HELP!! Find (ƒ – g)(x) if f(x) = 4x² – 5x and g(x) = 3x² + 6x − 4.
-
○ (ƒ − g)(x) = −x² + 11x − 4
○ (ƒ − g)(x) = −x² — x^4
○ (ƒ − g)(x) = 7x² + x − 4
○ (ƒ − g)(x) = x² − 11x +4

c) 2x^-3 + 5x^-1 - x

A polynomial is a mathematical expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication, and raised to non-negative integer powers.

Answer:

Only the (a) and (c) can be classified as polynomials here.

Reason is that  a polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, but not division by a variable. A polynomial can have one or more terms, where each term contains a product of a coefficient and a variable raised to a non-negative integer power. For example, 2x^3 + 5x^2 - 3x + 7 is a polynomial with four terms.

look up for a general expression for a polynomial for more info :

https://en.wikipedia.org/wiki/Polynomial

The selection of the appropriate immune suppressant is made by healthcare professionals based on the specific needs of each patient.

The most commonly used immune suppressant in medical practice is a medication called "cyclosporine." Cyclosporine belongs to a class of drugs known as calcineurin inhibitors and is primarily used to prevent organ transplant rejection.

The activity of T-cells, which are a type of immune cell involved in the body's immune response.

Cyclosporine is also used in the treatment of various autoimmune diseases, such as rheumatoid arthritis and psoriasis, where the immune system mistakenly attacks the body's own tissues.

T-cell activity, cyclosporine helps to reduce the inflammatory response and prevent further damage to the affected organs or tissues.

It's important to note that there are several other immune suppressants available, and the choice of medication depends on the specific condition being treated, the patient's overall health, and individual factors.

A commonly used immune suppressants include corticosteroid methotrexate, azathioprine, mycophenolate mofetil, and tacrolimus.

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Complete question:

While studying the T- and B-cell immune suppressors, the nursing students learn that the most commonly used immune suppressant is what?

The intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

To show that a1 ≤ a2 ≤ ... ≤ an ≤ ..., we need to use the fact that the sequence of intervals is nested, meaning that each interval is contained within the next one.

First, we know that I1 contains I2, so every point in I2 is also in I1. That means that a1 ≤ a2 and b1 ≥ b2.

Now consider I2 and I3. Again, every point in I3 is also in I2, so a2 ≤ a3 and b2 ≥ b3.

We can continue this process for all the intervals in the sequence, until we reach In. So we have:

a1 ≤ a2 ≤ ... ≤ an-1 ≤ an

and

b1 ≥ b2 ≥ ... ≥ bn-1 ≥ bn

This shows that the endpoints of the intervals are ordered in the same way.

Given that I₁ ⊇ I₂ ⊇ ... In ⊇ ... is a nested sequence of intervals and In = [an; bn], we can show that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... as follows:

Since the intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

Continuing this pattern for all intervals in the sequence, we can conclude that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... .

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Answer:

the answer is3xy+9-4x. -3x+3xy

Answer:

3xy+9-4x-7+x. -2x+3xy-(x-2)

=3xy+(9-7)+(-4x+x). = -2x+3xy-x+2

=3xy+2-3x. = (-2x-x)+3xy+2

= -3x+3xy+2

Answer:

10.59%

Step-by-step explanation:

percentage of change is given by

{(old number - new number)/old number} * 100

_________________________

given

no. of student  went to the first school dance = 340

no. of student  went to the last school dance = 306

Percentage of change between two dance

= ((no. of student  went to the first school dance - no. of student  went to the last school dance)/ no. of student  went to the fist school dance)*100

= (340 - 306)/340 *100

= (36/340 )*100 = 10.59%

The percent of change between the two dances 10.59%.

56/120

Step-by-step explanation:

The body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

To express the body mass of the man's two children in terms of their father's body mass, we can use the given ratios.

Let the body mass of the man be x kg.

The first child's body mass is five-sixths of their father's body mass:

Body mass of the first child = (5/6) * x

= 5x/6 kg.

The second child's body mass is four-fifths of their father's body mass:

Body mass of the second child = (4/5) * x

= 4x/5 kg.

Therefore, the body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

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We have two points of the line, and we have to find the equation of the line in the slope-intercept form:

First, we find the slope as:

With the value of the slope, we can calculate b replacing the values of x and y with one of the know points:

Now, we have the two parameters (slope and y-intercept) to define the line, and we can write the equation as:

Answer:

28deg

Step-by-step explanation:

sin x deg = 15/32

x = sin^-1 (15/32) = 27.953 (3dp) = 28 (nearest deg)

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In a parallelogram, opposite sides are equal. Therefore, AB = CD.

5x * 3 = 15 * x

15x = 15

x = 1

Therefore, the value of x is 1.

To find the area of parallelogram ABCD, we can use the formula A = base x height, where the base is the length of side AB and the height is the perpendicular distance between side AB and the opposite side CD. Since the height of parallelogram ABCD is given as 6, we need to find the length of side AB.

From the given information, we know that AB = 5x * 3, where x = 1. Therefore, AB = 15. Now we can calculate the area of parallelogram ABCD as:

A = base x height

A = 15 x 6

A = 90 square units

Therefore, the area of parallelogram ABCD is 90 square units.

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A spherical astroid has a radius of approximately 8.5 x 10^2 m. Using  the formula 4/3 π r^3 to find the approximate volume of the asteroid, we get volume = 2.57 x 10^9 m^3.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

a spherical astroid has a radius of approximately 8.5 x 10^2 m.

we know,

the volume =  4/3 π r^3

so, by calculating, we get.

volume = 2.57 x 10^9 m^3

Hence, a spherical astroid has a radius of approximately 8.5 x 10^2 m. Using  the formula 4/3 π r^3 to find the approximate volume of the asteroid, we get volume = 2.57 x 10^9 m^3.

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Answer:

If f(x)=x^3, evaluate f(x+h)-f(x)÷h, Where h* 0. Use your result to find the derivative of f(x) with respect to x. Differentiate with respect to x (x²-3x+5)(2x-7) .Find with respect to x the derivative of sinx ÷1– cosx​

Step-by-step explanation:

We are given f(x) = x^3. We need to find the value of (f(x+h) - f(x))/h.

f(x+h) = (x+h)^3 = x^3 + 3x^2h + 3xh^2 + h^3

Therefore, (f(x+h) - f(x))/h = [x^3 + 3x^2h + 3xh^2 + h^3 - x^3]/h

= 3x^2 + 3xh + h^2

Taking the limit of the above expression as h approaches 0, we get:

lim(h→0) [(f(x+h) - f(x))/h] = 3x^2

Therefore, the derivative of f(x) = x^3 with respect to x is 3x^2.

Next, we need to differentiate (x^2-3x+5)(2x-7) with respect to x.

Using the product rule, we get:

d/dx [(x^2-3x+5)(2x-7)] = (2x-7)(2x-3) + (x^2-3x+5)(2)

Simplifying, we get:

d/dx [(x^2-3x+5)(2x-7)] = 4x^2 - 20x + 11

Therefore, the derivative of (x^2-3x+5)(2x-7) with respect to x is 4x^2 - 20x + 11.

Finally, we need to find the derivative of sin(x)/(1-cos(x)) with respect to x.

Using the quotient rule, we get:

d/dx [sin(x)/(1-cos(x))] = [(1-cos(x))cos(x) - sin(x)(sin(x))]/(1-cos(x))^2

Simplifying, we get:

d/dx [sin(x)/(1-cos(x))] = cosec(x/2)^2

Therefore, the derivative of sin(x)/(1-cos(x)) with respect to x is cosec(x/2)^2.

The three third roots of the complex number -1 + 4i, expressed in polar form with angles in ascending order (in radians), are:

∛17  (cos(-0.441) + i sin(-0.441)) , ∛17 (cos(1.201) + i sin(1.201)) , ∛17  (cos(2.842) + i sin(2.842))

To find the third roots of the complex number -1 + 4i, we can represent the number in polar form and use De Moivre's theorem.

