What is the solution to -2(8x-4) < 2x + 5?
x > 2/1/20
x < 1/1/20
x>6
x<6

Answer:

Step-by-step explanation:

BAD = 42

x + 103 + 42 = 180

x = 180 - 145

x = 35

The expansion of the function \((3x - 4)^4\) simplifies to \(81x^4 - 432x^3 + 864x^2 - 768x + 256.\)

To expand the function \(f(x) = (3x - 4)^4\), we can use the binomial theorem. According to the binomial theorem, for any real numbers a and b and a positive integer n, the expansion of \((a + b)^n\) can be written as:

\((a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^{(n-1)} b^1 + C(n, 2)a^{(n-2)} b^2 + ... + C(n, n-1)a^1 b^{(n-1)} + C(n, n)a^0 b^n\)

where C(n, k) represents the binomial coefficient, which is given by C(n, k) = n! / (k!(n-k)!).

Applying this formula to our function \(f(x) = (3x - 4)^4\), we have:

\(f(x) = C(4, 0)(3x)^4 (-4)^0 + C(4, 1)(3x)^3 (-4)^1 + C(4, 2)(3x)^2 (-4)^2 + C(4, 3)(3x)^1 (-4)^3 + C(4, 4)(3x)^0 (-4)^4\)

Simplifying each term, we get:

\(f(x) = 81x^4 + (-432x^3) + 864x^2 + (-768x) + 256\)

Therefore, the expanded form of the function \(f(x) = (3x - 4)^4\) is \(81x^4 - 432x^3 + 864x^2 - 768x + 256\).

Note that the coefficient of \(x^3\) is -432, the coefficient of \(x^2\) is 864, the coefficient of x is -768, and the constant term is 256.

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Note the complete question is

The amount of water the farmer can put in the tank increase when the larger tank is built is 106.33%.It takes 4days for the horses to drink all the water in the larger tank.

Percentage is a way of expressing a proportion or a fraction out of 100. It represents the number of parts per hundred of a quantity.

Dimension refers to a measurable aspect of an object or a system, such as length, width, height, depth, volume, area, or mass. In mathematics, dimension also refers to the number of coordinates required to specify a point in a space. For example, a two-dimensional shape like a square has two dimensions, length and width, while a three-dimensional object like a cube has three dimensions, length, width, and height.

To find the percentage increase in the amount of water the farmer can put in the larger tank, we need to calculate the volume of the original tank and the volume of the larger tank, and then compare the two.

The original tank has dimensions of 2 4/5 ft, 2 2/5 ft, and 2 1/2 ft. We can convert these mixed numbers to improper fractions for easier calculations:

2 4/5 ft = (2 x 5 + 4)/5 ft = 14/5 ft

2 2/5 ft = (2 x 5 + 2)/5 ft = 12/5 ft

2 1/2 ft = (2 x 2 + 1)/2 ft = 5/2 ft

The volume of the original tank is then:

Volume = Length x Width x Height = 14/5 ft x 12/5 ft x 5/2 ft

Now, the farmer plans to increase measurement  by 25%. To do this, we multiply each measurement by 1.25.

The dimensions of the larger tank would be:

Length = 14/5 ft x 1.25 = 3.5 ft

Width = 12/5 ft x 1.25 = 3 ft

Height = 5/2 ft x 1.25 = 3.125 ft

The volume of the larger tank is then:

Volume = Length x Width x Height = 3.5 ft x 3 ft x 3.125 ft

To find the percentage increase, we can compare the two volumes:

Percentage increase = ((Volume of larger tank - Volume of original tank) / Volume of original tank) x 100

Plugging in the values we found:

Percentage increase = ((3.5 ft x 3 ft x 3.125 ft - 14/5 ft x 12/5 ft x 5/2 ft) / (14/5 ft x 12/5 ft x 5/2 ft)) x 100

After calculating the above expression, we find that the percentage increase is approximately 106.33%. So, the amount of water the farmer can put in the larger tank will increase by approximately 106.33% when the larger tank is built.

Now, to find how many days it will take the horses to drink all the water in the larger tank, we can assume that the rate at which the horses drink water remains constant. Since the volume of the larger tank is approximately 106.33% more than the original tank, it will take the horses approximately the same amount of time to drink all the water in the larger tank, which is 4 days.

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The formula for finding the area of the unshaded segment is given as

Given the following parameters,

π = 3.14

θ = 80°

r = 5 cm

Substituting,

To find the area of the shaded portion, we would subtract the area of the unshaded segment from the area of the circle.

Area of circle = πr²

Therefore,

The area of the shaded region = 78.5 - 5.1 = 73.4 cm²

Answer:

obtuse

Step-by-step explanation:

Let 5 = a, 7 = b, 10 = c

if a^2 + b^2 = c^2, then the triangle is a right triangle by the converse of the Pythagorean Theorem

If a^2 + b^2 > c^2, then the triangle is an acute triangle by Theorem 8-4

if a^2 + b^2 < c^2, then the triangle is an obtuse triangle by Theorem 8-3

a^2 = 25

b^2 = 49

c^2 = 100

25 + 49 < 100, therefore the triangle is an obtuse

Answer:

This identity holds as long as \(\displaystyle \theta \ne k\, \pi + \frac{\pi}{2}\) for all integer \(k\).

For the proof, make use of the fact that:

\(\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\) (definition of tangents,) and

\(\cos(\theta) = \sqrt{1 - \sin^{2}(\theta)}\) (Pythagorean identity,) which is equivalent to \(1 - \cos^{2}(\theta) = \sin^{2}(\theta)\).

Step-by-step explanation:

Assume that \(\displaystyle \theta \ne k\, \pi + \frac{\pi}{2}\) for all integer \(k\). This requirement ensures that the \(\tan(\theta)\) on the left-hand side takes a finite value. Doing so also ensures that the denominator \(\sqrt{1 - \sin^2(\theta)}\) on the right-hand side is non-zero.

Make use of the fact that \(\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\) to rewrite the left-hand side:

\(\begin{aligned} & \tan(\theta) \cdot \sin(\theta) \\ =&\; \frac{\sin({\theta})}{\cos({\theta})} \cdot \sin(\theta) \\ =&\; \frac{\sin^{2}(\theta)}{\cos(\theta)}\end{aligned}\).

Apply the Pythagorean identity \(\sin^{2}(\theta) = 1 - \cos^{2}(\theta)\) and \(\cos(\theta) = \sqrt{1 - \sin^{2}(\theta)}\) to rewrite this fraction:

\(\begin{aligned} & \frac{\sin^{2}(\theta)}{\cos(\theta)}\\ =\; &\frac{1 - \cos^{2}(\theta)}{\cos(\theta)}\\ =\; & \frac{1 - \cos^{2}(\theta)}{\sqrt{1 - \sin^{2}(\theta)}}\end{aligned}\).

Hence, \(\displaystyle \tan(\theta) \cdot \sin(\theta) = \frac{1 - \cos^{2}(\theta)}{\sqrt{1 - \sin^{2}(\theta)}}\).

Answer:

Step-by-step explanation:

x = hamburgers

x - 58 = cheeseburgers

392 = total of both sold

x + (x - 58) = 392

x + x - 58 + 58 = 392 + 58

x + x = 450

2x = 450

Divide both sides by 2

2x/2 = 450/2

x = 225

The number of hamburgers sold was 225

Using Maxwell's equations, we can determine the magnetic flux density. One of the Maxwell's equations is:

\(\displaystyle \nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}}{\partial t}\),

where \(\displaystyle \nabla \times \mathbf{H}\) is the curl of the magnetic field intensity \(\displaystyle \mathbf{H}\), \(\displaystyle \mathbf{J}\) is the current density, and \(\displaystyle \frac{\partial \mathbf{D}}{\partial t}\) is the time derivative of the electric displacement \(\displaystyle \mathbf{D}\).

In this problem, there is no current density (\(\displaystyle \mathbf{J} =0\)) and no time-varying electric displacement (\(\displaystyle \frac{\partial \mathbf{D}}{\partial t} =0\)). Therefore, the equation simplifies to:

\(\displaystyle \nabla \times \mathbf{H} =0\).

Taking the curl of the given magnetic field intensity \(\displaystyle \mathbf{R} =2\cos( 10^{10} t-600x)\hat{a}_{z}\, \text{Am}\):

\(\displaystyle \nabla \times \mathbf{R} =\nabla \times ( 2\cos( 10^{10} t-600x)\hat{a}_{z}) \, \text{Am}\).

Using the curl identity and applying the chain rule, we can expand the expression:

\(\displaystyle \nabla \times \mathbf{R} =\left( \frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial y} -\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial z}\right) \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Since the magnetic field intensity \(\displaystyle \mathbf{R}\) is not dependent on \(\displaystyle y\) or \(\displaystyle z\), the partial derivatives with respect to \(\displaystyle y\) and \(\displaystyle z\) are zero. Therefore, the expression further simplifies to:

\(\displaystyle \nabla \times \mathbf{R} =-\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial x} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Differentiating the cosine function with respect to \(\displaystyle x\):

\(\displaystyle \nabla \times \mathbf{R} =-2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Setting this expression equal to zero according to \(\displaystyle \nabla \times \mathbf{H} =0\):

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z =0\).

