Find the tangent line of xlog(x), when x=10

The value of a that makes u parallel to v is a = 4 and  the value of a that makes u perpendicular to v is -7.

a. For two vectors to be parallel, their direction ratios must be equal. In other words, their components must have the same ratio. For vectors u = (a, 7) and v = (4, 4), we have:

u1/u2 = a/7 = v1/v2 = 4/4

So the value of a that makes u parallel to v is a = 4.

b. For two nonzero vectors to be perpendicular, their dot product must be equal to zero. The dot product of u = (a, 7) and v = (4, 4) is given by:

u · v = a * 4 + 7 * 4 = 4a + 28

To make this equal to zero, we can solve for a:

4a + 28 = 0

4a = -28

a = -7

So the value of a that makes u perpendicular to v is -7.

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Answer:

AB=12 AD= 27

Step-by-step explanation:

According to the solution we have come to find that, the man's tax rate is 38.98%.

Tax rate is the percentage of income or value of goods and services that is paid as tax. It is the ratio of the tax paid to the taxable income or value of goods and services.

The man's taxable income is equal to his total income minus his tax-free allowance:

Taxable income = $9,000 - $3,100 = $5,900

We also know that he paid $2,300 in tax. The tax rate can be calculated as follows:

Tax rate = (Tax paid ÷ Taxable income) x 100%

Tax rate = ($2,300 ÷ $5,900) x 100%

Tax rate = 38.98%

Therefore, the man's tax rate is 38.98%.

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The Fourth Choice

\(x > -7\)

Please refer to the attached image for the graph

Given:

\(2x +5 > -9 \text{ or } -3x +2 < 14\)

Let's solve for the \(2x +5 > -9\) part of the Compound Inequality first.

\(2x +5 > -9 \\ 2x > -9 -5\\ 2x > -14 \\ x > \frac{-14}{2} \\ x > -7\)

Now, let's solve \(-3x +2 < 14\):

\(-3x +2 < 14 \\ -3x < 14 -2\\ -3x < 12 \\ x > \frac{12}{-3} \\ x > -4\)

We can now rewrite our Compound Inequality as \(x > -7 \text{ or } x > -4\). However, we can further simplify it by rewriting it as \(x > -7\) only since the values \(-7 < x \leqslant -4\) are already greater than \(-7\) anyway.

Using the power reducing formulas the expression \(5cos^4(x) = 5(1 + cos(2x))^{2/4}\).

We can define higher powers of a trigonometric function in terms of lower powers of the same function using the power-reducing formulas, which are trigonometric identities. Higher powers of cosine can be expressed using this formula in terms of sine and cosine's initial powers. For the other trigonometric functions, such as sine and tangent, there are equivalent formulas. These formulas can be used to solve trigonometric equations and to simplify trigonometric expressions.

The given function is 5cos^4(x).

Now, the power reducing formulas are given by:

\(cos(2x) = cos^2(x) - sin^2(x) = 2cos^2(x) - 1\\cos^2(x) = (1 + cos(2x))/2\)

Substituting the value of second equation in 1 we have:

cos(2x) = 2(1 + cos(2x))/4 - 1

\(cos(2x) = (2cos^2(x) - 1) = cos^2(x) - sin^2(x)\)

Now we have:

\(cos^2(x) = (1 + cos(2x))/2\)

Thus,

\(cos^4(x) = (1 + cos(2x))/2)^2\)

Now multiplying by 5:

\(5cos^4(x) = 5(1 + cos(2x))^{2/4}\)

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The number of rows and columns in the specified matrix and the matrix element are; 2 rows and 3 columns, the correct option is therefore;

a. 2 × 3; 1, which is option A

The common form of denoting the elements in a matrix is by using a letter and two subscripts in the form; A\(_{ij}\).

The specified matrix can be presented as follows;

\(\begin{bmatrix}-4 &1 &-3 \\ 2& 1& 0 \\\end{bmatrix}, a_{12}\)

The size of a matrix is indicated by the number of rows and columns in the matrix. The size of a matrix is usually indicated as m × n where;

m × n = Number of rows × Number of columns

Where;

m = The number of rows

n = The number of columns

The number of rows in the specified matrix are two rows

The number of columns in the matrix are three columns

The size of the specified matrix therefore is; 2 × 3

The position of a matrix element is similarly indicated by two subscripts, the first indicating the row number of the element and the second indicating the column number of the matrix.

Therefore;

a₁₂ is the element in the first row and in the second column, which is the number 1

The correct option is therefore;

a. 2 × 3; 1

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Step-by-step explanation:

x = number of cards

the production costs (PC) per day are

PC(x) = 264 + 1.1x

the sales (S) are

S(x) = 5.1x

the profit (P) per day is sales minus costs

P(x) = S(x) - PC(x) = 5.1x - (264 + 1.1x) =

= 5.1x - 264 - 1.1x = 4x - 264

we need to find the value of x, so that P(x) = 52.

52 = 4x - 264

316 = 4x

x = 316/4 = 79

79 cards must be delivered daily to make a profit of $52.

Answer:

-3

Step-by-step explanation:

x - (x+3)

x - x -3

-3

Hubble's constant in units of km/s/million LY is approximately 21.47.

what is  approximately ?

Approximately means close to or nearly, but not exactly. It is used to indicate that a value or number is an estimation or approximation, rather than an exact value. It is often used when a precise value is not necessary or when the exact value is unknown or difficult to determine.

In the given question,

To convert Hubble's constant from km/s/Mpc to km/s/million LY, we need to multiply it by a conversion factor that accounts for the difference in distance units. We can use the fact that 1 Mpc is equal to 3.26 million LY:

1 Mpc = 3.26 million LY

Therefore, to convert Hubble's constant from km/s/Mpc to km/s/million LY, we can use the following conversion factor:

1 Mpc / 3.26 million LY

Multiplying Hubble's constant by this conversion factor gives:

H = 70 km/s/Mpc x (1 Mpc / 3.26 million LY) = 21.47 km/s/million LY

Therefore, Hubble's constant in units of km/s/million LY is approximately 21.47.

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The best statement that describes the amount of water in the pool is that it is decreasing during the time interval 4. That is option 3.

To determine the time interval of the water in the pool the following is carried out.

At 0 hour, the water is at the level of = 40 gallons

At 1 hour, the water decreased to = 25 gallons.

At 2 hours, the water decreased to = 10 gallons.

The water remained at a constant level till 4 hours.

Therefore, the amount of water in the pool is that it is decreasing during the time interval 4.

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Answer:

cos44=b/h

0.7193=x/11

x=0.7193×11=7.913=8ft is your answer

Answer:

the answer is D. F(x) = 1/x(x-3)

Step-by-step explanation:

Answer: The answer is A

Step-by-step explanation:

Two stockpots are similar cylinders. The smaller stockpot has a height of 10 inches and a radius of 2.5 inches, the volume of larger one is 628.32 cubic inches.

We know that, to find volume:

Volume = π * \(r^2\) * h

For the smaller stockpot:

Radius (r) = 2.5 inches

Height (h) = 10 inches

Volume = π * (2.5)² * 10 ≈ 196.35 cubic inches

For the larger stockpot:

Radius (r) = 2.5 inches

Height (h) = 16 inches

Volume = π * (2.5)² * 16

             ≈ 628.32 cubic inches

Thus, the volume of larger one is 628.32 cubic inches.

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Answer: the answer is x=72

Step-by-step explanation:

Step 1: simplify both sides we know 15=x/4 -3 (the x holds a invisible 1)

the equation should look something Like: 15=1/4x-3 then FLIP the equation such as:

1/4x-3=15 then add 3 on both sides so 15+3=18

step 2: our equation is now 1/4x=18  (we see 4 is being divided the opposite of division is multiply) therefor multiply the 18 with 4

18*4=72 which means x=72

Answer:

28

Step-by-step explanation:

So 1% of 350 would be 3.5 because 350 divided by 100 is 3.5. You then get 3.5 and multiply it 8 times, which would be 28. (You multiply it 8 times because 8% is 8 times 1%.)

Answer:

this is hard i think its is 28

Step-by-step explanation:

because i put 128 and got it correct

Answer:

bru tell me why i cant see that

Step-by-step explanation:

Answer:

The correct answer is C) Completing the square.

Step-by-step explanation:

In the first step of the derivation, the left-hand side of the equation is the standard form of a quadratic equation, with the variable x raised to the second power and the coefficient of x being 1. In the second step, the expression on the left-hand side is rewritten as the square of a binomial, with the constant term b/2a added to the binomial. This process of adding the constant term and then squaring the resulting binomial is called "completing the square." By completing the square, it is possible to rewrite the original quadratic equation in a form that can be easily solved using the quadratic formula.

3 arrows pointing up

because its like 123454321

Answer: A,E or F.

Step-by-step explanation: That's the only ones that have X's and then x is 0

3.1.1 The basic property of operations used is the commutative property of multiplication.

3.1.2 The basic property of operations used is the additive inverse property.

3.1.3 The basic property of operations used is the associative property of addition.

3.1.1 The basic property of operations used in this calculation is the commutative property of multiplication. It states that the order of the factors in a multiplication problem can be rearranged without changing the product. In this case, the numbers 25 and 4 were swapped, resulting in the same product of 100.

3.1.2 The basic property of operations used in this calculation is the additive inverse property. It states that for any number, there exists an additive inverse such that when the number and its additive inverse are added together, the result is zero. In this case, adding 412 and its additive inverse (-412) results in zero.

3.1.3 The basic property of operations used in this calculation is the associative property of addition. It states that the grouping of numbers being added does not affect the sum. In this case, the numbers 25, 37, 20, 5, 30, and 7 were regrouped to facilitate easier mental addition. By grouping 25 and 37, and then grouping 20, 5, 30, and 7, the final sum of 62 is obtained, which is the same as adding all the numbers together in the original order.

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The solution to the original equation is 1, 1/6

Equations are expressions separated by mathematical operations.

Given the equation below

x/x − 1 = 6x + 1/x − 1

From the given expression, the least common denominator is x -1

Multiply both sides by x-1 to have;

x = 6x(x-1) +1

Expand

x = 6x^2-6x + 1

Equate to zero

6x^2-6x-x + 1 = 0

6x^2-7x +1= 0

The resulting quadratic equation in general form is 6x^2-7x +1 = 0

Factorize

6x^2 -6x-x + 1 = 0

Group the result

6x(x-1)-1(x-1) = 0

(6x-1)(x-1) = 0

6x - 1 = 0 and x -1 = 0

x = 1 and 1/6

Hence the solution to the original equation is 1, 1/6

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Randy paid $16,111.75 of federal income tax on his taxable income last year.

What is arithmetic?

Arithmetic is a branch of mathematics that deals with the study of numbers, their properties, and their manipulation using basic operations such as addition, subtraction, multiplication, and division.

To find out how much federal income tax Randy paid on his taxable income of $64,447.00 at a tax rate of 25%, we can use the formula:

Tax amount = Tax rate x Taxable income

Plugging in the values we get:

Tax amount = 0.25 x $64,447.00

Tax amount = $16,111.75

Therefore, Randy paid $16,111.75 of federal income tax on his taxable income last year.

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Answer:

17.32 meters

Step-by-step explanation:

Let’s call the height of the tower H. The distance from the point to the base of the tower is 10 m. The angle of elevation from the point to the top of the tower is 60 degrees.

Using trigonometry, we can calculate that:

tan (60) = H / 10

H = 10 * tan (60)

H = 10 * √3

H = 17.32 m

Therefore, the height of the tower is 17.32 meters.

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The equation that could be used to determine x, the number of purses Paula must sell to pay for the new equipment is;

A. 5.00x - 2.25x = 5000

We are told the materials costs $2.25 per purse.

She sells the materials for $5 each.

If the number of materials she purchased was x, it means that;

Selling price - Cost price = 5.00x - 2.25x

Now, we are told that she wants to invest $5000 for some new equipment. This means that she must realize at least $5000 in profit from the sales she is making of the materials.

Since the formula for profit is;

Profit = Selling Price - Cost Price

Then, we will have;

5.00x - 2.25x = 5000

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Answer:  5.00x - 2.25x = 5000

Step-by-step explanation:

The slope which shows  the cost per guest is $35 per guest

The given cost for 50 guests is $2150.

The cost for 75 guests is $3025.

It can also be represented as:

(Guest, Cost) =(50, $2150) & (75, $3025)

The slope can now be calculated as

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (50, $2150) & (75, $3025)

Substituting the given values in the equation as follows:

Slope = (3025 - 2150)/(75 - 50)

Slope = 35

Hence, the slope is $35 per guest.

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Answer:

A  , B, and C

Step-by-step explanation:

i just did it