Simplify (2x-3y)^2-(3x+4y)(2x-3y).
Pls show working

The trigonometric ratios are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

5 is the hypotenuse length, while for angle A, we have that the sides are given as follows:

Hence the ratios are given as follows:

For angle B, we have that 4 is now the adjacent side, while 3 is the opposite side, hence:

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The proportion of rent that the friend with the smaller bedroom has to pay is 125/265. So his share of the rent is $540.35.

Suppose the distance from your house to your school is 2 miles, while the distance from your house to the nearest park is 3 miles.

Then we say that the ratio of the two distances s 2:3. To take another example suppose in today's hw, you have got 10 questions to answer, while in yesterday's hw you had 7 questions to answer. In this case we say that the ratio of the no of hw questions you have today, to the no questions you had yesterday is 10:7.

A ratio is a pair of numbers which gives the relative magnitudes of two similar quantities. A ratio of a:b is also represented by the fraction a/b.

Let us use the previous example. the ratio of the distances from your home to your school and to the nearest park is say 2:3 . Now consider the ratio of the time it takes to reach your school from your home by car to the time it takes to reach the park by car from your home. suppose this ratio a:b . Then it reasonable to assume that the two fractions a/b and 2/3 are equal, assuming the car moves at the same average speed.

This common ratio is called the proportion. we write it as follows,dist to school : dist to park : : time to school : time to park.

This is read as the distance to school IS TO distance to park AS time to school IS TO time to park.

if we write the ratios as fractions. Then they are proportional or equivalently they are the same proportion if and only if the two fractions are equal.

So The ratio of the bedroom sizes is 125 : 140.

Total rent that is to be divided between them is $1150.

if the share of the rents are a,b. then as fractions a/b = 125/140

So. a/a+b = 125/125+140 = 125/265

but a + b = 1150

So a = 125/265 (1150) = 542.452

The closest option is $540.35. So this is our answer.

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Answer:

See below

Step-by-step explanation:

Mr. Hedges added the denominators together when he shouldn't have.

-12/14 + -7/14 DOES NOT EQUAL -19/28, you can't add denominators in fractions. Instead, they stay the same, while the numerators are added together.

The correct answer should be -19/14, by leaving the denominator alone and adding the numerators.

Hope this helps!

Both statements imply each other, we can conclude that ∃x(p(x) ∨ q(x)) and ∃xp(x) ∨ ∃xq(x) are logically equivalent.

We'll demonstrate that they imply each other.

1. First, let's assume ∃x(p(x) ∨ q(x)). This means that there exists an x such that either p(x) is true or q(x) is true (or both).

2. Since p(x) or q(x) is true for some x, we can say that either there exists an x for which p(x) is true or there exists an x for which q(x) is true. This can be written as ∃xp(x) ∨ ∃xq(x).

Now, let's assume ∃xp(x) ∨ ∃xq(x).

3. This statement means that there exists an x for which p(x) is true, or there exists an x for which q(x) is true (or both).

4. From this, we can conclude that for some x, either p(x) is true or q(x) is true. So, we can write this as ∃x(p(x) ∨ q(x)).

Since we've shown that both statements imply each other, we can conclude that ∃x(p(x) ∨ q(x)) and ∃xp(x) ∨ ∃xq(x) are logically equivalent.

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The given series Σ (n+1)/(n² + 5n) from n=1 to infinity is divergent and the correct option is option A.

We have to determine if the following series converges or diverges: Σ (n+1)/(n² + 5n) from n=1 to infinity.

To determine the convergence or divergence of the series, we can use the comparison test. We can compare the given series to another series with known convergence properties.

Let's compare it to the series Σ 1/n.

For all n > 1, we have (n+1)/(n² + 5n) < 1/n since n² + 5n > n.

Now, we know that the series Σ 1/n, also known as the harmonic series, is a divergent series.

Since (n+1)/(n² + 5n) < 1/n for all n > 1, and the series Σ 1/n diverges, the given series also diverges by the comparison test.

The correct answer is:
A. Since (n+1)/(n² + 5n) < 1/n for all n > 1 and the series Σ 1/n diverges, the given series diverges by the comparison test.

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The dimensions of the closed cylinder that maximize its volume are radius=25 cm and height=40 cm. The maximum volume is 62,500 cubic cm.

Given that the total surface area of the closed cylinder is 5000 cm^2, we can write the equation for the total surface area as:

2πrh + 2πr^2 = 5000

We want to find the dimensions that maximize the volume of the cylinder. The volume of a cylinder is given by:

V = πr^2h

We can use the equation for the total surface area to solve for h in terms of r:

h = (5000 - 2πr^2) / (2πr)

Substituting this expression for h into the equation for the volume, we get:

V = πr^2[(5000 - 2πr^2) / (2πr)]

Simplifying this expression, we get:

V = (2500πr - πr^3)

To find the maximum volume, we take the derivative of V with respect to r and set it equal to zero:

dV/dr = 2500π - 3πr^2 = 0

Solving for r, we get r=25 cm.

We can then substitute this value of r into the expression for h to get h=40 cm.

Therefore, the dimensions of the cylinder that maximize its volume are radius=25 cm and height=40 cm.

Substituting these values into the equation for the volume, we get:

V = π(25)^2(40) = 62,500 cubic cm.

To verify that this is a maximum point, we can take the second derivative of V with respect to r:

d^2V/dr^2 = -6πr

At r=25 cm, this is negative, which indicates that we have a maximum point. Therefore, the dimensions calculated above do indeed maximize the volume of the cylinder.

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The ascending order of the expression from smallest to highest is: -39, -11, -8, -6, 2.

In the above case, we need to first break down or simplify the expressions and thus it will be:

9 + 3 = -6

-4 + 6 = 2

2(-4) = -8

1 - 7 - 31 = -39

-5 - 3 x 2 = -11

So now, we need to arrange them and this will be in ascending order from smallest to highest  and it will be: -39, -11, -8, -6, 2

Therefore, the ascending order of the expression is : -39, -11, -8, -6, 2.

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See correct question below

17. Arrange -9 +3, -4+6, 2(-4), 1-7-31, -5-3x2 in ascending order.

Okay, let's break this down step-by-step:

* Junhao left at 17:25

* He returned at 19:10

* So we need to calculate the total time he was walking.

Here are the conversion steps:

* 17:25 = 17 hours and 25 minutes

* 19:10 = 19 hours and 10 minutes

* So the total time = (19 hours 10 minutes) - (17 hours 25 minutes)

* = 19*60 + 10 - 17*60 - 25

* = 1140 - 1025  = 115 minutes

So Junhao was walking for 115 minutes.

Let me know if you have any other questions!

Answer:

1 hour 45 minutes.

Step-by-step explanation:

We can count up to determine the length of time.

from 1725 to 1800 is 35 minutes.  (Remember that time is in increments of 60 minutes).  Add another hour to 1900.  Add 10 minutes to 1910

We have a total of 35 minutes plus 1 hour plus 10 minutes

1 hour 45 minutes.

The point on the plane 4x + 7y + 8z - 14 = 0 closest to the point (-2,2,3) is (-1, 1, 1). This can be answered by the concept of Distance formula.

To find the point on the plane closest to the given point, we can use the formula for the distance between a point and a plane. The formula states that the distance between a point (x1, y1, z1) and a plane Ax + By + Cz + D = 0 is given by:

Distance = |Ax1 + By1 + Cz1 + D| / √(A² + B² + C²)

In this case, the coefficients of x, y, and z in the equation of the plane are A = 4, B = 7, and C = 8, and D = -14. The given point is (-2, 2, 3), so x1 = -2, y1 = 2, and z1 = 3.

Plugging these values into the formula, we get:

Distance = |4(-2) + 7(2) + 8(3) - 14| / √(4² + 7² + 8²)

Simplifying, we get:

Distance = 35 / √(189)

To find the point on the plane closest to the given point, we need to minimize this distance. Since the distance is a positive value, the point on the plane closest to the given point will be the one that minimizes the numerator of the distance formula, which is |4(-2) + 7(2) + 8(3) - 14|. This occurs when the numerator is equal to zero.

Setting the numerator equal to zero, we get:

4(-2) + 7(2) + 8(3) - 14 = 0

Solving for x, y, and z, we get:

x = -1

y = 1

z = 1

Therefore, the point on the plane closest to the given point (-2, 2, 3) is (-1, 1, 1).

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The surface will be a hyperboloid of two sheets, since it has one positive and two negative squared terms. The xz- and yz-planes will contain hyperbolas, while the xy-plane will contain an ellipse.

To sketch the surface given by the equation −x² + 7y² − z² = 7, we can start by analyzing its traces in the x-, y-, and z-planes:

1. x-trace: Set x = 0 in the equation:
7y² - z² = 7
Divide by 7:
y² - (z²/7) = 1
This is a hyperbola in the yz-plane.

2. y-trace: Set y = 0 in the equation:
-x² - z² = 7
Divide by -1:
x² + z² = -7
Since x² and z² are always non-negative, there is no y-trace.

3. z-trace: Set z = 0 in the equation:
-x² + 7y² = 7
Divide by 7:
-(x²/7) + y² = 1
This is an ellipse in the xy-plane.

Now that we have the traces, we can sketch the surface by visualizing how these traces intersect and extend in 3D space. The surface will be a hyperboloid of two sheets, since it has one positive and two negative squared terms. The xz- and yz-planes will contain hyperbolas, while the xy-plane will contain an ellipse.

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The number of possible passwords for a length of 5 to 7 characters, where each character can be any alphanumeric value, is 218,340,105,584. If each password must contain at least one digit, then the number of possible passwords is 577,311,447,520.

There are 62 possible alphanumeric characters (26 uppercase letters + 26 lowercase letters + 10 digits). Therefore, the total number of possible passwords for a length of 5 to 7 characters is:

Total number of passwords = 62^5 + 62^6 + 62^7 = 218,340,105,584,896

If each password must contain at least one digit, then there are 10 choices for the first character, and 62 choices for each of the remaining four to six characters. Therefore, the total number of possible passwords is:

Total number of passwords = 10 * 62^4 + 10 * 62^5 + 10 * 62^6 = 577,311,447,520.

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Answer:

Step-by-step explanation:

22

To convert a nominal value to a real value in dollar terms, the base year index must be set at 100.The answer: True

1. Nominal value represents the face value or stated value of a currency, security, or financial instrument without considering the effects of inflation or changes in the purchasing power of money.
2. Real value is the value adjusted for inflation, reflecting the purchasing power of a currency in a given base year.
3. To convert a nominal value to a real value in dollar terms, we need to adjust the nominal value for inflation using a price index.
4. The base year index is typically set at 100, which allows for easy comparison and calculation of the real value.
5. To convert the nominal value to a real value, divide the nominal value by the price index in the current year and then multiply by the base year index (100). This will give you the real value in dollar terms.

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To convert a nominal value to a real value in dollar terms, the base year index must be set at 100.The answer: True

1. Nominal value represents the face value or stated value of a currency, security, or financial instrument without considering the effects of inflation or changes in the purchasing power of money.
2. Real value is the value adjusted for inflation, reflecting the purchasing power of a currency in a given base year.
3. To convert a nominal value to a real value in dollar terms, we need to adjust the nominal value for inflation using a price index.
4. The base year index is typically set at 100, which allows for easy comparison and calculation of the real value.
5. To convert the nominal value to a real value, divide the nominal value by the price index in the current year and then multiply by the base year index (100). This will give you the real value in dollar terms.

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The value of CD for the circle O with tangent AB and the secant through A which intersect the circle at points C and D is equal to 8 cm

Circle theorems are a set of rules that apply to circles and their constituent parts, such as chords, tangents, secants, and arcs. These rules describe the relationships between the different parts of a circle and can be used to solve problems involving circles.

For the tangent AB and the secant through A which intersect the circle at points C and D;

AB² = AC × CD {secant tangent segments}

(4 cm)² = 2 cm × CD

CD = 16 cm²/2 cm

CD = 8 cm

Therefore, the value of CD for the circle O with tangent AB and the secant through A which intersect the circle at points C and D is equal to 8 cm.

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The measurement of angle A to the nearest tenth is equal to 40.8 degrees.

In order to determine the magnitude of tan A, we would apply the law of tangent because the given side lengths represent the adjacent side and opposite side of a right-angled triangle.

tan(θ) = Opp/Adj

Where:

Based on the information provided in the image, we can logically deduce the following parameters:

By substituting the parameters into the law of tangent formula, we have the following;

TanA = 19/22

A = tan⁻¹(0.8636)

A = 40.8 degrees.

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Answer:

Cevap C, yani 70 kişi olarak verilmiştir. Ankete katılan 200 kişinin yüzde 35'i, 200 x 0.35 = 70 kişiye denk gelir.

Step-by-step explanation:

The volume of the given region u in cylindrical coordinates is 72π cubic units.

To compute the volume of the region u using integration in cylindrical coordinates, we first need to express the equation of the region in terms of cylindrical coordinates.

In cylindrical coordinates, x = rcosθ and y = rsinθ. Therefore, we can rewrite the equation of the region as:

0 ≤ z ≤ 36 - [tex]r^2[/tex]

Next, we need to determine the bounds of integration for r and θ. Since the region is bounded by a cylinder of radius √36 = 6, we have 0 ≤ r ≤ 6. The angle θ ranges from 0 to 2π, as it covers the entire region.

The volume of the region u can then be computed as:

V = ∫∫∫ u dV
= ∫0^6 ∫[tex]0^2[/tex]π ∫0^(36-[tex]r^2[/tex]) r dz dθ dr
= ∫0^6 ∫[tex]0^2[/tex]π r(36-[tex]r^2[/tex]) dθ dr
= 2π ∫[tex]0^6[/tex] r(36-[tex]r^2[/tex]) dr
[tex]= 2π [18r^2 - (r^4)/4] evaluated from 0 to 6[/tex]
= 2π (648 - 54)
= 1188π

Therefore, the volume of the region u is 1188π cubic units.
To compute the volume of the region u = {(x, y, z) : 0 ≤ z ≤[tex]36 - x^2 - y^2[/tex]} using cylindrical coordinates, we first need to convert the given Cartesian coordinates into cylindrical coordinates. In cylindrical coordinates, we use variables (ρ, θ, z) with the following relationships:

x = ρ * cos(θ)
y = ρ * sin(θ)
z = z

Now, we can rewrite the inequality for the region u in cylindrical coordinates:

[tex]0 ≤ z ≤ 36 - (ρ * cos(θ))^2 - (ρ * sin(θ))^2[/tex]

Simplifying this inequality, we get:

[tex]0 ≤ z ≤ 36 - ρ^2[/tex]

Next, we need to determine the range for ρ and θ. Since the given region is symmetric about the z-axis, we have:

0 ≤ θ ≤ 2π

For ρ, it ranges from 0 to the maximum value at the outer edge of the region, which is the surface z = 36 - [tex]ρ^2[/tex], so:

0 ≤ ρ ≤ √36 = 6

Now we can set up the triple integral to compute the volume:

Volume = ∫∫∫ ρ * dρ * dθ * dz

The limits of integration for ρ, θ, and z are as follows:

ρ: 0 to 6
θ: 0 to 2π
z: 0 to 36 - [tex]ρ^2[/tex],

Now we can write the full integral:

Volume = ∫(θ=0 to 2π) ∫(ρ=0 to 6) ∫(z=0 to 36-[tex]ρ^2[/tex], , ) ρ * dz * dρ * dθ

Evaluating this triple integral, we get:

Volume = 72π cubic units

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Answer: the answer is f(3)=29

Step-by-step explanation:

The third option {(–5, 1), (–2, 0), (–1, 1), (2, 4), (6, 3)} is the only function, as every input (x value) has a unique output (y value).

To determine if a relation is a function, we have to check if each input (represented by x) has exactly one output (y). If any x value has more than one corresponding y value, then it is not a function.

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The height of the pyramid is 11 units.

What is a triangular pyramid?

A tetrahedron is a polyhedron in geometry that has four triangular faces, six straight edges, and four vertex corners. It is often referred to as a triangle pyramid. The simplest regular convex polyhedron is the tetrahedron.

Here, we have

Given: The volume of a triangular pyramid is 99 units³. If the base and height of the triangle that forms its base are 9 units and 6 units respectively.

We have to find the height of the pyramid.

The area of the triangular base = (9×6)/2

= 54/2 units

= 27units

The volume of the pyramid with a triangular base = 27units³ = area of base × height/3, or the height of the pyramid.

= 99×3/27

= 11 units

Hence,  the height of the pyramid is 11 units.

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A 90% confidence interval for the mean sale price in San Luis Obispo County is $635.6 to $802.4.

Using the given data, we can calculate the sample mean and sample standard deviation as follows:

Sample mean (x) = (662 + 609 + 834 + 702 + 741 + 766) / 6 = 719

Sample standard deviation (s) = √[(∑(xi - x)²) / (n - 1)] = √[((662 - 719)² + (609 - 719)² + (834 - 719)² + (702 - 719)² + (741 - 719)² + (766 - 719)²) / (6 - 1)] = 79.44

The degrees of freedom (df) for a 90% confidence interval with n = 6 is df = n - 1 = 5.

The t-value for a 90% confidence interval with df = 5 is found using a t-table or a calculator and is approximately 2.571.

Using the formula for a confidence interval for the population mean with a known standard deviation, we have:

Lower limit = x - (t-value) * (s / √n) = 719 - (2.571) * (79.44 /√6) ≈ 635.6

Upper limit = x + (t-value) * (s / √n) = 719 + (2.571) * (79.44/ √6) ≈ 802.4

Therefore, a 90% confidence interval for the mean sale price in San Luis Obispo County is $635.6 to $802.4.

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Written as a fraction, the amount is 17/20 .

But a fraction actually means "division".  When you see "17/20", it means "17 divided by 20".

If you actually go ahead and DO the division problem (with a pencil or on your calculator) that the fraction is talking about, the answer you get is the same amount as the fraction, but written as a decimal.

The same amount as 17/20, written as a decimal, is 0.85 .

The same amount as 17/20, written as a percent, is  85% .

The area of the resulting surface formed by rotating the curve y = 1/4 x^2 − 1/2 ln(x) about the y-axis is approximately 148.81 square units.

To find the area of the surface formed by rotating the curve y = 1/4 x^2 − 1/2 ln(x) about the y-axis, we can use the formula for the surface area of a solid of revolution

S = 2π ∫[a,b] y(x) √(1 + (y'(x))^2) dx,

where a and b are the limits of integration (in this case, 1 and 3), y(x) is the equation of the curve being rotated, and y'(x) is its derivative.

First, we need to find y'(x)

y'(x) = 1/2 x − 1/2x^(-1)

Next, we can substitute y(x) and y'(x) into the formula

S = 2π ∫[1,3] [(1/4 x^2 − 1/2 ln(x)) √(1 + (1/2 x − 1/2x^(-1))^2)] dx

Simplifying the integrand

S = 2π ∫[1,3] [(1/4 x^2 − 1/2 ln(x)) √(1/4 x^2 + 1/4x^(-2))] dx

S = π ∫[1,3] [x^2√(x^2+1) − 2x ln(x)√(x^2+1)] dx

This integral can be evaluated using integration by parts or a suitable substitution. After performing the integration, we get

S = π/6 (54√10 − 5 ln(27) − 6)

= 148.81 square units.

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The period of function is approximately 0.6465 days, which means that the pattern of daylight hours repeats approximately every 0.6465 days, or about every 15.55 hours.

A periodic function is a function that repeats its values in a regular pattern over a specified interval or set of input values.

More specifically, a function f(x) is said to be periodic with period P if, for all values of x in the domain of f(x), we have:

f(x + P) = f(x)

The period of a periodic function is the distance along the x-axis between two consecutive peaks or troughs of the graph of the function. For the given function f(x)=2.95sin(2π365x)+12.21, the coefficient of x in the argument of the sine function is 2π365, which represents the frequency of the oscillation.

The period P of a sine function with frequency f is given by:

P = 1/f

Therefore, for the given function, the period is:

P = 1/f = 1/(2π365) ≈ 0.00177 years

However, since the function is modeling the number of hours of daylight, it is more convenient to express the period in terms of days. One year has 365 days, so we can convert the period to days by multiplying it by 365:

P = 0.00177 × 365 ≈ 0.6465 days

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Answer:

Yes, by AA, since angle DEF is congruent to HEJ (vertical angles are congruent), and angle DFE is congruent to HJE.

So triangle DEF is similar to triangle HEJ.

6 choc bars and 2 iceblocks would cost a total of $28

Let's assign a variable to the cost of one chocolate bar, say "c", and a variable to the cost of one ice block, say "i". Then we can set up a system of equations based on the information given:

3c + 4i = 20

4c + 3i = 22

Using a graphing tool, we have

c = 4 and i = 2

So the cost of one chocolate bar is $4 and the cost of one ice block is $2

Finally, we can calculate the cost of 6 chocolate bars and 2 ice blocks:

6c + 2i = 6 * 4 + 2 * 2

6c + 2i = 28

Hence, the cost is $28

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the wavelength of the electron is approximately 122 nm To find the wavelength of an electron, we can use the de Broglie wavelength formula:

wavelength (λ) = h / (m * v)

where:
- h is Planck's constant (6.63 x 10^-34 Js)
- m is the mass of the electron (9.11 x 10^-28 g, which needs to be converted to kg)
- v is the speed of the electron (5.97 mm/s, which needs to be converted to m/s)

Step 1: Convert the mass of the electron to kg:
9.11 x 10^-28 g * (1 kg / 1000 g) = 9.11 x 10^-31 kg

Step 2: Convert the speed of the electron to m/s:
5.97 mm/s * (1 m / 1000 mm) = 5.97 x 10^-3 m/s

Step 3: Plug the values into the de Broglie wavelength formula:
λ = (6.63 x 10^-34 Js) / (9.11 x 10^-31 kg * 5.97 x 10^-3 m/s)

Step 4: Calculate the wavelength:
λ = (6.63 x 10^-34 Js) / (5.44 x 10^-33 kg m/s) ≈ 1.22 x 10^-10 m

Step 5: Convert the wavelength to nm:
1.22 x 10^-10 m * (1 x 10^9 nm / 1 m) ≈ 122 nm

So, the wavelength is approximately 122 nm.

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