The width of a rectangle is 4 units less than the length. The area of the rectangle is 21 square units. What is the length, in units, of the rectangle?

The inverse function of f(x) = - Vx+1+6 is f^-1(x) = - Vx-7. The domain of f^-1(x) is [-1, ∞), or in interval notation, [-1, ∞).

The inverse function of f(x) = -√x+1 + 6 can be found by following the steps below:

1. Swap the x and y values, so y = -√x+1 + 6 becomes x = -√y+1 + 6
2. Solve for y by isolating it on one side of the equation:
x - 6 = -√y+1
(x - 6)² = y+1
y = (x - 6)² - 1
3. The inverse function is therefore f^-1(x) = (x - 6)² - 1

The domain of f^-1(x) can be found by considering the restrictions on the original function. Since the original function has a square root, the value inside the square root must be greater than or equal to zero. This means that:

x+1 ≥ 0
x ≥ -1

So, the inverse function of f(x) = -√x+1 + 6 is f^-1(x) = (x - 6)² - 1, and the domain of f^-1(x) is [-1, ∞).

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Step-by-step explanation:

the height is 17 feet and the distance from the wall is 8 feet

using pythogras theorem

[tex] {h}^{2} + {b}^{2} = {hypotenuse}^{2} \\ {h}^{2} + {8}^{2} = {17}^{2} \\ h = \sqrt{( {17}^{2} - {8}^{2} } \\ h = 15[/tex]

The excluded values of u in the expression (u-7)/(u^2-14u+49) are 7.

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The correct answer is sine and cosine.

The parent functions that have D = (XER) and R = ([-1, 1], YER) (in interval form) are sine and cosine.

Both sine and cosine are periodic functions that oscillate between -1 and 1 on the y-axis, meaning that their range is [-1, 1]. They also have a domain of all real numbers (XER), as they can take on any value for x and still produce a valid output.

The other parent functions listed, such as linear, quadratic, exponential, reciprocal, absolute value, and square root, do not have the same domain and range as sine and cosine. For example, the quadratic function has a domain of all real numbers, but its range is limited to values greater than or equal to the vertex. The reciprocal function has a range of all real numbers except for 0, and its domain is also all real numbers except for 0.

Therefore, the correct answer is sine and cosine.

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The answer of decimal number that has the specified place values is 964.8.

To write the decimal number, we need to understand the place value of each digit.

The place values are as follows:

- 9 hundreds = 900
- 6 tens = 60
- 4 ones = 4
- 8 tenths = 0.8
- 0 hundredths = 0.00

To write the decimal number, we add the place values together:

900 + 60 + 4 + 0.8 + 0.00 = 964.8

Therefore, the decimal number that has the specified place values is 964.8.

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Answer:

area=22/7×13=40.85=41 is the nearest whole number

Answer:

I need a graph to answer this question

Step-by-step explanation:

Answer: The answer t your question is the second one

Step-by-step explanation:

The height of the kite from the ground is 620.5 feet.

The angle of elevation from your hand to a kite is 65∘ and the distance from your hand to the kite is 287 feet.

Therefore, the height of the kite when your hand is 5 feet from the ground can be found as follows:

The situation forms a right angle triangle. Therefore, the height of the kite can be found using Pythagoras's theorem.

Hence,

tan 65 = opposite / adjacent

tan 65 = h / 287

cross multiply

h = 287 × tan 65

h = 615.473486186

Therefore,

height of the kite = 615.473486186 + 5

height of the kite = 620.5 feet

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a) f(0) = 3(0)^2 + 3(0) - 3 = -3
b) f(3) = 3(3)^2 + 3(3) - 3 = 33
c) f(−3) = 3(-3)^2 + 3(-3) - 3 = 15
d) f(−x) = 3(-x)^2 + 3(-x) - 3 = 3x^2 - 3x - 3
e)−f(x) = -(3x^2 + 3x - 3) = -3x^2 - 3x + 3
f) f(x+2) = 3(x+2)^2 + 3(x+2) - 3 = 3x^2 + 12x + 15
g) f(3x) = 3(3x)^2 + 3(3x) - 3 = 27x^2 + 9x - 3
h) f(x+h) = 3(x+h)^2 + 3(x+h) - 3 = 3x^2 + 6xh + 3h^2 + 3x + 3h - 3

We are asked to find the following for the function f(x)=3x^2+3x−3: (a) f(0) (b) f(3) (c) f(−3) (d) f(−x) (e) −f(x) (f) f(x+2) (g) f(3x) (h) f(x+h)

(a) f(0) = 3(0)^2 + 3(0) - 3 = -3
(b) f(3) = 3(3)^2 + 3(3) - 3 = 33
(c) f(−3) = 3(-3)^2 + 3(-3) - 3 = 15
(d) f(−x) = 3(-x)^2 + 3(-x) - 3 = 3x^2 - 3x - 3
(e) −f(x) = -(3x^2 + 3x - 3) = -3x^2 - 3x + 3
(f) f(x+2) = 3(x+2)^2 + 3(x+2) - 3 = 3x^2 + 12x + 15
(g) f(3x) = 3(3x)^2 + 3(3x) - 3 = 27x^2 + 9x - 3
(h) f(x+h) = 3(x+h)^2 + 3(x+h) - 3 = 3x^2 + 6xh + 3h^2 + 3x + 3h - 3

I hope this helps! Let me know if you have any further questions.

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Answer: 415

83 = [tex]\frac{y}{5}[/tex]

83(5) = y

415 = y

Answer:

y = 415

Step-by-step explanation:

83 = y/5

83 x 5 = y

415 = y

Using the statements given for congruency the proof is -

TC ≅ TM                      Given

AT bisects ∠CTM        Given

∠ATC ≅ ∠ATM            Definition of bisect

AT ≅ AT                       Reflexive property

Δ ATC ≅ Δ ATM          SAS theorem

CA ≅ MA                      ≅ Δs → ≅ parts

What is congruency?

If two shapes are similar in size and shape, they are congruent. We can also state that if two shapes are congruent, then their mirror images are identical.

A diagram of a diamond ACTM is given.

The line segment TC is equal and congruent to line segment TM.

This statement is already given in the question.

The line segment AT bisects angle CTM.

This statement is already given in the question.

The angle ATC is equal and congruent to angle ATM.

This statement is the definition of bisect.

The line segment AT is equal and congruent to line segment AT.

This statement is true by the reflexive property of the triangles.

Triangle ATC is equal and congruent to triangle ATM.

This statement is true by Side-Angle-Side (SAS) theorem of the triangles.

The line segment CA is equal and congruent to line segment MA.

This statement is true as the triangles are congruent to each other and congruent triangles have congruent parts.

Therefore, the proof is complete.

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The answer is 106993205379072 different ways that the 12 people can order from the 13 items on the menu.

There are a total of 12 people at a Restaurant and each person can order one of the 13 items on the menu. Therefore, the total number of different ways that they can order is 1312 = 106993205379072.

This is because for each of the 12 people, there are 13 choices for what they can order. So for the first person, there are 13 choices, for the second person there are 13 choices, and so on. Multiplying all of these choices together gives us the total number of different ways that they can order:

13 * 13 * 13 * 13 * 13 * 13 * 13 * 13 * 13 * 13 * 13 * 13 = 106993205379072

So the answer is 106993205379072 different ways that the 12 people can order from the 13 items on the menu.

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Isaiah's allοwance fοr the week wοuld be $43.75.

In mathematics, a fractiοn represents a part οf a whοle οr a ratiο between twο quantities. It is written as a number οr expressiοn (the numeratοr) abοve a line and anοther number οr expressiοn (the denοminatοr) belοw the line, and is typically expressed as a/b.

The numeratοr represents the number οf equal parts being cοnsidered, while the denοminatοr represents the tοtal number οf equal parts that make up the whοle. Fοr example, the fractiοn 3/4 represents three οut οf fοur equal parts, οr three-quarters οf the whοle.

Fractiοns can be used tο express values between whοle numbers, and they can be used in οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn. Fractiοns can alsο be cοnverted tο decimals οr percentages fοr ease οf cοmparisοn οr calculatiοn.

Cοmmοn types οf fractiοns include prοper fractiοns (where the numeratοr is less than the denοminatοr, such as 1/2), imprοper fractiοns (where the numeratοr is greater than οr equal tο the denοminatοr, such as 5/3), and mixed numbers (where the fractiοn is represented as a whοle number and a prοper fractiοn, such as 3 1/2).

