orm the indicated operations and simplify the expressi (3(3x-2)^((1)/(3))-(x-1)(3x-2)^(-(2)/(3)))/((3x-2)^((2)/(3)))

We can see that the points of intersection occur at π/3 and 4π/3.

We will solve this equation on the interval [0,2π). To begin, we can break up the equation into two parts:

2cosθ - 1 = 0 and 5cotθ + 4 = 0

First, let's solve the equation 2cosθ - 1 = 0. We can solve this equation by adding 1 to both sides and then dividing both sides by 2. We get:

2cosθ = 1
cosθ = 1/2

To find the angle θ, we can take the inverse cosine of both sides to get:

θ = cos-1(1/2)
θ = π/3

Now, let's solve the equation 5cotθ + 4 = 0. We can solve this equation by subtracting 4 from both sides and then dividing both sides by 5. We get:

cotθ = -4/5

To find the angle θ, we can take the inverse cotangent of both sides to get:

θ = cot-1(-4/5)
θ = 4π/3

Therefore, the solution to the equation on the interval [0,2π) is θ = π/3 or θ = 4π/3. To confirm the solutions, we can produce a Desmos graph of the equation on the interval [0,2π). We can see that the points of intersection occur at π/3 and 4π/3, which are our solutions. See the screenshot below.

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The length of the midsegment of the given trapezoid is 16.

A trapezoid is necessarily a convex quadrilateral in Euclidean geometry. The parallel sides are called the bases of the trapezoid.

Given is a trapezoid TUVW, with bases UV and TW given by expressions, 3x-1, 8x and the midsegment XY is 3x+7.

We need to find the length of the midsegment,

We know,

Midsegment = (base 1 + base 2) / 2

Therefore,

XY = UV+TW / 2

3x+7 = 3x-1 + 8x / 2

6x+14 = 11x-1

5x = 15

x = 3

XY = 3(3)+7 = 16

Hence, the length of the midsegment of the given trapezoid is 16.

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Answer:

not sure but i think its 12

Step-by-step explanation:

if you look carefully one side witch is 6 is have of side x and 6 x 2 is 12

hope this helps.

Answer:I think its 15 but I'm not sure

Step-by-step explanation:

Answer:

3.6225

Step-by-step explanation:

7.5% = 0.075

48.30 x 0.075 = 3.6225

So, 7.5% of 48.30 is 3.6225

Answer: Stem-and-leaf plot, because you can see each individual data point.

Step-by-step explanation:im taking the test.

Answer:stem and leaf plot

Answer:

[tex] \sf \: x = 5[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 11 + 2x = 3(x + 2)

Then the value of x will be,

→ 11 + 2x = 3(x + 2)

→ 11 + 2x = 3x + 6

→ 2x - 3x = 6 - 11

→ -x = -5

→ [ x = 5 ]

Hence, the value of x is 5.

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

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[tex] \: [/tex]

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[tex] \: [/tex]

[tex] \: [/tex]

The value of x is 5 !

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

The company deposited $1,487.88 at the end of each quarter during the first six years.

The amount deposited quarterly during the first six years can be calculated using the formula for the future value of an annuity:

[tex]PMT = (FV / ((1 + r)^{n-1}) * (1 + r)^{-n[/tex]

where PMT is the equal quarterly deposit, FV is the final value of the account, r is the quarterly interest rate (APR / 4), and n is the number of quarters (6 years * 4 quarters per year = 24 quarters).

Plugging in the given values, we get:

[tex]PMT = ($50,000 / ((1 + 0.068/4)^{28-1}) * (1 + 0.068/4)^{-28}[/tex]

PMT = $1,487.88 (rounded to the nearest cent)

Therefore, the company deposited $1,487.88 at the end of each quarter during the first six years.

The problem involves finding the amount deposited quarterly by a company for a period of six years, given the final value of the account four years after the company stopped making deposits. This can be solved using the formula for the future value of an annuity, which calculates the total value of a series of equal payments made at regular intervals over a specified period, taking into account compound interest.

By plugging in the given values into the formula, we can solve for the equal quarterly deposit made by the company during the first six years. The resulting amount is $1,487.88, which represents the total value of all the quarterly deposits made by the company during the six-year period. This answer assumes that the interest rate remained constant throughout the entire period and that the company made no withdrawals or additional deposits after the initial six years.

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Answer: A

Area of a circle=[tex]\pi r^2\\[/tex]

Now that we have established this, we will now substitute the values in the equation.

[tex]\pi r^2\\=\frac{22}{7}\\ =\frac{396}{7}\\ =56.57 \\[/tex] OR 57 square yards

HOPE THIS HELPED PLEASE MARK BRAINLIEST IF IT DID!

Answer:

If your options are  110 square yards

220 square yards

3,850 square yards

15,400 square yards

then the correct answer is 3,850 square yards.

Step-by-step explanation:

I took the quiz and got it right.

By applying trigonometric function concept, it can be concluded that the solutions are:

31.  tan a = cot(a + 10°), a = 40°

32. cos θ = sin(2θ - 30°), θ = 40°

33. sin(2θ + 10°) = cos(3θ - 20°), θ = 20°

34. sec(B + 10°) = csc(2B + 20°), B = 20°

35. tan(3B + 4°) = cot(5B - 10°), B = 12°

36. cot(5θ + 2°) = tan(2θ + 4°), θ = 12°

Two angles are said to be complementary angles if their sum is 90°. Sin and Cosine are complementary, Tan and Cot are complementary, and sec and cosec are complementary.

Trigonometric functions of complementary angles:

sin(90° - θ) = cos θ

cos(90° - θ) = sin θ

tan(90° - θ) = cot θ

cot(90° - θ) = tan θ

sec(90° - θ) = csc θ

csc(90° - θ) = sec θ

31. To find one solution for the equation tan a = cot(a + 10°), we can use the fact that cot(90° - θ) = tan θ. Therefore, we can rewrite the equation as:

         tan a = cot(a + 10°)

cot(90° - a) = cot(a + 10°)

      90° - a = a + 10°

             2a = 80°

                a = 40°

32. To find one solution for the equation cos θ = sin(2θ - 30°), we can use the fact that sin(90° - θ) = cos θ. Therefore, we can rewrite the equation as:

        cos θ = sin(2θ - 30°)

 sin(90° - θ) = sin(2θ - 30°)

θ + 2θ - 30° = 90°

              3θ = 120°

                θ = 40°

33. To find one solution for the equation sin(2θ + 10°) = cos(3θ - 20°), we can use the fact that sin(90° - θ) = cos θ. Therefore, we can rewrite the equation as:

sin(2θ + 10°) = cos(3θ - 20°)

sin(2θ + 10°) = sin(90° - (3θ - 20°))

sin(2θ + 10°) = sin(110° - 3θ)

      2θ + 10° = 110° - 3θ

               5θ = 100°

                 θ = 20°

34. To find one solution for the equation sec (B + 10°) = csc(2B + 20°), we can use the fact that sec θ = csc(90° - θ). Therefore, we can rewrite the equation as:

          sec(B + 10°) = csc(2B + 20°)

csc(90° - (B + 10°)) = sec(2B + 20°)

                 80° - B = 2B + 20°

                        3B = 60°

                          B = 20°

35. To find one solution for the equation tan(3B + 4°) = cot(5B-10°), we can use the fact that tan a = cot(90° - a). Therefore, we can rewrite the equation as:

           tan(3B + 4°) = cot(5B - 10°)

cot (90° - (3B + 4°)) = cot(5B - 10°)

                86° - 3B = 5B - 10°

                         8B = 96°

                           B = 12°

36. To find one solution for the equation cot(5θ + 2°) = tan(2θ + 4°), we can use the fact that cot(90° - θ) = tan θ. Therefore, we can rewrite the equation as:

          cot(5θ + 2°) = tan(2θ + 4°)

tan (90° - (5θ + 2°)) = tan(2θ + 4°)

                 88° - 5θ = 2θ + 4°

                           7θ = 84

                              θ = 12°

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The midline or midsegment theorem calculate the value of P. the value of the variable, P that base length in the trapezoid is equals to the 13.

