9(8s - 5f) use f = 3 and s = 4

9514 1404 393

Answer:

  x² +3x -3 +3x/(5x² +6x +2)

Step-by-step explanation:

As with any long division, you formulate a partial quotient, then subtract the product of that and the divisor from the dividend. The result is a new dividend. You're done when the degree of the dividend is less than the degree of the divisor.

The partial quotient term is simply the ratio of the highest-degree terms in the dividend and the divisor. (That is what makes it easier than numerical long division.)

_____

Web page formatting cut off part of the "Hints" in the first attachment. The second attachment shows the full "Hints."

The work required to lift the rope and the weight up to the level of the balcony is 1200 foot-pounds.

To calculate the work, we need to consider the gravitational potential energy gained by lifting the rope and the weight. The weight of the rope can be calculated by multiplying its linear density (0.1 pounds per foot) by its length (40 feet), resulting in 4 pounds. The total weight to be lifted is the sum of the weight of the rope and the weight attached (4 pounds + 20 pounds = 24 pounds).

The work done to lift an object is given by the formula: Work = Force × Distance. In this case, the force is equal to the weight (24 pounds) and the distance is the height of the balcony, which is not provided in the question. Let's assume the balcony height is h feet. Therefore, the work is given by: Work = 24 pounds × h feet.

Since we don't have the specific height, we cannot calculate the exact work value. However, the main answer provides a general formula to calculate the work required, which is 24h foot-pounds. If the height of the balcony is 50 feet, for example, the work required would be 24 pounds × 50 feet = 1200 foot-pounds. The actual work value depends on the height of the balcony.

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Answer:

49 degrees

Step-by-step explanation

Answer:

I think 49 °F

Step-by-step explanation:

42 - (-7) = 49 °F

So the temperature raised 49 degrees since 7pm last night.

I think thats right. :)

The statement is False.

Let A = {1,3,5,7). B = {5, 6, 7, 8). C = {5, 8} D = (2,5,8), and U = {1,2,3,4,5,6,7,8).

To determine whether the expression DCB is true or false, we need to know the content of these sets.

To determine the content of DCB:

DCB contains all elements of D, all elements of C, and all elements of B except those that are already in D and C.

D = {2,5,8} C = {5, 8} B = {5,6,7,8}

DCB = {2,5,8,6,7}

Thus, DCB is false because not all elements in D are in B, and all elements in D are not in B.

Therefore, the answer is option B.False; all elements in D are not in B.

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Answer:

1080°

Step-by-step explanation:

hope it's helpful

Answer:

i say the 3rd row

Step-by-step explanation:

The number of small boxes purchased is 4.

The number of large boxes purchased is 2.

The number of nails in a small box is 50, and the number of nails in a large box is 450.

The total number of nails bought is 1100.

Let the number of large boxes be "x".

The number of small boxes is "2x".

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equal sign.

The equation can be formed as given below :

x*450 + 2x*50 = 1100

450x + 100x = 1100

550x = 1100

x = 2

The number of small boxes purchased is 2*x = 2*2 = 4.

The number of large boxes purchased is x = 2.

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Answer:

4 boxes of small nails.

2 boxes of large nails.

Step-by-step explanation:

Define the variables:

Given information:

Create a system of equations with the given information and defined variables:

\(\begin{cases}x=2y\\50x+450y=1100\end{cases}\)

Substitute the first equation into the second equation and solve for y:

\(\implies 50(2y)+450y=1100\)

\(\implies 100y+450y=1100\)

\(\implies 550y=1100\)

\(\implies \dfrac{550y}{550}=\dfrac{1100}{550}\)

\(\implies y=2\)

Substitute the found value of y into the first equation and solve for x:

\(\implies x=2(2)\)

\(\implies x=4\)

Therefore the contractor purchased:

Since the two equations are of line and coincident to each other so the equations will have an infinite number of solutions.

The equation which have a degree of one will be called as the linear equation the graph of the equation will be always a straight line.