Isaiah's allοwance fοr the week can be calculated by adding up the amοunt he earned fοr each chοre he cοmpleted. Since he earned 1/8 οf his weekly allοwance fοr each chοre, the amοunt he earned fοr a single chοre can be calculated as:

1/8 * $70.00 = $8.75

Therefοre, if Isaiah cοmpleted n chοres in a week, his tοtal earnings fοr the week wοuld be:

Tοtal earnings = n * $8.75

Fοr example, if he cοmpleted 5 chοres in a week, his tοtal earnings wοuld be:

Tοtal earnings = 5 * $8.75 = $43.75

Sο Isaiah's allοwance fοr the week wοuld be $43.75 if he cοmpleted 5 chοres. The amοunt οf his allοwance wοuld depend οn the number οf chοres he cοmpleted during the week.

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Yes, according to the Rational Zero Theorem, the possible zeros of the polynomial p(x) are +-(1,5/1,7). The only factorization that works in this case is p/q = 1.5/1.7, which yields the zeros +-(1,5/1,7).

The Rational Zero Theorem states that any rational zero of a polynomial can be expressed in the form p/q, where p and q are factors of the constant term (an) of the polynomial and q does not divide a0.

In our case, the constant term of p(x) is a3=5, so the possible rational zeros are of the form p/q, where p is a factor of 5, and q is a factor of 8.

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The value of the function at x = 2 is 11.8.

We can start by using the given values for f(0) and f(1) to create a system of equations and solve for a and k.
f(0) = 2 = a + 5ek(0)
f(1) = 9 = a + 5ek(1)
Simplifying the first equation gives us a = 2 - 5ek(0) = 2. Substituting this value of a into the second equation gives us:
9 = 2 + 5ek
7 = 5ek
k = ln(7/5)/e
Now we can substitute this value of k back into the first equation to find a:
2 = a + 5e^(ln(7/5)/e)(0)
2 = a
So, our function is f(x) = 2 + 5e^(ln(7/5)/e)x.
To evaluate f(2), we simply plug in x = 2:
f(2) = 2 + 5e^(ln(7/5)/e)(2)
f(2) = 2 + 5(7/5)^2
f(2) = 2 + 5(49/25)
f(2) = 2 + 9.8
f(2) = 11.8
Therefore, the value of the function at x = 2 is 11.8.

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The coordinates of the pre-images are (-7, 8); (-7, 5); (4, 8), and (2, 5), and the pre-image is given below.

Transformation:

A transformation of a quadrilateral refers to any process that changes the size, position, or shape of a four-sided polygon.

To draw the pre-mage, find the coordinates of the pre-mage as given below and plot the points in a graph

Here we have

The coordinates of the quadrilateral are (-4, 5); (-4, 2); (7, 5), and (5, 2)

Given T < -3, 3 > (x, y)

Hence, the coordinates of the pre-images are

(-4, 5)  => (-4 -3, 5 + 3 ) = (-7, 8)

(-4, 2) => (-4 -3, 2 + 3) = (-7, 5)

(7, 5) => (7 -3, 5 + 3) = (4, 8)

(5, 2) => (5 - 3, 2+3) = (2, 5)  

Therefore,

The coordinates of the pre-images are (-7, 8); (-7, 5); (4, 8), and (2, 5), and the pre-image is given below.

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Agree with the statement " it does have a variability because someone could be absent".

What is meant by variability?

The degree to which the data points in a statistical distribution or data collection deviate from the average value and from one another is virtually by definition the measure of variability. A mean is a common tool used by analysts to describe the centre of a population or a process. Although the mean is important, variability elicits stronger reactions in people. Values in a dataset are more consistently distributed when a distribution has less variability. The data points are more diverse and extreme values are more probable when the variability is bigger. As a result, comprehension of variability aids in understanding the possibility of uncommon events.

Peirce says that there is variability because someone could be absent.

I agree with Peirce's statement.

Because when someone is absent, the number of students changes and there is variability.

Now the range of variability changes with how many students are absent.

If there are only a few students absent, then the variability can be low.' But if there are many students absent in the class, then will be a higher variability.

Therefore there can be variability when someone could be absent.

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Answer:

How are we supposted to do your homework if we dont have a picture or explanation of it??

Step-by-step explanation:

The values of the constant λ that will make y = e^(λx) a solution of the differential equation y′′ −3y′ + 2y = 0 are λ = 1 and λ = 2.

To find the value(s) of the constant λ that will make y = e^(λx) a solution of the differential equation y′′ −3y′ + 2y = 0, we can substitute y = e^(λx) into the differential equation and solve for λ.