First, let's find the magnitude and argument of the complex number. The magnitude, denoted as r, is given by the formula r = √(a² + b²), where a and b are the real and imaginary parts, respectively. In this case, a = -1 and b = 4, so r = √((-1)² + 4²) = √(1 + 16) = √17.

The argument, denoted as θ, can be found using the formula θ = arctan(b/a). In this case, θ = arctan(4/(-1)) = arctan(-4) = -1.3258 radians (approximately).

Now, we can express the complex number -1 + 4i in polar form as z = √17 (cos(-1.3258) + i sin(-1.3258)).

To find the third roots, we need to take the cube root of the magnitude and divide the argument by 3. Let's call the cube root of the magnitude as r^(1/3) and the angle divided by 3 as θ/3.

The three third roots are then given by:

r^(1/3)  (cos(θ/3) + i sin(θ/3))

r^(1/3)  (cos((θ + 2π)/3) + i sin((θ + 2π)/3))

r^(1/3)  (cos((θ + 4π)/3) + i sin((θ + 4π)/3))

So, the three third roots of -1 + 4i in polar form, with angles in ascending order (in radians), are given by the above expressions.

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The output of the statement: cout << pow(2.0, pow(3.0, 1.0)) << endl; is

c. 8.0.

Given statement:

output :

The output of a computer or word processor is the information that it displays on a screen or prints on paper as a result of a particular program.

cout << pow ( 2.0 , pow ( 3.0 , 1.0 )) << endl;

= pow ( 3.0 , 1.0 )

= 3^1

= 3.0

cout << pow ( 2.0 , 3.0 ) << endl;

= pow ( 2.0 ,3.0 )

= 2.0^3.0

= 8.0

Therefore The output of the statement: cout << pow(2.0, pow(3.0, 1.0)) << endl; is  c. 8.0.

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Answer:

The answer is B. The sample was biased because the survey was only given to a select group (the males). An unbiased sample would be a large group of random people (all genders included).

Answer:

B

Step-by-step explanation:

It is wat is is my boy

Answer:

39.50

Step-by-step explanation:

If the new tub has the same cylindrical shape, with a radius that is twice as large and a height that is 20 % taller, then the volume of bigger tub is 3.8 times greater.

The volume of a cylinder is given by the formula:

V = πr^2h

where V is the volume, r is the radius, and h is the height of the cylinder.

Let the current hot tub have radius r and height h, so its volume is:

V1 = πr^2h

The new hot tub has a radius that is twice as large, which means the new radius is 2r. The height is 20% taller than the current height, which means the new height is (1 + 0.2)h = 1.2h. So, the volume of the new hot tub is:

V2 = π(2r)^2(1.2h) = 4πr^2(1.2h) = 4.8πr^2h

The difference in volume between the new and current hot tubs is:

V2 - V1 = 4.8πr^2h - πr^2h = 3.8πr^2h

So the volume of the new hot tub is 3.8 times greater than the volume of the current hot tub. Therefore, the volume of the bigger tub is 3.8 times greater than the volume of the smaller tub.

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Answer:

39 gym, 21 pool, 19 track.

Step-by-step explanation:

Subtract these from the 3 sports areas

15 people use the gym and the pool.

14 people use the pool and the track.

10 people use the gym and the track.

1 person uses all three facilities.

gym. 65-15-10-1=39

pool. 51-15-14-1=21

track. 44-14-10-1=19

Answer:

y= -10x + 5

Step-by-step explanation:

i did some math

The numbers of the jerseys of 5 randomly selected Carolina Panthers would fall under the category of quantitative discrete data.

Quantitative data are numerical measurements or counts that can be added, subtracted, averaged, or otherwise subjected to arithmetic operations. Discrete data, on the other hand, can only take on specific, whole number values, as opposed to continuous data which can take on any value within a range.

