Use inverse trigonometric measures to find the measure of the indicated angle to the nearest degree.

Let's simplify the expression step by step: Expand the squared term:

(x - 3y)² = (x - 3y)(x - 3y) = x² - 6xy + 9y²

Expand the second term:

3(x + y)(x − 4y) = 3(x² - 4xy + xy - 4y²) = 3(x² - 3xy - 4y²)

Expand the third term:

x(3x + 4y + 3) = 3x² + 4xy + 3x

Now, let's combine all the expanded terms:

(x - 3y)² + 3(x + y)(x − 4y) + x(3x + 4y + 3)

= x² - 6xy + 9y² + 3(x² - 3xy - 4y²) + 3x² + 4xy + 3x

Combining like terms:

= x² + 3x² + 3x² - 6xy - 3xy + 4xy + 9y² - 4y² + 3x

= 7x² - 5xy + 5y² + 3x

The simplified form of the expression is 7x² - 5xy + 5y² + 3x.

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The description of the transformation of z on the complex plane that gives the product of and is to scale by a factor of 4, then rotate counterclockwise by /6 radians.

To understand this transformation, let's break it down into its components. Scaling by a factor of 4 means multiplying by 4. This scales the magnitude of by a factor of 4 but does not change its direction. Next, rotating counterclockwise by /6 radians means rotating around the origin by an angle of /6 in the counterclockwise direction. By performing these two transformations in succession, we first scale by a factor of 4, which stretches or compresses it depending on whether it is inside or outside the unit circle, respectively. Then, we rotate counterclockwise by /6 radians, which changes its angle in the counterclockwise direction by /6 radians.

The resulting transformation gives the product of and because scaling and rotation are commutative operations when applied to complex numbers. The order in which the transformations are performed does not affect the result. Therefore, scaling by a factor of 4, then rotating it counterclockwise by /6 radians, will yield the same result as scaling by a factor of 4, then rotating it counterclockwise by /6 radians.

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Answer:

52°

Step-by-step explanation:

360 - 33 - 165 - 20 - 90 = x

x = 52

Answer:

Step-by-step explanation:

Let's find the size of angle x

The angle in a complete turn add up to 360°

\( \mathsf{x + 20 + 165 + 33 + 90 = 360}\)

Add the numbers

\( \mathsf{x + 308 = 360}\)

Move constant to R.H.S and change it's sign

\( \mathsf{x = 360 - 308}\)

Calculate the difference

\( \mathsf{x = 52}\) °

Hope I helped!

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The parabola shown is symmetric about the y axis.  y-intercept = -18 and Zeros: x = -2, -2.5 and 2.5.

The value of a can be used to calculate the parabola's direction. If an is true, the parabola will face upward (making a u shaped). If an is negative, the parabola will be downward (upside down u).

The graph for the given quadratic function  f(x) = ax² + bx + c .

As the graph is open both upward as well as downward, the parabola shown is symmetric about the y axis.

From the graph:

y-intercept - is the point on the y axis where value of x becomes zero.

y-intercept = -18

Now,

Zeros of the equation are the points satisfying the curve.

Take the values of x that lies on curve when y = 0.

Zeros: x = -2, -2.5 and 2.5

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The amount of money paid in interest will be $3,292.56

The total amount of money borrowed is $14,825.00 - (8/100) × $14,825.00= $14,825.00 - $1,186.00= $13,639.00. Therefore, the monthly payment can be determined as follows:

Using the formula, Monthly payment = Principal × i (1 + i)n / (1 + i)n - 1

Where i = r / n, r is the rate of interest per year, and n is the number of payments per year,

the monthly payment will be; i = r / n

= 4% / 1

2= 0.00333

n = 6 × 12 = 72.

Thus we have; Monthly payment = $13,639.00 × 0.00333 (1 + 0.00333)72 / (1 + 0.00333)72 - 1

Monthly payment = $222.92

Therefore, the monthly payment will be $222.92Total cost of the car

The total cost of the car will be equal to the amount borrowed plus interest.

Since the amount borrowed is $13,639.00, the total cost can be computed as follows:

Total cost = $13,639.00 + interest

The interest can be calculated using the formula;

I = P × r × nI = $13,639.00 × 0.04 × 6= $3,292.56

Therefore, the total cost will be;

Total cost = $13,639.00 + $3,292.56= $16,931.56

Thus, the total cost of the car is $16,931.56

Therefore, The amount of money paid in interest will be $3,292.56

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Answer:

50 Fahrenheit (F) 10 Celsius (C)

1 F = -17.222 C 1 C = 33.800 F

Answer:

50 Fahrenheit (F) 10 Celsius (C)

1 F = -17.222 C 1 C = 33.800 F

Answer:

option plz

Step-by-step explanation:

where is the option

Answer:

x=39.76693372

Step-by-step explanation:

Subtract 2187 from 3.

54.92x−2184=0

Add 2184

to both sides of the equation.

54.92x=2184

Divide each term by 54.92

and simplify.

x=39.76693372

The distance between coordinates is d = 7.1 units.

The intersection of two perpendicular lines results in the formation of the cartesian plane, a two-dimensional coordinate plane. The X-axis is the horizontal line, and the Y-axis is the vertical line. The Cartesian coordinate point (x, y) indicates that the distance from the origin is x in the horizontal direction and y in the vertical direction. The point is to the right of the origin if the sign of x is positive; otherwise, it is to the left.

Given coordinates,

(3, 11) and (4, 3)

the distance between coordinates is

d=√((x₂ – x₁)² + (y₂ – y₁)²)

here x₁ = 3, x₂ = 4, y₁ = 11 and y₂ = 3

d=√((x₂ – x₁)² + (y₂ – y₁)²)

d=√((4 – 3)² + (4 – 11)²)

d = √(1 + 49)

d = √50

d = 7.0710 units

d = 7.1 units nearest tenth

Hence the distance is d = 7.1 units nearest tenth.

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Answer:

m∠1 = 112°

Step-by-step explanation:

To solve for m∠1, we need to find the supplementary angle and subtract from 180°.  We also know that m∠2 = 44° and the remaining two angles inside the triangle are the same because of the congruent sides, let's call each angle x.

Therefore m∠2 + x + x = 180; combine x's

m∠2 + 2x = 180; substitute m∠2 = 44°

44 + 2x = 180; subtract 44 from both sides

2x = 136; divide by 2

x = 68°

Therefore using the supplementary angle

x + m∠1 = 180 (because it is supplementary)

68 + m∠1 = 180; subtract 68 from both sides

m∠1 = 112°

If the columns of matrix B are linearly dependent, then the columns of AB are also linearly dependent.

Suppose the columns of matrix B are linearly dependent, which means there exist constants c₁, c₂, ..., cₙ (not all zero) such that c₁b₁ + c₂b₂ + ... + cₙbₙ = 0, where b₁, b₂, ..., bₙ are the columns of B.

Now, let's consider the product AB. Suppose A is an m × n matrix.

The jth column of AB is given by the product AB(:, j) = A(b₁j) + A(b₂j) + ... + A(bₙj), where b₁j, b₂j, ..., bₙj are the jth columns of B.

Substituting the linear dependence relation for the columns of B into the expression for AB(:, j), we get:

AB(:, j) = A(c₁b₁ + c₂b₂ + ... + cₙbₙ)

         = c₁A(b₁) + c₂A(b₂) + ... + cₙA(bₙ)

Since matrix multiplication distributes over column vectors, we have:

AB(:, j) = c₁A(b₁) + c₂A(b₂) + ... + cₙA(bₙ)

This shows that the jth column of AB can be expressed as a linear combination of the columns of A, multiplied by the corresponding coefficients c₁, c₂, ..., cₙ. Therefore, if the columns of B are linearly dependent, the columns of AB are also linearly dependent.

In conclusion, if the columns of matrix B are linearly dependent, then so are the columns of the product AB.

Complete Question:

Show that if the columns of B are linearly dependent, then so are the columns of AB.

