(x+3)^2=4

solve the following equation,giving your answer correct to 2 decimal places
where necessary
​

Answer:

14m+10i+7p-92

The sale price 's' of a book is $3.50 less than the original price 'p'. This situation is represented by the given equation s = p - 3.5.

Two or more expressions with an Equal sign is called as Equation.

The given equation is s = p - 3.5, where 's' represents the sale price and 'p' represents the original price of a book.

The equation shows that to get the sale price 's', the original price 'p' is reduced by $3.50.

If the sale price 'p' of a book is $3.50 less than the original price 's', then we can rewrite the equation as p = s + 3.5.

This situation is not represented by the given equation.

If the sale price 's' of a book is $3.50 more than the original price 'p', then the equation would be s = p + 3.5.

This situation is also not represented by the given equation.

Hence, the sale price 's' of a book is $3.50 less than the original price 'p'. This situation is represented by the given equation s = p - 3.5.

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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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Completing the square – can be used to solve any quadratic equation. It is a very important method for rewriting a quadratic function in vertex form. Quadratic formula – is the method that is used most often for solving a quadratic equation.

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 statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

Any quadratic problem may be solved by completing the square. It is a critical way for expressing a quadratic function in vertex form. The quadratic formula is the most often used method for solving a quadratic problem.

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Carl is correct the value of x by using the side splitter theorem is 6

\(\frac{6}{3} = \frac{12}{x}\)

Required

Is Carl correct?

The side splitter theorem is a theorem that states that when a line passes through the two sides of a triangle and is parallel to the third remaining side, the line divides the two sides proportionally.

Using the side splitter theorem, the proportion is:

\(\frac{AB}{BC} = \frac{AE}{ED}\\\)

This gives:

\(\frac{6}{3} = \frac{12}{x}\)

This proportion is equivalent to Carl's.

Hence, Carl is correct.

Solving further: Cross Multiply

6 * x = 12 * 3

6x = 36

Make x the subject

\(x=\frac{36}{6}\)

x =6

Carl is correct the value of x by using the side splitter theorem is 6

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The measure of angle ZCOD is 27°.

Since A, O, and B are collinear, angles AOC and COB form a linear pair, which means their sum is 180°. Therefore:

x + 50° = 180°

Solving for x, we get:

x = 130°

Next, we can use the fact that angles AOC and BOA are vertical angles, which means they are congruent. Therefore:

x = 103°

Substituting x with 130°, we get:

130° = 103° + COD

Solving for COD, we get:

COD = 27°

Finally, since angles AOD and COB are alternate interior angles, they are congruent. Therefore:

77° = 50° + ZCOD

Solving for ZCOD, we get:

ZCOD = 27°

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--The complete question is, Given that points A, O, and B are collinear, find the measure of angle ZCOD, where:

Angle AOC is denoted by x and measures 90°

Angle BOA measures 103°

Angle AOD measures 77°

Angle COB measures 50°.

Please note that point O is located between points A and B.--

8.5 units³

Step-by-step explanation:

The volume can be found as the product of the two given values.

In fact, for any right angled 3D figure, we can find its volume as area of one face times the height or length.

Thus, we get volume as

V = 4 × 17/8 (converting 2 1/8)

V = 17/2 units³ or 8.5 units³

Hope this helps!

All the values with exactly three significant digits are: 0.0807, 1990

Significant digits of a number tell us what the actual meaningful representation of a number is. There are certain rules to figure out which digits in a number are significant such as

Thus the numbers with 3 significant digits are: 0.0807, 1990

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Answer:

5

Step-by-step explanation:

Pythagoras theorem is a² = b² + c² (where a is the hypotenuse or the longest side)

To find the shorter side, you rearrange it so it becomes c² = a² - b² (whether it is c or b doesn't matter)

So √13² - 12² = 5

Answer:

\(\s\frac{143}{18}\)

Step-by-step explanation:

Fractions are easier to add when in improper form.

2 1/2 = 5/2

3 2/3 = 11/3

1 7/9 = 16/9

Now, we need to find a common denominator for these fractions.

18 is a multiple of 2, 3, and 9, so we can use it.

Convert all the fractions to have 18 as denominator:

5/2 = 45/18 (multiply by 9)

11/3 = 66/18 (multiply by 6)

16/9 = 32/18 (multiply by 2)

Now that all the fractions are converted to having the same denominator, we can add them.

\(\frac{45 + 66 + 32}{18}\) = \(\s\frac{143}{18}\)

Answer:

7 51/54, find simplest form on your own.

Step-by-step explanation:

Sorry, I can't explain right now. I might edit my post later.

