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If f(x) and g(x) are inverse functions, use the information shown to find g(x)

f(2x - 10) = x + 1

f(-10) = 1

f(-12) = 0

f(2x - 12) = x


Answer Choices:

g(x) = -12

g(x) = 2x - 10

g(x) = -10

g(x) = 2x - 12

The products that result in a difference of squares or a perfect square trinomial are Quadratic Equations, Perfect Square Binomials, and Difference of Squares. Difference of Cubes is incorrect.

Those apply:

All three of these products can be used to solve a variety of problems involving algebraic equations.

The task:

Which products result in a difference of squares or a perfect square trinomial?

Check all that apply:

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Using Scalar multiplication, If all the conditions are satisfied, then the set is a subspace of R³

The result of multiplying a real number by a matrix is known as a scalar multiplication. Each entry of the matrix is multiplied by the specified scalar in scalar multiplication.

The following requirements must be met in order to establish whether a set is a subspace of R3 under addition and scalar multiplication:

Closure under addition: If elements u and v are present, then u plus v must also be present.

If u is a member of the set and k is any scalar, then ku must likewise be a member of the set. Closure under scalar multiplication.

The zero vector is contained in: The set must contain the zero vector (0, 0, 0).

includes all negative vectors; if u is in the set, then -u must also be.

These conditions must be checked for each set, and your response must be supported.

The set is a subspace of R³ if all the conditions are met.

The set is not a subspace of R³ if any of the requirements are not met.

Consequently, the set is a subspace of R³ if all of the conditions are met.

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Complete question -

The decimal inch scale is based on tenths and hundredths of an inch. This scale is a common unit of measurement used for industrial, mechanical, and construction purposes.

The formula for a decimal inch is 1 inch = 0.1 decimal inch. This means that every 0.1 decimal inch is equal to 1 inch. To calculate a decimal inch, simply divide the number of inches by 10. The decimal inch scale is based on tenths and hundredths of an inch. This scale is a common unit of measurement used for industrial, mechanical, and construction purposes. For example, if you have a measurement of 6 inches, the decimal inch measurement would be 0.6. You can also convert decimal inches to inches by multiplying the decimal number by 10. For example, if you have a measurement of 0.6 decimal inches, the inch measurement would be 6 inches.

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By applying inverse function concept, it can be concluded that the table that could be used to verify that the function modeling Fahrenheit temperature, F(C), based on a given Celsius temperature, C, is the inverse of C(F) is option A:

C           -20      -15      -5

F(C)        -5         4       23

An inverse function can be defined as a type of function that is obtained by inverting (undoing) the operation of the given function f(x).

In Mathematics, if f(x) is a given function, its inverse function has the following property f⁻¹(f(x)) = x.

We already have this table:

F       -4        5       23

C(F)   20    -15      -5

By applying the concept of inverse function, we can form a new table to represent the inversion function of the above table:

C           20      -15      -5

F(C)        -4        5       23

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Full question attached.

The equation of the trend line to estimate the​ hiker's elevation after 165 minutes is 2291.3 feet.

What is linear equation ?

Linear equation can be defined as equation in which highest degree is one.

Given that,

The equation of a trend line for the​ hiker's elevation is y = 9.82x + 671​.

We have to determine,

The equation of the trend line to estimate the​ hiker's elevation after 165 minutes.

According to the question,

The equation of a trend line for the​ hiker's elevation is y = 9.82x + 671​.

Where, x represents the number of minutes and y represents the​ hiker's elevation in feet.

To find the trend line to estimate the​ hiker's elevation after 165 minutes, substitute the value of x = 165 minute in the given equation.

Hence, The equation of the trend line to estimate the​ hiker's elevation after 165 minutes is 2291.3 feet.

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Since the sum is given to be equal to 9, then the exact value of c must be equal to 9/1.

The given equation is ∑ n = 0 c n 1 = 9. This means that the sum of all of the terms beginning at n = 0 and continuing for infinity is equal to 9. Therefore, the exact value of c must be equal to 9/1. In other words, c must have a value of 9 in order for the given equation to be true. As such, the exact value of c is 9/1. Since the sum is given to be equal to 9, then the exact value of c must be equal to 9/1.

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The remaining ratios for the angle are:

sin θ = 2/√7

cos θ = √3 /√7

tan θ = 2/√3

sec θ = √7 /√3

cot θ = √3 /2

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. Trigonometry is used to determine the lengths of the sides of a triangle when one or more angles and/or the lengths of one or more sides are known.

