Compare the rates of change of the following items.


A.
The rate of change of item I is greater than the rate of change of item II.

B.
The rate of change of item II is greater than the rate of change of item I.

C.
The rate of change of item I is equal to the rate of change of item II.

values that are excluded from the domain of a rational expression are values that make the denominator 0, since if that's so, the rational will be undefined.  That happens when the denominator is zero out, let's do so

[tex]\bf mn+3m=0\implies m(n+3)=0\implies \begin{cases} m=0\\ n=-3 \end{cases}[/tex]

so, if ever m = 0, the denominator will become 0 and the rational becomes undefined, and whenever n = -3, the same will happen to the rational, thus those values are excluded.

Final answer:

The excluded values for the expression (m + 5) / (mn + 3m) are m = 0 and n = -3, as these would make the denominator equal to zero, which is undefined.

Explanation:

The question appears to relate to the concept of excluded values in an algebraic expression, specifically one that involves division by a variable term. The excluded values are the values that the variables cannot take on because they would make the denominator equal to zero, which is undefined in mathematics. However, the given information seems to be related to physics, particularly quantum mechanics, which involves quantum numbers and the Pauli exclusion principle. It is important to have the correct expression to identify the excluded values properly. Assuming the expression is (m + 5) / (mn + 3m), we need to determine the values of m and n that would make the denominator zero.

To find the excluded values for the variable m and n, we need to set the denominator equal to zero and solve for the variables:

mn + 3m = 0

m(n + 3) = 0

From this, we can see that m must not be zero, and when m is not zero, n must not be -3. Therefore, the excluded values are m = 0 and n = -3.

Answer:

4x + 9 = 20

Step-by-step explanation:

4x + 9 = 20 is the pertinent equation.

9 more than (this means the same thing as addition or sum, so replace this with an addition sign) the product of (product of means that it's multiplying two numbers together. In this case the two numbers are 4 and x) 4 and x is (this is another word for equal to, so replace with an equal sign) 20

This said the algebraic equation is:

9 + 4x = 20

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Option 4 (If it is fall, then the trees have no leaves).

Step-by-step explanation:

Conditional Statements are the statements which involve "if" and "then". It contains two sets of statements in it. The statement after the word "if" is the hypothesis, and the statement after the word "then" is the conclusion. Conditional statements are written in the form "If A, then B"; where A is the hypothesis, and B is the conclusion. The converse of a conditional statement is the opposite of the original statement: hypothesis and conclusion replace each other. So the converse of the above statement will be "If B, then A".

In this case, A=The trees have no leaves and B=It is fall. Therefore, the converse will be:

If it is fall, then the tress have no leaves. Option 4 is the right answer!!!

Answer:

t(12)=40 t(24)=-3.2

Step-by-step explanation:

t(12)=40 because, if you replace 12 with t in the equation, everything but 40 cancels out.

t(24)=-3.2 because, if you plug in 24 for t it will be the same as the first equation where t is 0.

Answer:

PY = PZ is true.

Step-by-step explanation:

We are given a figure of a regular square pyramid and we are to determine whether PY is equal to PZ or not.

From the figure, we can see that ∠PXY and ∠PXZ are right angles and since the base is a square so sides AB and BC are equal in length and Y and Z are their mid points respectively.

Therefore, the hypotenuses created by PY and PZ are equal.

Check the picture below.

all slant-heights are the same in a square pyramid, so yes, PY = PZ.

if you notice in the picture, the green line is longer than the black dashed line, now, we're using some values for the sake of examplifying, so the side at the base for the slant-height is shorter than the the side at the base for the corner of the pyramid, and therefore PY > PB.

must the slant-height be greater than the altitude?  well, notice on that yellow triangle, the slant-height is the hypotenuse and the hypotenuse is always greater than the other sides in a right-triangle.

could the edges be the same length?  well, we can squeeze that well for the base sides and the slant-heights, but we can't for the corners, the corners must always be longer than the slant-heights, so nope.

Answer:  b. 6

Step-by-step explanation:

The maximum value is the y-value of the vertex.

Step 1: Find the x-value (aka Axis Of Symmetry) using the formula: [tex]x=\dfrac{-b}{2a}[/tex]

[tex]x=\dfrac{-(2)}{2(-1)}=\dfrac{-2}{-2}=1[/tex]

Step 2: input the x-value (above) into the given equation to solve for y:

[tex]y=-x^2+2x+5\\y=-(1)^2+2(1)+5\\y=-1 + 2 + 5\\y = 6[/tex]

$16,462.58 (rounded from $16462.575)

By subtracting 13%, you leave 87%, because [tex]100-13=87[/tex].

So, the expression we need to simplify is [tex]25000 * 0.87^3[/tex], because you need to multiply 25000 by 87% three times.

Answer:

$16,462.58

Step-by-step explanation:

100 - 13 = 87

So, then it becomes 87% of its value each year.

25000 * 0.87 = 21,750

21750 * 0.87 = 16,462.575

16,462.575 = $16,462.58 (round up)

Answer is $16,462.58

Final answer:

The expected number of peaks in the distribution of exam scores for the described student group would be three, correlating to the clusters of the grades A, B, and C.

Explanation:

The question asks how many peaks we would expect in the distribution of exam scores for a given set of students. Given the information that 35 students got an A, 25 students got a B, and 18 students got a C, it would be reasonable to expect that there would be three peaks in this distribution. This is assuming that the scores that correlate with these grades tend to cluster around a certain range or value, which is common in educational grading systems.

In this scenario, the likely three peaks would correspond to the ranges or average scores that are designated for the grades of A, B, and C. Since these are the only grades mentioned and no other grades such as D, E, or F are indicated, one would not expect additional peaks.

Therefore, the most appropriate answer to the question is Option C: There would probably be three peaks because the only grades received were A, B, and C.

Answer:

112 adults

20 children

Step-by-step explanation:

In order to solve this problem, we must create system of equations. By definition, system of equations are two equations which help you find unknown variables.

As for this problem, we need to set two variables for each type of person.

Let x represent adults

Let y represent children

We can break the question apart, and form equations based on the information given.

"tickets for adults cost $3.25 while tickets for children cost $2.25 and total receipts for the concert was $364"

$3.25x + $2.25y = $364

Now, we must form our second equation based on the information given.

"If 132 people attend a concert" "how many of each went to the concert"

x + y = 132

Solve for x, or the total number of adults

x = -y + 132

3.25(-y + 132)+ 2.25y = $364

Distribute 3.25

3.25 * -y = -3.25y

3.25 * 132  = 429

-3.25y + 429 = $364

Subtract 429 from both sides

364 - 429 = -65

-3.25y = -65

Now divide both sides by -3.25 to find the value of y.

y = 20

Therefore, 20 children attended the concert.

In order to find the total amount of adults who attended, subtract 20 from the total number of people that attended.

132 - 20 = 112

So, 112 adults attended as well as 20 children.

To find the number of adults and children who attended the concert, we can set up a system of equations and solve for the variables. Using the given information, we can determine that there were 67 adults and 65 children at the concert.

To solve this problem, we can use a system of equations. Let's assume that the number of adults who attended the concert is 'a' and the number of children is 'c'. We can form two equations from the given information:

Now, we can solve the system of equations to find the values of 'a' and 'c'.

Solving Equation 1 for 'a', we get a = 132 - c.

Substituting this value of 'a' into Equation 2, we get 3.25(132 - c) + 2.25c = 364.

Expanding and simplifying the equation gives us 429 - 3.25c + 2.25c = 364.

Combining like terms, we get -c = -65.

So, c = 65.

Substituting this value of 'c' into Equation 1, we get a + 65 = 132.

Solving for 'a', we get a = 67.

Therefore, there were 67 adults and 65 children at the concert.

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Answer:

(x-2)/3 = g

Step-by-step explanation:

First you move the 2 over to the same side as the x by subtracting it on both side, because you are trying to make the g "alone". Then you move the 3 by doing the inverse, just like with the 2. Since you are multiplying 3 on one side to move to the other side you have to divide both sides by 3.

Answer:

g= (x-2)/3

Step-by-step explanation:

x=3g+2

Subtract 2 from each side

x-2=3g+2-2

x-2 = 3g

Divide each side by 3

(x-2)/3 = 3g/3

(x-2)/3 =g

g= (x-2)/3

Answer: 15

Step-by-step explanation:

Answer:

Step-by-step explanation:

EH =15

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we know that } \begin{cases} y=8\\ x=4 \end{cases}\implies 8=k4\implies \cfrac{8}{4}=k\implies 2=k \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=2x~\hfill[/tex]

For this case we have that by definition, a direct variation is represented as:

[tex]y = kx[/tex]

Where:

k: It is the constant of proportionality

So:

[tex]k = \frac {y} {x}[/tex]

Substituting the values we have:

[tex]k = \frac {8} {4}[/tex]

Finally, the proportionality constant is:

[tex]k = 2[/tex]

Answer:

[tex]y=2x[/tex]

Answer:

Step-by-step explanation:

Note that (x^a)^b = x^ab.

Thus,  (x^2/3)^4/5 = x^(2/3 * 4/5) = x^(8/15)

To simplify the expression (x^2/3)^4/5, multiply the exponents and provide the resulting exponent x^8/15.

To simplify the expression (x2/3)4/5, we can use the rule of exponents which states that when raising a power to another power, we multiply the exponents. In this case, the exponent 4/5 applies to both the x and the 2/3. Multiplying the exponents gives us 2/3 * 4/5 = 8/15. Therefore, the simplified expression is x8/15.

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The formula for slope is

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

In this case...

[tex]y_{2} =3\\y_{1} =7\\x_{2} =2\\x_{1} =-2[/tex]

^^^Plug these numbers into the formula for slope...

[tex]\frac{3-7}{2 - (-2)}[/tex]

[tex]\frac{-4}{4}[/tex] -------------------> Simplifies to -1

                                                ^^^This is your slope

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

C is correct

Step-by-step explanation:

On edg

Answer:

Step-by-step explanation:

First you must calculate the module or the magnitude of both vectors

The module of u is:

[tex]|u|=\sqrt{(8)^2 + (-3)^2} \\\\|u|=\sqrt{64 + 9}\\\\|u|=8.544[/tex]

The module of v is:

[tex]|v|=\sqrt{(-3)^2 + (-8)^2} \\\\|u|=\sqrt{9 + 64}\\\\|u|=8.544[/tex]

Now we calculate the scalar product between both vectors

[tex]u*v = 8*(-3) + (-3)*(-8)\\\\u*v = -24+ 24=0[/tex]

Finally we know that the scalar product of two vectors is equal to:

[tex]u*v = |u||v|*cos(\theta)[/tex]

Where [tex]\theta[/tex] is the angle between the vectors u and v. Now we solve the equation for [tex]\theta[/tex]

[tex]0 = 8.544*8.544*cos(\theta)\\\\0 = cos(\theta)\\\\\theta= arcos(0)\\\\\theta=90\°[/tex]

the answer is 90°

Whenever the scalar product of two vectors is equals to zero it means that the angle between them is 90 °

Answer:

B

Step-by-step explanation:

edge answer

Answer:

To find the value of missing exponent, we have to split the number which is in other side of equal sign (which is not having power) as the multiple of base of the missing exponent.

On both sides, powers have the same base, so their exponents must be equal.

Step-by-step explanation:

Write the missing exponent:

25=5^x

Let x be the missing exponent.

To find the value missing exponent, we have to split the number which is in the left side as the multiple of the base of the missing exponent.

That is,

25=5*5 or 5^2

Now,

5^2=5^x

Powers have the same base so their exponent must be equal.

Hence the missing exponent is 2

Answer:

9

Step-by-step explanation:

So we need to find the point on 3x+4y+1=0 such that when connecting that point to (8,5) the lines that interest are perpendicular ones.

First step solve 3x+4y+1=0 for y.

subract 3x and 1 on both sides: 4y=-3x-1

divide both sides by 4:   y=-3/4x-1/4

So a line that is perpendicular to this one is 4/3

So we have the perpendicular line is in the form of y=4/3 x+ b

now we do want this to go through (8,5)

5=4/3 (8)+b

5=32/3+b

5-32/3=b

(15-32)/3=b

-17/3=b

So the perpendicular line we are looking at is y=4/3 x -17/3 .

Now I can find the point I talked about in my first sentence if I find the intersection of the line I just got and the line we started with. I'm going to just sub one into the other since they are both solve for y now.

-3/4 x-1/4=4/3 x-17/3

add 1/4 on both sides

-3/4 x      =4/3 x-65/12

subtract 4/3 x on both sides

-3/4 x-4/3 x=-65/12

simplify

-25/12 x =-65/12

25x=65

x=65/25

x=13/5

Now find y by plugging this into y=-3/4 x-1/4 giving you y=-11/5

So we want to actually just find the distance between (13/5,-11/5) and (8,5)

which is sqrt((27/5)^2+(36/5)^2)=9

Answer:

The greatest common divisor (gcd) of two or more numbers referst to the largest positive integer that divides each of the integers. Also, two integers are said to be relatively prime, mutually prime, or coprime if the only positive integer that divides both of them is 1. Therefore, If the GCD of 5 and 12 is one, it means that the two numbers are mutually prime.