Answer: 4:3 (4 being the baseballs, and 3 being the golf balls)

I hope this helps, and Happy Holidays! :)

Answer:

There are no coefficients.

Step-by-step explanation:

To apply the Gram-Schmidt process to find an orthonormal basis for the subspace W of R3, spanned by the given vectors, we can follow these steps:

Let v1 be the first vector in the basis for W.

Step 1: Normalize v1 to get the first vector in the orthonormal basis.

v1* = v1 / ||v1||, where ||v1|| is the magnitude or length of v1.

Step 2: Project the second vector v2 onto the subspace orthogonal to v1.

Let u2 = v2 - proj(v2, v1), where proj(v2, v1) is the projection of v2 onto v1.

Step 3: Normalize u2 to get the second vector in the orthonormal basis.

v2* = u2 / ||u2||, where ||u2|| is the magnitude or length of u2.

Step 4: Project the third vector v3 onto the subspace orthogonal to both v1 and v2.

Let u3 = v3 - proj(v3, v1) - proj(v3, v2), where proj(v3, v1) and proj(v3, v2) are the projections of v3 onto v1 and v2, respectively.

Step 5: Normalize u3 to get the third vector in the orthonormal basis.

v3* = u3 / ||u3||, where ||u3|| is the magnitude or length of u3.

The set {v1*, v2*, v3*} is an orthonormal basis for the subspace W.

Note that the choice of v1 affects the resulting orthonormal basis, but any choice of v1 that spans W will result in an orthonormal basis for W.

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Answer:

B

Step-by-step explanation:

Answer:

B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)

Step-by-step explanation:

Answer:

Step-by-step explanation:

a. 100 divided by 75 = 1.3333333333333333333333333333333

1.3333333333333333333333333333333 times 43 = 57.333333333333333333333333333332

round it to the nearest whole number: ≅ 57%

Answer:

i think that she might be able to build 2

Step-by-step explanation:

but if you multiply them both you will get forty.

Answer:

5g-8

Step-by-step explanation:

i don't know

have a great day

Answer:

C.  37.5

Step-by-step explanation:

From inspection of the given triangle, we can see that the straight line that divides the triangle into two smaller triangles is an angle bisector since it divides the angle into two congruent angles.

Angle Bisector Theorem

An angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.

\(\implies x:15=40:16\)

Solve for x:

\(\implies \dfrac{x}{15}=\dfrac{40}{16}\)

\(\implies \dfrac{x}{15}=2.5\)

\(\implies x=2.5\times 15\)

\(\implies x=37.5\)

Answer:

5/3 is the slope. slope is the same thing as rate of change

Step-by-step explanation:

We differentiated the given functions, proved an identity involving cot(x) and csc(x), and found the limit of a given expression as x approaches infinity.

Differentiate the function:

a) y = 4e^x

To differentiate y with respect to x, we use the chain rule. The derivative of e^x with respect to x is simply e^x. Since 4 is a constant, its derivative is 0. Therefore, the derivative of y with respect to x is:

dy/dx = 4e^x

b) f(x) = 1 - e^x

Using the constant rule, the derivative of 1 with respect to x is 0. To differentiate -e^x with respect to x, we use the chain rule. The derivative of e^x with respect to x is e^x, and since it's multiplied by -1, the overall derivative is -e^x. Therefore, the derivative of f(x) with respect to x is:

f'(x) = 0 - (-e^x) = e^x

Differentiate:

cosec(x), f(0) = 1 + sin(x)

To differentiate cosec(x) with respect to x, we use the chain rule. The derivative of sin(x) with respect to x is cos(x), and since it's in the denominator, the negative sign is present. Therefore, the overall derivative is -cos(x) / sin^2(x). To find f'(0), we substitute x = 0 into the derivative:

f'(0) = -cos(0) / sin^2(0) = -1 / 0, which is undefined.

Prove that cot(x) = -csc(x):

We know that cot(x) is the reciprocal of tan(x), and csc(x) is the reciprocal of sin(x). Using the trigonometric identities, we have:

cot(x) = cos(x) / sin(x) (1)

csc(x) = 1 / sin(x) (2)

Multiplying both numerator and denominator of (1) by -1, we get:

-cos(x) / -sin(x) = -csc(x)

Therefore, we have proved that cot(x) = -csc(x).

