HELP!!


Given f(x)= x^2 -3 and g(x)= x+2/x , find (g-f)(4). Show all work.

Answer:

Step-by-step explanation:

The number 2145 is not even, so will not be divisible by 2 or 6. It ends in 5 so is divisible by 5. Its sum of digits is 12, which is divisible by 3, so the number is divisible by 3.

2145 is divisible by 3 and 5.

2.145 is divisible by all of these numbers:

  2.145/2 = 1.0725

  2.145/6 = 0.3575

  2.145/5 = 0.429

  2.145/3 = 0.715

_____

Here, we take the mixed number to be divisible if the decimal representation of the quotient is a terminating decimal fraction.

Answer:

$20 of credit left on the card

Step-by-step explanation:

If we say that the prepaid phone card has 25 minutes on it since Maya paid 25 dollars for it. We can multiply 25 times 4 which equals 1 dollar per 4 minutes. Then, we can divide 20 by 4 to get 5 which means that she used 5 dollars of call time. We can now subtract 25-5 and we get 20. This tells us that there is 20 dollars left on the card.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

b

Step-by-step explanation:

Answer:

1.5

Step-by-step explanation:

For the forecasting process to be effective, internal data should be highly disaggregated

Predicting the future based on historical and current facts is the forecasting process. The most popular method for doing this is trend analysis. It is typically ideal to use internal data that is significantly disaggregated for forecasting to be successful. This means that rather than aggregating or summarizing the data at a high level, it should be broken down into as much detail as feasible.

Since highly disaggregated data presents a more complete and precise picture of the variables that may impact future events, forecasting can be done more accurately and dependably. This can include information about previous sales, manufacturing rates, inventory levels, costs, and other elements that can be important for forecasting. Whereas, using highly aggregated data can lead to less accurate and reliable forecasts, as it may not capture the full range of factors that may influence future outcomes.

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The required value of the given function are, as follows:

\(f_x\) = [ y(x-y)/(1 + x²y²) - arc tan(xy) ] / (x-y)²

\(f_y\) = [x(x-y)/ (1 +x²y²) + arc tan(xy)] / (x-y)²

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The given function is as follows:

f(x,y) = arc tan (xy) / (x-y)

We know that derivative of arc tan(x) = 1/(1+x²)

To differentiate arctan(xy), we use the chain rule:

U/V = V U' - U V' / V²

f(x,y) = arc tan (xy) / (x-y)

a)

\(f_x\) = derivative with respect to 'x' and we get:

\(f_x\) = (x-y) * [1/(1+(xy)²) ]y - arc tan(xy) 1 / (x-y)²

\(f_x\) = [ y(x-y)/(1 + x²y²) - arc tan(xy) ] / (x-y)²

b)

\(f_y\) = derivative of f(x,y) with respect to 'y' and we get:

\(f_y\)= (x-y) * [1/(1+(xy)²) ]*x - arc tan(xy) *(-1) / (x-y)²

\(f_y\) = [x(x-y)/ (1 +x²y²) + arc tan(xy)] / (x-y)²

Thus, the required value of the given function are, as follows:

\(f_x\) = [ y(x-y)/(1 + x²y²) - arc tan(xy) ] / (x-y)²

\(f_y\) = [x(x-y)/ (1 +x²y²) + arc tan(xy)] / (x-y)²

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The complete question as follows:

For the function: f (x y) = arctan(xy )/ ( x - y ) ,

Find

a. \(f_x\)

b. \(f_y\)

Responder:

x=6

espero haber ayudado

Answer:

90 square feet.

Step-by-step explanation:

Let's set up an equation!

SA= 2(xy)+2(xz)+2(yz).

Lets say that x=3 y=6 and z=3

We plug it in.

2(18)+2(9)+2(18)= SA

36+18+36=SA

72+18=SA

90=SA

90 square feet = Surface area.

You can identify that the number given in the exercise is a Decimal Number because it has a decimal point.

