There are an infinite number of vector and parametric equations for a given plane. Why is the scalar equation of a given plane unique?

The value of in the form y = f(x) by eliminating the parameter is y(t) = x - 2.

Identify the parameter that needs to be eliminated. Determine what type of parameter it is (independent, dependent, etc.). Determine how the parameter relates to the other variables in the equation.

Use algebraic manipulation techniques to eliminate the parameter. Check the final result to ensure that the parameter has been eliminated.

The expressions are x(t) = 3 + t² - 1 and y(t) = t².

We represent x(t) as x.

Now the expression is:

x = 3 + t² - 1

Simplify the expression

x = 2 + t²

Subtract 2 on both side, we get

t² = x - 2

Take square root on both side, we get

t = √x - 2

Now substitute the value of t in y(t) = t².

y(t) = (√x - 2)²

y(t) = x - 2

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The complete question is:

Express x(t) = 3 + t² - 1 and y(t) = t² in the form y=f(x) by eliminating the parameter. (express numbers in exact form. use symbolic notation and fractions where needed.)

Y =

Answer:

  0

Step-by-step explanation:

Multiplying the first equation by xy, we have ...

  x^2 +y^2 = -xy

Factoring the expression of interest, we have ...

  x^3 -y^3 = (x -y)(x^2 +xy +y^2)

Substituting for xy using the first expression we found, this is ...

  x^3 -y^3 = (x -y)(x^2 -(x^2 +y^2) +y^2) = (x -y)(0) = 0

The value of x^3 -y^3 is 0.

The answers to all the subparts are shown:

(A) So, we know that: 1 liter = 10 decilitre

So, the consumption of the fuel = 60 - 34 = 26 litres.

(B) Cost of 60 liters of fuel if 1 liter is € 1.45:

(C) Liters of fuel he could buy from € 58:

Therefore, the answers to all the subparts are shown:

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The correct question is given below:
Giorgio fills up his car which is 60 liters. After a certain distance, 340 deciliters remained in the tank.

(A) How many liters did it consume?

(B) How much did you spend if 1-liter costs € 1.45?

(C) How many liters of petrol can you buy for € 58?

The internal rate of return on the investment for Burgundy Basins is 13.33%.

The internal rate of return on the investment for Burgundy Basins represents the percentage return expected from the investment, which is 13.33% in this case. It indicates the rate at which the investment's net present value is zero, meaning it is expected to generate returns equal to its cost. This makes the investment financially attractive as it offers a return higher than the company's cost of capital.

Burgundy Basins, a sink manufacturer, is considering an average-risk investment worth $36 million. The investment is projected to generate a perpetual annual return of $4.8 million. To evaluate the attractiveness of the investment, the internal rate of return (IRR) is calculated. The IRR represents the rate at which the net present value of the investment becomes zero.

In this case, the IRR is determined to be 13.33%, indicating that the investment offers a return higher than its cost. This implies that the investment is financially viable and can potentially enhance the company's profitability. However, it's important to note that other factors such as market conditions and potential risks should also be taken into consideration before making a final decision.

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A significance level of 0.10, we have enough evidence to conclude that the new copy machines have a significantly faster mean repair time compared to the older model.

To test if the new copy machines are faster to repair, we can set up the following null and alternative hypotheses:

Null Hypothesis (H₀): The mean repair time for the new copy machines is the same as the mean repair time for the older model.

Alternative Hypothesis (H₁): The mean repair time for the new copy machines is less than the mean repair time for the older model.

Let's perform a one-sample t-test to test these hypotheses. The test statistic is calculated as:

t = (sample mean - population mean) / (sample standard deviation / √(sample size))

Given:

Population mean (μ) = 93 minutes

Sample mean (\(\bar x\)) = 86.8 minutes

Sample standard deviation (s) = 14.6 minutes

Sample size (n) = 18

Significance level (α) = 0.10

Calculating the test statistic:

t = (86.8 - 93) / (14.6 / sqrt(18))

t = -6.2 / (14.6 / 4.24264)

t ≈ -2.677

The degrees of freedom for this test is n - 1 = 18 - 1 = 17.

Now, we need to determine the critical value for the t-distribution with 17 degrees of freedom and a one-tailed test at a significance level of 0.10. Consulting a t-table or using statistical software, the critical value is approximately -1.333.

Since the test statistic (t = -2.677) is less than the critical value (-1.333), we reject the null hypothesis.

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In order to create a diagram that represents the quantities of each ingredient adde, could be:

CM = X X X

FB = X X

CS = x

Where CM is Cups of Milk, FB is Frozen Bananas and CS is Chocolate Syrup. There, x representent the ammount of each ingredient.

Now, we determine the proportions of the ingredients:

There are 3 cups of milk per two frozen bananas (3:2)

There are 2 frozen banas per tablespoon of chocolate syrup (2:1).

There are 3 cups of milk per tablespoon of chocolate syrup (3:1).

Now, in order to write 3 sentences that contain the ratio of the ingredients we could think of it as a recipe:

*"In order to get this smoothie we will need 3 cups of milk and a tablespoon of chocolate syrup."

*"We will also add 2 frozen bananas for each tablespoon of chocolate syrup."

*"Remember that that is the ammount of ingredients per serving, so if you want more servings you will also need another extra 3 cups of milk, 2 frozen bananas and 1 tablespoon of chocolate syrup for each extra serving."

Using equations, we can find that the number of sale-priced songs is 5 and the number of regularly priced songs is 7.

Equations are mathematical statements with the equals (=) symbol and two algebraic expressions on either side. This illustrates the equality of the relationship between the expressions printed on the left and right sides. The formula LHS = RHS (left hand side equals right hand side) is utilised in all mathematical equations. To determine the value of an unknown variable that represents an unknown quantity, you can solve equations. A statement is not regarded as an equation if it has no "equal to" symbol.

As per the question, equation given are:

x + y = 12

x = 12 - y

Now, substituting the value in:

0.99x+1.25y = 13.7

= 0.99(12-y) +1.25y = 13.7

= 11.88 - 0.99y + 1.25y = 13.7

= 0.26y = 13.7 - 11.88

0.26y = 1.82

y = 1.82/0.26

y = 7

Now, substitute this value,

x = 12 - 7

x = 5

As a result, there are 5 songs on sale and 7 songs that are regularly priced.

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Answer:

I will go with the first box

Answer:

hope this helps please mark me as brainlist

Answer:

5

Step-by-step explanation:

By process of elimination, we can say for sure that C and D are not the right answers because as x- the numbers on the top- increases, y- the numbers on the bottom- increases. This means that the slope is not negative, because the slope is the rate of change and it does not have a negative rate of change.

The equation for slope is y2-y1 / x2-x1. Meaning, y is on top and x is on bottom. This creates a fraction. So let's take 0 and 1 for X, the first and second values, and 3 and 8 for y, the first and second values. We swap them, because the second y value comes first, so we have 8 - 3 for the top, the numerator. Then we have 1 - 0 for the bottom, the denominator. Solving 8 - 3 and 1 - 0, we have 5/1. 5/1 simplifies to 5, and thus 5 is your slope.

Answer:

22.7

Step-by-step explanation:

9³-8*6 = 729-48= 681

(8²-4) / 2 = 30

681/30 = 22.7

Answer:

\( \huge \boxed{ \blue{ \text{22.7}}}\)

Step-by-step explanation:

\(step - 1 : define\)

\( \frac{ {9}^{3} - 8 \times 6 }{ ({8}^{2} - 4 ) \div 2} \)

\(step - 2 : simplify\)

Answer:

This one is easy its y=3x-1.5

Step-by-step explanation:

I did this assignment

Answer:

25

Step-by-step explanation:

Answer: 25

Step-by-step explanation:

Answer:

➢ 0.9

➢ -95

➢ -79

\(BlackSparkles...\)

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a) Using the principles of a normal distribution, the percentage of data that lies between 7 and 16 is 95%.

b) The two numbers that 68% of the data lie between are 7 and 10.

c) The percentage of numbers that are larger than 13 is 32%.

A normal distribution is a probability distribution where the values of a random variable show a symmetrical distribution.

A symmetrical distribution implies that the values are equally distributed on the left and right side of the central tendency.

This symmetrical relationship means that a bell-shaped curve is formed.

The mean of the normal distribution = 10

The standard deviation = 3

z = (x - μ) / σ

Where:

z = the z-score

x = the value

μ = the mean

σ = the standard deviation.

For x = 7:

z = (7 - 10) / 3

z = -1

This means that 7 is one standard deviation below the mean.

For x = 16:

z = (16 - 10) / 3

z = 2

This means that 16 is two standard deviations above the mean.

Using the empirical rule, about 68% of the data falls within one standard deviation of the mean, and about 95% of the data falls within two standard deviations of the mean.

The percentage of data that lies between 7 and 16 is 95% (100% - 5%)

b) Mean = 10

Standard deviation = 3

A number below = 7 (10 - 3)

A number above = 13 (10 + 3)

Thus, 68% of the data lie between 7 and 13.

c) The percentage of numbers that are larger than 13, using the z-score formula to find how many standard deviations away from the mean is 13.

z = (x - μ) / σ

For x = 13:

z = (13 - 10) / 3

z = 1

This means that 13 is one standard deviation above the mean.

The empirical rule says that about 68% of the numbers fall within one standard deviation of the mean, and about 95% of the numbers fall within two standard deviations of the mean.

