Graph the function.

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

Exponential and logarithmic functions are one-to-one functions due to the unique relationship between x and y values. When x and y values are interchanged, their inverses maintain this one-to-one relationship. The blanks in your statement can be filled in as follows:

All exponential functions of form f(x) = b^x and logarithmic functions of form f(x) = log_b(x) are _one-to-one functions_ because these functions have exactly one _y-value_ for each _x-value_. So when the x and y values are _interchanged_, the inverses will also have _one y-value_ for each _x-value_.

In summary, exponential and logarithmic functions are one-to-one functions due to the unique relationship between x and y values. When x and y values are interchanged, their inverses maintain this one-to-one relationship.

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Answer:

10 dimes i think this is the answer hope it helps  

Step-by-step explanation:

1)

8. ∠ABC, 5. \(\overrightarrow{BA}\), 9. Point C, 3. Plane W, 6. \(\overline{AB}\), 2. \(\overrightarrow{BC}\) and \(\overrightarrow{BA}\), 1. \(\overleftrightarrow{AB}\), 7. Plane ABC, 4. line m.

2)

a) The output of the rule is (-6,9)

b) The output of the rule is (-3,0)

c) No.

3) The image is attached below.

What is a line?

A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things.

1)

Angle: An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.

Therefore first image is ∠ABC.

In mathematics, a ray is a segment of a line with a fixed starting point but no ending.

The fixed point is B. Then second image represents \(\overrightarrow{BA}\). The sixth image represents two rays that are \(\overrightarrow{BC}\) and \(\overrightarrow{BA}\),

A point is a basic concept in traditional Euclidean geometry that represents an exact place in space and has no length, breadth, or thickness. In contemporary mathematics, a point more broadly refers to a component of a set known as a space.

The image represent point C.

A plane is an infinitely long, Euclidean, two-dimensional surface in mathematics. A plane is a point, a line, and three-dimensional space's equivalent in two dimensions.

The fourth image represent Plane W. The eighth image represents Plane ABC.

The seventh image represents  \(\overleftrightarrow{AB}\) and the ninth image represents line m.

2)

The translation rule is

(x,y) → (x-3, y+4)

(a) The translation of the point (-3,5) is (-3 -3, 5 + 4) = (-6,9).

(b) The translation of the point (0,-4) is (0 -3, -4 + 4) = (-3,0)

(c) No, since a function consists of one variable. But in the translation, there is two variables.

3)

The vertices of △PQR are P(1,-1), Q(3,-2), R(3,-4).

The rule of 180° rotation about origin is (x,y) → (-x,-y)

After rotation, P'(-1,1), Q'(-3,2), R(-3,4).

The rule reflection about x-axis is (x,y) → (x,-y)

After reflection,  P''(1,1), Q''(3,2), R''(3,4).

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AB = DC

BC = BC

both have an angle of 90°

not only are they congruent, they're also completely identical.

Answer:

The first one is

\(x=\frac{3}{a }\)

The second one is

\(x=- \frac{a }{6 }\)

The third is

\(x=-\frac{6}{a}\)

Hope this helps, it's just simple rearrangement for x!

Answer:

I would recommend a Samsung TV but that is just what I think oh nvm a TV show um Big mouth on Netflix

The woman tells Lela and Devon that she's sorry because she feels bad that her children took the ring.

The woman's apology could stem from a sense of responsibility and guilt for her children's actions. She may feel remorseful because her children took the ring without her knowledge or permission. She could feel a sense of personal accountability for their behavior as their parent, believing that she should have been more vigilant or instilled better values in them.

Additionally, the woman's apology might also be driven by her empathy and understanding of the impact the incident has had on Lela and Devon. She could be aware of the emotional distress caused by the loss of the ring and genuinely regretful that her children were involved in the situation.

By apologizing, the woman may be expressing her regret and remorse for the unfortunate events surrounding the ring. It signifies her recognition of the wrongdoing and a desire to convey empathy and understanding towards Lela and Devon.

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The total distance traveled by bus is 420 miles.

Let's denote the distance traveled by car as "x" miles.

The time taken for the car journey can be calculated by dividing the distance by the speed:

Time taken by car = x miles / 30 mph = x/30 hours.

The remaining distance, which was traveled by bus, would be the total distance of 630 miles minus the distance traveled by car:

Distance traveled by bus = 630 miles - x miles = (630 - x) miles.

The time taken for the bus journey can be calculated by dividing the distance by the speed:

Time taken by bus = (630 - x) miles / 60 mph = (630 - x)/60 hours.

Given that the total time was 14 hours, we can write the equation:

Time taken by car + Time taken by bus = Total time

x/30 + (630 - x)/60 = 14.

To solve this equation and find the value of x, we can multiply all terms by 60 to eliminate the denominators:

2x + 630 - x = 840,

x + 630 = 840,

x = 840 - 630,

x = 210.

