The equation for the pH of a substance is pH = -log[H*], where H+ is the concentration of hydrogen ions. A basic
solution has a pH of 11.2. An acidic solution has a pH of 2.4. What is the approximate difference in the concentratic
of hydrogen ions between the two solutions?
1.6x10-9
O4.0x10-3
O 6.7x10-1
O 1.6x10¹11

Part A

The notation [tex]\lim_{x \to 2^{+}}f(x)[/tex] means that we're approaching x = 2 from the right hand side (aka positive side). This is known as a right hand limit.

So we could start at say x = 2.5 and get closer to 2 by getting to x = 2.4 then to x = 2.3 then 2.2, 2.1, 2.01, 2.001, etc

We don't actually arrive at x = 2 itself. We simply move closer and closer.

Since we're on the positive or right hand side of 2, this means we go with the rule involving x > 2

Therefore f(x) = (x/2) + 1

Plug in x = 2 to find that...

f(x) = (x/2) + 1

f(2) = (2/2) + 1

f(2) = 2

This shows [tex]\lim_{x \to 2^{+}}f(x) = 2[/tex]

Then for the left hand limit [tex]\lim_{x \to 2^{-}}f(x)[/tex], we'll involve x < 2 and we go for the first piece. So,

f(x) = 3-x

f(2) = 3-2

f(2) = 1

Therefore, [tex]\lim_{x \to 2^{-}}f(x) = 1[/tex]

===============================================================

Part B

Because [tex]\lim_{x \to 2^{+}}f(x) \ne \lim_{x \to 2^{-}}f(x)[/tex] this means that the limit [tex]\lim_{x \to 2}f(x)[/tex] does not exist.

If you are a visual learner, check out the graph below of the piecewise function. Notice the gap or disconnect at x = 2. This can be thought of as two roads that are disconnected. There's no way for a car to go from one road to the other. Because of this disconnect, the limit doesn't exist at x = 2.

===============================================================

Part C

You'll follow the same type of steps shown in part A.

However, keep in mind that x = 4 is above x = 2, so we'll deal with x > 2 only.

So you'd only involve the second piece f(x) = (x/2) + 1

You should find that f(4) = 3, and that both left and right hand limits equal this value. The left and right hand limits approach the same y value. The limit does exist here. There are no gaps to worry about when x = 4.

===============================================================

Part D

As mentioned earlier, since [tex]\lim_{x \to 4^{+}}f(x) = \lim_{x \to 4^{-}}f(x) = 3[/tex], this means the limit [tex]\lim_{x \to 4}f(x)[/tex] does exist and it's equal to 3.

As x gets closer and closer to 4, the y values are approaching 3. This applies to both directions.

See the attached truth tables.

• A ∧ B is true only when both A and B are true

• A ⇒ B is true only when both A and B are true, or A is false. This logically equivalent to ¬A ∨ B

• ¬A is true only when A is false

• A ⇔ B is true only when both A ⇒ B and B ⇒ A are true. Equivalently, (¬A ∨ B) ∧ (¬B ∨ A)

Answer: x = 23, y = 40

Step-by-step explanation:

By the same-side interior angles theorem, y+30 and 110 are supplementary.

We know that the 3x + 1 angle and y + 30 are also congruent, so:

Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

The exponential equation with a base of e is:

[tex]f(x) = 6*e^{2.639*x}[/tex]

We start with:

[tex]f(x) = 6*(14)^x[/tex]

We want to rewrite this to:

[tex]f(x) = 6*(e^n)^x[/tex]

So we only need to find the value of n such that:

[tex]e^n = 14[/tex]

If we apply the natural logarithm to both sides:

[tex]ln(e^n) = ln(14)\\n = ln(14) = 2.639[/tex]

Then the exponential equation with base of e is:

[tex]f(x) = 6*e^{2.639*x}[/tex]

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The equation of the given polynomial is f(x)=(x+2)(x+1)(x-3).

here we have given the graph of the

The roots of the given polynomial is

x=-2,x=-1 and x=3

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Therefore the equation of the polynomial is

f(x)=(x+2)(x+1)(x-3)

Therefore the equation of the given polynomial is f(x)=(x+2)(x+1)(x-3).

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The equation for this polynomial graphed will be P(x) = a(x + 2)(x + 1)(x – 3)³.

A polynomial expression is an algebraic expression with variables and coefficients.

The graph of the polynomial is given below.

From the graph, the roots of the polynomial will be -2, -1, and 3.

Then the factor of the polynomial will be

(x + 2), (x + 1), and (x – 3)

Then the polynomial will be

P(x) = a(x + 2)(x + 1)(x – 3)³

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Answer:

Step-by-step explanation:

You are given a system of equations and asked to solve it by the method of addition. That method requires you add a multiple of one equation to the other so that one of the variables is eliminated. In some cases, this is easier if multiples of both equations are added together. The resulting single-variable equation is then solved in the usual way.

__

The given system of equations is ...

We notice the first equation has the variables on opposite sides of the equal sign, and both their coefficients are 1. The second equation has the variables on the same side of the equal sign, and their coefficients are 0.08 and 0.02.

To eliminate a variable by the "addition method," we need to have the variable on the same side of the equal sign with opposite coefficients. Or, we need to have the variable on opposite sides of the equal sign with the same coefficient.

Both of the x-variables are on the left side, so we need opposite coefficients. We can get that by multiplying the first equation by -0.08, or by multiplying the second equation by -12.5. We judge the first of these choices to be easier.

The y-variables are on opposite sides of the equal sign, so we need equal coefficients. We can get that by multiplying the first equation by 0.02, or the second equation by 50.

We choose to multiply the first equation by 0.02, so we can eliminate the y-variable. Here is the result of doing that, then adding the results

  (0.02)(x) +(0.08x +0.02y) = (0.02)(y +1300) +(350)

  0.10x +0.02y = 0.02y +376 . . . . . eliminate parentheses

  0.10x = 376 . . . . . . . . . subtract 0.02y from both sides. y is eliminated

  x = 3760 . . . . . . . . . divide by 0.10

  y = x -1300 = 2460

__

The amount invested at 8% was $3760; the amount invested at 2% was $2460.

_____

Additional comment

We chose to eliminate y for a couple of reasons. x is the amount at the higher rate. We have found that solving for the higher-rate amount usually works best for preventing errors. The other reason is that multiplying by 0.02 results in smaller numbers, which we consider easier to deal with.

Had we multiplied by -0.08 to eliminate x, we would have ...

  -0.08(x) +(0.08x +0.02y) = -0.08(y +1300) +(350)

  0.02y = -0.08y +246

We judge -0.08(1300) +350 harder to calculate mentally, than 0.02(1300) +350.

  0.10y = 246

  y = 2460; x = 2460+1300 = 3760

Answer:

Power of a quotient

Answer:yw

Step-by-step explanation:

Answer :Opposite numbers are the same distance from 0 on the number line, but in opposite directions. Steps I would follow:

first, check the directions to make sure they are opposite,

then read the digits, or count the tick marks or compare lengths with dividers or ruler or marks on a piece of paper to see if the distances are the same.

3 is not the opposite of -6

__

6 is the opposite of -6

Answer:

right angle

acute

acute

obtuse

obtuse

Step-by-step explanation:

Since angle <ABC is a straight line, the angle is 180 degrees. This means all the angles in between should also add up to 180 degrees. Using this knowledge you can solve for the value of angle <FBE which is going to be equal to 180 - (40 + 25 + 50) = 65.

< DBF = <DBE + <EBF

< DBF = 25 + 65 = 90 (right angle)

<EBD = 25 (given) (acute)

<DBC = 50 (given) (acute)

<ABE = <ABF + <FBE

<ABE = 40 + 65

<ABE = 105 (obtuse)

<CBF = <CBD + <DBE + <EBF

<CBF = 50 + 25 + 65

<CBF = 140 (obtuse)

Answer:

Is the question even complete ?

Step-by-step explanation:

The attached graph represents the graph of the constraints

The constraints are given as:

7x+11y≤ 1540

x+3y ≤ 360

x+y≤ 200

x ≥ 0, y ≥ 0

Next, we plot the graph of the constraints using a graphing calculator

From the graph (see attachment), we have the coordinates of the feasible region to be (66, 98), (120,80) and (165,35)

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Step-by-step explanation:

the answer is (c)

because 0 is 3 in number,

1 is 4 in number,

2 is 3in number

3 is 2 in number,

4 is 2 in number,

no 5,6,7

8 is 1 in number

and no 9

The dot plot ( C )is solved and each dot represents one student's response

A dot plot, also known as a dot chart or dot graph, is a type of data visualization that displays the frequency of values in a dataset. It is a simple graphing technique that uses dots to represent data points on a horizontal or vertical axis.

Each data point in the dataset is represented by a dot placed above the corresponding value on the axis. If there are multiple data points with the same value, the dots are stacked vertically above that value. The resulting plot shows the distribution of data points along the axis, with the height of the stack of dots representing the frequency of each value.

Given data ,

Let the data of the number of pets owned by student be represented as A

Now , the value of A = { 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 8 }

The frequency of 0 = 3

The frequency of 1 = 4

The frequency of 2 = 3

The frequency of 3 = 2

The frequency of 4 = 2

The frequency of 8 = 1

In this dot plot, each dot represents one student's response. The number on the left indicates how many pets the students reported owning, and the dots are arranged vertically above that number.

For example, three students reported owning 2 pets, so there are three dots arranged above the number 2. This type of plot is useful for displaying the frequency of different values in a dataset.

Hence , the dot plot is solved

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Answer:

E; 10% off %20 sweater with $6 shipping

Step-by-step explanation:

Similar to what I said last time,

this time is with percentages,

How to calculate percent off?

Divide the number by 100 (move the decimal place two places to the left).

Multiply this new number by the percentage you want to take off.

Subtract the number from step 2 from the original number. This is your percent off number.
________________________________________________________
A. 35% off a $35 sweater with 4 dollar shipping is basically
  0.35 x 35 = 12.25 and 35-12.25 = $22.75 + the $4 shipping fee (if no tax)
    which the total would be $26.75

B. 20% off $35 is
   0.2x35=7 and 35-7 = 28 so your total is $28

C. 30% off $30 with $6 for shipping is

   0.3x30=9 and 30-9 is $21 plus the shipping fee
   $27

D.  $20 sweater with $5 shipping is $25 no discount involved :D

E. 10% off %20 sweater with $6 shipping is

    0.1x20 is 2 which 20 - 2 = 18 and plus shipping fee 18+6 is $24
________________________________________________________
Hope this helped again.

The factor of the function will be x and (x³ – 6). Then the zeroes of the function will be 0 and √6.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The polynomial function is given below.

f(x) = x⁴ − 6x

Then the factor of the function will be

f(x) = x(x³ – 6)

Then the zeroes of the function will be

x = 0, √6

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Answer:

a whole number is a number with no decmils other than .0000 and is not a fraction where the top and bottom are equal

whole: a,c,e&f

not:b&d

the slope intercept form of the given points is  y = 2/3 (x-3).

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined on both sides of a point. A straight line does not have any curve in it.

Here, given passing points

(3, 0) and (6, 2)

We know that,

    (y - y₁) = (y₂-y₁)/(x₂-x₁) (x - x₁)

  (y - 0) = (2-0)/(6-3) (x-3)

    y = 2/3 (x-3)

Thus, the slope intercept form of the given points is  y = 2/3 (x-3).

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Answer:

jjjijijijiiijijijijijijij no pliss inglés. ;D.

Answer:

r = 1

Step-by-step explanation:

we know that :

[tex]Slope=\frac{y_{B}-y_{A}}{x_{B}-x_A}[/tex]

Then

[tex]\frac{5}{4} =\frac{16-r}{-3-(-15)}[/tex]

Then

[tex]\frac{5}{4} =\frac{16-r}{12}[/tex]

Then

5×12 = 4×(16-r)

Then

60 = 64 - 4r

Then

4r = 64 - 60

Then

4r = 4

Then

r = 1

Answer: Read attachment.

Step-by-step explanation: Attached is my work. Hope it helps!

If my answer was helpful, please mark as brainliest. Or not, it's fine.

Answer:

[tex]\fbox {f(16) = -10}[/tex]

Step-by-step explanation:

Given :

f(x) = -3/4x + 2

Substitute x = 16 :

f(16) = -3/4(16) + 2

f(16) = -12 + 2

f(16) = -10

Answer:

09999kjht

Step-by-step explanation:

tttttttttgtgr312345678909ytrewq

x = -3

[tex]6( {2x}^{2} - 5) \\ \\ 6(2 \times { (- 3)}^{2} - 5) \\ \\ 6(2 \times ( 9) - 5) \\ \\ 6( 18 - 5) \\ \\ 6 \times ( 13) \\ \\ 78.[/tex]

The graph of the linear inequality 2x – 3y < 12 is given below. Then the correct option is A.

The missing options are given below.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

2x – 3y < 12

Then the correct graph will be given below.

Then the correct option is A.

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Given :

Answer 1 :-

We know that,

>> Total no. of outcomes = 5 + 8 + 7 + 4

>> Total no. of outcomes = 24

As there are 4 green balls. Therefore,

Answer 2 :-

We know that,

>> Total no. of outcomes = 5 + 8 + 7 + 4

>> Total no. of outcomes = 24

As there are 8 red balls. Therefore,

Answer 3 :-

We know that,

>> Total no. of outcomes = 5 + 8 + 7 + 4

>> Total no. of outcomes = 24

As there are 15 balls that are neither green nor white. (Red balls+ yellow balls)

Lashawn's scrambled eggs have a stronger salsa taste than Gilberta's scrambled eggs. Then the correct option is A.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Lashawn makes scrambled eggs with 3 spoonfuls of salsa for every 2 eggs.

Gilberta adds 7 spoonfuls of salsa for every 5 eggs.

Then the scrambled eggs have a stronger salsa taste will be

Lashawn's eggs = 3/2 = 1.5

Gilberta's eggs = 7/5 = 1.4

Lashawn's scrambled eggs have a stronger salsa taste than Gilberta's scrambled eggs.

Then the correct option is A.

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Option: B

The area of a circle is pi times the radius squared (A = π r²).

Answer: It is possible to draw different lines to approximate the same data. The line of best fit is only an estimate.