A trapezoid is a 4-sided (square) shape in which some sides are parallels and others not. The midsection of a trapeze is the line that runs from the middle of one leg to the middle of the other. The midsection or Midsegment theorem of a trapezium states that if a line parallel to the two bases passes through the middle of one leg, it also passes through the middle of the other leg. Also, the length of the middle fragment is half the length of two bases. Now we see a trapezoid in the image above, the length of the midsegment = 25

One of the bases of the trapezium = 37

We need to calculate the value of the other base length P Using Midsigment or Midline Theorem, Midsigment = length of two bases/2

=> 25 = (37 + P)/2

=> 50 = 37 + P

=> P = 50 - 37

=> P = 13

Hence, required length is 13.

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Complete question:

Use the midline theorem to find the value of the variable in the trapezoid. See the above figure.

The magnitude and direction of the resultant force will be 7.829 N and the direction is opposite to the applied force.

A vector is an amount that has direction as well as magnitude and complies with the rule of vector addition.

A constant force of 18 newtons is supplied to an item at a constant angle of 56° while a constant force of 32 newtons is produced to the entity at a fixed angle of 124°.

Then the magnitude and direction of the resultant force are given as,

∑F = 0

∑F = 18 · cos 56° + 32 · cos 124°

∑F = 10.065 - 17.894

∑F = - 7.829 N

The magnitude and direction of the resultant force will be 7.829 N and the direction is opposite to the applied force.

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The equation for the exponential function is

The graph is attached

Exponential function is a function of the form  f(x) = a(b)ˣ

where

the starting = a

the base = b

the exponents = x

Using the table, f(x) = a(b)ˣ

a = 20

solving for b

10 = 20(b)¹

10 = 20b

b = 1/2

the equation for the function is f(x) = 20(0.5)ˣ

check

for x = 3

f(x) = 20(0.5)³ = 2.5

for x = 4

f(x) = 20(0.5)⁴ = 1.25

The graph of exponential decay is a decreasing function that approaches the x-axis, but never touches it. The rate at which the function decays depends on the value of b - the smaller the value of b, the slower the decay

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[tex]\stackrel{ \textit{Partial Variation} }{V=aD+bD^2}\qquad \impliedby \begin{array}{llll} \textit{V\textit{ varies partly}}\\ \textit{with D and partly with }D^2 \end{array} \\\\[-0.35em] ~\dotfill\\\\ \textit{we also know that} \begin{cases} V=5\\ D=2\\[-0.5em] \hrulefill\\ V=9\\ D=3 \end{cases}\implies \begin{array}{llll} 5=a2+b2^2&\qquad &5=2a+4b\\\\ 9=a3+b3^2&&9=3a+9b \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{5=2a+4b}\implies 5-2a=4b\implies \cfrac{5-2a}{4}=b \\\\\\ \stackrel{\textit{using the 2nd equation}}{9=3a+9b}\implies \stackrel{\textit{substituting from above}}{9=3a+9\left( \cfrac{5-2a}{4} \right)}\implies 9=3a+\cfrac{45-18a}{4} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4(9)=4\left( 3a+\cfrac{45-18a}{4} \right)}\implies 36=12a+45-18a\implies -9=-6a[/tex]

[tex]\cfrac{-9}{-6}=a\implies \boxed{\cfrac{3}{2}=a}\hspace{5em}b=\cfrac{5-2\left( \frac{3}{2} \right)}{4}\implies \boxed{b=\cfrac{1}{2}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill V=\cfrac{3}{2}D+\cfrac{1}{2}D^2~\hfill[/tex]

The scale of the map is 1 inch for 6 miles

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

Distance apart = 36 miles

Distance on the map = 6 inches

Using the above as a guide, we have the following:

Scale = Distance on the map/Distance apart

Substitute the known values in the above equation, so, we have the following representation

Scale = 6 inches/36 miles

Evaluate

Scale = 1 inch/6 miles

Hence, the scale is 1 inch per 6 miles

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The quadratic parent function is represented by the equation F(x) = [tex]x^{2}[/tex], so, the correct answer is D.

A quadratic function is a type of mathematical function that can be written in the form:

f(x) = a[tex]x^{2}[/tex] + bx + c

where a, b, and c are constants and x are the variable. The highest power of x in a quadratic function is 2, which is why it is called a "quadratic" function.

The graph of a quadratic function is a curve called a parabola. The shape of the parabola depends on the value of the coefficient a. If a is positive, the parabola opens upward and has a minimum point, and if a is negative, the parabola opens downward and has a maximum point.

Quadratic functions are used in many areas of mathematics and science, such as physics, engineering, and finance. They are also used in computer graphics to create curves and surfaces.

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They should sell each T-shirt for $27.80 to make a profit of $320.

Profit is the financial gain that a company or individual makes after deducting all the expenses from the revenue earned. It is the positive difference between the total revenue generated from the sale of goods or services and the total cost of producing and selling those goods or services.

Profit is one of the key indicators of a company's financial performance, and it is calculated by subtracting the total expenses from the total revenue. The expenses include the cost of raw materials, labor, rent, taxes, and other overhead costs associated with producing and selling the goods or services.

To make a profit of $320, they need to sell all 25 shirts for a total of $320 + ($15 x 25) = $695.

Therefore, the price they need to sell each T-shirt for is $695 ÷ 25 = $27.80 (rounded to the nearest cent).

So they should sell each T-shirt for $27.80 to make a profit of $320.

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Answer:

5/8

Step-by-step explanation:

GCF:

5/8 = 25/40 ( multiply both sides by 5)

11/20 = 22/40 ( multiply both sides by 2)

Missing number to make the binomial 9x² + X + 25 a perfect square is 30x.

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).

Given expression

9x² + X + 25

It can be written as

(3x)² + X + 5²

Comparing with a² + 2ab + b²

a = 3x

b = 5

X = 2ab

X = 2(3x)(5)
X = 30x

Hence, 30x is the missing number  to create a perfect-square binomial.

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The function seen on Cartesian plane has the following domain and range:

Domain: 0 ≤ t ≤ 100, Range: 450 ≤ q ≤ 1200

In this problem we find a representation of a linear function on a Cartesian plane, of which we need to derive the definitions of its domain and its range. The domain corresponds to the set of times (t), in minutes, and the range is the set of amounts of water (q), in liters.  The domain belongs to the horizontal axis and the range to the vertical axis.

Then, by direct inspection, the domain and the range of the function is:

Domain

0 ≤ t ≤ 100

t ∈ [0, 100]

Range

450 ≤ q ≤ 1200

q ∈ [450, 1200]

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Answer:

Customer A - 5 / 22.45 = $0.22 or 22 cents per quart

Customer B - 7 / 25.45 = $0.27 or 27 cents per quart

The possible rational roots are -1/6, -1/3, -1/2, -1, 1/6, 1/3, 1/2, 1 .

The polynomial 6x4 - 11x3 + 8x2 - 33x - 30 has 4 possible rational roots. To find them, use the Rational Root Theorem.

This theorem states that any rational roots of a polynomial must be in the form a/b, where a is a factor of the constant term and b is a factor of the leading coefficient.

In this case, the constant term is -30, so the possible factors are -1, -2, -3, -5, -6, -10, -15, -30. The leading coefficient is 6, so the possible factors are 1, 2, 3, 6.

Therefore, the possible rational roots are -1/6, -1/3, -1/2, -1, 1/6, 1/3, 1/2, 1.

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a)  The demand (price) function in terms of x : P(x) = 12 - 0.025(x - 1500)

b) the marginal revenue function is [tex]MR(x) = dR(x)/dx = 12 - 0.05(x - 1500)[/tex] The marginal revenue from the sales of 1800 T-shirts is -$3. This means that for each additional T-shirt sold after the 1800th, the revenue will decrease by $3 per T-shirt

To determine the demand (price) function, we need to find a relationship between the price of the T-shirts (P) and the number of T-shirts sold (x). We are given that for every $0.50 decrease in price, 20 more T-shirts will be sold.

Let's first find the decrease in price per T-shirt sold. If 20 more T-shirts are sold for every $0.50 decrease, then the decrease per T-shirt is $0.50/20 = $0.025. Now, we can set up the demand function. The base price is $12, and we decrease it by $0.025 for each additional T-shirt sold. So the demand function is:

P(x) = 12 - 0.025(x - 1500) To determine the marginal revenue function, we first need to find the total revenue function. Total revenue (R) is the product of the price (P) and the number of T-shirts sold (x):

R(x) = P(x) * x = (12 - 0.025(x - 1500)) * x Now we need to find the derivative of the total revenue function with respect to x, which will give us the marginal revenue function: MR(x) = dR(x)/dx = 12 - 0.05(x - 1500)

To determine the marginal revenue from the sales of 1800 T-shirts, we simply plug in x = 1800 into the marginal revenue function: MR(1800) = 12 - 0.05(1800 - 1500) = 12 - 0.05(300) = 12 - 15 = -$3

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The expression in terms of m and n is m^2+2/3n-3.

To rewrite the given expression in terms of m and n, we need to use the properties of logarithms to simplify the expression. The properties of logarithms that we will use are:

- log(ab) = log(a) + log(b)
- log(a/b) = log(a) - log(b)
- log(a^b) = b*log(a)

Using these properties, we can rewrite the given expression as follows:

\( \log \left(\frac{\left(M^{\log (M)} \cdot 10^{\log (N)}\right)}{1000 \sqrt[3]{N}}\right) = \log \left(M^{\log (M)} \cdot 10^{\log (N)}\right) - \log \left(1000 \sqrt[3]{N}\right) \)

\( = \log \left(M^{\log (M)}\right) + \log \left(10^{\log (N)}\right) - \log \left(1000\right) - \log \left(\sqrt[3]{N}\right) \)

\( = \log (M) \cdot \log (M) + \log (N) \cdot \log (10) - \log (10^3) - \frac{1}{3} \cdot \log (N) \)

Now, we can substitute m = log(M) and n = log(N) into the expression to get:

\( = m^2 + n - 3 - \frac{1}{3}n \)

\( = m^2 + \frac{2}{3}n - 3 \)

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Answer: 18

Step-by-step explanation:

9 kids each have two bags

9 x 2 = 18

9 + 9 = 18

Milo is 8.09 miles from the dock.

Here we can use the Law of Cosines,

which states that c² = a² + b² - 2abcos(C),

Where c is the side opposite the angle C in a triangle.

Call the distance from the dock to the point where Milo changes direction "a", the distance Milo sails in the new direction "b", and the angle between these two sides "C".

We know that a = 7 miles and b = 4 miles.

To find C, we can use the fact that Milo changes direction by 5π/36 radians.

Since he turned to the right, we can say that he turned by,

⇒ 360 - 5π/36 = 355π/36 radians.

This is the angle between the two sides of the triangle.

Now we can plug these values into the Law of Cosines to find the distance from Milo to the dock:

⇒ c² = a² + b² - 2abcos(C)

⇒ c² = 7² + 4² - 2(7)(4)cos(355π/36)

⇒ c² = 49 + 16 - 56cos(355π/36)

⇒ c² = 65.47

Taking the square root of both sides, we get:

c = 8.09 miles (rounded to 2 decimal places)

Therefore, Milo is 8.09 miles from the dock.

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Answer:

Step-by-step explanation:

Answer:

75:77

Step-by-step explanation:

5 is 2 more than 3

3+72=75

5+72=77

therefore: 3:5 = 75:77

If that's not what you meant, then I don't understand the question

The value of m∠A + m∠B is 90°. The angles that add up to 180 degrees are referred to as supplementary angles.

Option C is correct.

Given a figure, we must determine the sum of the angles A and B. The angle that forms a linear pair with the sum of the angles A and B is 90 degrees. Since we are aware that the linear pair with a 90 degree angle is 90 degrees, the value of the sum of the angles A and B, m  A + m  B, is also 90 degrees.

There can be no more than three angles. Two angles whose measurements add up to exactly 180 degrees are referred to as supplementary angles. It is possible to have three angles that add up to 180 degrees each, such as 60 degrees, 30 degrees, and 90 degrees; however, these angles are not considered supplementary.

Question incomplete:

What is the value of m∠A + m∠B? If ∠ C = 56° and ∠D =124°

A. 180

B. 120

C. 90

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Answer:

There were 30 x 30/100 = <<30*30/100=9>>9 first-year teachers at the meeting.

Answer: 9.

Answer:

9

Step-by-step explanation:

30% of 30 is 9. Therefore there are 9 teachers how were first year teachers.

Hope this helps :)