First, we need to find the first and second derivatives of y = e^(λx):

y′ = λe^(λx)

y′′ = λ^2e^(λx)

Now, we can substitute these derivatives into the differential equation:

λ^2e^(λx) − 3λe^(λx) + 2e^(λx) = 0

e^(λx)(λ^2 − 3λ + 2) = 0

Since e^(λx) cannot equal 0, we can set the expression in parentheses equal to 0 and solve for λ:

λ^2 − 3λ + 2 = 0

(λ − 1)(λ − 2) = 0

λ = 1 or λ = 2

Therefore, the values of the constant λ that will make y = e^(λx) a solution of the differential equation y′′ −3y′ + 2y = 0 are λ = 1 and λ = 2.

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The explanatory variable is the one that is thought to influence or cause changes in the response variable. In this case, the most logical explanatory variable would be the treatment (5).

Since it is the factor that is being manipulated to potentially affect the other variables. The response variable would be the health condition (2), An explanatory variable, is also known as an independent variable or predictor variable since it is the outcome that is being measured in response to the treatment. The other variables, cold (1), placebo (3), and vitamin C (4), are not considered variables in this case because they are not being manipulated or measured.

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The Lowest Common Factor (LCF) and Highest Common Factor (HCF) are concepts used in mathematics to find the factors that are common to two or more numbers.

The LCF is the smallest factor that two or more numbers have in common, while the HCF is the largest factor that two or more numbers have in common.

For example, consider the numbers 12 and 18--

The factors of 12 are 1, 2, 3, 4, 6, and 12.

The factors of 18 are 1, 2, 3, 6, 9, and 18.

The common factors of 12 and 18 are 1, 2, 3, and 6.

Therefore, the LCF of 12 and 18 is 6, and the HCF of 12 and 18 is 3.

Note that the LCF and HCF are also called the Lowest Common Denominator (LCD) and Highest Common Factor (HCF) respectively.

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The rank of At is the number of linearly independent rows or columns in the matrix. Since At has an inverse for all values of t, the rank of At is 3 for all values of t.

In order to determine the values of t for which At has an inverse, we need to find the determinant of At. If the determinant of At is not equal to 0, then At has an inverse. The determinant of At is given by:

|At| = (1)(5)(-6) + (3)(t)(4) + (2)(2)(7-t) - (4)(5)(2) - (7-t)(t)(1) - (-6)(2)(3)

Simplifying the above expression, we get:

|At| = -30 + 12t + 28 - 14t - 40 - 5t2 + 12

Combining like terms, we get:

|At| = -5t2 - 2t - 30

Setting the determinant equal to 0, we get:

-5t2 - 2t - 30 = 0

Using the quadratic formula, we can find the values of t for which the determinant is equal to 0:

t = (-(-2) ± √((-2)2 - 4(-5)(-30)))/(2(-5))

t = (2 ± √(4 - 600))/(-10)

t = (2 ± √(-596))/(-10)

Since the square root of a negative number is not a real number, there are no real values of t for which the determinant of At is equal to 0. Therefore, At has an inverse for all values of t.

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In the given window there are both acute and obtuse angles are shown.

a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space

We have to find the  types of angles are shown by the window-glass shapes

An angle is formed when two straight lines or rays meet at a common endpoint.

As we observe the angles are less than 180 degrees.

Angles between 0 and 90 degrees are called acute angles.

Angles between 90 and 180 degrees are known as obtuse angles.

Hence, In the given window there are both acute and obtuse angles are shown.

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The probability of no one getting a hole in one on the sixth hole during the 1989 U.S. Open golf tournament is 0.95431 and the probability of exactly one golfer getting a hole in one on the sixth hole is 0.04478.

The probability of an event occurring is the number of favorable outcomes divided by the number of possible outcomes. In this case, the probability of a professional golfer making a hole in one is 1/3,709.

a. To find the probability that no one gets a hole in one on the sixth hole, we need to find the probability that each of the 174 golfers does not get a hole in one. The probability of not getting a hole in one is 1 - (1/3,709) = 3,708/3,709. The probability that no one gets a hole in one is (3,708/3,709)^174 = 0.95431. Therefore, the probability that no one gets a hole in one on the sixth hole is 0.95431.

b. To find the probability that exactly one golfer gets a hole in one on the sixth hole, we need to find the probability that one golfer gets a hole in one and the rest do not. The probability of one golfer getting a hole in one is 1/3,709 and the probability of the rest not getting a hole in one is (3,708/3,709)^173. There are 174 ways this can happen, so the probability is 174 * (1/3,709) * (3,708/3,709)^173 = 0.04478. Therefore, the probability that exactly one golfer gets a hole in one on the sixth hole is 0.04478.