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The solution for b is y-mx in the equation y=mx+b.

The given equation is y=mx+b

y equal r=to m times of x plus b

We need to solve for b in the equation

To solve we have to isolate b from the equation

Subtract mx from both sides

y-mx=b

Hence, the solution for b is y-mx in the equation y=mx+b.

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Answer:

25x-5

Step-by-step explanation:

Answer:

x = 3.32

y = 2.11

Step-by-Step Explanation:

The required surface area of the sphere with radius 10 feet is given by option a. 1,256 ft².

Let us consider 'r' be the radius of the sphere.

Radius of the sphere 'r' = 10 feet

Surface area of the sphere = 4 π r²

Substitute the value of radius in the formula we get,

⇒ Surface area of the sphere = 4 π × ( 10 )²

Substitute value of π is equal to 3.14 we get

⇒ Surface area of the sphere = 4 × 3.14 × ( 10 )²

⇒ Surface area of the sphere =  12.56 × 100

⇒ Surface area of the sphere = 1,256 square feet.

Therefore, the surface area of the sphere is equal to option a. 1,256 ft².

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Answer:

The answer is 1500

Step-by-step explanation:

I multiplied 60 by 25

Answer:Its 1500

Step-by-step explanation:60 x 25

The roots of the function f(x) =\(x^3 + 3x^2 + x - 5\) are approximately x ≈ -2.27 (real root) and x ≈ -0.36 + 1.56i, x ≈ -0.36 - 1.56i,   \((x-1)(x^3+3x^2+x-5)\).

To find the roots of the function f(x) = x^3 + 3x^2 + x - 5, we need to solve for values of x that make the function equal to zero.

One approach to finding the roots is by using factoring or synthetic division, but in this case, the function does not have any obvious rational roots. Therefore, we can use numerical methods such as the Newton-Raphson method or graphing techniques to approximate the roots.

Using a graphing calculator or software, we can plot the function f(x) = x^3 + 3x^2 + x - 5. By analyzing the graph, we can estimate the x-values where the function intersects the x-axis, indicating the roots.

Upon analyzing the graph or using numerical methods, we find that the function has one real root approximately equal to x ≈ -2.27.

The other two roots are complex conjugates, which means they come in pairs of the form a + bi and a - bi. For this particular function, the complex roots are approximately x ≈ -0.36 + 1.56i and x ≈ -0.36 - 1.56i.

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Therefore, to maximize the volume of the box, a square with a side length of 5 inches should be cut out.

To determine the size of the square that should be cut out to maximize the volume of the box, we can follow these steps:

1. Let's assume that the side length of the square to be cut out is 'x' inches.

2. After cutting out the squares, the resulting box will have dimensions of length (20 - 2x) inches, width (12 - 2x) inches, and height 'x' inches.

3. The volume of the box can be calculated by multiplying these dimensions: V = (20 - 2x)(12 - 2x)x.

4. Simplifying the expression, we get \(V = 4x^3 - 64x^2 + 240x\).

5. To maximize the volume, we need to find the value of 'x' that maximizes the volume function V.

To find the maximum volume, we can take the derivative of V with respect to 'x' and set it equal to zero, then solve for 'x':

\(dV/dx = 12x^2 - 128x + 240\)

Setting dV/dx = 0:

\(12x^2 - 128x + 240 = 0\)

Factoring the quadratic equation: 12(x - 5)(x - 4) = 0

Solving for 'x', we find two possible values: x = 4 and x = 5.

To determine which value of 'x' maximizes the volume, we can compare the values of V at these points. Evaluating V for x = 4 and x = 5:

\(V(x=4) = 4(4)^3 - 64(4)^2 + 240(4) = 256\)cubic inches

\(V(x=5) = 4(5)^3 - 64(5)^2 + 240(5) = 300\) cubic inches

Comparing the volumes, we see that V(x=5) = 300 cubic inches is greater than V(x=4) = 256 cubic inches.

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Answer:

8,16,24,32,40,48,56,64,72,80,88,96,104,112,120,128,136,144,152,160,168,176,184,192

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96

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Answer:

6,12,18,24,30,36,42,48,54,60,66,72

8,16,24,32,40,48,56,64,72,80,88,96

Step-by-step explanation: hope i helped

Answer and Step-by-step explanation:

For question 1:

The net for the cylindrical candy container has a rectangle with a height of 0.7 inches and a length of the circumference of the circular bases, which is π(1.6) inches. The area of the rectangle is (0.7)(π(1.6)) = 1.12π square inches. The two circular bases each have an area of (1/2)π(0.8)^2 = 0.4π square inches. The total surface area covered by the plastic wrap is the sum of the area of the rectangle and the two circular bases, which is 1.12π + 0.4π + 0.4π = 1.92π square inches. Therefore, the answer is option A: 1.84π square inches (rounded to two decimal places).

For question 2:

The surface area of a cylinder is given by the formula 2πr(r+h), where r is the radius of the circular base and h is the height of the cylinder. Substituting the given values, we get 2π(5)(5+4) = 2π(5)(9) = 90π square inches. Therefore, the answer is option C: 282.6 in2.

For question 3:

The correct formula for the surface area of a cylinder is SA = 2πrh + 2πr^2, where r is the radius of the circular base and h is the height of the cylinder. The given cylinder has a diameter of 3.2 feet and a height of 3.8 feet, so its radius is 1.6 feet. Substituting these values into the formula, we get SA = 2π(1.6)(3.8) + 2π(1.6)^2 = 12.032π square feet. Therefore, the answer is option A: SA = 2π(1.6)2 + 3.2π(3.8) square feet.

For question 4:

The surface area of the circular bottom of the cake is πr^2, where r is the radius of the circular bottom. Substituting the given values, we get π(15)^2 = 225π square centimeters. The lateral surface area of the cake (everything but the circular bottom) is given by the formula 2πrh, where r is the radius of the circular bottom and h is the height of the cake. Substituting the given values, we get 2π(15)(12) = 360π square centimeters. Therefore, the total surface area of the cake is 225π + 360π = 585π square centimeters. Rounding to the nearest square centimeter, the answer is option B: 585 cm2.

For question 5:

The lateral surface area of the wheel of cheese (everything except the circular top and bottom) is given by the formula 2πrh, where r is the radius of the circular base and h is the height of the cylinder. Substituting the given values, we get 2(22/7)(20)(18) = 2520 square centimeters. The label covers the lateral surface area of the wheel, so it covers 2520 square centimeters. Therefore, the answer is option B: 15,840/7 square centimeters.

For question 6:

The surface area of a cylinder is given by the formula SA = 2πr^2 + 2πrh, where r is the radius and h is the height. Since the diameter is 6 inches, the radius is half of that, or 3 inches.

We are given that the surface area of the tub is 183.69 square inches, so we can write the equation:

183.69 = 2π(3^2) + 2π(3)h

Simplifying and solving for h, we get:

183.69 = 18π + 6πh

165.69 = 6πh

h = 165.69/(6π)

h ≈ 4.45 inches

Therefore, the height of the cylindrical gallon tub is approximately 4.45 inches. Rounded to the nearest hundredth, the answer is 4.5 inches. So the correct answer is B. 4.5 inches.

Question 7:

The surface area of a cylinder is given by the formula SA = 2πr(r+h), where r is the radius and h is the height of the cylinder.

Substituting the given values, we get:

SA = 2π(1.25)(1.25+2.75)

SA = 2π(1.25)(4)

SA = 10π

Therefore, the exact surface area of the cylinder in terms of π is 10π square centimeters. The answer is option B.

Answer:

21b + 9

Step-by-step explanation:

7b(2 + 7b) + (7b + 7)

7b+7b+7b=21b

2+7=9

21b + 9

The angle between vectors A and B is approximately 89.78 degrees.

