Let f(x)= x+3 and g(x)= 4x-3. Find (f+g)(3).

Answer: dy/dx = y^3 - 12x^2 - 2yx / x(x-3y^2)

Step-by-step explanation: Differentiate each term with respect to x, then solve for y.

I hope this helps you out!

divide them:

52.50 / 7 = 7.50 dollars per hour

The equation 5.5 - x = -4.5 - x has no solution. After cancelling out the variable x, we are left with 5.5 = -4.5, which is a contradiction.

To solve the equation 5.5 - x = -4.5 - x, we first notice that the variable x is present on both sides of the equation. We can simply subtract or add x to both sides to cancel it out. This will give us an equation without variables:

5.5 - x + x = -4.5 - x + x

5.5 = -4.5

This equation suggests that 5.5 is equal to -4.5, which is not true. Therefore, we can conclude that there is no solution to the equation since the two sides of the equation do not balance.

Moreover, this type of equation is an example of a contradiction, meaning that it presents a statement that is inherently false regardless of the value of x. As there is no value of x that can make the equation true, we say that the equation has no solution.

Final answer:

The equation 5.5 - x = -4.5 - x simplifies to 5.5 = -4.5 when the x terms are cancelled out. Since 5.5 does not equal -4.5, the equation has no solutions.

Explanation:

To solve the equation 5.5 - x = -4.5 - x, we can first try to simplify it by adding or subtracting the same value from both sides. This method is based on the principle that whatever you do to one side of the equation, you must do to the other to maintain balance.

In this case, if we add x to both sides of the equation, the x terms will cancel out on both sides, which leaves us with 5.5 = -4.5. Here, we notice that both sides of the equation represent constant values and no longer contain the variable x.

Therefore, since 5.5 and -4.5 are not equal, we can conclude that there is no value of x that can satisfy this equation. This equation is a contradiction, which means there are no solutions.

The required trinomial expression that is equivalent to  (2x+5)(3x-2) is 6x² + 11x - 10.

According to the question, we have to determine the trinomial expression that is equivalent to the  (2x+5)(3x-2).

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the quadratic equation, cubic equation, etc. ax+b is a polynomial.

Here,
Given expression in the question,
=  (2x+5)(3x-2)
Following the distributive property
= 2x (3x - 2) + 5 (3x - 2)
= 6x² - 4x + 15x - 10
= 6x² - 11x - 10

Thus, the required trinomial expression that is equivalent to  (2x+5)(3x-2) is 6x² + 11x - 10.

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Final answer:

The trinomial expression equivalent to (2x+5)(3x-2) is calculated using the FOIL method, resulting in 6x² + 11x - 10.

Explanation:

To write a trinomial expression equivalent to the product of two binomials, (2x+5)(3x-2), we perform the multiplication by using the distributive property (also known as the FOIL method).

Multiply the first terms: 2x × 3x = 6x²

Multiply the outside terms: 2x × (-2) = -4x

Multiply the inside terms: 5 × 3x = 15x

Multiply the last terms: 5 × (-2) = -10

Combine like terms:

6x² + (15x - 4x) - 10 = 6x² + 11x - 10

The trinomial expression equivalent to (2x+5)(3x-2) is 6x² + 11x - 10.

Answer:

C. [tex]x=50[/tex], [tex]y=10[/tex]

Step-by-step explanation:

We have been given an image of two intersecting lines. We are asked to find the value of x and y for our given diagram.

We know that when two line intersect each other, then vertical angles are congruent.

Using vertical angles theorem, we will get a system of equations as sown below:

[tex]3y=x-20...(1)[/tex]

[tex]5x-100=y+140...(2)[/tex]

From equation (1), we will get:

[tex]x=3y+20[/tex]

Upon substituting this value in equation (2), we will get:

[tex]5(3y+20)-100=y+140[/tex]

[tex]5*3y+5*20-100=y+140[/tex]

[tex]15y+100-100=y+140[/tex]

[tex]15y=y+140[/tex]

[tex]15y-y=y-y+140[/tex]

[tex]14y=140[/tex]

[tex]\frac{14y}{14}=\frac{140}{14}[/tex]

[tex]y=10[/tex]

Therefore, the value of y is 10.

To find the value of x, we will substitute [tex]y=10[/tex] in equation (1) as:

[tex]3*10=x-20[/tex]

[tex]30=x-20[/tex]

[tex]30+20=x-20+20[/tex]

[tex]50=x[/tex]

Therefore, the value of x is 50 and option C is the correct choice.

Answer:

Option C) x = 50, y = 10

Step-by-step explanation:

We are given a two pairs of vertically opposite angle in the image.

Vertically opposite angle is formed when two lines intersect anf they are always equal.

Thus, we can write:

[tex]3y = x -20\\\Rightarrow x - 3y = 20\\5x-100 = y +140\\\Rightarrow 5x - y =240[/tex]

Solving the two equations in two variable, we get:

[tex]x - 3y = 20\\5x - y =240\\\text{Multiplying first equation by 5}\\5x - 15y = 100\\\text{Subtracting the equations}\\5x - 15y-(5x-y) = 100-240\\-14y = -140\\y = 10\\ x - 3(10) = 20\\x = 20 + 30\\x =50[/tex]

The value of x is 50 and y is 10.

Bioelectrical impedance machine can be used to determine a patient's body fat percentage

The body fat percentage of a human or other living being is the total mass of fat divided by total body mass, multiplied by 100

A doctor can use a bioelectrical impedance machine to determine a patient's body fat percentage.

This machine works by sending a small electrical current through the body and measuring how quickly it travels through different types of tissue.

Since fat and muscle have different electrical conductivity, the machine can estimate the amount of fat in the body based on the resistance to the current.

Hence, Bioelectrical impedance machine can be used to determine a patient's body fat percentage

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The solution for ( y ) is ( y = 3.5 ).

To solve for y in the equation [tex]\( 10y + 3.8 = 38.8 \)[/tex], follow these steps:

Start with the given equation:

[tex]\[ 10y + 3.8 = 38.8 \][/tex]

Subtract 3.8 from both sides to isolate the term with  y:

[tex]\[ 10y + 3.8 - 3.8 = 38.8 - 3.8 \][/tex]

[tex]\[ 10y = 35 \][/tex]

Divide both sides by 10 to solve for  y :

[tex]\[ \frac{10y}{10} = \frac{35}{10} \][/tex]

y = 3.5

So, the solution for ( y ) is ( y = 3.5 ).

The distance from a to b if the units of the coordinated system are meters is 10m.

A line that has two endpoints and a fixed measurement is called a line segment.

It is given that point a is located at coordinates (5, 3) and point b is located at coordinates (-3, 9)

D = √[(x-p)² + (y-q)²]  

Substituting the points we get;

D = √[(-3 - 5)² + (9 - 3)²]  

D = √[(-8)² + (6)²]  

D = √[(64) + (36)]  

D = √100

D = 10

Hence, the distance from a to b if the units of the coordinated system are meters is 10 m.

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Final answer:

The distance between point A (5, 3) and point B (-3, 9) is calculated using the distance formula, resulting in a distance of 10 meters.

Explanation:

The question is asking for the distance between two points in a coordinate system. To find the distance between point A (5, 3) and point B (-3, 9), we can use the distance formula which is derived from Pythagorean theorem. The distance d between two points (x1, y1) and (x2, y2) is given by:

d = √((x2 - x1)² + (y2 - y1)²)

For point A and point B, we substitute the coordinates into the formula:

d = √((-3 - 5)² + (9 - 3)²)
= √(64 + 36)
= √100
= 10 meters

Therefore, the distance from A to B is 10 meters.

The instantaneous velocity of the ball when it hits the ground is found by deriving the height function and solving for the time of impact. The instantaneous rate of change of the surface area of a cylinder with respect to its radius when r = 4 is found by differentiating the surface area function and evaluating at r = 4.

The student's question involves two separate parts of physics and calculus related to kinematics and surface area calculations.

Part 1: Instantaneous Velocity of the Ball

The height, s, of a ball thrown straight down with initial speed 64 ft/sec from a cliff 80 feet high is given by s(t) = -16t2 - 64t + 80. The instantaneous velocity when the ball hits the ground is the derivative of position with respect to time, s'(t), evaluated at the time t when s(t) = 0 (when the ball hits the ground).

First, we find t by solving -16t2 - 64t + 80 = 0. Then, we find the derivative s'(t) = -32t - 64 and evaluate it at the found time, which gives us the instantaneous velocity.

Part 2: Rate of Change of Surface Area

The surface area of a right circular cylinder of height 4 feet and radius r feet is given by S(r) = 2πrh + 2πr2. The instantaneous rate of change of the surface area with respect to the radius, when r = 4, is the derivative dS/dr evaluated at r = 4. This is done by differentiating S(r) with respect to r and substituting r = 4 into the resulting expression.

Answer:

[tex] 5.15\times 3.16=16.2740[/tex]

Step-by-step explanation:

Maria wants to find the product of [tex]5\frac{3}{20}[/tex] multiplied by[tex]3\frac{4}{25}[/tex]

First we change mixed fraction to fraction and then change into decimal.

#First fraction:  

[tex]5\frac{3}{20}\Rightarrow \dfrac{103}{20}[/tex]

[tex]\dfrac{103}{20}\Rightarrow \dfrac{103\times 5}{20\times 5}=5.15[/tex]

#Secondfraction:  

[tex]3\frac{4}{25}\Rightarrow \dfrac{79}{25}[/tex]

[tex]\dfrac{79}{25}\Rightarrow \dfrac{79\times 4}{25\times 4}=3.16[/tex]

Now we find the product of both decimal

[tex]\Rightarrow 5.15\times 3.16[/tex]

Using calculator product of 515 and 316 = 162740

Both number has decimal digits two

So, total number of decimal digits is 4

In multiply result write decimal before 4 digits from right.

Therefore,

[tex] 5.15\times 3.16=16.2740[/tex]

The mathematical expression is,

⇒ 2x + 6 = - 24

And, The value of number = - 15

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

''The product of 2, and a number increased by 6, is -24''

Now,

Since, The algebraic expression is,

''The product of 2, and a number increased by 6, is -24''

Let a number = x

Hence, We can formulate;

⇒ 2x + 6 = - 24

Solve for x as;

⇒ 2x = - 24 - 6

⇒ 2x = - 30

⇒ x = - 15

Thus, The value of number = - 15

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Answer:

Step-by-step explanation:

From the given triangle DEF, we have

[tex](EF)^{2}=(ED)^{2}+(DF)^{2}[/tex]

[tex](10)^{2}=(8)^{2}+(DF)^{2}[/tex]

[tex]100-64=(DF)^2[/tex]

[tex]DF=6[/tex]

Now, we know that SinE=[tex]\frac{Perpendicular}{Hypotenuse}[/tex], thus

[tex]SinE=\frac{DF}{EF}[/tex]

[tex]SinE=\frac{6}{10}=\frac{3}{5}[/tex]

Therefore, the value of SinE is [tex]\frac{3}{5}[/tex].

y =-2x-4

x = 0, y = -2(0)-4 = -4

x=1, y = -2(1) -4 =-2-4 = -6

x=2, y = -2(2)-4 = -4-4 =-8

x=3, y = -2(3) - 4 = -6-4 =-10

Answer is B

Answer:

B

Step-by-step explanation: