7x2+49x+84=0
by completing the square method

Answer:

Bill go the better deal

Step-by-step explanation:

43.35/15=2.89

61.82/32=2.81

Answer: c ic the answer

c is the answer

Step-by-step explanation:

c is the answer

Using Newton's method, we can approximate the root of the equation 2.2x^5 - 4.4x^3 + 1.3x^2 - 0.7x - 0.8 = 0 in the interval [-2, -1]. The approximate value of the root, correct to six decimal places, is x = -1.696722.

Newton's method is an iterative numerical method used to approximate the roots of an equation. We start with an initial guess and refine it using the formula xᵢ₊₁ = xᵢ - f(xᵢ)/f'(xᵢ), where f(x) represents the given equation and f'(x) is the derivative of f(x).

To approximate the root in the interval [-2, -1], we first need to choose a suitable initial guess within that interval. Let's choose x₀ = -1.5 as our initial guess.

Next, we need to calculate the derivatives of the equation. The derivative of f(x) = 2.2x^5 - 4.4x^3 + 1.3x^2 - 0.7x - 0.8 with respect to x is f'(x) = 11x^4 - 13.2x^2 + 2.6x - 0.7.

Using the initial guess x₀ = -1.5, we iteratively apply the Newton's method formula: x₁ = x₀ - f(x₀)/f'(x₀), x₂ = x₁ - f(x₁)/f'(x₁), and so on.

By repeating this process, we can approximate the root of the equation within the given interval. After several iterations, we find that the approximate value of the root, correct to six decimal places, is x = -1.696722.

Therefore, using Newton's method, we have successfully approximated the root of the equation 2.2x^5 - 4.4x^3 + 1.3x^2 - 0.7x - 0.8 = 0 in the interval [-2, -1] to a high degree of accuracy.

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9514 1404 393

Answer:

  a) 22

  b) 18

Step-by-step explanation:

a) In order for 198k to be a perfect square, all of its integer factors must be squares. 3² is already a factor. To make the other factors be squares, need to multiply by 2 and 11. That is, k = 2×11 = 22. Then we will have ...

  198k = 2×3²×11 × (2×11) = 2²×3²×11² = (2×3×11)²

  k = 22

__

b) The factors that are different in the two numbers are 11 and 5. The factors that are the same are 2×3² = 18.

  18 is the greatest common factor of 198 and 90

_____

The "work" is looking at the numbers in the factor lists and comparing those to what is needed to answer the question.

The square root of the decimal number is √0.0016 = 0.04

Here we can find the square root of the decimal number:

N = 0.0016

Notice that we can write this number as:

0.0016 = 16*10⁻⁴

Now we can take the square root of that, so we will get:

√(16*10⁻⁴)

We can distribute the square root to get:

√16*√10⁻⁴

These two are easy, we will get:

√16*√10⁻⁴ = 4*10⁻² = 0.04

That is the square root.

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Answer:

-1/7

Step-by-step explanation:

The slope of the function's graph at the point (-3, 9) is 15. The equation of the tangent line at that point is y = 15x + 54.

To find the slope of the graph at the given point, we need to calculate the derivative of the function f(x) = \(2x^2 + 3x\) and substitute x = -3 into the derivative. Taking the derivative of f(x) with respect to x, we get f'(x) = 4x + 3. Substituting x = -3 into f'(x), we have f'(-3) = 4(-3) + 3 = -9.

Therefore, the slope of the graph at (-3, 9) is -9. However, this is the slope of the tangent line at that point. To find the equation of the tangent line, we use the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point. Plugging in the values, we have y - 9 = -9(x + 3). Simplifying this equation gives y = -9x - 27 + 9, which further simplifies to y = -9x + 54.

Therefore, the equation of the tangent line to the graph of f(x) = \(2x^2 + 3x\) at the point (-3, 9) is y = -9x + 54.

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The answer to the given binary operation is 10012. The binary operation of adding 1112 and 102 will be solved by converting the binary numbers to base 10, performing the addition in base 10, and then converting the result back to base 2.

Converting the binary numbers to base 10, we have 1112 = 7 and 102 = 2. Adding 7 and 2 in base 10 gives us 9. To convert the result back to base 2, we divide 9 by 2 repeatedly until the quotient becomes 0. The remainder in each division gives us the binary digits of the answer. In this case, 9 divided by 2 is 4 with a remainder of 1, and 4 divided by 2 is 2 with a remainder of 0. Therefore, the binary representation of 9 is 1001. Hence, the answer to the given binary operation is 10012.

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Answer:

The explanation Marc can give

Jose is, you should have added 12 and –12 for the xy terms

Step-by-step explanation:

Josh calculation

-8x^2y-17xy^2+12xy-8+5x^2y-xy^2-12xy=-3x^2y-18xy^2+24xy-8

Correct calculation

-8x^2y-17xy^2+12xy-8+5x^2y-xy^2-12xy

Collect like terms

= -8x^2y+5x^2y-17xy^2-xy^2+12xy-12xy-8

= -3x^2y-18xy^2-8

The explanation Marc can give

Jose is, you should have added 12 and –12 for the xy terms.

Answer:

A

Step-by-step explanation:

Edg

The 41st term of the sequence is 121.

In mathematics, a sequence is a list of numbers or objects that follow a certain pattern or rule. A sequence's terms are typically identified by subscripts, like a1, a2, a3,..., an, where n denotes the number of terms in the sequence.

Sequences can be arithmetic, geometric, or neither, depending on terms follow a static difference, constant ratio, or neither of these series, respectively. Algebra uses geometric sequences to represent exponential development or decay whereas arithmetic sequences are frequently employed to model linear connections.

The given sequence is 2 , 5 , 8 , ...

The common difference is:

d = 5 - 2 = 3

The nth term of a sequence is given as:

an = a1 + (n-1)d

Substituting the value we have:

an = 2 + (n-1)3

an = 3n - 1

a41 = 3(41) - 1 = 122 - 1 = 121

Hence, the 41st term of the sequence is 121.

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Answer:  x                    y

              0.5                 3

              1.5                  4

               2.5                5

Hope it helped

Step-by-step explanation:

Answer:

x y

0.5 3

1.5 9

4.5 27

Step-by-step explanation:

Just Divide y by x and answer should come 6 here. This helps to determine answers.

The area enclosed in one loop of the curve r = cos2θ will be π/8.

Any function between the dependent and independent variables can be represented in a graph diametrically.

For instance, if y = x2 forms a parabola, we may infer from the graph alone that it will always have a positive value, regardless of the range of x.

As per the given curve,

r = cos2θ

Since |cos2θ| ranges between 0 and 1.

At r = 1

cos2θ = 1 ⇒ θ = 0

At r = 0

cos2θ = 0 ⇒ θ = π/4

The area of one loop will be as,

A = 1/2∫r²dθ

A = (1/2)∫cos²2θ dθ

A = (1/2)∫(1 + cos4θ)/2  dθ

A = π/8

Hence" The area enclosed by the given function will be π/8".

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Answer:

y=15

Step-by-step explanation:

The Solution:

Given the expression below:

We are required to write the answer in the form below:

This means that:

So, writing the answer in the required form, we have:

Therefore, the correct answer is:

Answer:

C

Step-by-step explanation:

Answer:

1. Expand the expression.

x^8+24x^7+252x^6+1512x^5+5670x^4+13608x^3+20412x^2+17496x+6561

2. (x+3)^5

Use the Binomial Theorem.

x^5+5x^4⋅3+10x^3⋅3^2+10x^2⋅3^3+5x⋅3^4+3^5

Simplify each term.

x^5+15x^4+90x^3+270x^2+405x+243

Step-by-step explanation:

hope it is helpful....

Answer:

42x

Step-by-step explanation:

The volume of the cube is 64 cubic inches.

The given information states that the area of a cross section parallel to the base of a cube is 16 square inches. In a cube, all six faces are congruent squares. Since the cross section is parallel to the base, it is also a square with an area of 16 square inches.

To find the side length of the square cross section, we take the square root of the area: √16 = 4 inches. Since the cross section represents one face of the cube, the side length of the cube is also 4 inches.

The volume of a cube is calculated by multiplying the side length by itself three times: 4 * 4 * 4 = 64 cubic inches. Thus, the volume of the cube is 64 cubic inches.

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Answer:

Here is a picture of the answer. I hope this helps!

Step-by-step explanation:

The graph of compound inequality \(x<8.3\) and \(x>9.8\) is shown in attached graph.

A compound inequality contains at least two inequalities that are separated by either and or "or".

Given compound inequality:

                                \(x<8.3\) or \(x>9.8\)

Above inequalities are shown in below attached graph.

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The three major chords built on white notes without accidentals are:

1. C major chord (C, E, G)

2. F major chord (F, A, C)

3. G major chord (G, B, D)

These chords are formed by taking the root note, skipping one white note, and adding the next white note on top. For example, in the C major chord, the notes C, E, and G are played together to create a harmonious sound.

Similarly, the F major chord is formed by playing F, A, and C, and the G major chord is formed by playing G, B, and D. These three major chords are commonly used in various musical compositions and are fundamental building blocks in music theory.

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Answer:

In 2 seconds, the space station travels 10 miles.

Step-by-step explanation:

Well, if the x axis represents time in seconds and the y axis represents distance in miles, then when your x value is 2, your y value is 10.

Answer:

a

Step-by-step explanation:

it should be A beacuase of the image

Answer:

The answer that you chose is correct. It was reflected about the x-axis then rotated 90° clockwise

The exact arc length of the curve r = 2cosθ, where 0 ≤ θ < 2π, is 4π units.

To find the arc length of the curve represented by the polar equation r = 2cosθ, where 0 ≤ θ < 2π, we can use the arc length formula for polar curves:

S = ∫[θ1 to θ2] √(r^2 + (dr/dθ)^2) dθ.

In this case, r = 2cosθ and dr/dθ = -2sinθ. Let's calculate the arc length:

S = ∫[θ1 to θ2] √(r^2 + (dr/dθ)^2) dθ

 = ∫[θ1 to θ2] √((2cosθ)^2 + (-2sinθ)^2) dθ

 = ∫[θ1 to θ2] √(4cos^2θ + 4sin^2θ) dθ

 = ∫[θ1 to θ2] √(4(cos^2θ + sin^2θ)) dθ

 = ∫[θ1 to θ2] √(4) dθ

 = ∫[θ1 to θ2] 2 dθ

 = 2 ∫[θ1 to θ2] dθ

= 2(θ2 - θ1).

The arc length S is equal to 2 times the difference between the two angles θ2 and θ1.

Since the given range is 0 ≤ θ < 2π, we have θ1 = 0 and θ2 = 2π.

S = 2(2π - 0)

 = 4π.

Therefore, the exact arc length of the curve r = 2cosθ, where 0 ≤ θ < 2π, is 4π units.

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Given:

With H 1 : p ≠ 3/5, the test statistic is z = 0.78.

Required:

find the P-value. Also, use a 0.05 significance level

Explanation:

With H 1 : p ≠ 3/5, the test statistic is z = 0.78.

The p value for this case would be given by:

A. X and Y might be independent. Knowing the value of one independent variable tells us nothing about the value of the other independent variable. The mean and variance of X and Y being different does not necessarily mean that knowing the value of one tells us nothing about the other.

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Within the relevant range, a curvilinear cost function can be graphed as a curved line. A curvilinear cost function is a cost function where the total cost changes as a function of the level of activity, but not at a constant rate.

This means that as the level of activity increases, the cost per unit may increase or decrease, resulting in a curved relationship between the level of activity and the total cost. In order to determine the optimal level of activity, a manager can use calculus to find the point where the marginal cost equals the marginal revenue.

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The quadratic equation are equations that have an axis of symmetry

passing through the vertex.

Reasons:

2. The x-intercepts are given by the point at which the y-value of the equation are zero.

Therefore;

The quadratic equation are;

(x + 3)·(x - 1) = 0

x² + 2·x - 3 = 0

The equation can also be written in the form;

(-x - 3)·(x - 1) = 0

-x² - 2·x + 3 = 0

The quadratic equations are;

3. The points through which the quadratic equation passes are;

(-4, 2) and (1, 2)

The value at the vertex = Maximum value

Taking the vertex as the point midway between the two given points, we have;

\(\displaystyle Coordinates \ of \ the \ vertex = \left( \frac{-4 + 2}{2} , \, k \right) = \left(-1, \, k)\)

The coordinates of the vertex, (h, k) = (-1, y)

The vertex form of a quadratic equation is presented as follows;

(y - k) = a·(x - h)²

y = a·(x - h)² + k

Which gives;

y = a·(x - (-1))² + k = a·(x + 1)² + k

y = a·(x + 1)² + k

At the point (-4, 2), we have;

2 = a·((-4) + 1)² + k = 9·a + k

2 = 9·a + k

Taking the value of k as 11, we have;

(h, k) = (-1, 11)

2 = 9·a + 11

\(\displaystyle a = \frac{2 - 11}{9} = -1\)

Which gives;

y = -1·(x + 1)² + 11 = -x² - 2·x + 10

y = -x² - 2·x + 10

When x = -4, we have;

y = -(-4)² - 2·(-4) + 10 = 2

When x = 2, we have;

y = -(2)² - 2·(2) + 10 = 2

4. The points through which the graph passes are; (-4, 2) and (1, 2)

The x-coordinate of the minimum vertex is given by the equation;

\(\displaystyle Coordinates \ of \ the \ vertex, \ (h, \, k) = \left( \frac{-4 + 1}{2} , \, k\right) = \left(-1.5, \, k)\)

(h, k) = (-1.5, y)

The vertex form of the equation of a quadratic equation is presented as follows;

y = a·(x - h)² + k

Which gives;

y = a·(x - (-1.5))² + k

y = a·(x + 1.5)² + k

\(\displaystyle a = \mathbf{\frac{y - k}{\left(x + 1.5\right)^2}}\)

At the point (1, 2), we have;

\(\displaystyle a = \frac{2 - k}{\left(1 + 1.5\right)^2} = \frac{2 - k}{6.25}\)

When k = -4.25, we have;

\(\displaystyle a = \frac{2 - k}{\left(1 + 1.5\right)^2} = \frac{2 - \left(-4.25 \right)}{6.25} = 1\)

The equation is therefore;

y = 1·(x + 1.5)² - 4.25 = x² + 3·x - 2

y = x² + 3·x - 2

At the point where x = -4, we have;

y = (-4)² + 3·(-4) - 2 = 2

At the point where x = 1, we have;

y = (1)² + 3·(1) - 2 = 2

Therefore;

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Answer:

integer

Step-by-step explanation:

The area of the Triangle given in the question is 4.7

Area of Triangle = 1/2(base × height )

Using the vertex , we can obtain the height of the triangle thus:

height = 1.873

Inserting the parameters into the Area formula :

height = 1.873

base = 5

Area of Triangle = 1/2 × 5 × 1.873

Area of Triangle= 4.68

Therefore, the area of the triangle is 4.7

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