Here we have the equation:

x-5=-5+x

or

x-5=x-5

Here we can see that the ratios are same:

\(\dfrac{a_1}{b_1}=\dfrac{a_2}{b_2}\\\\\\\\\dfrac{1}{-5}=\dfrac{1}{-5}\)

So the equations will be coincident to each other or line one will coincide with line 2. Hence the two equations are of line and coincident to each other so the equations will have an infinite number of solutions.

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The given matrix A is diagonalizable, and the matrix P such that P⁻¹AP = D is:

P = [[1, 1],

    [0, 1]

D = [[2, 0],

    [0, 3]]

To determine whether a given matrix is diagonalizable, we need to check if it has a full set of linearly independent eigenvectors. If it does, then it is diagonalizable.
To determine if a matrix is diagonalizable and find the diagonal matrix D:
1. Compute the eigenvalues of matrix A by solving the characteristic equation det(A - λI) = 0, where λ is an eigenvalue and I is the identity matrix.
2. For each eigenvalue λ, find the corresponding eigenvectors by solving the equation (A - λI)X = 0, where X is a vector.
3. If the number of linearly independent eigenvectors is equal to the size of the matrix (i.e., the matrix has n linearly independent eigenvectors), then the matrix A is diagonalizable.
4. Once you have found a set of linearly independent eigenvectors, construct the matrix P using these eigenvectors as columns.
5. Find the inverse of matrix P, denoted as P⁻¹.
6. Compute the diagonal matrix D by using the equation D = P⁻¹AP.
If the matrix A is diagonalizable, then matrix P will be the matrix of eigenvectors, and D will be a diagonal matrix consisting of the corresponding eigenvalues on the diagonal.

Example:
Let's say we have a matrix A:
A = [[2, 1],
    [0, 3]]
1. Compute the eigenvalues:
  The characteristic equation is det(A - λI) = 0:
  |2-λ  1   |
  |0    3-λ |
  Setting this determinant equal to zero, we get:
  (2-λ)(3-λ) - 0 = 0
  Expanding and simplifying, we have:
  λ² - 5λ + 6 = 0
  Factoring, we get:
  (λ - 2)(λ - 3) = 0
  So, the eigenvalues are λ = 2 and λ = 3.

2. Find the eigenvectors:
  For λ = 2, we solve the equation (A - 2I)X = 0:
  |0  1| |x1|   |0|
  |0  1| |x2| = |0|
  Solving this system of equations, we get one eigenvector:
  X1 = [1, 0]
  For λ = 3, we solve the equation (A - 3I)X = 0:
  |-1  1| |x1|   |0|
  |0   0| |x2| = |0|
  Solving this system of equations, we get one eigenvector:
  X2 = [1, 1]
3. Since we have found two linearly independent eigenvectors (X1 and X2) and the matrix A is a 2x2 matrix, it is diagonalizable.
4. Construct matrix P:
  P = [X1, X2] = [[1, 1],
                  [0, 1]]
5. Find the inverse of matrix P:
  P⁻¹ = [[1, -1],
          [0,  1]]
6. Compute the diagonal matrix D:
  D = P⁻¹AP = [[2, 0],
                [0, 3]]
Therefore, the given matrix A is diagonalizable, and the matrix P such that P⁻¹AP = D is:
P = [[1, 1],
    [0, 1]]
D = [[2, 0],
    [0, 3]]

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Answer:

-1x -3

Step-by-step explanation:

(3x+4)+(-4x-7)

3x + 4 -4x -7

3x - 4x +4 -7

-1x -3

Answer:

Reflection and Translation

Step-by-step explanation:

1 is reflected to 2, and then 2 is translated to 3

Answer:

p = 2

Step-by-step explanation:

First, simplify:

