an Ace on one draw is 4/52.

The probability of not drawing an Ace in 4 draws is (48/52) * (47/51) * (46/50) * (45/49) = 0.264.

The probability of winning is the complement of not winning, which is 1 - 0.264 = 0.736.

So, the probability of winning the game with at least one Ace among the four draws is 0.736.

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Answer: B: They are perpendicular

Step-by-step explanation:

First, you have to convert the equations into y=mx+b form; thankfully, one is already done for us. x+y=2, to convert into y=mx+b form, you have to subtract x. then y=2-x, or in other words, y=-x+2. now that the equations are both in y=mx+b form, we can start graphing them. As I don't have a phone, I will try my best to explain how it is graphed rather than take a picture. For the first equation, y=-x+2, it will start at the height of 2 units. since we can substitute values for x, we can substitute x for 1, and immediately we have to multiply 1 by -1, which is -1. add 2 to -1, and you get 1. so when x increases by 1, y decreases by 1. This trend will continue with different numbers. The second equation, or y=x+4, is pretty straightforward. the y-value starts at a height of 4, and every time the x-value increases by 1, so does the y-value. Now notice how these equations have different meanings, and slopes. this means that they aren't parallel as they don't have the same slope, and they cannot be the same line as they are different equations. This only leaves B or D. When you graph it, you see that the two equations form two lines that cross together and form 4 90-degree angles, which is exactly what perpendicular means. Hope this helps!

As per the given domain the behavior of f'(x) near that point to determine if the function is increasing or decreasing.

The domain of a function is the set of all possible input values (x-values) for which the function is defined and produces a valid output (y-value). In this case, the domain of f(x) is all real numbers.

(a) To determine the intervals over which f(x) is increasing or decreasing, we need to consider the sign of f'(x) and  the behavior of f'(x) near that point to determine if the function is increasing or decreasing.

(b) From the information given, we know that

=> f'(x)=0 at x=1

and that f'(x) is only undefined at x=−3 within the domain of the function. Hence, x=1 is a critical point.

(c) To determine the intervals over which f(x) is concave up or concave down, we need to consider the sign of f''(x).

If f''(x) is positive over an interval, then the function is concave up over that interval.

If f''(x) is negative over an interval, then the function is concave down over that interval.

(d) An inflection point is a point in the domain of the function at which the concavity of the function changes.

If the sign of f''(x) changes from positive to negative or from negative to positive, then the point is an inflection point.

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The bee's path can be modeled as a complex number sequence.

The bee started flying from the point facing east and flies a distance of 1 foot due east. For, once the bee reaches a point, turns counterclockwise, and flies two-thirds of the previous distance it flew to point

The first step is 1 + 0i. Each subsequent step is two-thirds of the previous step rotated by -90 degrees, which is equivalent to multiplying by -1/3 + i√3/3.

The bee's final position is the limit of this sequence, which is 0.5 + 0.5i√3. The distance from the starting point is |0.5 + 0.5i√3| = 0.5√(0.5² + (0.5√3)²) = √(0.25 + 0.75) = √(1).

Therefore, = √(1), and = 1.

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grid <- seq(from = 1, to = 2, by = (2-1)/(106-1)).  # Creates a numeric vector of 106 equispaced points between 1 and 2.

grid <- seq(from = 1, to = 2, by = (2-1)/(106-1))  #This will create a numeric vector called grid containing 106 equispaced points between 1 and 2 (inclusive). #The command takes three arguments. 'from' indicates the starting point for the sequence, in this case 1; 'to' indicates the ending point for the sequence, in this case 2; 'by' indicates the increment size between each number, which is calculated as (2-1)/(106-1). This is because there are a total of 106 numbers, so to get the distance between each number, we divide the total range (2-1) by the total number of points (106-1). This provides a numeric vector of 106 equispaced points between 1 and 2.

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Answer:

x ≈ 2.8

Step-by-step explanation:

using the sine ratio in the right triangle

sin40° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{PQ}{OQ}[/tex] = [tex]\frac{1.8}{x}[/tex] ( multiply both sides by x )

x × sin40° = 1.8 ( divide both sides by sin40° )

x = [tex]\frac{1.8}{sin40}[/tex] ≈ 2.8 ( to the nearest tenth )

Answer:2.8

Step-by-step explanation:

By using sine ratio , sine40°=opposite/hypotenuse

or, sine40°= 1.8/

or, x= 1.8/sine40°

or,x= 2.8003.......

or,x =2.8

Step-by-step explanation:

First, let's find 1% of 550.

