What are the leading coefficient, constant term and degree, if any, of the algebraic expression (x+√3)(x-√3)?
a. leading coefficient: 1; constant term: -3;
degree: 2
b.
leading coefficient: -1; constant term: 3;
degree: 2
c. leading coefficient: 1; constant term: 3;
degree: 2
none, expression is not a polynomial

Answer:

$25000 * 40% = 100.000

Step-by-step explanation:

Answer:

25.749504 kilometers

Step-by-step explanation:

16miles  x 1.609(constant) = 25.749504

Step-by-step explanation:

When x = 1, then y = _-2___

Answer:

bro ngl idek

Step-by-step explanation:

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Answer: 398m

Step-by-step explanation: 1,000 - 602 = 398

Answer:

Step-by-step explanation:

We know that 1 kilometre is equivalent to 1,000 metres.

So Peg rode 1,000 metres and Lauren rode 602 metres.

Now we must find the difference between the distances.

To find the difference, we need to subtract Peg's distance by Lauren's distance

1,000 - 602 = 398 metres

So 398 metres is your final answer.

The number that will occupy the denominator is 8

Divide the two real numbers of the denominators between themselves:

-5/8 + 9/2

8 ÷ 2 = 4

With this number - we will multiply the terms of the second fraction with it:

-5/8 + 9/2

-5/8 + 9*4/2*4

-5/8 + 36/8

So we'll join these two fractions into one and then we'll do the sum:

-5/8 + 36/8

-5+36/8

31/8

Therefore, the value of this expression is 31/8, with denominator 8

answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

Answer:

Step-by-step explanation:

If you would like to know how much water did Elena drink each practice if she drank the same amount each time, you can calculate this using the following steps:

5 bottles of water ... 7 practices

x bottles of water = ? ... 1 practice

5 * 1 = 7 * x

5 = 7 * x /7

x = 5/7 bottle of water

The correct result would be 5/7 bottle of water.

Answer:

Let's go step-by-step ⇒

\(\frac{10x + 4}{7} = 8\)

= \((\frac{7}{1})\frac{10x+4}{7} = \frac{8}{1}(\frac{7}{1})\)

= \(10x+4=56\)

= \(10x = 52\)

= \(x = 5.2\)

Your answer is x = 5.2

I hope this helps!

- sincerelynini

It takes the toy car 2.43 seconds to fall to the bottom floor,  answer choice is B. 9/4 seconds, which is equal to 2.25 seconds.

An equation is a mathematical statement that asserts that two expressions are equal. An equation consists of two sides, the left-hand side and the right-hand side, separated by an equal sign (=).

For example, 2x + 5 = 11 is an equation, where the left-hand side is 2x + 5 and the right-hand side is 11. This equation asserts that the expression 2x + 5 is equal to 11, and the value of x can be determined by solving for x.

Equations can be simple or complex, and they can involve one or more variables. They can also be linear or nonlinear, depending on the nature of the expressions involved.

Solving an equation involves finding the values of the variables that make the equation true. This may involve applying algebraic operations and simplification techniques to isolate the variable on one side of the equation.

Equations are used in many areas of mathematics, science, engineering, and economics, and they provide a powerful tool for modeling and analyzing real-world situations. They are also used extensively in computer programming and cryptography, where they play a critical role in the development of algorithms and data encryption methods.

We have the equation \(h = 94 - 16t^2\), where h is the height of the toy car in feet and t is the time in seconds.

When the toy car reaches the bottom floor, its height will be h = 0. So we can set the equation equal to 0 and solve for t:

\(0 = 94 - 16t^216t^2 = 94t^2 = 94/16\)

\(t = \sqrt{(94/16)} = \sqrt{(23.5/4)} = 2.43 seconds\) (rounded to two decimal places)

Therefore, it takes the toy car 2.43 seconds to fall to the bottom floor.

The closest answer choice is B. 9/4 seconds, which is equal to 2.25 seconds.

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Answer:

Step-by-step explanation:

ac=3.14/p==\(\beta \alpha\)ty

a) The smallest number of tiles needed to make a square is 3.

b) The smallest number of tiles needed to make a square is 11.

a) To make a square using rectangular tiles that are 12 cm long and 4 cm wide, we need to find the side length of the square that is divisible by both 12 and 4. The smallest common multiple of 12 and 4 is 12, so a square with a side length of 12 cm can be made.

To calculate the number of tiles needed, we divide the side length of the square by the length of each tile. In this case, 12 cm ÷ 4 cm = 3.

Therefore, the smallest number of tiles needed to make a square is 3.

b) To make a square using rectangular tiles that are 11 cm long and 3 cm wide, we need to find the side length of the square that is divisible by both 11 and 3. The smallest common multiple of 11 and 3 is 33, so a square with a side length of 33 cm can be made.

To calculate the number of tiles needed, we divide the side length of the square by the length of each tile. In this case, 33 cm ÷ 3 cm = 11.

Therefore, the smallest number of tiles needed to make a square is 11.

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The length of one side of the equilateral triangle in terms of x is 6x.

To find the length of one side of the equilateral triangle in terms of x, we need to consider the perimeter of both the rectangle and the equilateral triangle.

The perimeter of a rectangle is given by the formula:

Perimeter of rectangle = 2(length + width)

In this case, the length of the rectangle is 7x cm, and the width is 2x cm. Substituting these values into the formula, we have:

Perimeter of rectangle = 2(7x + 2x) = 2(9x) = 18x

We are told that the equilateral triangle has the same perimeter as the rectangle.

Since an equilateral triangle has all sides equal, the perimeter can be calculated by multiplying the length of one side by 3.

Therefore, we have:

Perimeter of equilateral triangle = 3(side length)

Since the perimeter of the equilateral triangle is equal to the perimeter of the rectangle (18x), we can set up the equation:

3(side length) = 18x

Dividing both sides of the equation by 3, we get:

side length = 6x

Hence, the length of one side of the equilateral triangle in terms of x is 6x.

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The complete question may be like: A rectangle measures 2x cm by 7x cm. An equilateral triangle has the same perimeter as the rectangle. What is the length of one side of the triangle in terms of x?

Answer:

Initial amount: 934 g

After 80 years: 147 g

Step-by-step explanation:

\( A(t) = 934 (\dfrac{1}{2})^\frac{t}{30} \)

The initial amount occurs at t = 0.

\( A(0) = 934 (\dfrac{1}{2})^\frac{0}{30} \)

\( A(0) = 934 (\dfrac{1}{2})^0 \)

\( A(0) = 934 \times 1 \)

\( A(0) = 934 \)

After 80 years, t = 80.

\( A(80) = 934 (\dfrac{1}{2})^\frac{80}{30} \)

\( A(80) = 934 (\dfrac{1}{2})^\frac{8}{3} \)

\( A(80) = 934 (0.15749) \)

\( A(80) = 147 \)

Answer:

(0, 0.5)

Step-by-step explanation:

Let M is the midpoint of the line

x-coordinate of the midpoint:

xM = ( xA + xB ) / 2 = (-6 + 6) / 2 = 0

y-coordinate of the midpoint:

yM = (yA + yB) / 2 = (8 - 7) / 2 = 1/2 = 0.5

Answer: M (0, 0.5)

Answer:

(0, 0.5)

Step-by-step explanation:

The number of bows that Penny makes per hour and the price the firm sells at shows that the value of the marginal product is $24.95 per hour.

The highest wage the firm will pay is $24.95 per hour.

This can be found by the formula:

= Price x Marginal product of Penny

= 4.99 x 5

= $24.95 per hour

The highest wage the firm can pay would be the wage amount that equals their marginal revenue as this is the only way they can maximize profit.

Their marginal revenue in this case is the $24.95 per hour that they pay to Penny so this will be their highest wage to her as well.

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1. In this case, we want the reliability to be 95%, so the probability of not breaking down is 0.95.

2. Probability of no breakdowns = (reliability of a single machine)^3. Probability of at least one breakdown = 1 - Probability of no breakdowns

1. To determine how often the computer should be scheduled for maintenance, we need to consider the reliability and the desired level of operational condition. Since the duration for trouble-free operation follows a gamma distribution with a mean of 40 days, this means that, on average, the computer can operate for 40 days before a breakdown occurs.

To ensure operational condition with a 95% probability, we can calculate the maintenance interval using the concept of reliability. The reliability represents the probability that the machine will not break down within a certain time period. In this case, we want the reliability to be 95%, so the probability of not breaking down is 0.95.

Using the gamma distribution parameters, we can find the corresponding reliability for a specific time duration. By setting the reliability equation equal to 0.95 and solving for time, we can find the maintenance interval:

reliability = 0.95

time = maintenance interval

Using reliability and the gamma distribution parameters, we can calculate the maintenance interval.

2. To calculate the probability that at least one of the three machines will break down within the first scheduled maintenance time, we can use the complementary probability approach.

The probability that none of the machines will break down within the first scheduled maintenance time is given by the reliability of a single machine raised to the power of the number of machines:

Probability of no breakdowns = (reliability of a single machine)^3

Since the breakdown times between the machines are statistically independent, we can assume that the reliability of each machine is the same. Therefore, we can use the reliability calculated in the first part and substitute it into the formula:

Probability of at least one breakdown = 1 - Probability of no breakdowns

By calculating this expression, we can determine the probability that at least one of the three machines will break down within the first scheduled maintenance time.

