find the value of x and y

Step-by-step explanation:

it's a right angled triangle

B. acute

C. scalene ( as all sides are different)

E. right

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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To find the length of the model, we need to use the given scale, which states that 1 inch on the model represents 1.5 feet in reality.

The length of the actual object is given as 18 feet. Let's calculate the length of the model:

Length of model = Length of actual object / Scale factor

Length of model = 18 feet / 1.5 feet/inch

Length of model = 12 inches

Therefore, the length of the model is 12 inches. Therefore, the correct option is (a) 12 inches.

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Given:

The angles are:

Example \(54^\circ\)

1. \(63^\circ\)

2. \(87^\circ\)

3. \(45^\circ\)

4. \(72^\circ\)

5. \(5^\circ\)

To find:

The complimentary angle of the given angles.

Solution:

If two angles are complimentary, then their sum is 90 degrees.

Example: Let x be the complimentary angle of \(54^\circ\), then

\(x+54^\circ=90^\circ\)

\(x=90^\circ -54^\circ\)

\(x=36^\circ\)

Similarly,

1. The complimentary angle of \(63^\circ\) is:

\(90^\circ -63^\circ=27^\circ\)

2. The complimentary angle of \(87^\circ\) is:

\(90^\circ -87^\circ=3^\circ\)

3. The complimentary angle of \(45^\circ\) is:

\(90^\circ -45^\circ=45^\circ\)

4. The complimentary angle of \(72^\circ\) is:

\(90^\circ -72^\circ=18^\circ\)

5. The complimentary angle of \(5^\circ\) is:

\(90^\circ -5^\circ=85^\circ\)

Therefore, the complimentary angles of \(54^\circ, 63^\circ, 87^\circ, 45^\circ, 72^\circ, 5^\circ\) are \(36^\circ, 27^\circ, 3^\circ, 45^\circ, 18^\circ, 85^\circ\) respectively.

Answer:

Using the section formula, if a point (x,y) divides the line joining the points (x

1

,y

1

) and (x

2

,y

2

) in the ratio m:n, then

(x,y)=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

3AC=CB

CB

AC

=

3

1

Since, A(1,1) and B(2,3) & m:n=1:3

Therefore, we have

C(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

(

1+3

(1)(2)+3(1)

,

1+3

(1)(3)+3(1)

)

C→(

4

5

,

2

3

).

Answer:

270

Step-by-step explanation:

so u would take 6 and 45 and multiplay

The smallest number would be 2520 which is divisible by 126 and 120 which is determined by the LCM.

Prime Factorization is defined as any number that may be expressed as a product of prime numbers that has been said to be prime factorized. Any integer with exactly two factors 1 and the number itself. is said to be a prime number.

We need to write 126 and 120 as the product of their prime factors,

126 = 2×3×3×7

120 = 2×2×2×3×5

LCM = 2×2×2×3×3×5×7 = 2520.

Therefore, the smallest integer would be 2520 which is divisible by 126 and 120.

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Hey there!

Assuming you meant:

9^3

IF SO, LETS SOLVE FOR IT!

9^3

= 9 * 9 * 9

= 81 * 9

= 729

Therefore, your answer is most likely:

[729] So, the base number is probably 5 and the exponent is probably 3

Random note:

Your base number is always that number that will be repeated by what the exponent is telling it!

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:  339.3 grams

Work Shown:

y = 1400(1-0.08)^x

y = 1400(1-0.08)^17

y = 339.25097192703

y = 339.3

Answer:

60m2

Step-by-step explanation:

I just dd it on edge 21 :)

The area of the triangle will be equal to 60 square meters. The correct option is B.

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.

The space occupied by any two-dimensional figure in a plane is called the area. The two-dimensional space occupied by the triangle is called the area of the triangle.

Given that right triangles, MNP and QRS are congruent. Right triangles M N P and Q R S are shown. The length of side Q S is 8 meters. The length of M N is 17 meters and the length of P N is 15 meters.

The area of the triangle is calculated as,

Area = (1/2) x PN x QS

Area = (1/2) x 8 x 15

Area = 4 x 15

Area = 60 square meters

Therefore, the area of the triangle will be equal to 60 square meters. The correct option is B.

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Answer:

it’s not a it’s D

Step-by-step explanation:

i took the quiz and got it correct

The equation for the plane consisting of all points that are equidistant from the points (−7, 1, 1) and (3, 3, 5) is 20x + 4y + 8z = -9.

In order to determine the distance of this plane (x, y, z) with the given points, we would use the distance formula.

Mathematically, the distance between three (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

For these points (x, y, z) and (−7, 1, 1), the distance is given by:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Distance = √[(x₂ - (-7))² + (y₂ - 1)² + (z₂ - 1)²]

Distance = √[(x₂ + 7)² + (y₂ - 1)² + (z₂ - 1)²]

By using the algebraic formulas, the expanded expression is given by:

(a - b)² = a² - b² - 2ab

(a + b)² = a² + b² + 2ab

Distance = √[(x² + 14x + 49) + (y² - 2y + 1) + (z² - 2z + 1)]   .......equation 1.

For these points (x, y, z) and (3, 3, 5), the distance is given by:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Distance = √[(x - 3)² + (y - 3)² + (z - 5)²]

Distance = √[(x² - 6x + 9) + (y² - 6y + 9) + (z² - 10z + 25)]    .....equation2.

Since both distances are equidistant, we would equate eqn. 1 and eqn. 2 and then simplify:

√[(x² + 14x + 49) + (y² - 2y + 1) + (z² - 2z + 1)] = √[(x² - 6x + 9) + (y² - 6y + 9) + (z² - 10z + 25)]

(x² + 14x + 49) + (y² - 2y + 1) + (z² - 2z + 1) = (x² - 6x + 9) + (y² - 6y + 9) + (z² - 10z + 25)

x² + 14x + 49 + y² - 2y + 1 + z² - 2z + 1 = x² - 6x + 9 + y² - 6y + 9 + z² - 10z + 25

14x + 6x - 2y + 6y - 2z + 10z + 52 - 43 = 0

20x + 4y + 8z + 9 = 0

20x + 4y + 8z = -9.

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The amount of investment will be $8183.24 after compound interest.

Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.

A = P(1+r/100)ⁿ

Where:

A = the future value of the investment or loan

P = the principal investment or loan amount

r = the interest rate (decimal)

n = the number of compound periods

As per the question, an initial investment of $5575 is appreciated for 12 years in an account that earns 3.25% interest, compounded semiannually.

The compounded amount will be calculated as:

A = 5575 ( 1 + 0.0325 )¹²

A = 5575 × 1.4678

A = $8183.24

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Answer:

P < -1

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

Step 2: Add 4 to both sides.

Therefore, the answer is P < -1! (Also, the graphed solution is below.)

To bring the 2,000 kg wagon to rest, the buffer stop needs enough springs to absorb its kinetic energy. The number of springs and their stiffness can be calculated using given parameters and formulas.



To calculate the number of springs required in the buffer stop, we need to find the energy of motion that needs to be absorbed. The kinetic energy (KE) of the wagon is given by KE = (1/2)mv^2, where m is the mass (2,000 kg) and v is the velocity (0.69 m/s). The KE is 477.9 J.Next, we calculate the potential energy stored in the compressed springs. The compression distance is 15 cm, which is 0.15 m. The potential energy (PE) stored in each spring is given by PE = (1/2)kx^2, where k is the stiffness of the spring and x is the compression distance.

The total energy absorbed by all the springs is equal to the kinetic energy of the wagon. Therefore, the number of springs required is given by N = KE / PE, where N is the number of springs.To determine the stiffness of the spring, we use the formula k = (Gd^4) / (8nD^3), where G is the shear modulus (0.8 x 10^5 N/mm^2), d is the wire diameter (2 cm), n is the number of coils (15), and D is the mean diameter of the coils (20 cm).

By substituting the values into the equations, we can find the number of springs and the stiffness of each spring.

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Answer:

● 23.55 units

Step-by-step explanation:

Arc length = 5( 270 π/ 180)

= 7.5 π units

= 7.5 (3.14)

= 23.55 units

OAmalOHopeO.

============================================================

Explanation:

For now, we'll just find the perimeter of the full circle. The term "circumference" is the same as the perimeter of the circle.

Use the circumference formula to get

C = 2*pi*r

C = 2*3.14*5

C = 31.4

The distance around the full circle is approximately 31.4 units. It's approximate because pi = 3.14 is approximate.

We don't want the full distance around the circle. Instead, we want just the length of the green arc shown in the drawing. This is exactly 3/4 of the full circle, aka 3/4 = 0.75 = 75% of the full perimeter.

The length of the green arc is about 0.75*C = 0.75*31.4 = 23.55 units long. Imagine using a cloth ruler (used in tailoring clothes) as one way to confirm that this arc length is roughly 23.55 units long. Or you could imagine unwrapping this curved portion to lay it completely straight and flat against a ruler.

Answer:

$30

Step-by-step explanation:

To find the cost, plug in 10 for x, then simplify

1.5x + 15

1.5(10) + 15

= 30

So, it will cost Johnny $30 to download 10 songs

The total amount of money that Johnny will have to pay is f(10) = 30.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Given is that it costs Johnny $15 a month plus $1.50 per song to download music. This situation is represented by the expression →

1.5(x) + 15.

The expression is given by -

f(x) = 1.5(x) + 15

where [x] is the number of songs downloaded.

For [x] = 10 songs, the total amount of money that Johnny will have to pay is -

f(10) = 1.5 x 10 + 15

f(10) = 15 + 15

f(10) = 30

Therefore, the total amount of money that Johnny will have to pay is f(10) = 30.

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The adding the polynomials we get -4x2 - 11x - 5.

Given, the polynomials are (-x2 + 9) and (-3x2 - 11x + 4).

The sum of the polynomials = (-x2 - 9) + (-3x2 - 11x + 4)

The sum of the polynomials is found by removing the parathesis and grouping the like terms.

-x2 - 9 + -3x2 - 11x + 4

= -x2 - 3x2 - 11x - 9 + 4

= -4x2 - 11x - 5

Therefore, the adding the polynomials we get -4x2 - 11x - 5.

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Answer:

-5/2

Step-by-step explanation:

Answer:

x= 3

Step-by-step explanation:

x on triangle 1 is 5 times less than 15

x on triangle 2 is 3 times bigger than 10

Hope this helps!

Answer:

x = 5

Step-by-step explanation:

The small triangle has been dilated by 2 making it twice as big as before.

The side that measures 10 would be dilated by 0.5 to find x which is half a big.

10 x 0.5 = 5

Now check your work. On one side it asks 6x. So, 6 x 5 = 30. Since 30 is twice as much as 15. The rule applies that x = 5.

5 x 2 = 10

6 x 5 = 30

15 x 2 = 30

Once you have the required numerical values, plug them into the formula and calculate the minimum sample size needed for Big Corporation to be confident in their estimate of the mean amount of coffee dispensed per cup

We need to determine the minimum sample size required for Big Corporation to estimate the mean amount of coffee dispensed per cup with a certain level of confidence and margin of error.

Unfortunately, some of the numerical values are missing in question.

Step 1: Determine the desired confidence level (e.g., 90%, 95%, 99%).
Step 2: Identify the desired margin of error (e.g., within 0.1 ounces).
Step 3: Given the standard deviation of cup amounts (missing in the question, let's assume it as "σ").

Now, use the formula for determining the minimum sample size needed:

n = (Z² * σ²) / E²

where:
n = minimum sample size
Z = Z-score corresponding to the desired confidence level (e.g., 1.96 for 95% confidence)
σ = standard deviation of cup amounts
E = margin of error

Step 4: Calculate the minimum sample size (n) using the formula and round up to the nearest whole number.

By numerical values, plug them into the formula and calculate the minimum sample size needed for Big Corporation to be confident in their estimate of the mean amount of coffee dispensed per cup.

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The description of the cosine function is \(\mathrm{f(x) = -10 \cos( \frac{2\pi}{3}) x + 10}\).

A cosine function's general form is given by:

\(\mathrm{f(x) = A \times cos(Bx + C)) + D}\)

where:

A stand for amplitude, or the ratio of the maximum to the minimum value.

B = 2π / period

C stands for horizontal phase shift.

(Midpoint between the Maximum and Minimum Values) D = Vertical Shift

We can determine the parameters for the specified function given the information given:

Period = 3 (This means B = 2π / 3)

Maximum value = 20

This means the amplitude A is half of this, so A = 20 / 2 = 10

Minimum value = 0

This means the vertical shift D is half of the difference between the maximum and minimum.

So, D = (20 - 0) / 2

= 10

The amplitude is negative because the function is a mirror of its parent function over the x-axis, hence A = -10.

Putting it all together, the function is:

\(\mathrm{f(x) = -10 \cos( \frac{2\pi}{3}) x + 10}\)

Hence the final expression after the transformation is \(\mathrm{f(x) = -10 \cos( \frac{2\pi}{3}) x + 10}\).

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Answer:

11.9

Step-by-step explanation:

just add the two numbers :)

Answer:

the answer 11.9

Step-by-step explanation:

add by lining up the decimals

To determine the price that would maximize revenue, we need to find the price point at which the product of price and sales is highest. In this scenario, the relationship between the price and monthly sales is assumed to be linear.

Let's define the price as x and the monthly sales as y. We are given two data points: (11, 26000) and (10, 33000). We can use these points to find the equation of the line that represents the relationship between price and monthly sales.

Using the two-point form of a linear equation, we can calculate the equation of the line as:

(y - 26000) / (x - 11) = (33000 - 26000) / (10 - 11)

Simplifying the equation gives:

(y - 26000) / (x - 11) = 7000

Next, we can rearrange the equation to solve for y:

y - 26000 = 7000(x - 11)

y = 7000x - 77000 + 26000

y = 7000x - 51000

The equation y = 7000x - 51000 represents the relationship between price (x) and monthly sales (y). To maximize revenue, we need to find the price (x) that yields the highest value for the product of price and sales. Since revenue is given by the equation R = xy, we can substitute y = 7000x - 51000 into the equation to obtain R = x(7000x - 51000).

To find the price that maximizes revenue, we can differentiate the revenue equation with respect to x, set it equal to zero, and solve for x. The resulting value of x would correspond to the price that maximizes revenue.

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Answer:

85.71 %

Step-by-step explanation:

26-14=12

12/14= 0.8571

0.8571x100= 85.71

Answer:

A change from 14 to 26 represents a positive change (increase) of 85.7142857143%

Step-by-step explanation:

Use the formula:

New - Old / Old x 100%

In other words, new(26) minus old(14) divided by old(14) time 100%

14 is the old value and 26 is the new value. In this case we have a positive change (increase) of 85.7142857143 percent because the new value is greater than the old value.