---------------------------------------------

HOW TO FIND 1% OF 550:

                                       (see the point?)

                                               (see it?)

---------------------------------------------

     Now, let's multiply the "new" number amount we have. ($5.50)

-------------

         (yeah, I don't think I need to explain this but I did lol)

You got the answer! Congrats!

-eliana44ever

The chair-to-table ratio is 104:13 = 8.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

A wedding planner rented 13 tables and 104 chairs for an upcoming wedding.

The chair-to-table ratio,

= 104/13

= 8

Therefore, the ratio is 104:13 = 8.

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The numerical value of y in the equation y = x² - 8 when x = -4 is 8.

Given the equation in the question;

y = x² - 8

To determine the numerical value of y, replace all the occurrence of x with -4 in the equation and simplify.

y = x² - 8

Plug in x = -4

y = ( -4 )² - 8

First take the square of -4

y = 16 - 8

Subtract 8 from 16

y = 8.

Therefore, the value of y is 8.

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AS per the concept of vectors, two vectors f1 and f2 , where f1 is parallel to u and f2 is orthogonal to u .

In mathematics, vectors are quantities that have both magnitude and direction. They are often used to represent physical quantities such as forces and velocities.

In this case, we are given a vector u and another vector f, and we want to decompose the vector f into two separate vectors, f1 and f2. The first vector, f1, will be parallel to u, meaning that it will have the same direction as u but possibly a different magnitude.

The second vector, f2, will be orthogonal to u, meaning that it will be perpendicular to u.

Next, we will subtract the projection from f to find the vector f2.

This vector will be orthogonal to u because the projection is parallel to u, and the difference between the two vectors will be perpendicular to u.

The final answer will be the vectors f1 and f2, which together form the original vector f.

This process of decomposing a vector into its parallel and orthogonal components is an important tool in mathematics and physics.

Complete Question:

Let u=〈−6,2,3〉. Decompose F=〈4,0,6〉 into two vectors F1 and F2, where F1 is parallel to u and F2 is orthogonal to u and Prove it.

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Answer:  9:5

Step-by-step explanation:

A. greater than 180°. A major arc is an arc of a circle that has a measure greater than 180°.

Arc is a curved line which is part of the circumference of a circle or other curved shape. In mathematics, an arc is defined as a continuous segment of a circle. It is a line that joins two points on a circle's circumference. The length of an arc is proportional to the circle's circumference and is measured in radians or degrees. An arc can also be a part or section of a different type of curve such as an ellipse or parabola.

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Assuming the length line is made of copper, the resistance would be 0.667.

The following formula can be used to determine the resistance of the diagonal line that passes through the corners of the 10mm by 10mm silicon integrated die: Resistance is equal to resistivity times length (cross-sectional area). The cross-sectional area of the line, which is 1 m thick and 5 m wide, may be calculated as 5 x 1 m = 5 m2. The Pythagorean Theorem, which asserts that the hypotenuse of a right triangle is equal to the square root of the sum of the squares of the other two sides, can be used to determine the length of the line. The line itself serves as the hypotenuse in this instance, while the other two sides measure 10 mm apiece. As a result, the square is equal to the length of the line.

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Answer:

First we distribute the -5:

-5(7+x) = -5(7) - 5(x) = -35 - 5x

Then we combine like terms:

-35 - 5x + 2 5/6x = -35 + 2/6x - 5x = -35 + 1/3x - 5x

So:

-5(7+x)+2 5/6x = -35 + 1/3x - 5x

As per the given number nine billion is 8.9 x 10⁹ greater than one hundred million

Numbers are a fundamental part of our lives and the world around us. Understanding how to compare and perform arithmetic with large numbers is an important skill.

In this question, we are comparing two large numbers: nine billion and one hundred million.

The correct answer is (a) 8.9 x 10⁹.

The number nine billion can be written as

=> 9 x 10⁹,

where 10⁹ means 10 raised to the 9th power, or 10 multiplied by itself 9 times, which is equal to 1,000,000,000.

Meanwhile, one hundred million can be written as 100 x 10⁶, or 100 million.

To compare these two numbers, we subtract 100 million from nine billion, which gives us 8.9 x 10⁹.

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We can make 5 pies with one pack of apples as the number of pies should be an integer.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, A bushel of apples weighs about 42 pounds and there are four packs in a bushel.

So, The weight of one pack of apples is (42/4) = 10.5 pounds.

Now, It takes 2 pounds of apples to make one pie,

Therefore, We can make (10.5/2) = 5.25 pies but we can only make 5 pie from one pack of apples.

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Check the picture below, so the ellipse looks more or less like so, with a major axis of 4, namely a = 4, and a "c" distance of 2√3, so

[tex]\textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=3\\ k=1\\ a=4 \end{cases}\implies \cfrac{(x- 3)^2}{ 4^2}+\cfrac{(y- 1)^2}{ b^2}=1[/tex]

[tex]\stackrel{\textit{we know that}}{2\sqrt{3}=\sqrt{4^2 - b^2}}\implies \sqrt{12}=\sqrt{4^2 - b^2}\implies 12=16-b^2\implies 12+b^2=16 \\\\\\ b^2=4\hspace{5em}\cfrac{(x- 3)^2}{ 4^2}+\cfrac{(y- 1)^2}{ 4}=1\implies \boxed{\cfrac{(x- 3)^2}{ 16}+\cfrac{(y- 1)^2}{ 4}=1}[/tex]

The equation of the ellipse with center (3,1), vertex (7,1), and focus (3+2√3,1) is (x - 3)² / 16 + (y - 1)² / 4 = 1.

To write the equation of the ellipse with the given center (3,1), vertex (7,1), and focus (3+2√3,1),  to determine some key properties of the ellipse.

Center (h, k) = (3, 1)

The center of the ellipse is (h, k) = (3, 1).

Major axis length = 2 × distance between center and vertex

The distance between the center and vertex is given by |3 - 7| = 4 units.

So, the major axis length is 2 × 4 = 8 units.

Distance between center and focus = c = |3 + 2√3 - 3| = 2√3 units

Now, we have all the information needed to write the equation of the ellipse in standard form:

(x - h)² / a² + (y - k)² / b² = 1

where (h, k) is the center of the ellipse, and a and b are the semi-major and semi-minor axes lengths, respectively.

Since the center is (3, 1),  (h, k) = (3, 1). We already know that the major axis length is 8 units, so a = 4.

To find b, we use the relationship between a, b, and c in an ellipse:

c² = a² - b²

(2√3)² = 4² - b²

4 × 3 = 16 - b²

12 = 16 - b²

b² = 16 - 12

b² = 4

b = 2

Now we have the values of a and b, so the equation of the ellipse is:

(x - 3)² / 4²+ (y - 1)² / 2² = 1

Simplifying further:

(x - 3)² / 16 + (y - 1)² / 4 = 1

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Por lo tanto, la segunda cuadrilla de 20 obreros de doble eficiencia completará la misma obra en 0,3 días, lo que equivale a 6 horas.

La fórmula para calcular el tiempo de trabajo necesario para una cuadrilla de obreros es:

Tiempo = Cantidad de trabajo / (Rendimiento de la cuadrilla)

Por lo tanto, el tiempo necesario para la segunda cuadrilla de 20 obreros de doble eficiencia sería:

Tiempo = Cantidad de trabajo / (2 x Rendimiento de la primera cuadrilla)

Tiempo = 12 días / (2 x 20 obreros)

Tiempo = 12 días / 40 obreros

Tiempo = 0,3 días

Por lo tanto, la segunda cuadrilla de 20 obreros de doble eficiencia completará la misma obra en 0,3 días, lo que equivale a 6 horas.

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The inequality that can be used to find the possible length, x, Ricky could make his quilt is x > 8.

An inequality is a mathematical statement indicating the relative size or order of two values, where one value is not equal to the other. It uses symbols such as > (greater than), < (less than), ≥ (greater than or equal to), ≤ (less than or equal to), or ≠ (not equal to) to compare the values. The solution of an inequality is the set of values that make the inequality true.

Let x = length of the quilt

The quilt is a rectangle, hence the area of the quilt is equal to the product of the length and the width.