Qualitative data, on the other hand, are non-numerical data that cannot be measured or counted numerically. Examples include colors, names, opinions, and preferences. Since the numbers of the jerseys are specific numerical values, they are considered quantitative data.

Since they can only take on specific, whole number values (i.e. the jersey numbers are not continuous values like weights or heights), they are considered discrete data. Therefore, the correct option for the given question is option "quantitative discrete".

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The interest rate would be = 8.9%

An interest rate is defined as the percentage of money that should be received by an individual for a particular period of time following an investment made.

The principal amount (p) = £9400

The simple interest = £11,907 - 9400 = 2507

The time given(T) = 3 years

The rate (R)= x%

The rate can be calculated from the formula of simple interest = P×T×R/100

make R the subject of formula;

R = 100×SI/P×T

R = 100× 2507/9400×3

R = 250700/28200

R = 8.89%

R= 8.9%

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1. The gradient of AB is 0.5

2. The gradient of BC is tan θ

The gradient is the amount of vertical movement for each unit of horizontal movement to the right.

The gradient can also be called the slope and it expressed as;

S = y2-y1)/x2 -x1

1. The gradient of line AB

= 0-5)/-8-2

= -5/-10

= 1/2

therefore the gradient of AB is 1/2

2. using analytical method , the gradient of BC can be found by finding the value of θ

tan θ= gradient.

line AB = √ -10² + 5²

AB = √ 125

AB = 11.2

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Answer:

These line segments can form a triangle, because the longest side of the triangle can be exactly 4 inches long.

Step-by-step explanation:

Answer:

35°

Step-by-step explanation:

x= 180°-145° = 35°

______

Answer: it is 32.6

Step-by-step explanation:

The orginal number that Gavin was thinking of is 32.60.

Let the orginal number be represented with y

Gavin adds 9 to the original number: 9 + y

The answer is doubled: 2(9 + y)

The answer is 83.2: 2(9+y) = 83.2

In order to determine the value of y, take the following steps:

Divide both sides of the equation by 2

9 + y = 41.60

Subtract 9 from both sides of the equation

y = 41.60 - 9

y = 32.60

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Answer:

- Angle 'a' is an alternating exterior angle with one angle in the triangle and therefore congruent to one angle in the triangle formed by lines m, x, and y.

- Angles 'b' and 'c' are vertical angles with the other two angles in the triangle and therefore congruent to two other angles in the triangle

Step-by-step explanation:

Vertical angles are angles that are equal to each other but in opposite direction. The angles b and c have vertical angles on the triangle Q while alternate exterior angles are equal angles that lie on different lanes cutting through an axis.

Angles on a plane can be congruent if they are vertical equals or alternating exterior angles.

Just after her payment at the 2 1/2 year mark, Maria will owe approximately $7,722.63 on her loan.

To calculate the amount Maria will owe just after her payment at the 2 1/2 year mark, we need to determine the remaining balance on her loan.

First, we convert the loan duration to months:

2 1/2 years = 2.5 * 12 = 30 months.

Next, we use the formula for the remaining balance on a loan:

Remaining balance = Principal * (1 + monthly interest rate)^remaining months - Monthly payment * [(1 + monthly interest rate)^remaining months - 1] / monthly interest rate.

Principal = $10,000

Monthly interest rate = 7.8% / 12 = 0.065

Remaining months = 48 - 30 = 18

Plugging in the values, we have:

Remaining balance = $10,000 * (1 + 0.065)^18 - $243.19 * [(1 + 0.065)^18 - 1] / 0.065

Calculating this expression step by step:

Remaining balance = $10,000 * (1.065)^18 - $243.19 * [(1.065)^18 - 1] / 0.065

≈ $7,722.63

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Answer:

23

Step-by-step explanation:

It appears that you want to find the value of the expression 4x - 6 ÷ x when x = 6.  Replacing each instance of x with 6, we get:

4(6) - 6 ÷ (6)

Order of opertions rules require that we perform multiplication and division before addition or subtraction.  Thus, our

4(6) - 6 ÷ (6) becomes 24 - (6/6), or 24 - 1, or 23.