Find the limit:

lim (sin(2x)) / (2405x - 3x)

x -> ∞

To find the limit as x approaches infinity, we need to evaluate the behavior of the expression as x becomes extremely large. In this case, as x approaches infinity, the denominator becomes very large compared to the numerator. The term 2405x grows much faster than 3x, so we can neglect the 3x term in the denominator. Therefore, the expression can be simplified as:

lim (sin(2x)) / 2402x

x -> ∞

Now, as x approaches infinity, sin(2x) oscillates between -1 and 1, but it does not grow or shrink. On the other hand, 2402x becomes extremely large. Dividing a bounded value (sin(2x)) by a very large value (2402x) tends to zero. Hence, the limit is 0.

lim (sin(2x)) / (2405x - 3x) = 0

x -> ∞

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The quotient of 3/4 and 5/6, expressed in its simplest form, is 9/10 .To find the quotient of fractions, we need to divide the numerator of one fraction by the denominator of the other fraction.

To simplify the process, we can convert the division into multiplication by taking the reciprocal of the second fraction. The reciprocal of a fraction is obtained by interchanging the numerator and the denominator. So, the reciprocal of 5/6 is 6/5.

Now, we can multiply the fractions:

3/4 * 6/5 = (3*6)/(4*5) = 18/20

However, we need to simplify the fraction to its simplest form. To do this, we find the greatest common divisor (GCD) of the numerator and denominator, which is the largest number that divides both without leaving a remainder. In this case, the GCD of 18 and 20 is 2.

By dividing both the numerator and denominator of 18/20 by 2, we get the simplest form of the fraction:

18/20 ÷ 2/2 = 9/10

The quotient of 3/4 and 5/6, expressed in its simplest form, is 9/10.

It's important to note that simplifying fractions involves dividing both the numerator and denominator by their greatest common divisor. This ensures that the fraction is in its simplest form, where the numerator and denominator have no common factors other than 1.

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Answer:

3(a+2b)=11b

3a+6b=11b

3a=5b

a/b=5/3

a:b=5:3

Answer:

a:b = 5:3

Step-by-step explanation:

I do RSM too, just type in 5:3! Good luck and have a wonderful day.

The points that can be connected to draw a line of symmetry through the figure shown are: C. points, E, and , F.

A line of symmetry, can be described as any line that divides a figure into two parts, in such a way that the divided parts are identical to each other, which implies that they can be folded onto each other.

A line of symmetry is also called a mirror line or axis of symmetry of a shape. The line simply creates mirror images that are identical to each other when the figure is cut across.

The figure given is a rectangle having the indicated points. If we connect point E to point F, the figure will be divided into equal halves. Therefore, the answer is: C. points, E, and , F

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Answer:

Step-by-step explanation:

1/2x - y = 8

1/2x = 8 + y

2(1/2x = 8 + y)

x = 16 + 2y

Answer:

Answer is A

Step-by-step explanation:

I don't really know if am right but can u give a like to this answer that will really make me happy :)

Answer:$84

Step-by-step explanation:196/9.80=20

20x4.20=$84

hoping im right

Answer:

C

Step-by-step explanation:

Answer:

C) ΔJIL ≅ ΔKLI by HL

Step-by-step explanation:

Answer:

Step-by-step explanation:

The loop will run an infinite number of times

a) The nth derivative for f(x) = xⁿ is n!.

b) The nth derivative for expression f(x) is (-1)^(n+1) * n! / x^(n+1).

(a) f(x) = xⁿ:

To find the nth derivative of f(x) = xⁿ, we can start by calculating the first few derivatives and looking for a pattern:

f(x) = xⁿ

f'(x) = n x^(n-1)

f''(x) = n(n-1)x^(n-2)

f'''(x) = n(n-1)(n-2)x^(n-3)

...

From this pattern, we can observe that the nth derivative of f(x) is given by:

f ⁿ(x) = n(n-1)(n-2)...(n-(n-1)) x^(n-n)

f ⁿ(x) = n!

Therefore, the nth derivative of f(x) = xⁿ is n!.

(b) f(x) = 1/x:

To find the nth derivative of f(x) = 1/x, we can again start by calculating the first few derivatives and observing the pattern:

f(x) = 1/x

f'(x) = -1/x^2

f''(x) = 2/x^3

f'''(x) = -6/x^4

f''''(x) = 24/x^5

...

From this pattern, we can observe that the nth derivative of f(x) alternates between positive and negative values, and is given by:

f ⁿ(x) = (-1)^(n+1) * n! / x^(n+1)

Therefore, the nth derivative of f(x) = 1/x is (-1)^(n+1) * n! / x^(n+1).

In summary, to find the nth derivative of a function, we can start by calculating the first few derivatives and looking for a pattern. Once we have identified the pattern, we can use it to derive a formula for the nth derivative of the function.

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