Then, to convert to a Mixed Number, you can follow the steps shown below:

1. Identify the decimal part of the number and the whole part.

2. Separate them using the symbol + :

2. Let's focus on the decimal part. Write 1 is its denominator:

3. To express the numerator as an Integer, multiply the numerator and the denominator by 100 (to move the decimal point to places to the right):

4. Reduce the fraction:

5. Now you can write the Mixed Number as follows:

Therefore, the answer is:

Answer:

6 $50 bills and 9 $5 bills

Step-by-step explanation:

Let's let x = the number of $5 bills, and y = the number of $50 bills. With this, we can set up two equations:

5x + 50y = 345

x + y = 15

Because there is $345 total in the register, that means that 5 times the number of $5 bills plus 50 times the number of $50 bills would equal 345. And there are 15 bills total, so the numbers added is 15. Now, we can solve these equations through substitution:

x + y = 15

x = 15 - y

Now, plug in (15 - y) for x into the other equation, and solve for y:

5(15 - y) + 50y = 345

75 - 5 y + 50y = 345

75 + 45y = 345

45y = 270

y = 6

Since y is 6, that means we have 6 $50 bills. And there are 15 bills total, so there are 9 $5 bills. (15 - 6 = 9)

Answer:

x=-5,6

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

Answer:

1, -6

Step-by-step explanation:

Since there are alike numbers, add them together.

4x+x= 5x

Now the function is: f(x)= \(x^{2}\)+5x-6

The function is in  \(a^{2}\)+bx+c form.

So find the factors of a x c = b.

Factors of -6(a) that fits (b)5 is (-1,6).

Then you just factor it:

f(x)= \(x^{2}\)+5x-6

(x-1)(x+6)

x-1= 0  x+6=0

 +1 +1     -6  -6

x=1      x=-6

Those are the real zeroes: 1, -6

Using it's concept, it is found that the probability that a randomly selected student is in music/drama is:

P(Music/Drama) = 0.25.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, the number of students is given by:

N = 20 + 7 + 3 + 20 + 13 + 2 + 25 + 5 + 5 = 100.

Of those, the number involved in music/drama is:

D = 7 + 13 + 5 = 25.

Hence the probability is given by:

p = 25/100 = 0.25.

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Answer:

(-3 , -7)

Step-by-step explanation:

The values of (a + b)(a - b) is a²-b² = (a-b) (a+b) and (x+7)² is x² + 14x+49 =  (x+7)(x+7)

Any equation using the formula ax² + bx + c = 0 is a quadratic equation.

where a, b and c are constants, and x is an unknown variable.

It is called "quadratic" because the variable is squared (in other words, raised to the power of 2).

The most common way to solve a quadratic equation is to factor it into two linear equations, which can then be solved using the methods of linear algebra.

Another way is to use the quadratic formula, which expresses the roots of the equation in terms of the coefficients a, b and c.

It is called a quadratic equation because it can be written in the form

ax² + bx + c = 0

which is the standard form for a quadratic equation.

Examples:

1) x² + 4x – 5 = 0

2) 4x² – 7x + 3 = 0

3) 2x² + 3x – 4 = 0

Therefore , The values of (a + b)(a - b) is a²-b² = (a-b) (a+b) and (x+7)² is x² + 14x+49 =  (x+7)(x+7)

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As per given by the question,

There are given that a circle for finding the arc AD.

Now,

And,

Then,

The total sum of the semicircle is 180 degree.

So,

Then,

So,

x - 2 < 5   ⇒   x < 7

x + 7 > 6   ⇒   x > -1

Together, we have -1 < x < 7, which in set notation is

\(\left\{x \mid -1 < x < 7\right\}\)

(third choice)

The 6th partial sum of the geometric sequence is 63/4.

To find the 6th partial sum of a geometric sequence, we first need to determine the common ratio (r) of the sequence.

Given that the 1st term (a₁) is -1/4 and the 8th term (a₈) is -1/512, we can use these values to find the common ratio.

We have the formula for the nth term of a geometric sequence:

aₙ = a₁ * r^(n-1)

Using this formula, we can write two equations based on the given information:

a₈ = a₁ * r⁸⁻¹

-1/512 = -1/4 * r⁷

Simplifying the equation:

r⁷ = (1/4) / (1/512)

r⁷ = (1/4) * (512/1)

r⁷ = 128

r = ∛(128)

r = 2

Now that we have the common ratio (r = 2), we can find the 6th partial sum (S₆) using the formula:

Sₙ = a₁ * (1 - rⁿ) / (1 - r)

Plugging in the values:

S₆ = (-1/4) * (1 - 2⁶) / (1 - 2)

S₆ = (-1/4) * (1 - 64) / (-1)

S₆ = (-1/4) * (-63) / (-1)

S₆ = 63/4

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Answer:

B. -1; C. -6; D. -7; E. -3

Step-by-step explanation:

Given the inequality, \( 3x - 1 \) > \( -7 \), solve to find the possible values of the solution as follows:

\( 3x - 1 \) > \( -7 \)

Add 1 to both sides of the inequality

\( 3x - 1 + 1 \) > \( -7 + 1 \)

\( 3x \) > \( -6 \)

Divide both sides by 3

\( \frac{3x}{3} \) > \( \frac{-6}{3} \)

\( x \) > \( -2 \)

This means the values of x are greater than -2, therefore, the solution of these inequality includes all values that rangers from -1 and above. Therefore, -1, -6, -7, -3 are all solutions to the inequality.

The restricted domain of the function is 0≤s≤25

The equation is a(s) = 37.5s - 1.5s²  models the function represented in the table

a(s) = s(37.5 - 1.5s)

The critical points are s=0 or

37.5 - 1.5s

37.5 = 1.5s

s=25

As area can not be negative, the area should be positive

s< 0 and s>25

Therefore, restricted domain is 0≤s≤25

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Answer:

The answer is B.

Step-by-step explanation:

Given that the total angle in a triangle is 180°. So in order to find x, you have to subatract 95° and 57° from 180°

\(x + 95 + 57 = 180\)

\(x = 180 - 95 - 57\)

\(x = 28\)

In order to explain why -4 - 2 equals -8, let's start with the equation 0.2 = 0. By analyzing this equation, we can uncover the reason behind this seemingly counterintuitive result.

1. Begin with the equation 0.2 = 0.

2. Subtract 0.2 from both sides of the equation to isolate the variable: 0.2 - 0.2 = 0 - 0.2.

  This simplifies to 0 = -0.2.

3. Observe that the right side of the equation, -0.2, is a negative number.

4. Recall that subtracting a negative number is equivalent to adding its positive counterpart. Therefore, -0.2 is the same as +0.2.

5. Rewrite the equation as 0 = +0.2.

6. Notice that 0 on the left side of the equation is equal to 0 + 0, since any number added to zero remains unchanged.

7. Substitute 0 + 0 for 0 in the equation: 0 + 0 = +0.2.

8. Simplify the equation to 0 = +0.2.

9. Finally, recognize that a positive number cannot equal zero. Hence, the equation 0 = +0.2 is false.

10. As a result, the original equation 0.2 = 0 is invalid.

11. Therefore, the logical consequence is that any subsequent deductions based on this invalid equation would also be incorrect.

12. Consequently, -4 - 2 does not equal -8, as per the explanation derived from the flawed equation.

To summarize, by analyzing the equation 0.2 = 0, we can determine that subsequent deductions based on this equation are incorrect. Hence, -4 - 2 does not equal -8.

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Step-by-step explanation:

the volume of a regular shape like a cylinder is

ground area × height.

the ground area is the area of a circle.

the area of a circle is

pi × r²

r is half of the diameter, so, 17/2 = 8.5 ft

so, the volume is

pi × (8.5)² × 50 = 3.14 × 72.25 × 50 = 11,343.25 ft³

rounded to the nearest whole number

11,343 ft³

Given: A speed of 15 meters per seconds

To Determine: The equivalent expression for the speed in kilometers per hour

Solution

Please note that 1000 meters is equivalent to 1 kilometers

Also, 1 minutes is equivalent to 60 seconds, and 1 hour is equivalent to 60 minutes

Hence, the expression to express 15 meters per second in kilometers per hour is

From the given options, the correct answer is circled and ticked as shown below

Answer:

6x

take sqrt of 36 which is x and x^2 becomes x. there you go

Answer:

\(r \geqslant - 16\)

Step-by-step explanation:

\( \frac{ - 10 + r}{2} \geqslant - 13\)

multiply both sides by 2:

\( - 10 + r \geqslant - 26\)

add 10 on both sides:

\(r \geqslant - 16\)

Answer:

\(r \ge -16\)

Step-by-step explanation:

To solve any equation/inequality:

1. get the variable to show up exactly once

2. isolate it

\(\frac{-10+r}{2} \ge -13\)

Multiply both sides by 2 and simplify (note that we're multiplying by a positive, not a negative, so the direction of the inequality stays the same, whereas multiplying or dividing by a negative would have changed the direction of the inequality)

\(\frac{-10+r}{2} *2 \ge -13 *2\)

\(-10+r \ge -26\)

Add 10 to both sides, and simplify

\((-10+r)+10 \ge (-26)+10\)

\(r \ge -16\)

Answer:

81

Step-by-step explanation:

2

27

x 3

------

8 1

Answer:

81

Step-by-step explanation:

27 × 3

81