Since the equation should hold for any arbitrary values of \(\displaystyle \mathrm{d} x\), \(\displaystyle \mathrm{d} y\), and \(\displaystyle \mathrm{d} z\), we can equate the coefficient of each term to zero:

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x) =0\).

Simplifying the equation:

\(\displaystyle \sin( 10^{10} t-600x) =0\).

The sine function is equal to zero at certain values of \(\displaystyle ( 10^{10} t-600x) \):

\(\displaystyle 10^{10} t-600x =n\pi\),

where \(\displaystyle n\) is an integer. Rearranging the equation:

\(\displaystyle x =\frac{ 10^{10} t-n\pi }{600}\).

The equation provides a relationship between \(\displaystyle x\) and \(\displaystyle t\), indicating that the magnetic field intensity is constant along lines of constant \(\displaystyle x\) and \(\displaystyle t\). Therefore, the magnetic field intensity is uniform in the given medium.

Since the magnetic flux density \(\displaystyle B\) is related to the magnetic field intensity \(\displaystyle H\) through the equation \(\displaystyle B =\mu H\), where \(\displaystyle \mu\) is the permeability of the medium, we can conclude that the magnetic flux density is also uniform in the medium.

Thus, the correct expression for the magnetic flux density in the given medium is:

\(\displaystyle B =6\cos( 10^{10} t-600x)\hat{a}_{z}\).

Answer:

140.22

Step-by-step explanation:

(a) The local extrema of the polynomial are: Local maximum at x = -0.68 and Local minimum at x = -0.32

(b) There is no global minimum or maximum.

To find the local extrema and absolute extrema of the given polynomial 10x⁵ + 22x⁴ + 20x³ - 0x² + 6, we need to take the first and second derivatives of the polynomial and find the critical points.

The first derivative is:

50x⁴ + 88x³ + 60x²

The second derivative is:

200x³ + 264x² + 120x

Setting the first derivative to zero, we get:

50x⁴ + 88x³ + 60x² = 0

Factoring out x², we get:

x²(50x² + 88x + 60) = 0

Using the quadratic formula to solve for the roots of the quadratic equation 50x² + 88x + 60 = 0, we get:

x = -0.68 or x = -0.32

These are the critical points of the polynomial. To determine whether they correspond to local extrema or inflection points, we need to look at the sign of the second derivative at each point.

Substituting x = -0.68 into the second derivative, we get:

200(-0.68)³ + 264(-0.68)² + 120(-0.68) = -148.68

Since the second derivative is negative at x = -0.68, this critical point corresponds to a local maximum.

Substituting x = -0.32 into the second derivative, we get:

200(-0.32)³ + 264(-0.32)² + 120(-0.32) = 9.48

Since the second derivative is positive at x = -0.32, this critical point corresponds to a local minimum.

To find the absolute extrema, we also need to evaluate the polynomial at the endpoints of the interval we are interested in. Since the polynomial does not have any real roots, we can assume that the interval of interest is the entire real line.

Taking the limit of the polynomial as x approaches positive or negative infinity, we see that the leading term dominates and the polynomial goes to positive infinity as x approaches infinity and negative infinity.

Therefore, there is no global minimum or maximum.

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The total number of each zone for a three-week period is between 1200 and 1300, 1:2 is the ratio of customer from Zone 1 to customers from Zone 3.

​

1) During 3 weeks bound

Customers from zone 3 = 900

Customers from zone 4 = 320

So, total customers = (900 + 320)

= 1220

Hence, option D is correct i.e between 1200 and 1300.

2) Customer from zone 1 = 450

Customers from zone 3 = 900

So, Customer from zone 1 / Customer from zone 3 = 450/900

= 1/2

Hence, option 2 i.e., 1:2 is correct.

3) 3/5 pound of clay is used to make = 1 bowl

So, 1 bound of clay is used to make = 5/3 bowl

By unitary method,

10 pounds of clay is used to make = 10 *(5/3)

= 16.66

= 17 bowls (approx)

Hence, option d is correct answer.

Therefore, The total number of each zone for a three-week period is between 1200 and 1300, 1:2 is the ratio of customer from Zone 1 to customers from Zone 3.

​

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Answer:

h = 5.318 m

Step-by-step explanation:

6.5/11 = h/9

0.5909 = h/9

h = 5.318

Answer:

Height: 5.32

Step-by-step explanation:

Area=29.24

Heron's Formula

Answer:

-6

Step-by-step explanation:

Answer:

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

There are two triangular faces with base of 16 cm and height of 15 cm and three rectangular faces.

Find the sum of areas of all five faces:

Answer:

8.7 cm

Step-by-step explanation:

Since all sides of the given shape are equal, so it is a cube.