To find the angle between vectors A and B, we can use the dot product formula:

A · B = |A| |B| cos(θ)

Given that Ā· B = 4 and knowing the magnitudes of vectors A and B:

|A| = √(22² + 33²)

    = √(484 + 1089)

    = √(1573)

    ≈ 39.69

|B| = √((-1)² + 23² )

    = √(1 + 529)

    = √(530)

    ≈ 23.02

Substituting the values into the dot product formula:

4 = (39.69)(23.02) cos(θ)

Now, solve for cos(θ):

cos(θ) = 4 / (39.69)(23.02)

cos(θ) ≈ 0.0183

To find the angle θ, we take the inverse cosine (arccos) of 0.0183:

θ = arccos(0.0183)

θ ≈ 89.78 degrees

Therefore, the angle between vectors A and B is approximately 89.78 degrees.

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Answer:

arc WVY = 250°

Step-by-step explanation:

The tangent- tangent angle YXW is half the difference of the intercepted arcs

\(\frac{1}{2}\) ( WVY - WY) = 70

\(\frac{1}{2}\) (10a - (4a + 10) ) = 70 ( multiply both sides by 2 )

10a - 4a - 10 = 140

6a - 10 = 140 ( add 10 to both sides )

6a = 150 ( divide both sides by 6 )

a = 25

Then

arc WVY = 10x = 10 × 25 = 250°

Answer: 10

Step-by-step explanation:

6-5 = 1

-2 x 1 = -2

-2 x -5 = 10

Instrumental values refer to the means or behaviors that individuals adopt to achieve their desired goals. They are the guiding principles or traits that people consider important in their actions.

On the other hand, terminal values are the desired end states or outcomes that individuals strive to achieve. They reflect the ultimate goals or objectives that people aspire to fulfill. Examples of terminal values include happiness, success, freedom, peace, and wisdom.

Values play a crucial role in work settings as they shape individual attitudes, behaviors, and decision-making. They guide employees' choices and actions, influencing their work ethic, motivation, and job satisfaction. When employees share common values with their organization, it creates a sense of alignment and cohesion, leading to greater employee engagement and commitment.

Values also influence organizational culture, as they define the norms, beliefs, and expectations within the workplace. Organizations often establish value statements to communicate their core principles and attract employees who align with those values. In summary, values provide a framework for individuals and organizations to define their purpose, guide their actions, and create a positive work environment.

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The ball will achieve the maximum height after 2.5 seconds.

Equation modelling is a process of writing a given mathematical statement in the form of a mathematical expression for the correct analysis and results of the parameters existing in that problem.

Given is that the height of the football can be modelled by the function as -

y = - 16x² + 80x

For maximum height -

dy/dx = 0

d/dx (- 16x² + 80x) = 0

- 32x + 80 = 0

32x = 80

x = 80/32

x = 2.5

Therefore, the ball will achieve the maximum height after 2.5 seconds.

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The Ferris wheel's graph can be a sinusoidal curve with an amplitude of 40 feet as well as a period of 1/3 minutes (or 20 seconds), oscillating between 20 feet and 100 feet.

The procedures can be used to graph the Ferris wheel, which has axle height of 60 feet, a diameter of 80 feet, along with a rotational speed of three spins per minute:

Find the equation that describes how a rider's height changes with time on a Ferris wheel.

The equation referred to as h(t) = a + b cos(ct), where is the height of the axle, b is the wheel's half-diameter, as well as c is the number of full cycles per second substituting the values provided.

The vertical axis shows height in feet, as well as the horizontal axis shows time in minutes.

Thus, the graph will usually have a sinusoidal curve with an amplitude of 40 feet, a period of 1/3 minutes, and an oscillation between 20 feet and 100 feet.

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In a certain isoceles triangle, the sum of the measures of the base angles is 88 degrees less than the measure of the remaining angle. Then the measure of each angle is 44° and 92°.

Determine the measure of each angle

These are the specified parameters:

The sum of the measures of the base angles is 88° less than the measure of the remaining angle.

Large pedestal angle

a + a = 88

2a = 88

 a = 88/2

 a = 44°

Peak angle

a + a + b = 180

88 + b = 180

       b = 180 - 88

       b = 92°

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Answer:

3x-5=81

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