The percentage of numbers that are larger than 13 = 32% (100% - 68%).

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To calculate the amount you pay for the loan, we need to calculate the simple interest over the loan term.

The formula for simple interest is: I = P * r * t, where I is the interest, P is the principal (loan amount), r is the interest rate per period, and t is the number of periods.

Given:

Principal (P) = $45,000

Interest rate (r) = 8% = 0.08 (expressed as a decimal)

Time (t) = 6 years

Plugging the values into the formula, we have:

I = $45,000 * 0.08 * 6

Calculating the interest:

I = $45,000 * 0.48

I = $21,600

Therefore, the amount you pay for the loan is $21,600.

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Answer:

(\(\sqrt{5}\) n - 4)(\(\sqrt{5}\) n + 4)

Step-by-step explanation:

Using the factorising method, difference of 2 squares

a² - b² = (a - b)(a + b) , then

5n² - 16

= (\(\sqrt{5}\) n )² - 4²

= (\(\sqrt{5}\) n - 4)(\(\sqrt{5}\) n + 4)

Answer:

The 2 numbers = 81 and 83

Step-by-step explanation:

As, one number = x

The other, because it's an even number and consecutive = x + 2

So the larger numbef here is x + 2

And they are saying 3 times x + 2 plus x = 330

So let's solve!

3 times x + 2 = 3(x+2) = 3x + 6

So we will add it to x = (3x + 6) +(x) = 4x + 6

So they are saying the sum of them will be 330

So, 4x + 6 = 330

4x = 330 - 6

4x = 324

x = 324/4

x = 81

So x is the first number = 81

And the second is x + 2 = 81 + 2 = 83

So the 2 numbers are 81, 83

Lets check!

3 times the bigger number = 83 x 3 = 249

We will add it to 81 and we will get 330

So, 249 + 81 = 330

So the answer is right

Answer:

A receipt is a record of a transaction that apready happened.

Step-by-step explanation:

since there is no graph it's a bit hard to answer this question, but I'll try. I can help solve the equation that represents the ratio of the two numbers:

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

This can be simplified to:

x + 1/2 = y/3

To graph this equation, you would need to plot points that satisfy the equation. One way to do this is to choose a value for y and solve for x. For example, if y = 6, then:

x + 1/2 = 6/3

x + 1/2 = 2

x = 2 - 1/2

x = 3/2

So one point on the graph would be (3/2, 6). You can choose different values for y and solve for x to get more points to plot on the graph. Once you have several points, you can connect them with a line to show the relationship between x and y.

(Like I said, it was a bit hard to answer this question, so I'm not 100℅ sure this is the correct answer, but if it is then I hoped it helped.)

The triangles AEB and DEC describes AA similarity .

What is AA Similarity ?

Two triangles are said to be congruent by AA Similarity when two angles in one triangle are congruent to two angles in another triangle .

In the question ,

a figure is given .

in triangle AEB and triangle DEC ,

we can see that ,

∠AEB ≅ ∠DEC    ,   because they are vertically opposite angles .

On rotating triangle CED by  180° around the point E, then the translate point D to point A confirms  ∠EAB ≅ ∠EDC.

Since two angles are Congruent

So , By AA Similarity , triangles AEB and DEC are Congruent .

Therefore , the triangles AEB and DEC are Congruent .

The given question is incomplete , the complete question is

Which of the following triangles in the given figure describes AA similarity ?

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Answer:

81-1 nine

90-81

9

Step-by-step explanation:

Answer:

\(9 \times 9 = 10nines - 1nine \\ 9 \times 9 = 90 - 9 \\ 9 \times 9 = 81 \\ thank \: you\)

Answer:

27 is 30% of what number?

D. 90

Step-by-step explanation:

You're welcome.

Answer:

28 shirts

Step-by-step explanation:

Let's see what we are given.

there are x amount of shirts ($616 total)

there are 12 in a dozen

the regular shirts are $16

the last 12 shirts are $14

Lets make an equation.

616= 14(12) + 16x

616=168+16x

448=16x

x=28

(Sorry if this explanation is bad)

Answer:

994

Step-by-step explanation:

First, let's translate the statement into a mathematical expression.

Now, we can evaluate the expression when t = 2.

Answer:

994

Step-by-step explanation:

(8+2)=10

(10) to the power of 3=1000

100-6=994

Answer:

M = 12.5

Step-by-step explanation:

Multiply each one by 12.5

Answer:

The answer is 4

Either 4 is equal to 16 or 4 is equal to 1.

Answer:

1 . x(x+1)
2.(3a-1)(5a+8)
3.(4x + 3y) ( 3x - 3y)
4.(a+b)

Answer:

x = 2    y = 0

Step-by-step explanation: