(Pls Need Help with 2 questions ASAP)

If the difference between the squares of two numbers is 10 and the difference between the two numbers is 2, their sum would be 5.

An equation is an expression that can be used to show the relationship between variables and numbers.

Let a and b represent the two numbers.

The difference between the squares of two numbers is 10. Hence:

a² - b² = 10

(a - b)(a + b) = 10    (1)

The difference between the two numbers is 2, hence:

a - b = 2

Substituting:

(a - b)(a + b) = 10    

2(a + b) = 10    

(a + b) = 5

Their sum is 5.

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The representation of D in the form D_x, D_y, where the x and y components are separated by a comma will be D[6.08,7.27]

Any vector oriented in two dimensions can be understood to have an impact in both directions. This implies that it may be divided into two halves. A component is a portion of a two-dimensional vector. The components of a vector assist to represent the vector's effect in a certain direction. The total impact of these two components is equivalent to the influence of the separate two-dimensional vectors. The two vector components can substitute the single two-dimensional vector.

Determine the x and y components for each vector A & B for vector A

Ax=sin (15) * 2=0.5176

Ay=cos (15) * 2=1.9318

for Vector B

Bx=cos (15) * 4=3.8637

By=sin (15)* 4=1.0352

The vector addition and scalar multiplication for x and y individually D=4.3 * A+B

Dx=4.3 *(sin (15) * 2)+cos (15) * 4

Dx=4.3 * 0.5176+3.8637

Dx=6.0893

Dy=4.3 *(cos (15) * 2)-sin (15) * 4

Dy=4.3 * 1.9318-1.0352

Dy=7.2715

D[6.08,7.27]

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The actual question may be:

Express D in the form D_x, D_y, where the x and y components are separated by a comma using two significant figures.

To find a recursive Nevill's method when interpolating a table using a polynomial at x = 4.1, we can use the following steps:

Step 1: Set up the given data in a table with two columns, one for f(x) and the other for x.

f(x)             x

36               1.16164956

3.80201036       4.0

0.30663842       4.2

0.35916618       -123926000.4

Step 2: Begin by finding the first-order differences in the f(x) column. Subtract each successive value from the previous value.

Δf(x)            x

-32.19798964     1.16164956

-3.49537194      4.0

-0.05247276      4.2

Step 3: Repeat the process of finding differences until we reach a single value in the Δf(x) column. Continue subtracting each successive value from the previous one.

Δ^2f(x)          x

29.7026177       1.16164956

3.44289918       4.0

Step 4: Repeat Step 3 until we obtain a single value.

Δ^3f(x)          x

-26.25971852     1.16164956

Step 5: Calculate the divided differences using the values obtained in the previous steps.

Divided Differences:

Df(x)             x

36                1.16164956

-32.19798964     4.0

29.7026177       4.2

-26.25971852     -123926000.4

Step 6: Apply the recursive Nevill's method to find the interpolated value at x = 4.1 using the divided differences.

f(4.1) = 36 + (-32.19798964)(4.1 - 1.16164956) + (29.7026177)(4.1 - 1.16164956)(4.1 - 4.0) + (-26.25971852)(4.1 - 1.16164956)(4.1 - 4.0)(4.1 - 4.2)

Solving the above expression will give the interpolated value at x = 4.1.

Q2: To construct an approximation polynomial using the Hermite method, we follow these steps:

Step 1: Set up the given data in a table with three columns: f(x), f'(x), and x.

f(x)             f'(x)              x

2.572152         7.615964          1.2

3.602102         13.97514          1.3

5.797884         34.61546          1.4

14.101442        199.500           1.5

Step 2: Calculate the divided differences for the f(x) and f'(x) columns separately.

Divided Differences for f(x):

Df(x)            \(D^2\)f(x)           \(D^3\)f(x)

2.572152         0.51595           0.25838

Divided Differences for f'(x):

Df'(x)           \(D^2\)f'(x)

7.615964         2.852176

Step 3: Apply the Hermite interpolation formula to construct the approximation polynomial.

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Answer:

\(-9x-10y\)

Step-by-step explanation:

\(10yi^2-9x \\ \\ =10y(-1)-9x \\ \\ =-9x-10y\)

Answer:

it's 9x^6.

hope it may help you

Given the equation:

8x + 7y = -50

We will check the options to find which order pair is the solution of the equation

Point (-6 , -1)

8 * -6 + 7 * -1 = -48 - 7 = -55 ≠ -50

Point ( 0 , -6)

8 * 0 + 7 * - 6 = -42 ≠ -50

Point (-6, 0 )

8 * - 6 + 7 * 0 = -48 ≠ -50

Point (-1 , -6)

8 * -1 + 7 * -6 = -8 - 42 = -50

so, the order pair which is a solution for the equation is (-1 , -6 )

Step-by-step explanation:

remember the definitions of these 2 types of numbers ?

rational numbers are all numbers that can be written as

a/b

where a and b are integers, and b <> 0.

this includes all real fractions, but also all whole or integer numbers, as they can be written as a/1.

if they have digits after the decimal point, they are either finite, or they have a repeating pattern for all eternity.

irrational numbers are all numbers with an infinite series of digits after the decimal point without any repeating patterns.

that includes all squares roots of non-squared numbers or any other roots of numbers that are not the product of correspondingly many multiplications with themselves. and trigonometric function and logarithm results, and the special numbers in math and physics : pi and e.

so,

4/7 is rational

sqrt(30) is irrational

21/sqrt(4) is a trick question, as sqrt(4) = 2.

so, this is actually

21/2 is rational

pi is irrational

-27 = -27/1 is rational

To predict a linear regression score, you first need to train a linear regression model using a set of training data.

Once the model is trained, you can use it to make predictions on new data points. The predicted score will be based on the linear relationship between the input variables and the target variable,

A higher regression score indicates a better fit, while a lower score indicates a poorer fit.

To predict a linear regression score, follow these steps:

1. Gather your data: Collect the data p

points (x, y) for the variable you want to predict (y) based on the input variable (x).

2. Calculate the means: Find the mean of the x values (x) and the mean of the y values (y).

3. Calculate the slope (b1): Use the formula b1 = Σ[(xi - x)(yi - y)]  Σ(xi - x)^2, where xi and yi are the individual data points, and x and y are the means of x and y, respectively.

4. Calculate the intercept (b0): Use the formula b0 = y - b1 * x, where y is the mean of the y values and x is the mean of the x values.

5. Form the linear equation: The linear equation will be in the form y = b0 + b1 * x, where y is the predicted value, x is the input variable, and b0 and b1 are the intercept and slope, respectively.

6. Predict the linear regression score: Use the linear equation to predict the value of y for any given value of x by plugging the x value into the equation. The resulting y value is your predicted linear regression score.

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Answer:

400 km

Step-by-step explanation:

distance = speed * time

d = 100km/h * 4h

d = 400km

Answer:

equilateral

Step-by-step explanation:

all sides are even to each other

Answer: Equilateral triangle

Step-by-step explanation: This is because it has 3 equal sides

Answer:

D. Everyone 10+

Step-by-step explanation:

This is the most popular age group when it comes to age ratings. For example, Mario Kart is an Everyone 10+ game.

To factor a trinomial when a is greater than 1, we can use the AC method

To factor a trinomial when a is greater than 1, follow these steps

Multiply the coefficient of a (the first term) by the constant (the third term).

Find two numbers that multiply to the product obtained in step 1 and add up to the coefficient of b (the second term).

Replace the middle term with the two terms found in step 2.

Factor the resulting four-term polynomial by grouping.

Factor out the greatest common factor from each group.

Factor the resulting binomials.

Combine the factors to obtain the final factorization of the trinomial.

This method is known as the AC method, and it can be used to factor trinomials of the form ax^2 + bx + c, where a is greater than 1.

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The following operations are used to transform the quadratic equation y = x² into parabolas in standard form:

Case 1

Horizontal translation, vertical translation. Horizontal stretch.

Case 2

Horizontal translation, vertical translation. Reflection in the x-axis, vertical stretch.

Case 3

Horizontal translation, vertical translation. Horizontal stretch.

In this question we find three cases of parabolas in standard form, that is, quadratic equations of the form:

y - k = a · (x - h)²

Where:

This parabola is translated both horizontally and vertically by using the following definitions:

Horizontal translation

x → x - a, where a > 0 for rightward translation.

Vertical translation

y → y - b, where b > 0 for upward translation.

Horizontal dilation

f(x) → f(k · x), where k is a non-negative real number.

Vertical dilation

f(x) → k · f(x), where k is a non-negative real number.

Reflection in the x-axis

f(x) → - f(x)

The procedure is summarize below:

Finally, we summarize the procedure for each case:

Case 1

g(x) = x²

g(x) = [(1 / 2) · x²]

g(x) + 4 = [(1 / 2) · (x - 2)]²

Horizontal shift: 2 units right, vertical shift: 4 units down. Horizontal stretch.

Case 2

f(x) = x²

f(x) = - (1 / 2) · x²

f(x) - 2 = - (1 / 2) · (x - 4)²

Horizontal shift: 4 units right, vertical shift: 2 units down. Reflection in the x-axis, vertical stretch.

Case 3

h(x) = x²

h(x) = 2 · x²

h(x) - 5 = [2 · (x + 2)]²

Horizontal shift: 2 units left, vertical shift: 5 units up. Horizontal stretch.

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The $1314^\text{th}$ digit past the decimal point is 2.

To find the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$, we can use long division to compute the decimal expansion of the fraction.

The long division of $\frac{5}{14}$ is as follows:

```

0.35    <-- Quotient

-----

14 | 5.00

   4.2    <-- Subtract: 5 - (14 * 0.3)

   -----

     80   <-- Bring down the 0

     70    <-- Subtract: 80 - (14 * 5)

     -----

     100   <-- Bring down the 0

      98    <-- Subtract: 100 - (14 * 7)

      -----

       20   <-- Bring down the 0

       14    <-- Subtract: 20 - (14 * 1)

       -----

        60   <-- Bring down the 0

        56    <-- Subtract: 60 - (14 * 4)

        -----

         40   <-- Bring down the 0

         28    <-- Subtract: 40 - (14 * 2)

         -----

         120   <-- Bring down the 0

         112    <-- Subtract: 120 - (14 * 8)

         -----

           80   <-- Bring down the 0

           70    <-- Subtract: 80 - (14 * 5)

           -----

           ...

```

We can see that the decimal expansion of $\frac{5}{14}$ is a repeating decimal pattern with a repeating block of digits 285714. Therefore, the $1314^\text{th}$ digit past the decimal point is the same as the $1314 \mod 6 = 0^\text{th}$ digit in the repeating block.

Since $1314 \mod 6 = 0$, the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$ is the first digit of the repeating block, which is 2.

So, the $1314^\text{th}$ digit past the decimal point is 2.

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Answer:

6 one rupee and 12 two rupee coins.

Step-by-step explanation:

If the number of rupee coins is x then the number of 2 rupee coins is 2x.

x +  2*2x = 30

5x = 30

x = 6.

Answer:

1.96

Step-by-step explanation:

\( \frac{q}{7} + 1 > - 5➡q > - 42\)

\(\dfrac q7 + 1 > -5\\\\\implies \dfrac q7 > -5-1\\\\\\\implies \dfrac q7 > -6\\\\\\\implies q > -42\\\\\text{Interval,} ~ (-42, \infty)\)

96

Step-by-step explanation:

Your formula for parallelograms are: (B•H) which means base times height...

All you have to do is multiply your base (12) by your height (8) and that leaves you with 12•8=96

Hope this helped!

We can conclude that limsup \((x_n)^{(\frac{1}{n}) }\) ≤ ε + limsup (x_n)(x_n+1) for any positive ε.

To prove that limsup \((x_n)^{(\frac{1}{n}) }\)≤ limsup (x_n)(x_n+1), we can follow the hint and show that for any positive ε, limsup (x_n)(1/n) ≤ ε + limsup (x_n)(x_n+1).
Let's begin by assuming that limsup \((x_n)^{(\frac{1}{n}) }\)> ε + limsup (x_n)(x_n+1), and aim to derive a contradiction.
By the definition of limsup, we know that for any ε > 0, there exists an index N such that for all n ≥ N, x_n < limsup (x_n) + ε.
Consider the sequence (y_n) = (x_n)(x_n+1). Since (x_n) is bounded, (y_n) is also bounded.
Now, let's choose an arbitrary positive ε' such that 0 < ε' < ε.
By the definition of limsup, there exists an index M such that for all n ≥ M, y_n < limsup (y_n) + ε'.
Let's define M' = max(N, M).

Then for all n ≥ M', we have:
x_n < limsup (x_n) + ε        (by the definition of limsup)
x_n+1 < limsup (x_n+1) + ε    (by the definition of limsup)
y_n = x_n * x_n+1 < (limsup (x_n) + ε) * (limsup (x_n+1) + ε)    (by the above inequalities)
Now, let's consider the inequality:
\((y_n)^{(\frac{1}{n}) }\) = (x_n * x_n+1)(1/n) ≤ ((limsup (x_n) + ε) * (limsup (x_n+1) + ε))^(1/n)   (raising both sides to the power of 1/n)
By the properties of limits, we can rewrite the right-hand side as:
((limsup (x_n) + ε) * (limsup (x_n+1) + ε))(1/n) = (limsup (x_n) + ε)(1/n) * (limsup (x_n+1) + ε)(1/n)
Since ε' can be chosen to be arbitrarily small, we have:
limsup \((x_n)^{(\frac{1}{n}) }\) ≤ limsup (x_n) + ε' ≤ limsup (y_n) + ε'   (using the above inequality)
But this contradicts our assumption that limsup \((x_n)^{(\frac{1}{n}) }\) > ε + limsup (x_n)(x_n+1).
Therefore, we can conclude that limsup \((x_n)^{(\frac{1}{n}) }\)≤ ε + limsup (x_n)(x_n+1) for any positive ε.

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y = - 8

I hope this helps!

Step-by-step explanation:

by subtracting 2 from both sides we get

Answer:

s+0

Step-by-step explanation:

h.o mean of f= S =0

H.a mean of F=S >0

The eigenvalues are λ1 = -3 with eigenvector | 1 | -47/15 | 2/5 |

To find the eigenvalues and eigenvectors of the matrix:

| 8 1 4 |

| 4 5 -1 |

| -9 -1 1 |

We need to solve the characteristic equation:

det(A - λI) = 0

where A is the matrix, λ is the eigenvalue, and I is the identity matrix.

Expanding the determinant, we get:

| 8 - λ 1 4 |

| 4 5 - λ -1 |

| -9 -1 1 - λ |

= (8 - λ)[(5 - λ)(1 - λ) + 1] - (1)[(4)(1 - λ) - (-1)(-9)] + (4)[(4)(-1) - (-9)(5 - λ)]

= (8 - λ)(λ^2 - 6λ + 6) + 13(λ - 1) - 64(λ - 5)

= -λ^3 + 14λ^2 - 47λ - 15

Now we solve for the roots of the characteristic equation, which are the eigenvalues:

λ1 = -3, λ2 = 1, λ3 = 5

To find the eigenvectors, we substitute each eigenvalue into the matrix equation:

(A - λI)x = 0

For λ1 = -3, we have:

| 11 1 4 |

| 4 8 -1 |

| -9 -1 4 |

Solving for the eigenvector x, we get:

11x1 + x2 + 4x3 = 0

4x1 + 8x2 - x3 = 0

-9x1 - x2 + 4x3 = 0

Taking x1 = 1, we get:

x2 = -47/15

x3 = 2/5

So the eigenvector corresponding to λ1 = -3 is:

| 1 |

| -47/15 |

| 2/5 |

For λ2 = 1, we have:

| 7 1 4 |

| 4 4 -1 |

| -9 -1 0 |

Solving for the eigenvector x, we get:

7x1 + x2 + 4x3 = 0

4x1 + 4x2 - x3 = 0

-9x1 - x2 = 0

Taking x1 = 1, we get:

x2 = -9

x3 = 2

So the eigenvector corresponding to λ2 = 1 is:

| 1 |

| -9 |

| 2 |

For λ3 = 5, we have:

| 3 1 4 |

| 4 0 -1 |

| -9 -1 -4 |

Solving for the eigenvector x, we get:

3x1 + x2 + 4x3 = 0

4x1 - x3 = 0

-9x1 - x2 - 4x3 = 0

Taking x1 = 1, we get:

x2 = 13

x3 = -4

So the eigenvector corresponding to λ3 = 5 is:

| 1 |

| 13 |

| -4 |

Therefore, from smallest to largest, the eigenvalues are:

λ1 = -3 with eigenvector | 1 | -47/15 | 2/5 |

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Based on the truth conditions of conditional and logical equivalencies, it can be concluded that Dr. Santos did not lie to Mark.

In this scenario, Dr. Santos did not lie to Mark. The statement made by Dr. Santos is a conditional statement, where the antecedent is "If you do not give me your cheat sheet" and the consequent is "then you will fail the course." In order for this conditional statement to be false, the antecedent must be true and the consequent must be false. In this case, Mark did give Dr. Santos the cheat sheet, therefore the antecedent of the conditional statement is false. As a result, the truth value of the entire conditional statement is true, even though Dr. Santos did fail Mark after reviewing the cheat sheet. Furthermore, Dr. Santos' statement can also be expressed using logical equivalencies. "If A, then B" is logically equivalent to "not A or B." Using this equivalence, Dr. Santos' statement can be rewritten as "Either you give me your cheat sheet or you will fail the course." Again, this statement is true because Mark did give Dr. Santos the cheat sheet.
Therefore, based on the truth conditions of conditional and logical equivalencies, it can be concluded that Dr. Santos did not lie to Mark.

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The two-sample t-test tests for the difference between two population means, x1 and x2, and their respective standard deviations. The test statistic is given as t = (x1 - x2) / (s12/n1 + s22/n2). If the t-value falls in the rejection region, the null hypothesis is rejected, indicating there is evidence to support the alternative hypothesis.

The given hypothesis tests for the difference between two population means, denoted as µ1 and µ2. Here, the null hypothesis h0: µ1=µ2 states that the difference between the means is zero, whereas the alternative hypothesis ha: µ1≠µ2 states that the means are different from each other.

The following results are for two independent samples taken from the two populations. It is possible to test the hypothesis using a two-sample t-test, where the test statistic is given as:

t = (x1 - x2) / (s1²/n1 + s2²/n2)½

Here, x1 and x2 are the sample means of the two groups, whereas s1 and s2 are their respective standard deviations. Also, n1 and n2 are the sample sizes of the two groups.

In order to conduct the test, the t-value is calculated and compared to the critical value of the t-distribution for a given level of significance. If the calculated t-value falls in the rejection region, then the null hypothesis is rejected, indicating that there is significant evidence to support the alternative hypothesis.

However, if the calculated t-value falls in the acceptance region, then the null hypothesis is accepted, indicating that there is not enough evidence to reject the null hypothesis.

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Answer: ITS 10!!!!

Step-by-step explanation:

Answer:8x+10y cannot be simplified

Step-by-step explanation: They have different variables.

Answer:

322, 468, 35, 48, 28.5

Step-by-step explanation:

23 times 14 is 322, 18 times 26, 5 times 7, 8 times 6, 3 times 9.5

Answer:

23x14=322ft

18x28=468ft

5x7=35ft

8x6=48ft

3x9.5=28.5

Step-by-step explanation:

hejdbsisugebe

Answer:

x = \(\sqrt{x+6}\)

Step-by-step explanation:

The question states that it is the square root of the sum of both n and 6. That means n and 6 are added first before square rooted. Between B and C, choose the answer that has the parenthesis around x and 6, like (x + 6).

Answer:

Step-by-step explanation:

Its in the image.

I used Pythagoras theorem in solving for the unknown side.

Sorry for the rough working

Amount of water produced in 6 days is 15.6×10⁶.

We will simply perform multiplication to find the amount of water produced in 6 days.

Amount of water produced in 6 days = amount of water produced in one day × 6

Amount of water produced in 6 days = 2.6×10⁶×6

Performing multiplication to find the amount of water produced in 6 days

Amount of water produced in 6 days = 15.6×10⁶

The answer is in scientific notation as 15.6 is coefficient, 10 is base and 6 is exponent. Therefore, amount of water produced by plant in 6 days is 15.6×10⁶.

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