Find the values of x and y in parallelogram PQRS. PT=​y, TR=4x+​1, QT=2​y, TS=3x+12 In parallelogram PQRS, diagonals PR and QS cross at point T. Q P S R T x=nothing and y=nothing

a) The cosine equation that models the board position is given as follows: y = 4.8cos(2πx/7).

b) The cosine function was chosen as it has a maximum point at the origin, hence no phase shift is needed.

The standard definition of the sine function is given as follows:

y = Acos(B(x - C)) + D.

For which the parameters are given as follows:

The board moves 9.6 feet from its low point to its high point, hence the amplitude is given as follows:

2A = 9.6

A = 4.8.

The period is of 7 seconds, hence the coefficient B is given as follows:

2π/B = 7

7B = 2π

B = 2π/7.

Hence the equation is given as follows:

y = 4.8cos(2πx/7).

The board moves 9.6 feet from its low point to its high point, returning to its low point every 7 seconds.

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Answer:

f(t)= (9.6/2)cosBt

= 4.8cosBt

where B=2pi/period

use cosine to avoid a phase shift

Answer:

If none of the input values are repeated, the relation is a function.

Step-by-step explanation:

When all outputs have a different input, its a function.

Answer:

B

Step-by-step explanation:

Did it on edge 100%

Answer:

if 24miles in 2gallons the 12 miles per gallon is one gallon

Answer:

-9

Step-by-step explanation:

(6+3) divided by (4-5)

9/-1

-9

Step-by-step explanation:

\(6(17x) = 102\)

A linearly independent set that generates the subspace of diagonal matrix in M2x2(F) is {[1,0;0,0], [0,0;0,1]}.

A subspace of M2x2(F) is a set of all diagonal matrices, which are matrices of the form [a,0;0,b] with a, b∈F.

A linearly independent set of vectors that generate this subspace is {[1,0;0,0], [0,0;0,1]}. Any diagonal matrix can be written as a linear combination of these two vectors.

A subspace of M2x2(F) is a set of all diagonal matrices, which are matrices of the form [a,0;0,b] with a,b∈F. This means that all the diagonal entries in the matrix must be non-zero. To find a linearly independent set that generates this subspace, we can start by considering the simplest form of a diagonal matrix, which is [1,0;0,0]. This vector is linearly independent, as it cannot be expressed as a linear combination of any other vector in the space. Similarly, [0,0;0,1] is also linearly independent, as it can't be expressed as a linear combination of any other vector.

These two vectors form a linearly independent set that generates the subspace of diagonal matrices in M2x2(F). Any diagonal matrix can be written as a linear combination of these two vectors. For example, the matrix [2,0;0,3] can be expressed as 2[1,0;0,0]+3[0,0;0,1]. Thus, this set of vectors is sufficient to generate the entire subspace.

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Answer:

D

Step-by-step explanation:

Clockwise would mean a rotation to the right, and since the triangle is already plotted, just use the little picture turning icon( in the top right corner of the photo of the problem) to turn, and look at the triangle in the original graph to see how it moved.

Then click the button three more time until you get the photo right-side-up, and choose which option is the best answer.

The value of SV, given that point J is the centroid, would be A. 9.

Seeing as we have point J as the centroid for triangle SZU, we can then tell that JV would be:

JV = 1 / 3 x SV

Knowing this, we can make SV the subject of the formula to become:

(JV = 1 / 3 x SV ) / 1 / 3

3 x JV = SV

SV = 3 JV

SV would then be:

SV = 3 x JV

SV = 3 x 3

SV = 9

In conclusion, SV would be 9.

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Answer:

answer is B. 9 :)

Step-by-step explanation:

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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The value of angle x and angle y is determined as 78⁰ and 115⁰ respectively.

The value of angle x and angle y is calculated by applying principle of angles formed by parallel lines as follows;

The value of angle adjacent x = 102⁰

The value of angle x   is calculated as;

x = 180 - 102 ( sum of angles on a straight line)

x = 78⁰

The value of angle y is calculated as follows;

y = 115⁰ (corresponding angles are equal)

Thus, the value of angle x and angle y is determined as 78⁰ and 115⁰ respectively.

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Answer:

Step-by-step explanation:

You want to know a thermometer's reading 4 minutes and 9 minutes after begin brought into a room with a temperature of 36 °C if its initial reading is 10 °C, and it rises to 14 °C after 2 minutes.

Newton's law of cooling tells you the temperature difference of 36 -10 = 26 °C will decline exponentially. If it declines to 36 -14 = 22 °C after 2 minutes, then the temperature reading can be modeled by ...

  T = 36 -26·(22/26)^(t/2)

At times of t=4 and t=9, the temperature readings will be ...

__

Additional comment

The time constant of this thermometer is about 12 minutes, so it will take about 67 minutes to read within 0.1 °C of the room temperature.

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Yes, isosceles triangle ABC has a 130 angle at vertex B.

What is an isosceles triangle?

Any triangle with (at least) two equal sides is said to be an isosceles. The remaining side in the illustration has a length in addition to the two equal sides. This characteristic equates to the triangle's two angles being equal. Therefore, an isosceles triangle has two equal sides as well as two equal angles.

Here, we have

The isosceles triangle has 2 angles of the same length.

All angles in a triangle add to 180

if the angles are m∠A, m∠B, m∠C, then

either m∠A = m∠B or m∠B = m∠C or m∠A = m∠C

If we assume that vertex B is the one that has a twin then

130+130+x = 180

260+x = 180

x = -80, we can't have a negative angle measure.

so 130 must be the odd one

x+x+130 = 180

2x+130 = 180

2x = 50

x = 25

so

m∠A=m∠C=25°

let's test the 2nd answer choice

m∠A+m∠B=25+130 = 155,

Hence, isosceles triangle ABC has a 130 angle at vertex B if m∠A+m∠B=25+130 = 155.

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Answer:

V = 1/3 * π * r^2 * h OR V = π * r^2 * h/3

Step-by-step explanation:

hope it will help you dear

you told only formula if you need derevation then say :)

Answer:

About 154 Square

Explanation:

To find an area of a circle you multiply pi by the radius squared so 7² = 49 and 49 x 3.14 = 153.86 which is the closest to 154.

In order to find the height of 2 different 3-D shapes, we must identify which dimension represents the height for each individual shape and then add them together.

The first thing is that we must identify which dimension represents the height for each individual shape, for instance, if one shape is a rectangular prism, its height would be the length of one of its sides.

After we identified the height for each shape, you can add them together to get the total height of the composite figure, but, we must understand that this method assumes that the two shapes are stacked vertically on top of each other with their bases aligned.

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Using the cross product for the proff of Pythagoras theorem, the correct step is

By the cross product property, AB² =  BC multiplied by BD

The cross product property is typically used to solve equations with two values, where the product of the extremes (the outer terms) is equal to the product of the means (the inner terms).

For the similar triangles, the ratio is as follows

BD / BA = BA / BC

BA² = BD * BC

and AB = BA, hence

BA² = BD * BC

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The joint relative frequency for school children who plan to attend camp and have swimming lesson is 44%.

The correct option to the given question is option d.

We are required to find the joint relative frequency for school children who plan to attend camp and have swimming lessons, rounded to the nearest percent.

To find the joint relative frequency, we use the formula as follows:

Joint relative frequency = frequency of interest / total frequency

Joint relative frequency for school children who plan to attend camp and have swimming lessons = 42 / 96

(As we are looking for the students who plan to attend camp and have swimming lessons, we are interested in the first column of the table and the entry at the intersection of the first row and second column.)

Joint relative frequency for school children who plan to attend camp and have swimming lessons = 0.4375

Joint relative frequency for school children who plan to attend camp and have swimming lessons (rounded to the nearest percent) = 44%(option d).

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Answer: 48 qt

Step-by-step explanation:

The conversion factor between pints and quarts is two which means there are 2 pints in every quart. divide the number of pints by two to find the number of quarts.

96/2 = 48

EX: 24 pints = 12 quarts

24/2 =12

EX 8 quarts = 16 pints

The same rule works in reverse but instead of dividing you multiply.