3p = 6

Then, divide 3 on both sides:

p = 2

Hope this helps ^^

Answer:

p=2

Step-by-step explanation:

add -p to 4p and you get 3p

then divide both sides by 3 to get p alone so you get p=2 bc 6/3=2

Answer:

x ≈ 14.4 cm

Step-by-step explanation:

the third angle of the triangle = 180° - 40° - 46° = 94°

Using the Sine rule in the triangle

\(\frac{x}{sin46}\) = \(\frac{20}{sin94}\) ( cross- multiply )

x × sin94° = 20 × sin46° ( divide both sides by sin94° )

x = \(\frac{20sin46}{sin94}\) ≈ 14.4 cm ( to the nearest tenth )

Answer:

14 cm (rounded to nearest whole number)

Step-by-step explanation:

Law of Sine:

\(\displaystyle \large{\dfrac{\sin A}{a} = \dfrac{\sin B}{b} = \dfrac{\sin C}{c} = 2R}\)

Given angles are:

Definition of Euclidean Triangle:

Find another angle:

So another angle is 94°.

To find:

Determine:

Therefore:

\(\displaystyle \large{\dfrac{\sin 46^{\circ}}{x} = \dfrac{\sin 94^{\circ}}{20}}\)

Multiply both sides by 20x:

\(\displaystyle \large{\dfrac{\sin 46^{\circ}}{x} \cdot 20x = \dfrac{\sin 94^{\circ}}{20} \cdot 20x}\\\displaystyle \large{20\sin 46^{\circ}= x\sin 94^{\circ}}\)

Divide both sides by \(\displaystyle \large{\sin 94^{\circ}}\):

\(\displaystyle \large{\dfrac{20\sin 46^{\circ}}{\sin 94^{\circ}} = \dfrac{x\sin 94^{\circ}}{\sin 94^{\circ}}}\\\displaystyle \large{\dfrac{20\sin 46^{\circ}}{\sin 94^{\circ}} = x}\)

Evaluate the expression, hence:

\(\displaystyle \large{x = 14.42...}\)

Round to nearest whole number:

\(\displaystyle \large{x = 14}\)

Therefore, the value of x is 14 cm.

Answer:

192 servings in two gallons

Step-by-step explanation:

16 cups= 1 gallon

32 cups= 2 gallons

find the unit rate

1 cup: __ servings

4:24

divide by 4

1:6

multiply by 32

=32:192

192 servings

Answer: Needs more of an answer to explain

Step-by-step explanation:

Answer:

Chunkysdead Is the leader of this organization.

Step-by-step explanation:

Answer:

y=0.5x-7

Step-by-step explanation:

x-2y=8

2y=x-8

y=0.5x-4 m1=0.5

m1=m2=0.5 - the slope for parallel lines are equaly

y=m2x+b

-6=0.5*2+b

b=-7

y=0.5x-7

After adding bonus amount, the graph of an employee’s earnings is translated upward by 75 units.

In this question, we have been given the minimum wage for employees of a company is modeled by the function f(x)=7.25x

Let h(x) be a function that models how much employee earns after a signing bonus of $75

The wage for the employees after signing the bonus would be 7.25x + 75

so, h(x) = 7.25x + 75 is the required function.

Here x is the number of working days, it can not be negative but must be greater than or equal to zero.

The graph of functions f(x) and h(x) are shown below.

The blue line represents the graph of the function which models an employee’s earnings after a signing a bonus.

The graph of f(x) is translated upward by 75 units.

The initial value of graph of h(x) is (0, 75) This means even if the employee works 0 days, he will get $75

Therefore, after adding bonus amount, the graph of an employee’s earnings is translated upward by 75 units.

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The statement is false .Hence, the only true statement is that t(x) is a decreasing Function

The functions f(x) = 1/x² and t(x) = -1/(x+2)² are used to determine if the following statements are true or false.

Let us evaluate the statements and see whether they are true or false.

a) f(x) is an even function since f(-x) = f(x)The statement is false.

A function is said to be even if it satisfies f(x) = f(-x).

However, we can see that f(-x) = 1/(-x)² ≠ f(x) = 1/x².

Therefore, f(x) is not an even function.

b) t(x) is an even function since t(-x) = t(x)

The statement is false. We have, t(-x) = -1/(-x+2)² = -1/(x-2)², which is not equal to t(x) = -1/(x+2)².

Therefore, t(x) is not an even function.c) t(x) is a decreasing functionThe statement is true.

We say that a function is decreasing if it satisfies f(x) > f(y) when x < y. Differentiating t(x) using the chain rule, we have t'(x) = 2/(x+2)³ which is always negative since (x+2)³ > 0 for all x.

Hence, t(x) is a decreasing function.d) f(x) and t(x) intersect at x = −1

The statement is false.

We can find the point of intersection by equating f(x) and t(x) and then solving for x. 1/x² = -1/(x+2)².

On cross multiplying, we obtain (x+2)² = -x².

Expanding the squares gives 4x+4 = 0, which implies x = -1.

However, this value of x does not satisfy the original equation, hence there is no intersection point.

Therefore, the statement is false .

Hence, the only true statement is that t(x) is a decreasing function.

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The formula for the height of the banner in terms of the side length of the cardboard square, the height of the grandstand, and the distances from the person's eye level to the grandstand and the ground.

Mathematically, we can write this as:

(height of banner) / (distance from eye level to top of grandstand) = (side length of cardboard square) / (distance from eye level to bottom of square)

So, the distance from the eye level to the top of the grandstand is "s + h". We also know the distance from the person's eye level to the bottom of the square, which is "d₂ - d₁".

Putting all of this together, we can write:

(height of banner) / (s + h) = s / (d₂ - d₁)

To solve for the height of the banner, we can cross-multiply and simplify:

(height of banner) = (s² / (d₂ - d₁)) * (1 + h/s)

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Complete Question:

Zach wants to order a banner that will hang over the side of his baseball stadium grandstand and reach the ground. And then he needs to find the height for the banner so he uses a cardboard square to line up the top and bottom of the grandstand. Then he measures the distance from the grandstand and from the ground to his eye level.

Find height of the banner.

The general antiderivative of g(t) = (t + 1)³ is: (1/4)(t + 1)⁴ + C.

The general antiderivative of g(t) = (t + 1)³ with respect to t can be found using the power rule for integration.

According to the power rule, the antiderivative of tⁿ with respect to t is (1/(n + 1))t^(n + 1).

Applying the power rule to g(t), we have:

∫(t + 1)³ dt = (1/4)(t + 1)⁴ + C,

where C is the constant of integration.

The integral of g(t) is represented by the antiderivative of (t + 1)³ with respect to t.

By applying the power rule and simplifying the expression, we obtain the general antiderivative of g(t) as (1/4)(t + 1)⁴ + C.

The constant of integration, C, represents any arbitrary constant and accounts for the family of antiderivatives.

It allows for the inclusion of the various possibilities that satisfy the differential equation associated with the original function g(t).

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the radius of convergence (R) is ∞, and the interval of convergence (I) is (-∞, ∞).

To find the radius of convergence (R) and the interval of convergence (I) of the series given by:

∑ 7(-1)^(n-1) n^n x^n

We can apply the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is L as n approaches infinity, then the series converges absolutely if L < 1, diverges if L > 1, and the test is inconclusive if L = 1.

Let's apply the ratio test to the given series:

L = lim(n→∞) |(7(-1)^(n-1) (n+1)^(n+1) x^(n+1)) / (7(-1)^(n) n^n x^n)|

Simplifying and canceling out common factors:

L = lim(n→∞) |(7(n+1) x) / (n^n)|

Taking the absolute value:

L = lim(n→∞) |7(n+1) x / n^n|

Now, let's evaluate the limit:

L = |7x| lim(n→∞) (n+1) / n^n

The limit can be further simplified by applying the ratio test for the sequence:

lim(n→∞) (n+1) / n^n = 0

Therefore, the limit L simplifies to:

L = |7x| * 0 = 0

Since L = 0, which is less than 1, the ratio test indicates that the series converges absolutely for all values of x. Thus, the series converges for all x.

For a series that converges for all x, the radius of convergence (R) is infinite (∞), and the interval of convergence (I) is the entire real number line (-∞, ∞).

