If ABCD was a kite, and P was the intersection of its diagonals, what must be true? (3 points)
There are two pairs of opposite congruent angles.

The diagonals each bisect the other diagonal.
The adjacent sides are equal.
The opposite sides are equal.

The volume of any rectangular prism (or solid) is given by:

Given that the dimnsions of the rectangular prism in question is:

Length = 62cm

Width = 3.5cm

Height = 10cm

Therefore, the volume is:

Therefore, the volume (in cubic centimeters) of the given rectangular prism is 2170

Answer: 2170cm3

Step-by-step explanation:

The volume of any rectangular prism (or solid) is given by:

Given that the dimensions of the rectangular prism in question is:

Length = 62cm

Width = 3.5cm

Height = 10cm

Answer:

\( {f}^{ - 1} (x) = \frac{1}{8} x + \frac{7}{8} \)

Inverse functions undo the operation of the original function. That is, if x undergoes function f to become f(x), then the inverse function (denoted by f⁻¹) reverse what function f does. Thus, the inverse function of f changes f(x) back into x.

The inverse of a function can be found in 3 main steps, which is to first let y= f(x), then make x the subject of formula before replacing x with f⁻¹(x) and y with x.

Let's apply the above steps to solve the question!

Given: f(x)= 8x +7

Step 1: Let y= f(x).

y= 8x +7

Step 2: Make x the subject of formula.

Start by subtracting 7 from both sides:

8x= y -7

Divide both sides by 8:

\(x = \frac{1}{8} y + \frac{7}{8} \)

Step 3: Replace x with f⁻¹(x) and y with x.

\( {f}^{ - 1} (x) = \frac{1}{8} x + \frac{7}{8} \)

Additional

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Answer:

x  = 7\(\sqrt{2}\)

Step-by-step explanation:

note the 2 legs are congruent and equal 7

using Pythagoras' identity in the right triangle

x² = 7² + 7² = 49 + 49 = 98 ( take square root of both sides )

x = \(\sqrt{98}\) = \(\sqrt{49(2)}\) = \(\sqrt{49}\) × \(\sqrt{2}\) = 7\(\sqrt{2}\)

Step-by-step explanation:

Since the side marked by the bar is 7, the other side marked by the bar is also 7. Since the angle is 90°, it is a right triangle. Apply the Pythagorean theorem:

\(i = \sqrt{c {}^{2} + c {}^{2} } \)

\(i = \sqrt{ {7}^{2} + {7}^{2} } \)

\(i = \sqrt{2 \times 7 {}^{2} } \)

\(i = 7 \sqrt{2} \)

Answer:

Allergic to chocolate

Step-by-step explanation:

I don't really eat chocolate that much lol.

Answer:

Well i think i would rather be alergic to chocolate

Step-by-step explanation:

The given statement " When the film is placed into the XCP (extension cone paralleling) holder with the smooth side of the film towards the throat, after processing, it will appear darker" is false because it will  lighter, not darker.

The smooth side of the film is the side that interacts with the X-ray radiation and receives the image, while the emulsion side contains the light-sensitive crystals that react to the radiation.

Placing the smooth side towards the throat ensures that the image is sharp and clear, as the X-ray beam travels through the teeth and soft tissues before reaching the film.

After processing, the exposed areas of the film turn dark, representing the captured X-ray image, while the unexposed areas remain light or clear.

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Answer:

Surface area of net = 310 cm²

Step-by-step explanation:

Given:

Dimension of two same rectangle = 11 cm by 9 cm

Dimension of single rectangle = 11 cm by 7 cm

Height of two triangle = 5 Cm

Base of two triangle = 7 Cm

Find;

Surface area of net

Computation:

Surface area of net = Surface area of two same rectangle + Surface area of single rectangle + Surface area of two same triangle

Surface area of net = 2[l x b] + [l x b] + 2[(1/2)(b)(h)]

Surface area of net = 2[11 x 9] + [11 x 7] + 2[(1/2)(7)(5)]

Surface area of net = 198 + 77 + 35

Surface area of net = 310 cm²

To determine the speed of the car at the bottom of the hill, we can use the principle of conservation of energy. As the car rolls down the hill, it will convert its potential energy at the top into kinetic energy at the bottom, neglecting any energy losses due to friction or air resistance.

The potential energy of the car at the top of the hill is given by the formula:

Potential Energy = mass × gravity × height

Since the mass of the car is not provided, we can assume it to be a constant value for the purpose of this calculation. Gravity is approximately 9.8 m/s².

The kinetic energy of the car at the bottom of the hill is given by the formula:

Kinetic Energy = (1/2) × mass × velocity²

Since the potential energy at the top is equal to the kinetic energy at the bottom, we can equate the two equations and solve for velocity.

mass × gravity × height = (1/2) × mass × velocity²

Simplifying the equation, we find:

velocity² = 2 × gravity × height

Taking the square root of both sides, we get:

velocity = √(2 × gravity × height)

Substituting the given values, with gravity as 9.8 m/s² and height as 50 m, we can calculate the velocity. Plugging the values into the equation, we find: velocity = √(2 × 9.8 m/s² × 50 m) ≈ 31.3 m/s

Therefore, the car will be going at approximately 31.3 meters per second (m/s) at the bottom of the hill.

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Graph

Procedure

This is due to the fact that the merry-go-round's passengers are being held in orbit by a gravitational force similar to that experienced by stars in a galaxy. People riding on a merry-go-round that is spinning. Thus, option D is correct.

The action that would best model the role gravity plays in the motions of stars within a galaxy is D. People riding on a merry-go-round that is spinning.

This is because, like stars in a galaxy, the riders on the merry-go-round are experiencing a gravitational force that keeps them in orbit around a central point.

This force, which is proportional to the mass of the objects and inversely proportional to the square of the distance between them, is similar to the force that holds stars in orbit around the centre of a galaxy.

The other options do not accurately model this gravitational force in the same way as a spinning merry-go-round.

Therefore, people riding on a merry-go-round that is spinning.

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50

Step-by-step solution:

    0.3x-42=0.1x-32

    -0.1x

    0.2x-42=-32

                   +42

      0.2x=10

               0.2                

        x=50

(x+x/2)*3=105 is the equation for "three times the sum of a number and half the number equals 105."

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical sentence with two equal sides separated by an equal sign is called an equation. 4 + 6 = 10 is an example of an equation. Linear equations are classified into three types: point-slope, standard, and slope-intercept.

Here,

Three more than twice the sum of a number and half the number equals 105,

The equation will be,

(x+x/2)*3=105

The equation for "Three more than twice the sum of a number and half the number equals 105" will be (x+x/2)*3=105.

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The probability that it does rain tomorrow is 0.6. The result is obtained by using the ratio of positive and negatif outcomes.

Probability is a numerical description of how possible an event to happen. Tha value of probability is between 0 to 1. Zero probability means something is impossible to happen. Probability 1 shows certainty.

If the probability is

p = a/n

Then, the negative outcome of the probability is

q = 1 - p

or

q = b/n

The odds of positive outcome is a/b and the odds of negative outcome is b/a, where a + b= n.

The odds against it raining tomorrow is 3 : 2. Determine the probability that it does rain tomorrow.

We have a = 3, b = 2.

n = a + b

n = 3 + 2

n = 5

The probability that it does rain tomorrow is

p = a/n

p = 3/5

p = 0.6

Hence, the probability of raining tomorrow is 0.6.

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Answer:

x = 20

y = 20√2  

Step-by-step explanation:

This is a 45 - 45 - 90° special right triangle

In a 45 - 45 - 90° triangle the legs are congruent and the hypotenuse = leg * √2

If one leg = 20 then the other leg also = 20

Thus, x = 20

If leg = 20

Then hypotenuse = 20 * √2 or 20√2

Thus, y = 20√2  

The average cost of all courses is It's $112.50, by substituting null values with 0, you ensure that they do not affect the average cost calculation.

To determine the average cost for all courses, you can follow these steps:
1. Sum up the costs of all courses.
2. Count the number of courses.
3. If any course cost contains a null value, substitute it with 0.
4. Divide the total cost by the number of courses to calculate the average cost.
If your course cost contains null values, you can replace them with a value of 0 before calculating the average.

Here is an example of calculating the average cost using a set of course costs.

Course 1 cost: $100

Course 2 cost: Zero

Course 3 cost: $150

Course 4 cost: $200

Step 1: Replace zero 0 value:

Course 1 cost: $100

Course Cost of 2: $0

Cost of Course 3: $150

Cost of Course 4: $200

Step 2: Calculate Total Course Cost:

Sum = $100 + $0 + $150 + $200 = $450

Step 3: Course Determine the total number of:

Number of courses = 4

Step 4: Calculate the average cost:

Average cost = Total / Number of courses = $450 / 4 = $112.50

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The proof for each theorem is matched as;

<EFC is a right angle: Definition of a right angle

m<EFC = 90; Definition of a tangent line

m<EFC + m<FEC + m<ECF = 180 degrees; triangle sum theorem

90 + m<FEC + m<ECF = 180; substitution property of equality

m<FEC + m<ECF = 90; substitution property of equality

m<FEC + m<ECF = definition of complementary angles

To determine the values, we need to know the following;

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In order to calculate the diameter of the soap bubble, we need to use the Laplace equation and solve for the radius of the bubble.The diameter of the soap bubble is 8.04 x 10⁻⁴ mm.

We will then double the radius to get the diameter of the bubble.Here's the solution:

Given that:

Radius of the soap bubble =

r = 0.065 mm

= 6.5 x 10⁻⁵ m

Surface tension of soap in air =

σ = 0.019 N/m

Pressure outside the bubble =

P₂ = 75.0 kPa

= 75,000 Pa

Ambient temperature =

T = 300 K

Atmospheric pressure =

P₁ = 1 atm = 101,325 Pa

Laplace's equation states that the pressure inside the bubble is given by:

Pinside = Poutside + (2σ/r)

where σ is the surface tension and r is the radius of the bubble.

Rearranging the above equation to solve for the radius of the bubble:

2σ/r = Pinside - Poutside

r = 2σ/(Pinside - Poutside)

Substituting the given values into the above equation:

r = [2 x 0.019] / [Pinside - 101325]

After the soap bubble rises up, the pressure outside the bubble becomes 75 kPa.

Therefore:

Pinside - 101325 = 75000

Pinside = 176325 Pa

Substituting this value of Pinside into the above equation:

r = [2 x 0.019] / [176325 - 101325]

= 4.02 x 10⁻⁷ m

The diameter of the soap bubble is twice the radius:

D = 2r = 2 x 4.02 x 10⁻⁷ m

= 8.04 x 10⁻⁷ m

Converting the diameter to mm:

D = 8.04 x 10⁻⁷ m x 1000 mm/m

= 8.04 x 10⁻⁴ mm (answer)

Therefore, the diameter of the soap bubble is 8.04 x 10⁻⁴ mm.

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Answer:

Step-by-step explanation

You would take 15 ft and divide it by how many feet are in a yard which is 3.

Answer - Jill has 5 yards of ribbon

Answer:

5 yards

Step-by-step explanation:

every 3 feet are 1 yard... 15 feet divided by the 3 = 5 yards

The standard deviation of a sample proportion is given by the formula:

σ = sqrt((p * (1 - p)) / n)

where σ is the standard deviation, p is the sample proportion, and n is the sample size.

If we want the standard deviation to be one-half of what it was for a sample of size 100, we can write the following equation:

(sqrt((p * (1 - p)) / n)) / 2 = sqrt((p * (1 - p)) / 100)

To simplify the equation, we can square both sides:

((p * (1 - p)) / n^2) / 4 = (p * (1 - p)) / 100

Simplifying further:

100 * n^2 = 4 * 1

n^2 = (4 * 1) / 100

n^2 = 0.04

Taking the square root of both sides:

n = sqrt(0.04)

n = 0.2

Therefore, the sample size should be 0.2. However, since the sample size must be a positive integer, we round it up to the nearest whole number. Therefore, the sample size should be 1.

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Answer:b

Step-by-step explanation:

l x w x h

Answer

=-15

v=-4

Step-by-step explanation:

0.000000000000000000000000000000000000

In order to find two equivalent expressions for the given expression, first let's add the like terms:

Now, instead of adding like terms, let's factor the expression using the common factor 4x:

So two equivalent expressions are 28x and 4x(3+4)

The required area of figure is 90 square centimeters.

Two of the edges of a right triangle are perpendicular to one another. Consequently, one of them will be the triangle's height and the other its base. Therefore, if you know the side lengths, you are given the height and base even if they are not mentioned. Therefore, to calculate the area, use the formula \(Area = \frac{1}{2}bh\).