Therefore, the distance traveled by bus is:

Distance traveled by bus = 630 miles - x miles = 630 miles - 210 miles = 420 miles.

So, the total distance traveled by bus is 420 miles.

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The general solution of the given system can be summarized as follows: The system has infinitely many solutions, where x₁ is fixed at zero and x₂ and x₃ are free variables.

To determine the general solution, we need to perform row reduction on the augmented matrix. Starting with the given matrix:

1  3  2  -1  |  3

9  4  7   x₁  |  0

We can perform row operations to simplify the matrix. First, we'll perform R2 - 9R1 to eliminate the coefficient 9 in the first column:

1  3   2   -1  |  3

0 -23 -11  x₁+9  | -27

Next, we'll divide R2 by -23 to obtain a leading coefficient of 1:

1   3    2    -1   |  3

0   1   11/23  -(x₁+9)/23  |  27/23

Now, we can perform R1 - 3R2 to eliminate the coefficient 3 in the first column:

1   0   -25/23   2/23   |  12/23

0   1   11/23   -(x₁+9)/23  |  27/23

From the row-reduced form, we can see that x₁ is fixed at 12/23, while x₂ and x₃ are free variables. This means that for any value of x₂ and x₃, we can find a solution for the system. Therefore, the system has infinitely many solutions, and the general solution can be expressed as:

x₁ = 12/23

x₂ = x₂ (free variable)

x₃ = x₃ (free variable)

where x₂ and x₃ can take any real values.

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The greatest difference we could observe in the solutions v and w is 2α.

Explanation:
To find the greatest difference between the solutions v and w, we need to determine the maximum value of |v(x, t) - w(x, t)|. Since α > 0, we can rewrite the given equation as:

v(t) - w(t) = α(v''(x) - w''(x))

By applying the maximum principle, we know that the maximum value of v''(x) - w''(x) occurs at the boundaries of the interval [0, π].

Since v(0, t) = w(0, t)

= 0 and

v(π, t) = w(π, t)

= 0, we can conclude that the maximum difference between v and w occurs at the interior points of the interval [0, π].

Now, let's consider the initial conditions. Given that 0 ≤ v0(x) ≤ 1 and 0 ≤ w0(x) ≤ 1, the maximum difference in the initial conditions would be when v0(x) = 1 and

w0(x) = 0, or vice versa.

Therefore, the maximum value of v(x, t) - w(x, t) is given by:
v(0, t) - w(0, t) = α(v''(0) - w''(0))
v(π, t) - w(π, t) = α(v''(π) - w''(π))

Since v''(0) = w''(0) = 0 and

v''(π) = w''(π) = 0, the maximum difference is 2α.

Conclusion:
The greatest difference we could observe in the solutions v and w is 2α.

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Answer:

Mapping C represents a function.

To be a function, there must be one and only one y value (output) for every input value (x value).

Mapping C matches this criteria, thus it is a function.

Let me know if this helps!

Answer:Pythagorean therome

Step-by-step explanation:a^2+b^2=c^2

Answer:

Step-by-step explanation:

S=a*b=12*14=168feet²

Answer:

x +7 =14 this is not enough information to solve so it probably an algebraic expression so here what i think it is

Step-by-step explanation:

x + 7 =14

a. sin(t+377) = -sin(t)

b. sin(2) = 0

c. sin- (undefined)

In trigonometry, the value of the trigonometric functions depends on the angle measured in degrees or radians. In this question, we are given that the sect (the sector angle) is 3, and 1 is in Quadrant IV.

Step 1: For part a, sin(t+377), we can apply the angle addition formula for sine, which states that sin(A + B) = sin(A)cos(B) + cos(A)sin(B). In this case, B is 377, and we know that sin(377) = sin(-360 - 17) = sin(-17). Since 1 is in Quadrant IV, the sine function is negative in this quadrant. Therefore, sin(-17) = -sin(17), and we can conclude that sin(t+377) = -sin(t).

Step 2: For part b, sin(2), we need to evaluate the sine of 2. Since 2 is not given in the context of an angle, we assume it represents an angle in degrees. The sine function is defined as the ratio of the length of the side opposite the angle to the hypotenuse in a right triangle. However, without knowing the specific angle measure, we cannot determine the ratio and therefore cannot calculate the sine of 2. As a result, the value of sin(2) is undefined.

Step 3: Part c, sin-, is not well-defined in the given question. It is important to note that sin- typically represents the inverse sine function or arcsine. However, without any angle provided, we cannot calculate the inverse sine or determine the corresponding angle. Therefore, sin- remains undefined in this context.

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The power of substitutes is one of the five forces in Porter's Five Forces framework and it is a measure of how easy it is for customers to switch to alternative products or services. The higher the power of substitutes, the more competitive the industry and the lower the profitability.

The power of substitutes is based on the premise that when there are readily available alternatives to a product or service, customers can easily switch to those alternatives if they offer better value or meet their needs more effectively. This poses a threat to the industry as it reduces customer loyalty and puts pressure on pricing and differentiation strategies.

The availability and quality of substitutes influence the degree to which customers are likely to switch. If substitutes are abundant and offer comparable or superior features, the power of substitutes is strong, increasing the competitive intensity within the industry. On the other hand, if substitutes are limited or inferior, the power of substitutes is weak, providing more stability and protection to the industry.

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Answer:

5 letters

Step-by-step explanation:

let x = # of packages

x+2 = # of letters

$0.37(x+2) + $0.88x = $4.49

.37x + .74 + .88x = 4.493

1.25x + .74 = 4.49

1.25x = 3.75

x = 3.75/1.25 = 3 = # of packages

# of letters = x+2 = 3+2 = 5

What are the next four multiples of 1/7​ ?

so, it will be :

Answer:

• Resolving horizontally:

\({ \rm{ \sum v _{x} = 2 \cos(23 \degree) }} \\ \\ { \boxed{ \rm{ v_{x} = 1.841}}}\)

• Resolving vertically:

\({ \rm{ \sum v _{x} = 2 \sin(23 \degree) }} \\ \\ { \boxed{ \rm{v _{x} = 0.781}}}\)

In vector notation:

\( \dashrightarrow \: { \boxed{{v = 1.841 \: i \: + 0.781 \: j }}}\)

False. The margin of error only accounts for sampling variability (the fact that my sample will be different that many other people's and therefore provide different statistics.

Statistics is a technique for interpreting, analyzing, and summarizing data in mathematics. In light of these characteristics, the various statistical types are divided into: Statistics that are descriptive and inferential. We analyze and understand data based on how it is presented, such as through graphs, bar graphs, or tables.

Inferential statistics, which draws conclusions from information using statistical tests like the student's t-test, is one of the two main statistical methods used in data analysis. Descriptive statistics presents data using indices like mean and median.

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The first step is to subtract $500 from $2000 and then you end up with $1500 which you then divide by 5.

Each payment will have to be $300

Answer:

36

Step-by-step explanation:

75/2700=36

Answer:

190

Step-by-step explanation:

20C2 = (20*19)/(1*2) = 190

Answer:  Let's just say that each of the units are 1 inch in sides, and since it's an irregular shape you have to separate each shape. So, the rectangle I separated is 14 inches.

The semicircle is 12.56.

Adding those two answers together comes out to 26.56.

The maximum number of possible effects that could be tested in a 2x2x2 factorial design with 3 main effects, 3 two-way interactions, and 1 three-way interaction is 7.

In a 2 x 2 x 2 factorial design, we can test the following maximum number of possible effects:
Main effects:

There are 3 main effects in this design, one for each factor (A, B, and C). You would analyze the effect of each factor independently on the outcome variable.

Two-way interactions:

There are 3 possible two-way interactions that can be tested in this design: AxB, AxC, and BxC.

These interactions examine the combined effects of two factors on the outcome variable.
Three-way interactions:

There is 1 possible three-way interaction that can be tested in this design: AxBxC.

This interaction examines the combined effect of all three factors (A, B, and C) on the outcome variable.

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The expression for the total cost of their trip is 7 + 2x + 3y.

As per the question, assuming the number of bottles to be x and number of bags to be y. The equation will have one time fee of admission, product of cost of bottles and number of bottles and product of cost of bags and number of chips bags.

The one time fee and two products will be added to form the expression. Forming the equation now -

Expression = 7 + 2x + 3y

Therefore, the expression of trip when x bottles of water were bought during the visit is 7 + 2x + 3y.

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Statement                Reason

m∠A ÷ 5 = m∠B       1. Given

m∠B = 20                 2. Given

m∠A ÷ 5 = 20           3. Substitution

m∠A = 100                4. Multiplication property of equality

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

m∠A ÷ 5 = m∠B  ____(1)

m∠B = 20 _____(2)

Substitute (2) in (1)

m∠A ÷ 5 = 20

m∠A / 5 = 20

Multiply 5 on both sides.

m∠A = 5 X 20

m∠A = 100

Thus,

Statement                Reason

m∠A ÷ 5 = m∠B       1. Given

m∠B = 20                 2. Given

m∠A ÷ 5 = 20           3. Substitution

m∠A = 100                4. Multiplication property of equality

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The rate of change of area is given as 27 π. The time at which radius of circle is increasing is 1.386 sec and change in radius is 3 cm.

What is rate of change?

The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity. In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another.

a) Given, radius of circle = 9 cm

rate of change of radius = 3/2

We know area of circle = πr^2

change in area =2πrr'

we get  2×π×9×2/3=27π

B) Given,

g(t) = 12 - 12e^0.5t

derivate it

g'(t) =-12×-1/2e^t/2

g'(t)=3

3= 6e^t/2

t = 1.386

c) f1(t) = t2-4t+4.

Integrate it we get

radius =3.

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Answer:

a is mark me as brainlist pls

Step-by-step explanation: