check if f(x)=4x³+4x²-x-1 is a multiple of (2x+1)​

Answer:

6.87 g/mL

Step-by-step explanation:

The density of an object can be found by dividing the mass by the volume.

\(density=\frac{mass}{volume}\\\\ d=\frac{m}{ v}\)

We know that the aluminum occupies a volume of 12.7 milliliters and weighs 87.3 grams. Therefore, the mass is 87.3 g and the volume is 12.7 mL.

\(m= 87.3 g\\\\v=12.7 mL\)

Substitute the values into the formula.

\(d= \frac{87.3 g}{12.7 mL}\)

Divide 87.3 g by 12.7 mL

\(d=6.87401575 g/mL\)

Round to the nearest hundredth. The 4 in the thousandth place tells us to leave the 7 in the hundredth place.

\(d= 6.87 g/mL\)

The density of the aluminum is about 6.87 grams per milliliter.

\(\displaystyle\bf (3-5\sqrt{5} )-(5\sqrt{3} -3)=3+3-5\sqrt{5} -5\sqrt{3} =\boxed{6-5\sqrt{5} -5\sqrt{3} } \\\\\\\\\sqrt{5} (\sqrt{5} -2x)=\boxed{-2x\sqrt{5} +5}\)

The probability of getting a number greater than 3 is:

P(greater than 3) = favorable outcomes / total outcomes

= 3 / 6

= 1 / 2

So, the correct answer is d. one-half.

A single, standard number cube has six sides, numbered from 1 to 6. To find the probability of getting a number greater than 3, we need to determine the favorable outcomes (numbers greater than 3) and divide it by the total number of possible outcomes (all numbers on the cube).

Favorable outcomes: {4, 5, 6} (three numbers greater than 3)

Total possible outcomes: {1, 2, 3, 4, 5, 6} (six numbers in total)

Therefore, the probability of getting a number greater than 3 is:

P(greater than 3) = favorable outcomes / total outcomes

= 3 / 6

= 1 / 2

So, the correct answer is d. one-half.

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Applying the trigonometry ratios, the missing lengths for right triangle ABC are: 12 and 8√3.

Trigonometric ratios are defined as the values of all trigonometric functions based on the right-angled triangle's side ratio. The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.

Reference angle (∅) = 60

Adjacent = 4√3

Opposite = ?

tan 60 = opp/adj

tan 60 = Opp/4√3

√3 = opp/4√3

Opposite = √3 × 4√3

Opposite = 12

Reference angle (∅) = 60

Adjacent = 4√3

Hypotenuse = ?

cos 60 = adj/hyp

cos 60 = 4√3/hyp

hyp = 4√3/cos 60

hyp = 4√3/1/2

hyp = 4√3 × 2

hyp = 8√3

Therefore, applying the trigonometry ratios, the missing lengths for right triangle ABC are: 12 and 8√3.

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Step-by-step explanation:

for a=

\( \frac{s - n}{n} \)

Answer:

6√3

Step-by-step explanation:

Spherical harmonics are an integral part of quantum mechanics. They describe the shape of the orbitals, which electrons occupy in atoms. Moreover, the spherical harmonics provide the angular distribution of a wave in spherical coordinates. In 3D, the spherical harmonics can be written as:

Ylm(θ, φ) = √(2l + 1)/(4π) * √[(l - m)!/(l + m)!] * Plm(cosθ) * e^(imφ)

Here, l and m are known as the angular quantum numbers. They define the shape and orientation of the orbital. Plm(cosθ) represents the associated Legendre polynomial, and e^(imφ) is the exponential function. The spherical harmonics have various forms, including:

Y1,1 = -Y1,-1 = 1/2 √(3/2π) sinθe^(iφ)

Y1,0 = 1/2 √(3/π)cosθ

Y2,2 = 1/4 √(15/2π)sin²θe^(2iφ)

Y2,1 = -Y2,-1 = 1/2 √(15/2π)sinθcosφ

Y2,0 = 1/4 √(5/π)(3cos²θ-1)

Y0,0 = 1/√(4π)

The spherical harmonics have various applications in physics, including quantum mechanics, electrodynamics, and acoustics. They play a crucial role in understanding the symmetry of various systems. Hence, the spherical harmonics are an essential mathematical tool in modern physics. Thus, this is how one can show another form for spherical harmonics.

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If one number is the multiple of another number, then the L.C.M. will be the smaller number (the number whose multiple the other number is).

The unknown angle x in the triangle is 80 degrees

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

The triangle

The unknown angle x is calculated using the sum of angles in a triangle theorem

So, we have

x + 60 + 40 = 180

Evaluate the like terms

x + 100 = 180

So, we have

x = 80

Hence, the unknown angle x is 80 degrees

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Answer:

\(x = [2644,8418)\)

Step-by-step explanation:

Given

\(f(x) = 86.3ln\ x - 680\)

\(x < 8418\)

Required

The domain of the function

The maximum value of x has been given.

So, the next step is to calculate its minimum value.

Since f(x) represents the % moisture. This value cannot go less than 0.

So, we set f(x) to 0; in order to calculate the minimum of x.

This gives:

\(f(x) = 0\)

\(86.3ln\ x - 680 = 0\)

Add 680 to both sides

\(86.3ln\ x - 680 + 680= 0 + 680\)

\(86.3ln\ x = 680\)

Divide both sides by 86.3

\(ln\ x = \frac{680}{86.3}\)

\(ln\ x = 7.88\)

Take exponent of both sides

\(e^{(ln\ x)} = e^{7.88\)

\(x = e^{7.88\)

\(x = 2644\)

Hence, the domain is:

\(x = [2644,8418)\)

or

\(2644 \le x< 8418\)

Equation of opened downward parabola is (x - 1) ²= - 4/5 (y - 25/4)

Parabola is a curve created by the intersection of a cone and a plane. Generally, parabola is U shaped and either open in downward or opened in upward direction.

The formula for opened downward parabola is given by (x - h) ² = - 4p (y - k)

as the parabola contains the points (0, 5) (2, 5) and (- 2, -5)

so, the equation can be (0 -h) ² = - 4p(5 - k)   [ put the value (0, 5)]

                                       h² = - 20p+4pk ..... equation 1

while putting the value (2, 5) we have the equation of parabola.

  (2 - h) ² = - 4p(5 - k)

   4 - 4h + h ² = - 20p + 4pk .... equation 2

from the equation 1 and 2, the right-hand side is similar.

hence, 4 - 4h +h² = h²

       4 = 4h

      h = 1

put h =1 in the equation 1 we get, 1 = - 20p + 4pk .... equation 3

when we put the value ( -2, -5) in the formula.

(- 2- h) ² = - 4p ( -5 -k)

( -2 -1) ² = 20p +4pk

9 = 20p +4pk ....... equation 4

from equation 4 and equation 3

we get, 9 = 20p +4pk

               1 = - 20p+ 4pk

               -      +       -

solve by addition method and we get, 8 = 40p

                                                           p = 1/5

  from h = 1 and p = 1/5 we get the value of k from equation 3

  1 = - 20/5 + 4/5k

 k = 25/4

now the equation of opened downward parabola will be.

(x - 1) ² = - 4/5 (y - 25/4)

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The statement also says that t finishes after p and before q. This means that t cannot have finished third, as that position is already occupied by q.

In a race involving five runners, p, q, r, s, and t, it is possible to deduce the order of finish based on the information given. According to the statement, p beats q and p beats r, indicating that p finished first in the race. Additionally, q beats s, so q must have finished second.

Therefore, t must have finished either fourth or fifth.One could also deduce that T could not have finished fourth in the race.

As T finishes before Q who is in the 2nd place and after P who is in the first place.It is important to note that this conclusion is based on the information given and cannot be confirmed without additional information.

For example, if it were specified that t finished just milliseconds after p and just before q, it would not be possible to determine whether t finished fourth or fifth.

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Answer:

  3

Step-by-step explanation:

The Roman numerals at left indicate generations I through III are shown on the chart. 3 generations are shown.

An equation of the line that passes through (1, 2) and is parallel to the given line is y=-5x+7.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

Given that, the coordinate point is (1, 2) and the line is y=-5x+4.

Here, slope of given equation is m₁= -5

We know that, the slope of parallel lines is equal. That is m₁=m₂.

Now, slope m₂=-5

Substitute, m=-5 and (x, y)=(1, 2) in y=mx+c, we get

2=-5(1)+c

c=7

Substitute, m=-5 and c=7 in y=mx+c, we get

y=-5x+7

Therefore, an equation of the line that passes through (1, 2) and is parallel to the given line is y=-5x+7.

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We get that a / b will also be less than e / f.

A rational number means a number that can be written in the form of p / q.

We are given the three rational numbers:

a / b , c / d and e / f.

We are also given that:

a / b < c / d  …(1)

c / d < e / f    …(2)

Multiply (1) and (2), we get that:

a / b × c / d < c / d × e / f

Dividing both sides by d / c, we get that:

a / b < e / f

So, a / b will also be less than e / f.

Therefore, we get that a / b will also be less than e / f.

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Answer:

i have no idea what the answer is

Step-by-step explanation:

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300% of 10 is 30.

30 x 100/300 = 10

It is important to be aware that the distribution of sample means x may not match the distribution of the original x values exactly, due to sampling variability.

if the original distribution of x values is known to be normalize size needs to be large, then the sample size does not need to be restricted in order to claim that the distribution of sample means x taken from random samples of a given size is normal. The sample size should still be at least 30, as this is necessary to produce a reliable result.

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Answer:

x = 14

y = 4

Explanation:

Ok so, just from looking at the two triangles i can tell they're congruent right triangles. I used different colors to show which sides of the triangle correspond and are equal to each other in my attatched photo.

So the side thats equal to x is the same length as the side that's equal to y+10 on the other triangle.

So we can write the equation x = y + 10.

Using this same method, the side that's equal to x + 2 is the same length as the side that's equal to 4y on the other triangle.

So, we can write the equation 4y = x + 2.

Now we have the equations \(\left \{ {{x=y+10} \atop {4y=x+2}} \right.\) you could rewrite to be in slope- intercept form so they're easier to graph. But a graphing calculator online would plot it just fine.

If you graph these two equations they'll intersect at the solution ( 14, 4 ). I'll include the graph in my images as well.

To check your answer, you can plug in x and y and see if the triangle sides end up being the same length. I did and it was correct.

Answer:

you have to start with you b which in your problem is 5 so put a point at 5 on the y-axis on your graph. then with the M (the fraction numbers) you have to move either up or down depending if there is a negative number. so yours is 1/2 so then you would start at the 5 point and go up 1 and right 2 then you just keep repeating till you get a few points and can make a line then you just do the same thing for the other equation. start at 3 on the y-axis and then go up 3 and right 4 then just keep repeating till you get a few point and can create a line at the end the lines should cross each other like perpendicular lines

Step-by-step explanation:

hope this helps:)

Answer:

$14.70

Step-by-step explanation:

31.50/15=2.10

2.10*7=14.70

Answer:

8

Step-by-step explanation:

16/8 × 2²

= 2 × 4

= 8

hope this helps

Step-by-step explanation:

16/8 ×2^2

=16/8 × 4

=2 × 4

=8

The integer that represents the scenario "Zach hiked 54 feet up the mountain" is the number 54.

A whole number that can be either positive, negative, or zero is known as an integer.In other words, it is a number that has no fractional or decimal part.

Examples of integers include -3, -2, -1, 0, 1, 2, 3, and so on.

Mathematical operations like addition, subtraction, multiplication, and division all use integers.

They are also used in everyday life situations, such as counting, measuring, and keeping score.

In this case, since Zach hiked up the mountain, the integer is positive.

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Answer:

Number of small boxes Sam made = Total piece of wood bought / Piece of wood used for each small box

Step-by-step explanation:

Total piece of wood bought = 7/8 foot

Piece of wood used for each small box = 3/16 foot

Number of small boxes Sam made = Total piece of wood bought / Piece of wood used for each small box

= 7/8 foot ÷ 3/16 foot

= 7/8 × 16/3

= 7×16 / 8×3

= 112 / 24

= 4 16/24

= 4 2/3 small boxes

The equation is:

Number of small boxes Sam made = Total piece of wood bought / Piece of wood used for each small box

A system of equation is 1680mi3hr = p−w×600×2hr -p + w  for a jet airliner travels 1680 miles in 3hours with a tail wind.

Let p be  the speed of the jet airliner

and w  be the speed of the tail wind

It takes the plane 3 hours to go 1680 miles when a jet airliner travels with a tail wind and and 3.5 hours to go 1680 miles against the wind.. So, using system of equations we get

1680mi3hr = p−w×600×2hr = p + w

Solving for the left sides we get:

200mph = p - w

300mph = p + w

Now solve for one variable in either equation, we use

200mph = p - w

Add w to both sides:

p = 200mph + w

Using the value of x, we can found the value of w using system of equations.

300mph = (200mph + w) + w

Combine like terms:

300mph = 200mph + 2w

Subtract 200mph on both sides:

100mph = 2w

On dividing by 2:

50mph = w

So the speed of the tail wind is 50mph.

Therefore, 200mph = p - 50mph

Add 50mph on both sides:

250mph = p

Hence, speed of jet airliner is 250mph.

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a. The equation can be written as \(3x^{(2)} - 75 = 0,\) where a = 3, b = 0, and c = -75.

b. The discriminant \(b^{(2)} - 4ac\)  is equal to 0, indicating that there are two real solutions.

c. Solving the equation, we find x = ±√(25), so the solutions are x = ±5.

a. To write the equation \(3x^{(2)} = 75\) as \(ax^{(2)} + bx + c = 0\) with a > 0, we can start by dividing both sides of the equation by 3:

\(x^{(2)}= 25\)

Now, we have the equation in the form \(x^{(2)} - 25 = 0.\)

Since the coefficient of \(x^{(2)\) is positive, we can say that a = 1, b = 0, and c = -25.

Therefore, the equation can be rewritten as:

\(x^{(2)} + 0x - 25 = 0\)

b. The discriminant, denoted by Δ, is given by the expression\(b^{(2)} - 4ac.\)

In this case, a = 1,  b = 0, and c = -25.

Substituting these values into the formula, we get:

Δ \(= (0)^{(2)} - 4(1)(-25)\)

= 0 - (-100)

= 100

The discriminant is positive (Δ > 0), which means that there are two distinct real solutions for this equation.

c. To solve the equation \(x^{(2)}- 25 = 0,\) we can factor it as a difference of squares:

(x + 5)(x - 5) = 0

Setting each factor equal to zero, we have:

x + 5 = 0 or x - 5 = 0

Solving for x in each equation, we get:

x = -5 or x = 5.

Therefore, the equation \(3x^{(2)} = 75\) has two real solutions: x = -5 and x = 5.

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