A = l x w

If the quilt is 7 feet wide and the area should be greater than 56 square feet, then we can write that as the inequality below.

A > 56 square feet

l x w > 56

x(7) > 56

x > 8

Therefore the inequality that shows the possible lengths of the quilt is x > 8.

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The total pay at the end of the week is $618.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign.

Thomas gets paid $15 per hour during regular time, hence for 40 hours he gets:

(15)(40) = 600

He works a total of 46 hours:

The additional time worked is 6 hours.

The payment for the additional hours is:

(1.5)(15) = 22.5

For 6 hours he gets:

(6)(22.5) = 135

Hence, the total income that he should get is 600 + 135 = 735.

He gets an deduction of $117, the final pay is:

735 - 117 = 618

Hence, the total pay at the end of the week is $618.

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Answer:

4x⁶ - 7

Step-by-step explanation:

[tex] \sf{( {2x}^{3} )}^{2} - 7[/tex]

[tex] \sf( {2}^{2} \times {x}^{3 \times 2} ) - 7[/tex]

[tex] \sf {4x}^{6} - 7[/tex]

Answer:

The ordered pair for the equation 3y=2(2)-9 is (x, -5/3).

Step-by-step explanation:

To find the ordered pair, you will first need to solve the equation for y. To do this, you can start by simplifying the right side of the equation:

3y = 2(2) - 9

3y = 4 - 9

3y = -5

Next, you will divide both sides of the equation by 3 to solve for y:

y = -5/3

So the value of y is -5/3.

The ordered pair is a set of coordinates on a coordinate plane, representing a point on the plane. It is usually represented by (x, y) where x is the value of x-coordinate and y is the value of y-coordinate. In this case, since you only have one variable, you don't have the value of x, so it would be (x, -5/3)

Please note that the above solution is based on the given equation, if you have any other information such as the context of the question or any other variables in the equation, it would be helpful to include that information in your question so I can help you better.

The number of candy that worth $1.05 per pound will be 5.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Given that One candy is worth $1.05 a pound, one is worth $1.35 a pound. The mixture is worth $1.17 a pound.

Consider that x be the number of candy that worth $1.05 per pound.

Then the number of candy that worth $0.85 per pound will be (20 - x). Then the equation will be;

1.05x + 0.85(20 - x) = 0.90 × 20

105x + 85 × 20 - 85x = 90 × 20

20x = 5 × 20

x = 5 pounds

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The graph of the function g(x) = (11.7)ˣ is plotted and attached with the answer.

A function describes a relationship between a dependent and independent variable. Example -

y = f(x) = 5x + 9

Given is the function f(x) = x.

It is given that -

f(x) = x

It is a linear function. It represents a straight line with slope 1.

The graph of the function -

g(x) = (11.7)ˣ

is plotted and attached with the answer.

Therefore, the graph of the function g(x) = (11.7)ˣ is plotted and attached with the answer.

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Answer:

B) 234 Letters

Step-by-step explanation:

Each number will be matched with 1 letter, and there is 26 letters in the alphabet, so each number can be used 26 different times. 26 * 9 is 234

The value of the function when evaluated is 1/2

From the question, we have the following parameters that can be used in our computation:

f(x)=2/√10-6

Express properly

So, we have the following representation

f(x)=2/√(10-x)

Substitute the known values in the above equation, so, we have the following representation

f(-6)=2/√10+6

Evaluate the like terms

f(-6)=2/√16

So, we have

f(-6) = 1/2

Hence, the function value is 1/2

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Correct option is B, function for the area of the circle in terms of the side of the square is A = [tex]\pi \frac{S^2}{4}[/tex].

Because the area of a square is one of its sides multiplied by itself, the area equals the square of the radius of a circle multiplied by two. Because the radius of the circle is a known quantity, the area of the inscribed square can be calculated numerically.

An “inscribed” square in a square is one in which all of the vertices of the smaller square are on the borders of the bigger square. To do this, the vertices of the smaller square will split each side of the bigger square into two segments, one on each side.

If a square is used to inscribe a circle, the square's side length will match the circle's diameter. As a result, the radius of an inscribed circle is S/2 for a square with length S. hence, the area of a circle is expressed as the square's sides,

= [tex]\pi \frac{S^2}{4}[/tex]

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