The remaining ratios are as follows

csc θ = √7 /2

Since sin θ = 1/cscθ

sin θ = 2/√7

Remember: sin θ= opposite/hypotenuse  = 2/(√7)

adjacent =  √((√7)² - 2²) = √3

cos θ = √3 /√7   (adjacent/hypotenuse)

tan θ = 2/√3  (opposite/adjacent)

sec θ = 1/cos θ

sec θ = √7 /√3

cot θ = 1/tan θ

cot θ = √3 /2

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Answer:

-1, 6

0, -3

1, -3.9

2, -3.99

f(x) = 5^2x+1

Step-by-step explanation:

for the first question, after plugging in the values of x, we get our answer to be the 2nd table

-1, 6

0, -3

1, -3.9

2, -3.99

for the second question

f(x) = 5^2x+1

after graphing, we can see it never passes x = 2

Just put your name on the check's back to complete a blank endorsement. The teller at the bank will ask if you want to cash it or deposit it after you arrive.

The three types of endorsements available for checks are blank, special, and restriction. When the payee signs their name on the check's top back, it becomes a blank endorsement.

To accomplish this, you just sign the check on the back and inform the bank teller whether you want to deposit it into a certain account or cash it. When depositing a check using mobile deposit or an ATM, a blank endorsement is also acceptable.

To be accepted for deposit, a check needs to have an endorsement on the back. Therefore, always add your signature to the document right before bringing it to the bank in the place provided next to the X.

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The solution for the given initial-value is 6ty + t² - 9t + 4y² - y = 12

An initial value problem is a differential equation that is accompanied by an initial condition that specifies the value of one or more variables at a particular time or at a particular point in space. The initial value problem is to find the solution of the differential equation that satisfies the given initial condition. The solution of the initial value problem describes the behavior of the system over time or as a function of space based on the given initial conditions.

The given initial value problem is a non-linear ordinary differential equation and can be solved using numerical methods such as Runge-Kutta methods or numerical integration.

The solution to the initial value problem gives the function y(t) that satisfies the differential equation and the initial condition y(-1) = 2.

Given that

(6y + 2t − 9)dt = (8y 6t − 1)dy = 0

and y = -2

As both = 0 then (6y + 2t − 9)dt = (8y + 6t − 1)dy

that is

(6(-2) + 2t − 9)dt = (8(-2) + 6t − 1)d(-2)

−21dt + 2dt² = 34d−12dt

2dt² − 9dt - 34d

d(2t² −9t−34)

Integration both sides

6ty + t² - 9t + 4y² - y = c

Using y(-1) = 2

-12 + 1 + 9 + 16 - 2 = c

c = 12

Thus, the solution for the given initial-value is 6ty + t² - 9t + 4y² - y -12 = 0

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Answer: n/a

Step-by-step explanation:

there are no numerical values given to derive an answer from.

to find the mean, take the sum of all numbers and divide it by the number of added numbers.

for the standard deviation, subtract every data point from the mean and square it. add all of those together and divide it by the number of data points. then find the square root of that number

There are 187.425 pounds in 85 kilograms. The solution has been obtained by using the unit conversion.

What is unit conversion?

The same feature is expressed in a different unit of measurement using a unit conversion. For instance, you may represent time in minutes rather than hours or distance in feet rather than miles. It happens frequently when measurements are given in one set of units, like feet, but are demanded in another set, like chains.

We are given 85 kilograms which are to be converted into pounds.

We know that 1 kilogram = 2.205 pounds(approx)

So,

⇒85 kilograms = 85 * 2.205

⇒85 kilograms = 187.425 pounds

Hence, there are 187.425 pounds in 85 kilograms.

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The solution to the equation are k = 2 or k = -3.5

From the question, we have the following parameters that can be used in our computation:

2k^2 - 14 = -3k

Express properly

So, we have the following representation

2k^2 + 3k - 14 = 0

Expand the equation

2k^2 + 7k - 4k - 14 = 0

So, we have

k(2k + 7) - 2(2k + 7) = 0

This gives

k - 2 = 0 or 2k + 7 = 0

Evaluate

k = 2 or k = -3.5

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Answer:

113

Step-by-step explanation:

the formula is: π(d/2)^2

so:

π(12/2)^2=113.09...

Rounded that equals 113.0

Hope that helped! Let me know if you have any other questions.

Answer:

113.0 ft²

Step-by-step explanation:

Solution Given:

diameter(d) :12 ft

radius(r) = d/2= 12/2=6 ft

now

we have

area of the circle= πr²=22/7*6²= 113. 14 ft² =113 ft²

You are right

Answer: 7

Step-by-step explanation:

Combine like terms

7^15/7/^14 = 7

The coefficient of q in the sum of these two expression is 1/2.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The given expressions are (2/3q −3/4) and (−1/6 q − 2).

We have to add these two expressions.

First arrange in such a way that like terms are together.

(2/3q −3/4) + (−1/6 q − 2) = (2/3q - 1/6q) + (-3/4 - 2)

                                        = (4/6q - 1/6q) + (-3/4 - 8/4)

                                        = 3/6q - 11/4

                                        = 1/2 q - 11/4

Hence the sum of the given expressions is 1/2 q - 11/4. And the coefficient of q is 1/2.

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The volume of the triangular region with vertices (0,0), (1,0), and (0, 1). Cross-sections perpendicular to the y-axis are isosceles triangles with height 3 is V = 3/4.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry.

From the given vertices we can write the equation of the base of the triangular region as:

x = 1 - y

The area of the triangular region is given as:

A = 1/2 (b)(h)

A = 1/2 (1-y)(3)

The volume of the region is calculated by taking the integration of the area:

[tex]V = \int\limits^1_0 {\frac{3}{2} [1 - y] } \, dx\\\\V = \frac{3}{2} [y - \frac{y^2}{2} ]_0^1[/tex]

Substituting the values of the limit we have:

V = 3/2 [ 1 - 1/2]

V = 3/2 [1/2]

V = 3/4

Hence, the volume of the triangular region with vertices (0,0), (1,0), and (0, 1). Cross-sections perpendicular to the y-axis are isosceles triangles with height 3 is V = 3/4.

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If 18 is the quotient of a number and 6, the value of the unknown number is 108.

Given the statement in the question;

18 is the quotient of a number and 6

Let the unknown number be represented by 'x'.

The quotient of a number and 6 the same as x / 6

Hence

18 = x / 6

Solve for x

Cross multiply the equation

18 × 6 = x

x = 18 × 6

Multiply 18 and 6

x = 108

Therefore, the value of x is 108.

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The x-intercept of the function is given by x=±9

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here: The function y=x²-81

To find x-intercepts of the functions we set y=0

Thus y=x²-81

x²-81=0

x=√81

x=±9

Hence, The x-intercept of the function is given by x=±9

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Answer:

A

Step-by-step explanation:

As x gets larger, the y-values became more and more negative. This means that as x approach infinity, y approaches negative infinity.

On the other side, as x gets smaller, the y-value also gets more and more negative. This means as x approaches negative infinity, y also approaches negative infinity.

This is shown in answer option A.

Using conditional probability, it is found that there is a 0.7921 = 79.21% probability that the body is attempting to reject the kidney.

Conditional Probability:

P(A|B)=P(A∩B)/P(A)

where:

P(B|A) is the probability of event B happening, given that A happened.

P(A∩B) is the probability of both A and B happening

P(A) is the probability of A happening.

Event A: Positive test.

Event B: Body attempting to reject the kidney.

The percentages associated with a positive test are:

80% of 30%(experience kidney rejection).

9% of 70%(do not experience kidney rejection).

Hence:

P(A)=0.8*0.3+0.09+0.7

P(A)=0.303

The probability of both a positive test and the body attempting to reject the kidney is:

P(A∩B)=0.8*0.3=0.24

Hence, the conditional probability is:

P(B|A)=0.24/0.303

P(B|A)=0.7921.

0.7921 = 79.21% probability that the body is attempting to reject the kidney.

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The truth value of a is False and after seeing the result of 1st statement b is true.

A mathematical statement like "3 is bigger than 4," "an infinite set exists," or "7 is prime" is referred to as a proposition.

A statement that is presumptively true is known as an axiom. Although there are several exceptions, mathematical logic can typically classify a claim as true or false given enough information (e.g., "This statement is false").

let p(x):x^2<=4

the domain for x is all positive integers (1, 2, 3, . . .).

(a) p(5)

p(5):25 not equal or less than 4

hence the truth value of a is False

(b)  negation for x;p(x)

after seeing the result of 1st statement b is true.

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The cost to rent each chair and table is $7.2 and $6.6 respectively.

Simultaneous equations are two or more algebraic equations with the same unknown variables and the same value of the variables that satisfies all such equations. This implies that the simultaneous equations have a common solution.

Let chairs = c

Let tables = t

5c + 3t = 36 --- 1

2c + 6t = 54 --- 2

From equation 2

2c + 6t = 54

c = 27 - 3t

Substitute c in equation 1

5(27 - 3t) = 36

135 - 15t = 36

135 - 36 = 15t

t = 99/15

t = $6.6

c = 27 - 3(6.6)

c = 27 - 19.8

c = $7.2

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The length of side x obtained using trigonometric ratios is 5 units

Trigonometric ratios are expressions that indicate the relationship between the lengths of two of the sides of a right triangle and the interior angles of the right triangle.

The specified triangle is a right triangle, therefore, if the interior angles, and the length of one of the sides is known, the lengths of the other sides can be found.

The right triangle is a 30°-60°-90° right triangle

The length of the hypotenuse side = 10

The length of the leg with measurement x, can therefore, be found using trigonometric ratios follows;

sin(θ) = Opposite/Hypotenuse

sin(30°) = x/10

Therefore; x = 10 × sin(30°)

x = 10 × 0.5 = 5

The length of the side x in the right triangle is 5 units

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Corn's market value  in 5 days will  be 64273.95.

What is exponential decay function?

A exponential decay is a function that, as the name implies, decays exponentially. So it decays fast at the beginning and slower as the value of the variable increases.

The form of the general exponential decay is:

f(x) = A*(r)ˣ

r is rate

A=initial value

Exponential decay:

y=a(1-r)ᵗ

a= initial value, r in decimal = 0.07, t = 5 days

y= 92389 (1-0.07)⁵

y=  92389(0.93)⁵

y= 64273.95

Corn's market value  in 5 days will  be 64273.95

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The algebraic expression is 2 + y.

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,

Sum of 2 and y

This can be written as,

2 + y

Thus,

The expression is 2 + y.

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As t increases without bound. N(t) approaches:

N(t) is limited by the number of people who started the rumor.

The correct answer is option (A).

The given exponential model is defined as follows:

[tex]N(t)=5501+49e^{-0.7t}[/tex]

For t = 0

Substitute the value of t = 0 in the above equation,

[tex]N(t)=5501+49e^{-0.7\times0}[/tex]

N(t) = 5501 + 49 × 1

N(t) = 5501 + 49

N(t) = 5550

Thus, 5550 people started the rumor.

Since [tex]49e^{-0.7t}[/tex] is greater than zero for all real t.

Then, [tex]5501+49e^{-0.7t} > 5501\\[/tex]

So, as t increases without bound.

N(t) approaches:

N(t) is limited by the number of people who started the rumor.

Therefore, the correct answer is option (A).

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The complete question is as follows:

The equation [tex]N(t)=5501+49e^{-0.7t}[/tex] models the number of people in a town who have heard a rumor after t days. As t increases without bound, what value does N(t) approach? Interpret your answer.

How many people started the rumor?

N(t) approaches:

A. N(t) is limited by the number of people who started the rumor.

B. N(t) is limited by the carrying capacity of the town.

C. N(t) is limited by the number of days it takes for the entire population to hear the rumor.

D. N(t) is limited by the rate at which the rumor spreads.

E. N(t) is not limited by any value and increases without bounds.

A general solution to the system Ax = 0 in parametric vector form is given by:

X = X_2 * [1 0 1 0 0] + X_3 * [0 1 0 1 0]

The matrix [2 -1 -4 2 6 -3] can be row-reduced to the row-echelon form [2 -1 -4 0 6 -9], which has a pivot in the first, second and fourth columns. This implies that the columns with zero entries in the row-echelon form correspond to free variables in the solution.

Since there are two free variables in the row-echelon form, the solution to the homogeneous linear system Ax = 0 will be in the form of a parametric vector, where X_2 and X_3 are the free variables and X_1, X_4, and X_5 are expressed in terms of X_2 and X_3.

A general solution to the system Ax = 0 in parametric vector form is given by:

X = X_2 * [1 0 1 0 0] + X_3 * [0 1 0 1 0]

where X_2 and X_3 are arbitrary constants. This represents a two-dimensional subspace in R^5, which consists of all linear combinations of the two linearly independent vectors [1 0 1 0 0] and [0 1 0 1 0].

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The probability of randomly drawing a vowel is 2/7, option C is correct.

Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.

Given a set of cards spell P, E, R, C, E, N, T, S

total cards = 8

so total outcome = 8

to find  the probability of randomly drawing a vowel,

set contains 2 vowels,

a favorable outcome for vowel = 2

probability =  favorable outcome/total outcome

P(vowel) = 2/7

Hence option C is correct.

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