Step-by-step explanation:

[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{We have the equation:}\\\\-3y=15-4x\\\\-3y=-4x+15\qquad\text{ivide both sides by (-3)}\\\\\boxed{y=\dfrac{4}{3}x-5}\\\\\boxed{slope=\dfrac{4}{3}}\\\boxed{y-intercept=-5}[/tex]

[tex]\text{To draw a graph we need only two points.}\\\text{We choose any value of x, put it to the equation of the line}\\\text{and calculate the value of y:}\\\\for\ x=0\\\\y=\dfrac{4}{3}(0)-5=0-5=-5\to(0,\ -5)\\\\for\ x=3\\\\y=\dfrac{4}{3}(3)-5=4-5=-1\to(3,\ -1)\\\\\text{The graph is in attachment}.[/tex]

Answer:

answer in picture

Step-by-step explanation:

Answer:

on edinuity, (3/8)^2 is the right answer

Step-by-step explanation:

:)

Answer:

g(x) = 3 square root of x + 7 is "The graph of the parent function is shifted 7 units up"

j(x) = 3 square root of x + 7 is "The graph of the parent function is shifted 7 units left"

h(x) = 3 square root of x - 7 is "The graph of the parent function is shifted 7 units down"

k(x) = 3 square root of x - 7 is "The graph of the parent function is shifted 7 units right"

Explantion:

Got this right on the test. And for square root of is supposed to mean the symbol for anyone who doesn't know that, I didn't have that thing on my keyboard.

The graph of the parent function f(x)=x^3 can be shifted up, down, left, or right by adding or subtracting constants to the function or its variables. The four variations of the function provided will result in vertical or horizontal shifts.

The graph of a parent function f(x)=x3, can be shifted in various ways by altering the function equation. When a positive or negative constant is added to the function, such as f(x)=x3+7 or f(x)=x3-7, it results in vertical shifts. Adding the constant shifts the function upward, while subtracting the constant shifts it downwards. On the other hand, if the constant alters the x-value (inside the parentheses), like in f(x-7)=x3 or f(x+7)=x3, it results in horizontal shifts. Adding the constant shifts the function to the left, while subtracting the constant shifts it to the right.

Match each function to the graph's shift:

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Answer:

16

Step-by-step explanation:

1/2 the linear term (which in this case is 8x) squared.

The linear term is one which may have a number in front of the x, but there is only 1 x.

x^2 does not qualify as a linear term

So for this question

1/2 8 = 4                    leave off the x.

squared = 4^2 = 16

You would add 16 to both sides.

Answer:

Add 16 to each side

Step-by-step explanation:

x^2 + 8x = 4

To complete the square, we take the coefficient of the x term, divide by 2, and then square it

8

8/2 =4

4^2 = 16

Add 16 to both sides of the equation

x^2 +8x +16 = 4+16

(x+4)^2 = 20

Answer:

The surface area is [tex]SA=(800+464\pi)\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of the half cylinder is equal to

[tex]SA=2B+PL[/tex]

where

B is the area of the half circle

P is the perimeter of the half circle plus the diameter of circle

L is the length of the structure

Find the area B

The area of the half circle is

[tex]B=\frac{1}{2} \pi r^{2}[/tex]

we have

[tex]r=16/2=8\ ft[/tex] -----> the radius is half the diameter

substitute

[tex]B=\frac{1}{2} \pi (8)^{2}[/tex]

[tex]B=32\pi\ ft^{2}[/tex]

Find the value of P (the perimeter of the half circle plus the diameter of circle)

[tex]P=\pi r+D[/tex]

we have

[tex]D=16\ ft[/tex]

[tex]r=8\ ft[/tex]

substitute

[tex]P=\pi (8)+16[/tex]

[tex]P=(8\pi+16)\ ft[/tex]

Find the surface area

[tex]SA=2B+PL[/tex]

[tex]L=50\ ft[/tex]

substitute

[tex]SA=2(32\pi)+(8\pi+16)(50)[/tex]

[tex]SA=64\pi+400\pi+800[/tex]

[tex]SA=(800+464\pi)\ ft^{2}[/tex]

see the attached figure to better understand the problem

Answer:

You would multiply by 1728.

So 10 cubic feet = 10 * 1728 = 17,280 cubic inches.

Step-by-step explanation:

There are  12 inches in a foot so there are 12^3 = 1728 cubic inches in a cubic foot.

Final answer:

To convert 10 cubic feet to cubic inches, multiply the volume in cubic feet (10) by the conversion factor of 1,728 to get 17,280 cubic inches.

Explanation:

To change 10 cubic feet into cubic inches, you need to use the conversion factor that 1 cubic foot equals 1,728 cubic inches (since 1 foot equals 12 inches, cubing both sides gives us 123 = 1,728). You then multiply the volume in cubic feet by this conversion factor.

Here is the calculation step by step:

Start with the volume in cubic feet: 10 cubic feet.

Multiply this amount by the conversion factor to get the volume in cubic inches: 10 cubic feet * 1,728 cubic inches/cubic foot = 17,280 cubic inches.

So, 10 cubic feet is equal to 17,280 cubic inches.

Answer:

The inverse g(x) = 2x + 2

Step-by-step explanation:

* Lets explain the inverse of a function

- To find the inverse of any function we switch the x and y then

 we solve to find the new y

- The domain of the function is the values of x and the range of

 the function is the values of y

- The domain of the inverse function is the values of y and the

 range of the inverse function is the values of x

- Lets solve the problem

∵ f(x) = {(8 , 3) , (4 , 1) , (0 , -1) , (-4 , -3)}

- To find the inverse g(x) lets find f(x) from the order pairs

∵ x-coordinates are decreases by 4 and y-coordinates are

  decreases by 2

∴ The relation represents the linear function

- The form of the linear function is f(x) = mx + c , where m is the

  slope of the line and c is the y-intercept

∵ The slope of the line whose endpoints are (x1 , y1) and (x2 , y2)

  is m = (y2 - y1)/(x2 - x1)

- We can find the slope from any two order pairs

∵ (x1 , y1) = (8 , 3) and (x2 , y2) = (4 , 1)

∴ m = [1 - 3]/[4 - 8] = -2/-4 = 1/2

∵ f(x) = mx + c

∴ f(x) = 1/2 x + c

- The y-intercept means the line intersect the y-axis

  at point (0 , c)

∵ There is a point (0 , -1)

∴ c = -1

∴ f(x) = 1/2 x - 1

- To find the inverse of the function switch x and y and solve to

  find the new y

∵ y = 1/2 x - 1 ⇒ switch x and y

∴ x = 1/2 y - 1 ⇒ add 1 to both sides

∴ x + 1 = 1/2 y ⇒ Multiply both sides by 2

∴ 2(x + 1) = y

∴ y = 2x + 2

∵ g(x) is the inverse of f(x)

∵ The inverse of f(x) is 2x + 2

∴ g(x) = 2x + 2

Answer:

g(x) = {(3, 8), (1, 4), (–1, 0), (–3, –4)}

Step-by-step explanation:

I got it right on edge

The volume is 90 if you add

Answer:

[tex]V = 983.73\ cm^3[/tex]  or [tex]V = 983\ ^{11/15}\ cm^3[/tex]

Step-by-step explanation:

By definition the volume of a rectangular prism is the product of its length (l) by its width (w) by its height (h). This is:

[tex]V = lwh[/tex]

In this case we know that

l = [tex]8\ ^{1/2}[/tex] centimeters

l = [tex]8 + \frac{1}{2}=8.5[/tex] centimeters

w=  [tex]9\ ^{1/3}[/tex] centimeters

w = [tex]9 + \frac{1}{3}=9.333[/tex]  centimeters

h=  [tex]12\ ^{2/5}[/tex] centimeters

h = [tex]12 + \frac{2}{5}=12.4[/tex]  centimeters

Then

[tex]V = (8.5)(9.333)(12.4)\ cm^3[/tex]

[tex]V = 983.73\ cm^3[/tex]

[tex]V = 983\ ^{11/15}\ cm^3[/tex]

Answer:

[tex]1\frac{1}{2}[/tex]

Step-by-step explanation:

If there is 1500 cellular phones per 1000 people, then the number of phones per person is:

[tex]\frac{1500}{1000} = \frac{15}{10} = \frac{3}{2}[/tex]

Now we know that [tex]\frac{3}{2} = 1 + \frac{1}{2} = 1\frac{1}{2}[/tex]

x+(6x+10)+(x+2)=180

8x=180-12

x=168÷8

x=21°

Hope i helped.

Answer:

a) x = 21

b) 136º

Step-by-step explanation:

The sum of all the angle measures within a triangle is equal to 180º. Therefore, we can use an equation to find x and find the measure of angle C.

x + 6x + 10 + x + 2 = 180

Let's add together all the x's.

8x + 10 + 2 = 180

Now let's add together 10 + 2.

8x + 12 = 180.

To solve for x, we must first isolate 8x. To do this, we subtract 12 from both sides.

8x + 12 - 12 = 180 - 12.

8x = 168

To solve for x, we must divide 8 from both sides.

8x / 8 = 168 / 8

x = 21

Now we have the answer to the first part.

We can use this answer to solve for the measure of angle C.

Angle C = 6x + 10.

We just have to plug in 21 for x and solve for angle C.

6(21) + 10 = 136.

Angle C has a measure of 136º.