Given figure is consist of rectangle and right angled triangle.

Base of triangle = 12 - 8 = 4 cm, Height of triangle = 5 cm

dimensions of rectangle are 10 by 8

Area of figure = area of rectangle + area of triangle

Area of figure = 10(8) + \(Area = \frac{1}{2}5(4)\)

Area of figure = 80 + 10

Area of figure = 90 square centimeters

Thus, required area of figure is 90 square centimeters.

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DE is equal to 6.

Let's use the given information to solve for DE.

We know that AC is equal to DB, so we can write AC = DB.

We also know that CB is equal to 3 times DB, so we can write CB = 3 * DB.

Using the information above, we can substitute DB for AC and 3 * DB for CB in the equation.

AC + CB = AD + DE

DB + 3 * DB = 15 + DE

4 * DB = 15 + DE

Next, we can substitute AC for DB:

4 * AC = 15 + DE

Since AC = DB, we have:

4 * DB = 15 + DE

Now we can substitute CB for 3 * DB:

CB = 15 + DE

But we also know that CB is equal to 3 * DB:

3 * DB = 15 + DE

Now we can substitute the given values:

3 * 7 = 15 + DE

21 = 15 + DE

To solve for DE, we subtract 15 from both sides:

21 - 15 = DE

6 = DE

Therefore, DE is equal to 6.

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The system has exactly one solution, which is (p, q) = (-0.2118, -8.0).

We are given the system of equations:

1.7p - 0.34q = 0

0.17(q+1) - 0.85(p-1) = 0

We can simplify the second equation by distributing the 0.17 and 0.85 terms:

0.17q + 0.17 - 0.85p + 0.85 = 0

0.17q - 0.85p = -0.72

Now we have two equations in two variables, which we can solve using substitution or elimination. We will use elimination here.

Multiplying the first equation by 5, we get:

8.5p - 1.7q = 0

Multiplying the second equation by 2, we get:

0.34q - 1.7p = -1.44

Adding these two equations, we get:

6.8p = -1.44

p = -0.2118

Substituting this value of p into either of the original equations, we get:

1.7(-0.2118) - 0.34q = 0

q = -8.0

So the system has exactly one solution, which is (p, q) = (-0.2118, -8.0).

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The distance from a point on a circle to its center is called the radius, and it plays a crucial role in defining the circle's characteristics.

The distance from a point on a circle to its center is the radius of the circle.

1. In a circle, the radius is the distance from the center to any point on the circle.
2. The radius is always the same length, no matter which point on the circle is chosen.
3. It is an essential property of a circle and helps determine the size and shape of the circle.

In conclusion, the distance from a point on a circle to its center is called the radius, and it plays a crucial role in defining the circle's characteristics.

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In linear equation , x = 36 is the total cost, y, depends on the number of students going, x.

What in mathematics is a linear equation?

Tickets cost  for the club adviser =  $21.25

cost for each student who goes = $14.75

Based on the given conditions, formulate x = $21.25 + $14.75

Calculate the sum or difference x = 36

get the result x = 36

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The figure with explanation is given below .

When two rays meet each other is at a common point is called angle.

Given:

- A Fence with parallel sides AB and EF  there is a point K on line AB point L on line EF

 Angle AKL

We need to prove , m\(\angle AKL = 116^0\)

Proof:

\(m\angle AKL +m\angle KLE = 116^0\)

1. To create triangle AKL to draw a line KL.

2. Since AB is parallel to EF, we know that m∠AKL and m∠KLE are corresponding angles and are congruent.

3. Let x be the measure of angle KLE.

4. Since triangle AKL is a triangle, we know that the sum of its angles is \(180 ^0\) Therefore, m∠AKL + x + 64° = 180° (since m∠EKL = 64°, as it is a corresponding angle to m∠AKL).

5. Simplifying the equation in step 4, we get m\(\angle AKL +116^0\)

6. Since m\angle\(\angle KLE\) and m\(\angle AKL\) are congruent (as shown in step 2), we can substitute m∠KLE with x in the equation from step 5 to get m∠AKL + m∠KLE = 116°.

7. Combining like terms in the equation from step 6, we get m∠AKL = 116°.

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Answer:

17

Step-by-step explanation:

subtract the half from the whole to find the other half

52-35=17

Answer:

2

Step-by-step explanation:

1/5*10