What is the domain of 2x+5

The composite function that converts temperatures from degrees Kelvin to degrees Fahrenheit is:

K to F = 9/5 * K - 241.15

The image shows a question about how to convert temperatures from degrees Celsius to degrees Fahrenheit using composite functions. The question provides two functions:

[tex]$F(x) = \frac{9}{5}x + 32$[/tex] converts from degrees Celsius to degrees Fahrenheit

[tex]$C(x) = x - 273.15$[/tex]converts from degrees Kelvin to degrees Celsius

We are asked to find the composite function [tex]$C \circ F$[/tex] that converts from degrees Kelvin to degrees Fahrenheit.

To find the composite function, we simply substitute the output of the first function, [tex]$F(x)$[/tex], into the input of the second function, [tex]$C(x)$[/tex]. This gives us:

[tex]```(C \circ F)(x) = C(F(x)) = F(x) - 273.15 = \frac{9}{5}x - 241.15```[/tex]

Therefore, the composite function that can be used to convert temperatures from degrees Kelvin to degrees Fahrenheit is:

[tex]```(C \circ F)(x) = \frac{9}{5}x - 241.15```[/tex]

A composite function is a function that is created by composing two or more other functions. In other words, it is a function that takes the output of one function as the input to another function. Composite functions are often used to solve complex problems that cannot be solved using a single function.

For example, the composite function that we found above,[tex]$(C \circ F)(x)$[/tex], can be used to convert temperatures from degrees Kelvin to degrees Fahrenheit. This is a useful function for scientists and engineers who work with temperatures in different units.

Another example of a composite function is the product rule in calculus. The product rule states that the derivative of the product of two functions [tex]$u(x)$[/tex]and [tex]$v(x)$[/tex] is equal to the sum of the product of the derivatives of [tex]$u$[/tex] and [tex]$v$[/tex] and the product of [tex]$u$[/tex] and the derivative of [tex]$v$[/tex]. This can be expressed mathematically as follows:

[tex]```\frac{d}{dx}[u(x)v(x)] = u'(x)v(x) + u(x)v'(x)```[/tex]

The product rule is a composite function because it takes the output of two functions, [tex]$u$[/tex] and [tex]$v$[/tex], and their derivatives,[tex]$u'$[/tex] and [tex]$v'$[/tex], and produces a new function, [tex]$\frac{d}{dx}[u(x)v(x)]$[/tex].

Composite functions are a powerful tool that can be used to solve a wide variety of problems in mathematics, science, and engineering.

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The equation 2m - nx = x + 4 is a linear equation solvable for x using algebraic manipulation. The solution is x = (2m - 4)/(nx + 1), requiring values for m and n to find x's specific value.

The given equation 2m - nx = x + 4 is a linear equation and can be solved for x by applying algebraic techniques. The question indicates that there is an element of differential equations involved, suggesting that it might be related to more advanced topics such as linear differential equations or characteristics equations. However, the provided context also mentions concepts like probability with positive and negative jumps, quadratic equations, and principles from physics, but these do not directly apply to the initial linear equation provided.

To solve for x in the given equation, we would rearrange the terms to isolate x:

2m - nx = x + 4

2m - 4 = x(nx + 1)

x = (2m - 4)/(nx + 1)

The solution for x is now expressed in terms of m and n. To find the specific value of x, values for m and n must be known.

The number is 30+ 3x².

When an integer is multiplied by itself, the resultant number is known as its square number. Basically, a square number is a number that is obtained by the product of two same numbers. In geometry, the area of a square with 'n' as the side length (where n is an integer) is the finest example of a square number.

When an integer is multiplied by the same integer, the resultant number is known as a square number. For example, when we multiply 5 × 5 = 52, we get 25. Here, 25 is a square number. Square numbers are always positive, they cannot be negative because when a negative number is multiplied by the same negative number, it results in a positive number.

let the number be x

Now, 3 times square of a number

3x²

and, 30 increased

=30+ 3x²

Hence, the number is 30+ 3x².

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Answer: 0.2

Step-by-step explanation:

To calculate the distance that Joanie run during her lunch break is necessary to multiply the total distance around the outside of Cedar Park (0,8) by the 1/4 of the total distance that she ran (0,25).

So, the expression is:

0,25 . 0.8 = 0,2

Joanie run 0,2 miles during  her  lunch break.

Instantaneous velocity is found by taking the derivative of the position function with respect to time, giving the velocity at a specific moment. Average velocity is calculated by dividing the total displacement by the total time elapsed.

To find instantaneous velocity, we take the derivative of the position function x(t) with respect to time t. This provides the velocity at any given moment. Mathematically, if the position x is a function of time t, then the instantaneous velocity v at time t is defined as:

v = lim_(Δt→0) (x(t + Δt) - x(t)) / Δt

For average velocity, we simply take the total displacement (the change in position) and divide it by the total time elapsed. Suppose we have an object that moves from position x1 to x2 over a time period from t1 to t2, the average velocity ū is:

ū = (x2 - x1) / (t2 - t1)

When the time interval becomes very small, the average velocity approaches the instantaneous velocity.

Let

x------> the number of men’s shirts

y----->  the number of women’s shirts

we know that

[tex]8x+12y \leq 240[/tex] ----> constraint A    

[tex]x\geq 3[/tex] ----> constraint B

[tex]y\geq 8[/tex] ----> constraint C  

[tex]y\geq 2x[/tex] ----> constraint D  

using a graphing tool

see the attached figure N[tex]1[/tex]

The solution is the shaded area

Remember that

if an ordered pair meets all restrictions and makes sense in the context of the situation, then the ordered pair is a system solution

we're going to proceed to verify each pair ordered

case A) [tex](4,9)[/tex]

Substitute the value of x and y in each  constraint

[tex]x=4\\y=9[/tex]

Verify constraint A

[tex]8*4+12*9 \leq 240[/tex]

[tex]140 \leq 240[/tex] -------> is true

Verify constraint B

[tex]4\geq 3[/tex] -------> is true

Verify constraint C

[tex]9\geq 8[/tex] ------> is true

Verify constraint D

[tex]9\geq 2*4[/tex]

[tex]9\geq 8[/tex] -----> is true

therefore

the ordered pair [tex](4,9)[/tex]  is a system solution

case B) [tex](7,13)[/tex]

Substitute the value of x and y in each  constraint

[tex]x=7\\y=13[/tex]

Verify constraint A      

[tex]8*7+12*13 \leq 240[/tex]

[tex]212 \leq 240[/tex] -------> is true

Verify constraint B

[tex]7\geq 3[/tex] -------> is true

Verify constraint C

[tex]13\geq 8[/tex] ------> is true

Verify constraint D

[tex]13\geq 2*7[/tex]

[tex]13\geq 14[/tex] -----> is not true

therefore

the ordered pair [tex](7,13)[/tex] is not a system solution

case C) [tex](2,15)[/tex]

Substitute the value of x and y in each  constraint

[tex]x=2\\y=15[/tex]

Verify constraint A

[tex]8*2+12*15 \leq 240[/tex]

[tex]196 \leq 240[/tex] -------> is true

Verify constraint B

[tex]2\geq 3[/tex] -------> is not true

Verify constraint C

[tex]15\geq 8[/tex] ------> is true

Verify constraint D

[tex]15\geq 2*2[/tex]

[tex]15\geq 4[/tex] -----> is true

therefore

the ordered pair [tex](2,15)[/tex] is not a system solution  

case D) [tex](5,12)[/tex]

Substitute the value of x and y in each  constraint

[tex]x=5\\y=12[/tex]

Verify constraint A

[tex]8*5+12*12 \leq 240[/tex]

[tex]184 \leq 240[/tex] -------> is true

Verify constraint B

[tex]5\geq 3[/tex] -------> is true

Verify constraint C

[tex]12\geq 8[/tex] ------> is true

Verify constraint D

[tex]12\geq 2*5[/tex]

[tex]12\geq 10[/tex] -----> is true

therefore

the ordered pair [tex](5,12)[/tex] is  a system solution  

case E) [tex](6,15)[/tex]

Substitute the value of x and y in each  constraint

[tex]x=6\\y=15[/tex]

Verify constraint A

[tex]8*6+12*15 \leq 240[/tex]

[tex]228 \leq 240[/tex] -------> is true

Verify constraint B

[tex]6\geq 3[/tex] -------> is true

Verify constraint C

[tex]15\geq 8[/tex] ------> is true

Verify constraint D

[tex]15\geq 2*6[/tex]

[tex]15\geq 12[/tex] -----> is true

therefore

the ordered pair [tex](6,15)[/tex] is  a system solution  

therefore

the answer is

[tex](4,9)[/tex]

[tex](5,12)[/tex]

[tex](6,15)[/tex]

see the attached figure N[tex]2[/tex] to better understand the solution

Answer:

(4,9) (5,12) (6,15)

Step-by-step explanation:

Those were the correct options.

To solve the inequality -138 greater than or equal to -6(6b-7), distribute the -6 to the terms inside the parentheses. Simplify the inequality by subtracting 42 from both sides. Divide both sides by -36, remembering to flip the inequality sign.

To solve the inequality -138 ≥ -6(6b-7), we need to distribute the -6 to the terms inside the parentheses. This gives us -138 ≥ -36b + 42. Next, we can simplify the inequality by subtracting 42 from both sides, resulting in -180 ≥ -36b. To isolate b, we divide both sides of the inequality by -36. Remember when dividing or multiplying an inequality by a negative number, the inequality sign flips. So the final answer is b ≤ 5.

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The measure for <ECA is 115 degree.

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as additional angles.

Given:

m <ACB = 65 degree

m <ECA = ?

As. <ACB and <ECA forms a linear pair.

So, m<ACB + m<ECA = 180

64 + m <ECA = 180

m <ECA = 180 - 65

m <ECA = 115

Hence, the measure of <ECA = 115 degree.

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Answer:

option B

Step-by-step explanation:

We have three different function for h(x)

[tex]h(x)= \frac{1}{4}x-4, x<=0[/tex]

WE have x<=0, so the graph starts at x=0 and goes down

Plug in 0 for x

[tex]h(0)= \frac{1}{4}(0)-4[/tex]

So h(0)= -4

When x=0, y= -4

The graph starts at (0,-4) and goes down

[tex]h(x)= \frac{1}{3}x-3, 0<x<=3[/tex]

x lies between 0  and 3, so the graph starts at x=0 and ends at x=3

Plug in 0 for x

[tex]h(0)= \frac{1}{3}(0)-3[/tex]

So h(0)= -3

When x=0, y= -4

Plug in 3 for x

[tex]h(3)= \frac{1}{3}(3)-3=-2[/tex]

When x=3, y= -2

The graph starts at (0,-4) and ends at (3, -2)

[tex]h(x)= \frac{1}{2}x-2, x>=4[/tex]

WE have x>=4, so the graph starts at x=4 and goes to the right

Plug in 4 for x

[tex]h(4)= \frac{1}{2}(4)-2[/tex]

So h(4)= 0

When x=4, y= 0

The graph starts at (4,0) and goes to the right.

SEcond graph is correct

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want the reasons for each of the final three steps in the solution of the inequality 7x +16 < -5(5 -5x).

2. 7x +16 < -20 +25x . . . . . . . given step 2

3.  16 < -20 +18x . . . . . Subtraction property of inequality

4.  36 < 18x . . . . . . . . . Addition property of inequality

5.  2 < x . . . . . . . . . . . . Division property of inequality

__

Additional comment

Subtraction of 7x is the same as adding -7x, so you can say the reason for step 3 is either of "subtraction property" or "addition property" The same would be true of step 4.

To figure this out, you compare the inequality on each line with the one before, and determine what was changed. If the same thing is done to both sides of the inequality (addition, subtraction, multiplication, division), the reason is the corresponding property of inequality.

The multiplication and division properties of inequality tell you to reverse the comparison symbol when the factor used is negative. Here, the factor is 18, a positive number, so the inequality symbol remains untouched.

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False, because the difference between two negative numbers is not always negative.

Here,

Given that, The difference between two negative numbers is always negative.

We have to prove this statement is true or false.

What is Negative number?

In the real number system, a negative number is a number that is less than zero.

Now,

We can prove it false with a counter example.

Let two negative number -6 and -8.

Hence, difference between -6 and -8 is,

⇒-6 - ( -8 )

⇒-6 + 8

⇒2

it is not negative number.

Hence, the difference between two negative numbers is not always negative.

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