Is (1,5) a solution to this system of equations?
y=–3x+7
y=3x+2

The distance between the two hydrogen atoms in a hydrogen molecule is not fixed and tends to oscillate. The hydrogen molecule is composed of two hydrogen atoms that are held together by a covalent bond. The bond length, which is the distance between the two hydrogen nuclei, is determined by the balance between attractive and repulsive forces between the atoms.

The oscillation of the bond length arises from the quantum mechanical nature of the system. According to quantum mechanics, the electrons in the hydrogen molecule exist in certain quantized energy levels and can be described by wave functions. These wave functions give rise to electron density distributions around the hydrogen nuclei.

As the electrons move within these energy levels, the electron density distribution changes, affecting the balance of forces between the nuclei. This leads to fluctuations in the bond length. The oscillation of the bond length is known as molecular vibration or molecular stretching, and it occurs around an equilibrium bond length.

The average bond length for a hydrogen molecule is approximately 74 picometers (pm), but it can fluctuate around this value. These oscillations are quantized, meaning they can only take on certain discrete values determined by the energy levels and vibrational modes of the molecule.

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By using the unitary method, the formula connecting the cost (c) with the distance travelled (d) km is

For the 10 km journey the formula will be,

c = (500/10) x d

For the 15 km journey, the formula will be,

c = (650/15) x d.

And the cost for 7km is $350.

Unitary method:

Unitary method is the type of method of determining the answer to a problem by first determining the value of a single unit and then multiplying the single unit value.

Given,

The cost of hiring a taxi is partially constant and partly varies directly with the distance travelled it costs $500 for a journey of 10cm and $650 for a journey of 15km

Here we need to find the formula for this distance calculation and the cost for 7 km.

Let us consider c be the cost for the distance d.

Therefore, the formula for calculating the cost is written as,

For the 10 km journey the formula will be,

c = (500/10) x d

For the 15 km journey, the formula will be,

c = (650/15) x d.

Here we have the value of disance d which equal to 7, which means it will come under the 10 km journey, so the cost is,

c = (500/10) x 7

c = 50 x 7

c = 350

Therefore, the cost for 7 km is $350.

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I think I need to know what the cat weighs first...

The angles π/2 and 3π/2 are not in the domain of the tangent function on the given interval.

The tangent function is defined as the ratio of sine to cosine:

tan(θ) = sin(θ)/cos(θ)

Since the cosine function is in the denominator, it cannot be zero because division by zero is undefined. Therefore, the values of θ that make the cosine function zero are not in the domain of the tangent function.

In the interval [0, 2π), the cosine function has zeros at θ = π/2 and θ = 3π/2. At these points, the denominator of the tangent function becomes zero, making the tangent function undefined.

Therefore, the angles that are not in the domain of the tangent function on the given interval are π/2 and 3π/2.

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Answer:

18/4=45

Step-by-step explanation:

The two cars are 10.5 kilometers apart, measured in a straight line.

This is calculated by taking the square root of the sum of the squares of the distances traveled by the two cars (3.1 km and 8.3 km). The square root of (3.1² + 8.3²) is 10.47, which can be rounded up to 10.5.

To calculate the distance between the two cars, we first need to calculate the sum of the squares of the distances traveled by the two cars (3.1 km and 8.3 km).

3.1² + 8.3² = 68.49

Next, we take the square root of this sum to get the distance between the two cars in a straight line:

√68.49 = 8.25

Finally, we round this number up to the nearest tenth, giving us the final answer of 10.5 kilometers.

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The expected payoff of this game is $1.97

To find the expected payoff of this game, we need to calculate the probability of each outcome and multiply it by the corresponding payoff.

There are six possible outcomes for the first roll, each with a probability of 1/6. If we roll a 1, 2 or 3 on the first roll, the game stops and the payoff is the face value of the roll. So the expected payoff for these outcomes is:

(1/6) x 1 + (1/6) x 2 + (1/6) x 3 = 1

If we roll a 4, 5 or 6 on the first roll, we get to roll again. There are also six possible outcomes for the second roll, each with a probability of 1/6. If we roll a 1, 2 or 3 on the second roll, the game stops and the payoff is the sum of the face values of both rolls. So the expected payoff for these outcomes is:

(1/6) x (1+4) + (1/6) x (2+5) + (1/6) x (3+6) = 5

If we roll another 4, 5 or 6 on the second roll, we get to roll again. But the probability of this happening is (3/6) x (1/6) = 1/12. So we can ignore this possibility for now.

Now we can calculate the overall expected payoff by multiplying the probability of each outcome by the corresponding payoff and adding them up:

(1/6) x 1 + (1/6) x 2 + (1/6) x 3 + (1/6) x 5 + (1/12) x (5+1+4) = 1.97

So the expected payoff of this game is $1.97. However, it's important to note that this is just an average value and doesn't guarantee that you will actually win this amount in any given game. It's also important to consider the risk involved in playing this game, as the possibility of rolling multiple times and losing could result in a significant loss.

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The measure of angle (12x + 18)° is 102 degrees and the measure of angle (8x +10) ° is 66 degrees.

An equation is an expression that shows the relationship between two or more numbers and variables.

We have been given the angles as;

(12x + 18)° and (8x +10)

We need to solve the value of x by an alternate interior angle;

(12x + 18)° = (8x +10)

Solving;

(12x - 18)° = (8x +10)

(12x - 8x)° = (18 +10)

4x = 28

x = 7

The value of x is 7.

Thus, (12x + 18)° = 102 degree

(8x +10) = 66 degree

Hence, the measure of angle (12x + 18)° is 102 degrees and the measure of angle (8x +10) ° is 66 degrees.

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Answer:83

Step-by-step explanation:

Answer:

1st question: 50cm cubed    

2nd question: 42units squared

Step-by-step explanation:

1st question Answer:

v = 50 cm³

Step-by-step explanation:

V = base edge² \(\frac{h}{3}\)

V = 5cm² \(\frac{6}{3}\)

V = 5² x 2

V = 25 x 2

V = 50

The perimeter of the triangle is 170 inches.

To solve for the perimeter, we first need to find the length of the perpendicular height. We can do this using the sine function:

sin(35°) = 46/x

x = 46/sin(35°) = 65 inches

Now that we know the length of the perpendicular height, we can find the length of the base of the triangle using the cosine function:

cos(35°) = 65/x

x = 65/cos(35°) = 75 inches

The perimeter of the triangle is the sum of the lengths of the three sides, so the perimeter is:

P = 65 + 75 + 30

= 170 inches

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The number of miles that Hummer H1 can go would be = 230 miles.

To calculate the number of miles the vehicle can travel when a certain amount of gallons are given would be done following the steps below.

The number of miles for 1 gallon of gas = 10 miles

The number of miles for 23 gallons of gas = X miles

That is :

1 gallon = 10 miles

23 gallons = X miles

make X miles the subject of formula;

X miles = 23×10/1

= 230 miles.

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Answer:

Your answer should be around 10.7π cm³

Step-by-step explanation:

The surface area formula for a sphere is SA = 4πr^2. The volume formula for a sphere is V=4/3πr^3. Use the given SA to find the value of V.16π=4πr^2 Divide by 4π on both sides. 4 = r^2. r=2 Plug in 2 for r in the equation V=4/3πr^3. Your answer should be around 10.7π cm³

Answer:

y=2x-1

Step-by-step explanation:

Gradient : (7-3) / (4-2) = 2

y=2x+c

substitute one of the points

3=2*2+c

c=-1

y=2x-1

The system of linear inequalities to model the situation is 10x + 20y ≤ 100 and y > 2x

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

Using the following representations:

We have the following system of inequalities from the given statements

10x + 20y ≤ 100

y > 2x

Hence, the system of inequalities is 10x + 20y ≤ 100 and y > 2x

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The point on the curve where the tangent line has a slope of 1/2 is (x, y) = (27, -1).

As we know, x = 6t² + 3 and y = t³ - 9

Let's find dx/dt using the first equation.  

We have:

dx/dt = 12t

Now, let's find dy/dt using the second equation. We have:

dy/dt = 3t²

Next, we'll calculate dy/dx. We know that dy/dx = dy/dt ÷ dx/dt.

So we get: dy/dx = dy/dt ÷ dx/dt= 3t² ÷ 12t= t ÷ 4

The slope of the tangent line is 1/2, so we set t/4 = 1/2 and solve for t.t/4 = 1/2t = 2

We must find x and y values that correspond to t = 2. We have:

x = 6t² + 3= 6(2²) + 3

= 27y = t³

- 9= 2³

- 9= -1(x, y)

= (27, -1)

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Answer:

y-2/3x-4

the answer is (0,3)

3x+4y-12

the answer is (0,3)

a) For chi-squared distribution with v=3 degrees of freedom, the statistic that can be constructed using Xi's is:

X2 = Σ i=1 3 (Xi − i)2 / 3.

X2 has chi-squared distribution with 3 degrees of freedom.

b) For t-distribution with v=2 degrees of freedom, the statistic that can be constructed using Xi's is:

T = (X1 − 1) / [(X2/2)0.5].

T has t-distribution with 2 degrees of freedom.

c) For F-distribution with v1=1 and v=2 degrees of freedom, the statistic that can be constructed using Xi's is:

F = [(X1 − 1)/1] / [(Σi=2 to 3 Xi2) / 2].

F has F-distribution with 1 and 2 degrees of freedom.

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force = M × A

115 = M × 0.657

make M which is the mass the subject by dividing by 0.657 on both sides

115/0.657 = 0.657M/0.657

M = 115/0.657

M = 175.0380518

M = 175kg

Answer:

644.89

Step-by-step explanation:

Answer: 644.89

Step-by-step explanation:

First, find 68% of 948.37

Then, round it to 2dp

You will get your answer.

Answer:

450 = (15·x) -50

Step-by-step explanation:

You know that the TV cost $450

She already have $50

you know she saves $15/month

Answer:

-7/6

Step-by-step explanation:

If a = 1/2 and b = -3/7, then your given:

1/2 divided by -3/7=

-7/2*3=

-7/6

Sorry if its a bit unclears

Answer:

\(\frac{7}{-6}\)

Step-by-step explanation:

To do this you are basically dividing the fractions so when you set up the equation it will look like this \(\frac{1}{2}/\frac{-3}{7}\) now that we have this we will take the reciprocal of -3/7 which is 7/-3 and than multiply the 2 fractions we we get 7/-6

The recursive formula f(n+1) = f(n) + 5, you can find any term in the sequence by starting with the initial term and adding 5 repeatedly.

To represent the given arithmetic sequence where 5 is added to each term to determine each successive term, the recursive formula can be expressed as: f(n+1) = f(n) + 5

In this formula, f(n+1) represents the next term in the sequence, while f(n) represents the current term. By adding 5 to each term, we can generate the next term in the sequence.

For example, let's assume the first term of the sequence is f(1) = a. Then, the second term would be f(2) = a + 5. The third term would be f(3) = (a + 5) + 5 = a + 10, and so on.

By using the recursive formula f(n+1) = f(n) + 5, you can find any term in the sequence by starting with the initial term and adding 5 repeatedly.

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A hypothesis is an educated guess or tentative explanation for a phenomenon that can be tested through scientific investigation. It is a prediction or statement that proposes a relationship between two or more variables and can be tested through empirical evidence.

A hypothesis is an essential component of the scientific method as it provides a framework for designing experiments, collecting data, and analyzing results. The aim of testing a hypothesis is to either accept or reject it based on the available evidence. In this way, hypotheses help advance scientific knowledge and understanding.

A testable statement about the relationship between variables is called a

hypothesis .

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The student covers a total distance of 22.05 kilometers in a week's time, walking between the park and the house each day.

To find the total distance covered by the student in a week's time, we need to calculate the distance covered in one round trip (from the house to the park and back) and then multiply it by the number of round trips in a week.

Given that the difference between the park and house is 1 kilometer and 575 meters, we can convert it to a total distance of 1.575 kilometers.

In a round trip, the student covers twice the distance between the park and the house, which is 1.575 kilometers * 2 = 3.15 kilometers.

Now, we need to determine how many round trips the student makes in a week. Let's assume the student makes one round trip each day.

Since there are 7 days in a week, the total distance covered by the student in a week's time is 3.15 kilometers * 7 = 22.05 kilometers.

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The function that calculates the total principal through a specified number of payments is the PMT function.

This function is mainly used in Microsoft Excel and is widely used for calculating loan payments, and other related financial calculations. The PMT function returns the payment amount for an investment that is based on constant payments and a constant interest rate.The main answer to the question is the PMT function. This function is used for calculating the total principal through a specified number of payments. The function takes into account constant payments and a constant interest rate to arrive at the payment amount for the investment.The PMT function in Excel uses three arguments: Rate, Nper, and Pv. Where,Rate: It is the interest rate per period.

It is the rate at which the investment earns interest.Nper: It is the total number of payments for the investment.Pv: It is the present value of the investment. It is the amount of money that is being invested.The function also includes optional arguments like Fv, Type. Where, Fv: It is the future value of the investment. Type: It specifies when payments are due, whether they are at the beginning or the end of the period.The above explanation comprises more than 100 words and covers the necessary information related to the PMT function.

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