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Answer:

C) $90.48

Step-by-step explanation:

72.39*.2=14.478

72.39*.05=3.6195

14.478+3.6195=18.0975

18.0975+72.39=90.4875

Answer:

a = -3

Step-by-step explanation:

Step 1:  Since we're told that 5 to the power of a = 1/125, we can use the following equation to solve for a:

5^a = 1/125

Step 2:  Take the log of both sides

log(5^a) = log(1/125)

Step 3:  According to the power rule of logs, we can bring a down and multiply it by log(5):

a * log(5) = log (1/125)

Step 4:  Divide both sides by log(5) to solve for a:

(a * log(5) = log(1/125)) / log(5)

a = -3

Optional 5:  We can check our answer by plugging in -3 for a and seeing if we get 1/125 when completing the operation:

5^-3 = 1/125

1/(5^3) = 1/125 (rule of exponents states that a negative exponent creates a fraction with 1 as the numerator and the base (5) and exponent (-3 becoming 3) as the denominator

1/125 = 1/125

The solution of the integral is  (-π, π].

Yes, Cauchy’s theorem will be applied on it.

The integral we need to evaluate is ∮_C Ln(1-z)dz, where C is the boundary of the parallelogram with vertices ±i,±(1+i). To evaluate this integral, we need to use complex analysis, which is a branch of mathematics that deals with complex numbers and functions.

Ln(1-z) is not analytic at z=1, so we cannot use Cauchy's theorem directly. However, we can use a technique called branch cutting to transform the integral into one that can be evaluated using Cauchy's theorem.

We can define a branch of the logarithm function as Ln(z) = ln|z| + i arg(z), where arg(z) is the argument of z, which is the angle between the positive real axis and the line joining the origin to z. We can choose arg(z) to be in the range (-π, π].

We can then choose a branch cut for Ln(1-z) along the negative real axis, so that arg(1-z) lies in the range (-π, π].

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Answer:

As a decimal 0.5

as a percentage 50%

Solution

Step 1

A)The domain refers to all values of x for which the function remains defined. Any value of x that makes the function undefined is out of the domain. This can be achieved by factorizing the denominator of the known function to get the values of x that make the function undefined. All other values of x that make the function defined are part of the domain.

Step 2

B)Factorize the denominator

Hence factorizing further we will have

Hence, the domain of the function given is all real values of x except -3 and 5/6

Check the picture below.

\(tan(\theta )=\cfrac{\stackrel{opposite}{282}}{\underset{adjacent}{137}}\implies \theta =tan^{-1}\left( \cfrac{282}{137} \right)\implies \theta \approx 64^o\)

Make sure your calculator is in Degree mode.

Answer:

144

Step-by-step explanation:

3+15=18

18 multiply 8=144 is the height after 8 years

Answer:

2.35

Step-by-step explanation:

Answer:

2.35

Step-by-step explanation:

I hope this helps you!

The ball with the least mass will have the longest time of travel, while the one with the greatest mass will have the shortest time of travel.

When objects are thrown straight up, the gravitational force that pulls them down is opposed by their initial velocity. Thus, they rise for a time before falling back to the ground. The amount of time each ball stays in the air is determined by the balance between gravitational force and initial velocity, which is dependent on their respective masses.

Air resistance is negligible; thus, it will not have any impact on the time of travel of the four balls. Since the balls are thrown straight up, the initial velocity of all the balls is zero, and they start falling back the moment they reach their maximum height, where the velocity of the ball becomes zero again.

Since all four balls have the same size and different masses, the ball with the greatest mass will have the greatest weight or gravitational pull, resulting in it falling down first.

The ball with the least mass, on the other hand, will take the longest time to reach its maximum height and will stay in the air for a longer period of time. The time in the air will be calculated using the formula t = 2 * √(h / g), where t is the time of travel, h is the maximum height reached, and g is the acceleration due to gravity.

Hence, the ball with the least mass will have the longest time of travel, while the one with the greatest mass will have the shortest time of travel.

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