Add Each pair of expressions
(4x-7) and (7-4x)
Answer ASAP

The standard format for electronic document submission in U.S. federal courts is PDF (Portable Document Format).

PDF, or Portable Document Format, is a widely used file format that allows for the electronic representation of documents. It is designed to be platform-independent, meaning it can be viewed and accessed on different devices and operating systems while retaining its original formatting. In the context of U.S. federal courts, PDF has become the standard format for attorneys to submit documents electronically.

The adoption of PDF as the standard format for electronic document submission in U.S. federal courts brings several advantages. PDF files are generally compact in size, making them easier to transmit and store. They also preserve the interest, fonts, and graphics of the original document, ensuring that the submitted materials are accurately represented.

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The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope. The equation of the line that is perpendicular to y = -2x + 4 and passes through the point (4, 2) is given by option D: y = -2x.

To determine which equation represents a line perpendicular to y = -2x + 4 and passes through the point (4, 2), we need to consider the slope of the given line. The equation y = -2x + 4 is in slope-intercept form (y = mx + b), where the coefficient of x (-2 in this case) represents the slope of the line.

Since we are looking for a line that is perpendicular to this given line, we need to find the negative reciprocal of the slope. The negative reciprocal of -2 is 1/2. Therefore, the slope of the perpendicular line is 1/2.

Now, we can use the point-slope form of a line to find the equation. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope.

Substituting the values (4, 2) for (x₁, y₁) and 1/2 for m, we get:

y - 2 = (1/2)(x - 4).

Simplifying this equation, we find:

y - 2 = (1/2)x - 2.

Rearranging the terms, we obtain:

y = (1/2)x.

Therefore, option D, y = -2x, represents the equation of the line that is perpendicular to y = -2x + 4 and passes through the point (4, 2).

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First square root: √(√2)(cos(22.5°) + isin(22.5°))
Second square root: √(√2)(cos(202.5°) + isin(202.5°))

Here are the steps:

1. Convert the complex number 1+i to polar form.
In polar form, a complex number is represented as r(cos(θ) + isin(θ)), where r is the modulus and θ is the argument.

Calculate the modulus (r):
r = √(Re² + Im²) = √(1² + 1²) = √2

Calculate the argument (θ) in degrees:
θ = arctan(Im/Re) = arctan(1/1) = 45°

So, the polar form of 1+i is:
√2(cos(45°) + isin(45°))

2. Find the square roots using De Moivre's Theorem.
De Moivre's Theorem states that for any complex number in polar form, (r(cos(θ) + isin(θ)))ⁿ = rⁿ(cos(nθ) + isin(nθ)), where n is any real number.

In this case, we're looking for square roots, so n = 1/2.

Calculate the new modulus:
r¹/² = (√2)¹/² = √(√2)

Calculate the new arguments:
(1/2) * 45° = 22.5°
(1/2) * (45° + 360°) = 202.5°

3. Write the two square roots in polar form:
First square root: √(√2)(cos(22.5°) + isin(22.5°))
Second square root: √(√2)(cos(202.5°) + isin(202.5°))

These are the two square roots of 1+i in polar form with the argument in degrees.

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Answer:

Now 7 remains without a pair and therefore 7 should be multiplied to 112 to make it a perfect square. Similarly 28 should be multiplied to 784 to make it a perfect cube.

Step-by-step explanation:

112 = 2⁴ * 7.

Next power after 2⁴ with a cube power = 2⁶.

Next power after 7 with a cube power = 7³.

Therefore k = 2² * 7² = 196.

(a) The statement is true , (b) The statement is false.

(a) The statement is true. If a function f is smooth (differentiable), then its gradient vector is defined as ∇f = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k,

where i, j, and k are the unit vectors in the x, y, and z directions, respectively.

Taking the curl of the gradient vector yields the expression

curl(∇f) = (∂(∂f/∂z)/∂y - ∂(∂f/∂y)/∂z)i + (∂(∂f/∂x)/∂z - ∂(∂f/∂z)/∂x)j + (∂(∂f/∂y)/∂x - ∂(∂f/∂x)/∂y)k.

∵ the second derivatives of f are continuous (smooth function), these partial derivatives commute, resulting in each term being zero.

∴ curl(∇f) = 0→i + 0→j + 0→k.

(b) The statement is false. If a vector field →G is a smooth curl field, it means that the curl of →G is zero, i.e., curl(→G) = 0. However, it does not imply that the divergence of →G is zero. The divergence of a vector field →G is defined as

div(→G) = ∂Gx/∂x + ∂Gy/∂y + ∂Gz/∂z,

where Gx, Gy, and Gz are the components of →G in the x, y, and z directions, respectively. Even if curl(→G) = 0, the individual partial derivatives in the divergence expression may not cancel out, resulting in a non-zero value. Therefore, in general, div(→G) ≠ 0 for a smooth curl field →G.

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If cos 3α is positive, it implies that α is an acute angle in the first or fourth quadrant of the unit circle.  if cos 3α is negative, α is an acute angle in the second or third quadrant.

We can find an acute angle β such that 3α ≠ 3β or 3α = 3(β + 90). Additionally, the sets of numbers cos β, cos (β + 120), cos (β + 240), and cos (β + 90), cos (β + 210), and cos (β + 330) are equal.

On the other hand, if cos 3α is negative, α is an acute angle in the second or third quadrant. We can find an acute angle β such that 3α = 3(β + 30) or 3α = 3(β + 60). Furthermore, the sets of numbers cos (β + 30), cos (β + 150), cos (β + 270), and cos (β + 60), cos (β + 180), cos (β + 270) coincide.

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To solve the problem, we can use the equations for the axial deformation of a bar under axial load:

ε = δ/L

σ = Eε

where ε is the strain, δ is the displacement, L is the length of the bar, σ is the stress, and E is the modulus of elasticity.

(a) To find the displacements at points B and C, we can use the equation:

δ = PL/AE

where P is the axial load, L is the length of the bar, A is the cross-sectional area, and E is the modulus of elasticity.

For point B, the axial load is 5000 lb and the cross-sectional area is 1 sq in. The length of the bar is 10 in (15 in - 5 in). The modulus of elasticity is 30x10^6 psi. Therefore, the displacement at point B is:

δB = (5000 lb x 10 in) / (1 sq in x 30x10^6 psi) = 0.0167 in

For point C, the axial load is 2000 lb and the cross-sectional area is 0.25 sq in. The length of the bar is 12 in (15 in - 3 in). The modulus of elasticity is 30x10^6 psi. Therefore, the displacement at point C is:

δC = (2000 lb x 12 in) / (0.25 sq in x 30x10^6 psi) = 0.008 in

(b) To find the axial load in each shaft, we can use the equation:

P = σA

where P is the axial load, σ is the stress, and A is the cross-sectional area.

For shaft AB, the stress is:

σAB = δB/LAB x E = 0.0167 in / 10 in x 30x10^6 psi = 50 psi

The cross-sectional area is 1 sq in. Therefore, the axial load in shaft AB is:

PAB = σAB x AAB = 50 psi x 1 sq in = 50 lb

For shaft BC, the stress is:

σBC = (δC - δB)/LBC x E = (0.008 in - 0.0167 in) / 3 in x 30x10^6 psi = -25 psi

The cross-sectional area is 0.196 sq in (π(0.375 in)^2 / 4). Therefore, the axial load in shaft BC is:

PBC = σBC x ABC = -25 psi x 0.196 sq in = -4.9 lb

The negative sign indicates that the load is compressive.

For shaft CD, the stress is:

σCD = -δC/LCD x E = -0.008 in / 3 in x 30x10^6 psi = -80 psi

The cross-sectional area is 0.049 sq in (π(0.25 in)^2 / 4). Therefore, the axial load in shaft CD is:

PCD = σCD x ACD = -80 psi x 0.049 sq in = -3.92 lb

The negative sign indicates that the load is compressive.

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Answer: 66

Step-by-step explanation:

I did it on khan

The durations of presentations whose difference is equal to 11/12 will be the correct answer.

The process of taking a matrix, vector, or other quantity away from another under specific rules to obtain the difference is called subtraction.

Given is that four presentations are being offered at a training seminar.

Since the durations of the presentations is not given, we will assume the general way of solving the problem.

The durations of presentations whose difference is equal to 11/12 will be the correct answer.

Mathematically, we can write -

x - y = 11/12

Therefore, the durations of presentations whose difference is equal to 11/12 will be the correct answer.

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Answer:

on which on do you need help on but let me know

Step-by-step explanation:

huh

When a coin is flipped 10 times, there are 1024 possible outcomes. Out of these, 286 outcomes contain at most three tails.

To calculate the number of possible outcomes containing at most three tails, we need to consider all the possible combinations of heads (H) and tails (T) in 10 flips. In each flip, we have two possibilities, so the total number of outcomes is 2^10 = 1024.

To find the number of outcomes with at most three tails, we can break it down into three cases:

1. Zero tails: There is only one outcome with all heads (HHHHHHHHHH).

2. One tail: There are 10 ways to choose the flip that results in a tail, and for each of these, the remaining flips are all heads. So, there are 10 outcomes with one tail.