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The solution to the inequality is -3 ≤ x ≤ -1/3

Given the inequality:

4|3x+5| ≤ 16

Let us simplify it by dividing both sides by 4 to get:

|3x+5| ≤ 4

Next, we can break the inequality into two cases, depending on whether 3x+5 is positive or negative:

First: 3x+5 ≥ 0

In this case, the inequality simplifies to:

3x+5 ≤ 4

Subtracting 5 from both sides, we get:

3x ≤ -1

Dividing by 3 (which is positive) gives:

x ≤ -1/3

Second: 3x+5 < 0

In this case, the inequality simplifies to:

-3x-5 ≤ 4

Adding 5 to both sides, we get:

-3x ≤ 9

Dividing by -3 (which is negative and requires us to flip the inequality), gives:

x ≥ -3

Therefore, the solution to the inequality is:

-3 ≤ x ≤ -1/3

The interval [-3,-1/3] is the solution set, and it includes all values of x between -3 and -1/3, including the endpoints.

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Step-by-step explanation:

Lets break this word problem down:

"The difference" means we're going to be finding x - y ("difference" means we're finding how much one value "differs" from the other)

"a number and it's opposite" so we're doing x - y, where y = -x. So already, we can re-write this as x - (-x) or x + x

"is 28" so x + x = 28 ("is" always means "equals")

"Find the number" so we're finding x.

x - (-x) = 28  (I went back a step so I could write everything out more plainly)

simplify

x + x = 28

add

2x = 28

divide both sides by 2 to get x on its own

x = 14

Answer:

14

The graph of f(x) = x(x+5)(x+3) / (x+3)(x+5) bears resemblance to the line y=x since both plots share similar linear characteristics.

Both the numerator and denominator of f(x) = x(x+5)(x+3) / (x+3)(x+5) cancel out the factors (x+3) and (x+5), giving us a simplified expression for the function, f(x) = x.

A line with a slope of 1 passes through the origin in an upward direction. When we examine the graph of y=x, which is a straight line passing through the origin with a slope of 1, it becomes apparent that adding 1 to x also adds 1 to y.

Since the simplified expression is merely f(x) = x, we can deduce that the graph of this function follows a linear path passing through the origin with a slope of 1.

In conclusion, the graph of f(x) = x(x+5)(x+3) / (x+3)(x+5) bears resemblance to the line y=x since both plots share similar linear characteristics.

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The inequality that represents the number of each type of calculator she can buy will be 25x + 65y ≤ 800

Given that teacher needs to purchase some scientific calculators for $25 each and some graphing calculators for $65 each.

Consider that x equal the number of scientific calculators and y equal the number of graphing calculators she buys She can only spend up to $800 for the calculators.

The inequality that represents the situation becomes as;

25x + 65y ≤ 800

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The solution to the trigonometric equation is sin( 6x ) = 2sin(3x)cos(3x)

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the equation be represented as A

Now , the value of A is

A = sin (6x)

From the trigonometric relations ,

The value of sin( 2x ) = 2sin(x)cos(x)

Now , when x is replaced by 6x

Substituting the values in the equation , we get

sin ( 6x ) = 2 sin ( 6x/2 ) cos ( 6x/2 )

On simplifying the equation , we get

sin ( 6x ) = 2 sin ( 3x ) cos ( 3x )

So , the value of the trigonometric relation is

sin(6x) = 2sin(3x)cos(3x)

Hence , the equation is sin(6x) = 2sin(3x)cos(3x)

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Step-by-step explanation:

Answer n=2

add 8n and -2n which is 6n and then divide 6n by 6 and 12 by 6 and you get n=2

The graph of the original triangle and the after the dilation are shown below:

Triangle dilation graph 8.

Dilation refers to the process of expanding or stretching an object or a space in one or more directions. In mathematics, dilation is a geometric transformation that changes the size of an object or a figure by either enlarging or reducing its dimensions, while preserving its shape and orientation.

In the context of image processing and computer vision, dilation is an operation that is commonly used to enhance and extract features from images. It involves convolving an image with a small structuring element or kernel, which slides over the image and replaces each pixel with the maximum value within the kernel.

For a dilation with a scale factor of 0.5 and centered at the origin, each coordinate of the triangle will be multiplied by 0.5. Thus:

J(8,0) will become J'(4,0)

L(-2,0) will become L'(-1,0)

K(4,4) will become K'(2,2)

The graph of the original triangle and the image after the dilation are shown below:

Triangle dilation graph 6

For a dilation with a scale factor of 2 and centered at the point (8,3), each coordinate of the triangle will be multiplied by 2 and then translated by the vector (8,3). Thus:

A (9,8) will become A'(26,14)

C (0,2) will become C'(8,7)

G (3,3) will become G'(14,9)

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Answer:

x=-1/4

Step-by-step explanation:

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

x=29

To solve for x in the equation 4x3 = -5x - 21, we can follow these steps:

1. Move all the terms containing x to one side of the equation, and move the constant term to the other side. We can do this by adding 5x to both sides and then adding 21 to both sides:

   4x3 + 5x = -21

2. Factor out x from the left-hand side of the equation:

   x(4x2 + 5) = -21

3. Divide both sides by (4x2 + 5):

   x = -21 / (4x2 + 5)

So the solution for x is x = -21 / (4x2 + 5). Note that this is a rational function, which means that the value of x depends on the value of the variable x. This equation has no real solutions because the denominator is always positive, and the numerator is negative.