8x2 = 16

Answer: First side is 40.5 meters. Second side is 121.5 meters. The third side is 159.

Step-by-step explanation:

x + 3x + 4x -3 = 321

8x - 3 =321

      +3     +3

8x = 324

x = 40.5

Second Side:   3(40.5) = 121.5

Third side:  4(40.5) - 3  = 159

Check: 159 + 121.5 + 40.5 =  321    

Answer:

  total cost = 8x^2 +17280/x

Step-by-step explanation:

Let x represent the base length. Then the area of the base is x^2, and the height is h = 720/x^2.

The area of the four sides is ...

  (4x)(h) = (4x)(720/x^2) = 2880/x

The cost of the base is ...

  base cost = 8x^2

And the cost of the sides is ...

  side cost = 6(2880)/x = 17280/x

The total cost of the box is ...

  total cost = base cost + side cost

  total cost = 8x^2 +17280/x

_____

Comment on the cost function

You will find this function has a minimum at x=∛1080 ≈ 10.260 in. The total cost is about $2526.35, and the box is 2/3 times as tall as wide. That aspect ratio makes any pair of opposite sides cost the same as the base, the generic solution to a cost optimization problem of this sort.

Answer:

21+10.5 which would equal 31.5

Step-by-step explanation:

Answer:

21+10.5 which would equal 31.5

Step-by-step explanation:

Okay so you put -6 in where y is then solve and youll get your answer

-8x-7(-6)=-6

1a. The percentage total return is -19.56%

1b. The dividend yield is 2.42%.

1c. The capital gains yield is -21.98%.

2a. The arithmetic average annual return on large-company stocks in nominal terms is 14.5%.

2b. The arithmetic average annual return on large-company stocks in real terms is 9.67%.

3a. The real return on long-term government bonds is 3.195%

3b. The real return on long-term corporate bonds is 3.291%

In Financial accounting, the percentage total return (P) can be calculated by using this formula;

P = [(Ending price - Initial price) + Dividend] ÷ Initial price

P = [(71 - 91) + 2.20] ÷ 91

P = -0.1956 or -19.56%

1b. For the dividend yield, we have:

Dividend yield = Dividend ÷ Initial price

Dividend yield = 2.20 ÷ 91

Dividend yield = 0.0242 or 2.42%

1c. For capital gains yield, we have:

Capital gains yield = (Ending price - Initial price) ÷ Initial price

Capital gains yield = (71 - 91) ÷ 91

Capital gains yield = -0.2198 or -21.98%.

Part 2.

a. The arithmetic average of annual return on large-company stocks in nominal terms is equal to 14.5%.

b. For arithmetic average annual return in real terms, we have:

(1 + 0.145) = (1 + r)(1 + 0.044)

r = (1.145/1.044) - 1

r = 9.67%

Part 3.

a. For real return on the long-term government bonds, we would apply Fisher equation:

(1 + i) = (1 + r)(1 + h)

Where:

(1 + 0.066) = (1 + r)(1 + 0.033)

1 + r = 1.066/1.033

r = 3.195%

b. For real return on long-term corporate bonds:

(1 + 0.067) = (1 + r)(1 + 0.033)

1 + r = 1.067/1.033

r = 3.291%

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Answer:

156 cm³

Step-by-step explanation:

The solid is a prism with a trapezoid base.

volume = (area of base) × height

V = (8 cm + 5 cm)(1/2)(4 cm) × 6 cm

V = 156 cm³

The given function is ,

The inverse of the function is ,

for x ,

if x= 1 the function will be undefined.

thus,

The correct equation of the circle with center (0,0) that passes through the point (-6,-6) is:

(x + 6)² + (y + 6)² = 72

Please note that the equation represents the circle with center (0,0) and radius √72.\(\)

Answer:

The equation of a circle with center (0,0) that passes through the point (-6,-6) is:

(x - 0)² + (y - 0)² = r²

where r is the radius of the circle. Since the center of the circle is (0,0), we can use the distance formula to find the radius:

r = √(0 - (-6))² + (0 - (-6))² = √(6² + 6²) = √72

Therefore, the equation of the circle is:

x² + y² = 72