So length of the diagonal of cube is give as:

\(l(diagonal) = l \sqrt{3} \\ \\ = 5 \times 1.732 \\ \\ = 8.66 \\ \\ l(diagonal) \approx8.7 \: cm\)

Answer:

B: rectangle JKLM ~ rectangle QRSP

Step-by-step explanation:

5/6=0.83

12.5=0.83

JK corresponds to QR

JM corresponds to PQ

rectangle JKLM ~ rectangle QRSP

This function represents a downward-opening parabola with a vertical shift of 6 units upward.

The given function is Ƒ(t) = –1/(2t²) + 2t + 6.

This is a quadratic function in terms of t. The general form of a quadratic function is f(t) = at² + bt + c, where a, b, and c are constants.

Comparing the given function Ƒ(t) = –1/(2t²) + 2t + 6 with the general form, we can see that a = -1/2, b = 2, and c = 6.

So, the function Ƒ(t) can be written as:

Ƒ(t) = (-1/2)t² + 2t + 6

This function represents a downward-opening parabola with a vertical shift of 6 units upward.

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Answer:

0.4332 = 43.32% probability of a rating that is between 200 and 275.

Step-by-step explanation:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

A bank's loan officer rates applicants for credit. the ratings are normally distributed with a mean of 200 and a standard deviation of 50

This means that \(\mu = 200, \sigma = 50\).

Find the probability of a rating that is between 200 and 275.

This is the pvalue of Z when X = 275 subtracted by the pvalue of Z when X = 200. So

X = 275

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{275 - 200}{50}\)

\(Z = 1.5\)

\(Z = 1.5\) has a pvalue of 0.9332

X = 200

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{200 - 200}{50}\)

\(Z = 0\)

\(Z = 0\) has a pvalue of 0.5

0.9332 - 0.5 = 0.4332

0.4332 = 43.32% probability of a rating that is between 200 and 275.

Answer:

So that's 75$ back.....

Answer: q=13

Step-by-step explanation:

add the separate the q, add 4 to the 9= 13

13=q

Answer:

Hugo has 10 songs in his music player. He will add 15 songs every month. Hugo collects songs for r months. For what values of r will Hugo have at most 135 songs?

Step-by-step explanation:

took test 100%

Since we have that 1 + 3i is one zero of p(x), then we have that its conjugate is also a root, then, we have the following complex roots for p(x):

also, notice that if we evaluate -1 on p(x), we get:

therefore, the zeros of p(x) are:

x = 1-3i

x = 1+3i

x = -1

Answer:

ok, here is your answer

Step-by-step explanation:

Using the formula for compound interest:

A = P (1 + r/n)^(nt)

where:

A = the total amount

P = the principal amount

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

Given:

P = €250

r = 9% = 0.09

n = 1 (compounded annually)

t = 3 years

Now, substituting the given values in the formula:

A = 250 (1 + 0.09/1)^(1*3)

A = 250 (1 + 0.09)^3

A = 250 (1.09)^3

A = 250 (1.29503)

A = €323.76 (rounded to two decimal places)

Therefore, the balance in the account at the end of 3 years would be €323.76.

5

1) Since this is a line of best fit, actually we are going to find an approximation for that.

2) Locating two points along the line, we've got (1,30) and (7,60) so let's find the rate of change:

So, the rate of change relative to the scatter plot is 5

Answer:

false because it only equal when b = n

Answer:

177 pounds

Step-by-step explanation:

Create an equation to represent the system.

Since it's 18% more than what was used last month an equation can be written such as the one below:

(118%)( last month's cheese ) = this month's cheese

Convert the percentages into decimals by moving the decimal place at the end of 118.00 two places to the left

118% = 1.18

( 1.18 )( last month's cheese ) = this month's cheese

Next, plug in the number for last month's cheese

( 1.18 )( 150 pounds) =

177 pounds

Answer:

The question is not complete

The first term of the sequence is u₁ = 2.

In a geometric sequence, each term is found by multiplying the previous term by a constant ratio. Let's denote the first term as u₁ and the common ratio as r.

Given information:

u₂ = 6

u₆ = 486

We can use the formula for the nth term of a geometric sequence:

uₙ = u₁ x r^(n-1)

Plugging in the values for the second term (n = 2) and the sixth term (n = 6), we get:

u₂ = u₁ x r²⁻¹ = u₁ x r

u₆ = u₁ x r⁶⁻¹ = u₁ x r⁵

We can set up a system of equations with these two equations:

u₂ = 6 --> u₁r = 6 ...(1)

u₆ = 486 --> u₁ r⁵ = 486 ...(2)

Dividing equation (2) by equation (1), we get:

(u₁r⁵) / (u₁r) = (486) / 6

Simplifying the equation:

r⁴ = 81

Taking the fourth root of both sides:

r = √(81)

Therefore,

u₁ = 6/3

u₁ = 2.

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