In conclusion, the probability of no one getting a hole in one on the sixth hole during the 1989 U.S. Open golf tournament is 0.95431 and the probability of exactly one golfer getting a hole in one on the sixth hole is 0.04478.

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The polynomial equation is solved and the value of A is given by the long division A = 3x³ + 6x² + 4x - 3 - 5/( x -2 )

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the polynomial equation be represented as A

Now , let the first equation be p

p = 3x⁴ - 8x² - 11x + 1

Let the second equation be q

q = ( x - 2 )

And , the value of A = p/q

On simplifying , we get

A = ( 3x⁴ - 8x² - 11x + 1 ) / ( x - 2 )

From the long division of polynomials , we get

Step 1 :

A = 3x³ + [ ( 6x³ - 8x² - 11x + 1 ) / ( x - 2 ) ]

The student went wrong while multiplying the quotient 3x³ with the divisor -2 , it should have been 6x³ instead of 6x²

Step 2 :

A = 3x³ + 6x² + [ ( 4x² - 11x + 1 ) / ( x - 2 ) ]

Step 3 :

A = 3x³ + 6x² + 4x + [ ( -3x + 1 ) / ( x - 2 ) ]

Step 4 :

A = 3x³ + 6x² + 4x - 3 - [ 5/( x -2 ) ]

Therefor , the long division is solved , A = 3x³ + 6x² + 4x - 3 - [ 5/( x -2 ) ]

Hence , the polynomial is A = 3x³ + 6x² + 4x - 3 - [ 5/( x -2 ) ]

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The arclength of the circular sector with radius r = 5.1 and central angle θ = 145º is 13.06. The area of the circular sector is 32.54.

The arclength and area of a circular sector can be calculated using the following formulas:

Arclength = (θ/360) * 2πr

Area = (θ/360) * πr²

Where θ is the central angle in degrees, r is the radius, and π is the constant pi.

Plugging in the given values for r and θ, we get:

Arclength = (145/360) * 2π(5.1) ≈ 12.90

Area = (145/360) * π(5.1)² ≈ 32.91

So, the arclength of the circular sector is approximately 12.90 units and the area is approximately 32.91 square units.

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Answer:

Step-by-step explanation:4.  12 divided by 3 is 4 so 4

Therefore, the order from least to greatest is:d<f<a<b<c<e

d. 2√2 x √5 ≈ 5.66, f. 3√2 x √3 ≈ 6.00, a. 4√3 = 4 x √(3) ≈ 6.93, b. 3√5 ≈ 6.71, c. 5√2 ≈ 7.07, e. 2√13 ≈ 7.21

To arrange these radicals in order from least to greatest, we need to simplify them and compare the values. We can start by simplifying the radicals using prime factorization.

a. 4√3 = 4 x √(3) = 4 x√(3)

b. 3√5 = 3 x √(5)

c. 5√2 = 5 x√(2)

d. 2√10 = 2 x √(25) = 2 x √(2) x √(5) = 2√2 x√5

e. 2√13 = 2 x √(13)

f. 3√6 = 3 x √(23) = 3 x √(2) x √(3) = 3√2 x √3

Now, we can compare the values of the radicals by comparing their coefficients and the values inside the radical:

a. 4√3 = 4 x √(3) ≈ 6.93

b. 3√5 ≈ 6.71

c. 5√2 ≈ 7.07

d. 2√2 x√5 ≈ 5.66

e. 2√13 ≈ 7.21

f. 3√2 x √3 ≈ 6.00

Therefore, the order from least to greatest is:

d. 2√2 x √5 ≈ 5.66

f. 3√2 x √3 ≈ 6.00

a. 4√3 = 4 x √(3) ≈ 6.93

b. 3√5 ≈ 6.71

c. 5√2 ≈ 7.07

e. 2√13 ≈ 7.21

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Total students=1,200

Total number of students whose favorite movie genre is Romance= 10%

So,

10% of total students= 10% of 1,200

Therefore, the Total students who chose romance= 10/100*1200=120

Similarly, 10% of students chose Science fiction, and the total number of students who chose science fiction=10/100*1200=120

Therefore,

Total students who chose romance=120

Total students who chose science fiction=120