3. Two tails: There are 10 choose 2 = 45 ways to choose the two flips that result in tails, and for each of these, the remaining flips are all heads. So, there are 45 outcomes with two tails.

Adding up these cases, we have 1 + 10 + 45 = 56 outcomes with at most two tails. However, this count includes the outcome with all heads, which we already counted in case 1. So, we subtract 1 to get 56 - 1 = 55 outcomes with at most three tails.

In conclusion, out of the 1024 possible outcomes when flipping a coin 10 times, there are 286 outcomes that contain at most three tails.

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Critical angle for the total internal reflection icrit, β =  78.28⁰

Critical angle for the total internal reflection crit, α = 17,22⁰

We have the refractive index of core, \(n_c_o_r_e\) = 1.46

We have the refractive index of clad , \(n_c_l_a_d\) = 1.4

Critical angle can be defined as the incidence angle which results in the refraction angle being equal to  at that angle of incidence.

For Total Internal Reflection to occur, the incidence angle must be greater than the critical angle.

We know that the critical angle, θ is given by:

sinθ = \(\frac{n_c_l_a_d}{n_c_o_r_e}\)

sinθ = \(\frac{1.4}{1.46}\)

sinθ = 0.959 = sin⁻¹(0.979) = 78.28⁰

β = θ = 78.28⁰

Now, for α:

\(\frac{sin(90-\alpha )}{sin\alpha } = \frac{1}{n_c_o_r_e}\)

sinα = sin(90⁰-78.28⁰) × 1.46

sinα = sin(11.72⁰) × 1.46

α = sin⁻¹(0.296)

α = 17,22⁰

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Critical angle for total internal reflection icrit β = 78.28⁰

Critical angle for total internal reflection crit, α = 17.22⁰

The refractive index of the core is ncore = 1.46.

The refractive index of clad is nclad = 1.4.

We know that the critical angle, θ is given by:

sinθ = nclad/ ncore

sinθ = 1.4/1.46

sinθ = 0.959

sin⁻¹(0.979) = 78.28⁰

β = θ = 78.28⁰

Now, for α:

sin(90- α) / sin α = 1 / ncore

sinα = sin(90⁰-78.28⁰) × 1.46

sinα = sin(11.72⁰) × 1.46

α = sin⁻¹(0.296)

α = 17.22⁰

Critical angle for icrit β = 78.28⁰

Critical angle for crit α = 17.22⁰

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Answer:

B.)

Step-by-step explanation:

A rational number is a number with no repeating decimals or decimals that go on “forever” like pi.  An expample of a rational number is 2 where 2.3333333... is not a rational number.  Pi isn’t a rational number either since forth there is no known end to that.  

So, when solved:

A.) = 1.58113883...  (irrational)

B.) = -8 (rational)

C.) = 8.94427191... (irrational)

D.) = 3.794733192... (irrational)

I hope you see the pattern.  Hope this helps!

Answer:

27

Step-by-step explanation:

13=g/3 +4

9=g/3

27=g

answer:27

The number formed by the digits 16, 06, and 68 is 160668, which is determined by concatenating them in the given order.

To determine the number formed by the given digits, we concatenate them in the given order. Starting with the first digit, we have 16. The next digit is 06, and finally, we have 68. By combining these three digits in order, we get the number 160668.

When concatenating the digits, the position of each digit is crucial. The placement of the digits determines the resulting number. In this case, the digits are arranged as 16, 06, and 68, and when they are concatenated, we obtain the number 160668. It's important to note that the leading zero in the digit 06 does not affect the value of the resulting number. When combining the digits, the leading zero is preserved as part of the number.

Therefore, the number formed by the digits 16, 06, and 68 is 160668.

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Answer: 3=-155.15

4=-224.05

Step-by-step explanation:

Answer: 155.15 then 223.75

Step-by-step explanation:

An equation for the boiling point of this liquid is y = -0.0015x + 215.55. Also, the boiling point of this liquid at 2500 ft is equal to 211.8°F.

In order to write an equation for the boiling point of this liquid, we would have to first calculate its slope because the relationship between altitude and the boiling point of this liquid is linear (direct proportion or proportional relationship).

Mathematically, the slope of any linear equation can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided about the altitudes and boiling points of this liquid, we have the following parameters:

Point (x, y) = (8500, 202.8)

Point (x, y) = (4200, 206.7)

Substituting the given points into the formula, we have;

Slope, m = (209.25 - 202.8)/(4200 - 8500)

Slope, m = 6.45/-4300

Slope, m = -0.0015

At point (8500, 202.8), the equation of this line is given by:

y - y₁ = m(x - x₁)

Where:

y - 202.8 = -0.0015(x - 8500)

y - 202.8 = -0.0015x + 12.75

y = -0.0015x + 12.75 + 202.8

y = -0.0015x + 215.55

Now, we can calculate the boiling point of this liquid at 2500 ft:

y = -0.0015(2500) + 215.55

y = -3.75 + 215.55

y = 211.8°F.

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Complete Question:

The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8500 ft, the liquid boils at 202.8°F. At an altitude of 4200 ft, the liquid boils at 209.25°F. Write an equation giving the boiling point b of the liquid, in degrees Fahrenheit, in terms of altitude a, in feet. What is the boiling point of the liquid at 2500 ft?

The probability of getting at least one head is 15/16.

What is probability?

The ratio of positive outcomes to all possible outcomes of an event is known as the probability.

Formula for probability = favourable outcomes/ total outcomes

Main body:

if 4 coins are tossed , total no. of outcomes = 2⁴ = 16

In a toss there are 2 outcomes T or H

so, Probability of getting Head = 1/2

The probability of getting at least 1 head = 1- probability of getting no heads

⇒1 - Probability of getting tail in 4 tosses

⇒ 1 - (1/2)⁴

⇒ 1 - 1/16

⇒ 15/16

So the probability of getting at least one head is 15/16.

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The customer will pay $32.25 for 9 pounds of blueberries with the coupon

At $3.75 per pound, 9 pounds of blueberries would cost $33.75 without the coupon. However, the customer has a coupon for $1.50 off the total cost of the blueberries. So, the customer can subtract $1.50 from the total cost, bringing it down to $32.25. Therefore, the customer will pay $32.25 for 9 pounds of blueberries with the coupon.

It's important to note that the price per pound of blueberries may vary at different grocery stores or at different times of the year. Additionally, coupons and discounts may have expiration dates or other terms and conditions that should be reviewed before use. When shopping, it's always a good idea to compare prices and use coupons and discounts to get the best possible deal

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Answer:

64

Step-by-step explanation:

because the formula for the volume of a cube is edge (4) to the power of 3

4 to the power of 3 is 64

Answer:

If you look up the equation on google there is a calculator for that and you should get ur answer there

Step-by-step explanation:

43% of elementary students chose something other than blue, red, or yellow as their favorite color.

Blue: 24%

Red: 17%

Yellow: 16%

Total: 24% + 17% + 16% = 57%

Percentage chose something other:

100% - 57% = 43%.

Therefore, 43% of elementary students chose something other than blue, red, or yellow as their favorite color.

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Answer:

D) cot(C) = 1/2.

Step-by-step explanation:

We can go through each choice and examine is validity.

Choice A)

We have:

\(\displaystyle \sec B=\frac{3}{7}\)

Recall that secant is the ratio of the hypotenuse to the adjacent.

With respect to B, the adjacent is 6 and the hypotenuse is 7.

Therefore, sec(B) should be 7/6 instead.

A is incorrect.

Choice B)

We have:

\(\displaystyle \cot B=\frac{3}{2}\)

Cotangent is the ratio of the adjacent side to the opposite.

With respect to B, the adjacent side is 6 and the opposite side is 3.

Therefore, cot(B) = 6/3 = 2.

B is incorrect.

Choice C)

C is incorrect for the reasons listed in A.

Choice D)

We have:

\(\displaystyle \cot C=\frac{1}{2}\)

Again, cotangent is the ratio of the adjacent side to the opposite.

With respect to C, the adjacent side is 3 and the opposite side is 6.

So, cot(C) = 3/6 = 1/2.

Therefore, D is the correct choice!

6 2/3 liters of water should be mixed with 10 juiced lemons to obtain the same result as Four liters of water are mixed with 6 juices lemons to make lemonade.

A single or distinct unit is referred to by the word unitary. Therefore, the goal of this method is to establish values in relation to a single unit. The unitary method, for instance, can be used to calculate how many kilometers a car will travel on one litre of gas if it travels 44 km on two litres of fuel.

A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4).

By using unitary method, 4 liters was water has 6 lemons

1 lemon will have 4/6 liter of water.

So 10 lemon will have

(4/6)*10=40/6

=20/3

=6 2/3 liters

Mix 10 freshly squeezed lemons with 6 2/3 liters of water to make lemonade as needed to combine the juice of six lemons with four liters of water.

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The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

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Hi there!

\(\large\boxed{\text{ She is incorrect.}}\)

The format of a logarithmic equation is:

\(a^{b} = c\\\\log_{a}c = b\)

In this instance:

a = e

b = 3x

c = 7

Rewrite as the logarithmic equation:

\(log_{e}7 = 3x\)

Solve. Evaluate \(log_{e}7\) and use algebra to find x:

\(1.946 = 3x\\\\x = 0.649\)