For the rational function f(x)=2−x4x+6, find the point on the graph at the function value f(x)=1.

Answer:

x=11

Step-by-step explanation:

let number =x

(8+3x)=41

group like terms

3x=41-8

3x=33

divide both side by the coefficient of x

3x/3=33/3

x=11

Answer:

25.12 cm

Step-by-step explanation:

The circumference of a circle can also be understood as the perimeter of the circle.

Circumference of circle= 2πr= πd

r refers to radius while d refers to diameter

Given that r= 4,

circumference of circle

= 2(π)(4)

= 8π

≈ 8(3.14)

= 25.12 cm

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The value of the composite functions, (h ° f)(1) = 0.5.

Given the function, (h ° f)(1), this means h(f(1)) as a composition of functions.

Using the table given for the function, f(x), f(1) = -1.

This means that, to find (h ° f)(1) = h(f(1)), we would find the value of h(x) in the table where x = -1.

Thus, from the table for h(x), when x = -1, h(-1) = 0.5.

Therefore, the value of the composite functions, (h ° f)(1) = 0.5.

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Answer:

See explanation

Step-by-step explanation:

3x/(-8)=-21/4

-3x/8=-21*8/4

-3x*8/8=-21*8/4    ==> multiply 8 on both sides to get rid of denominator

-3x=-21*2

-3x=-42

3x=42   ==> Multiply by -1 on both sides to get positive values on both sides

x=14

The value of full positive integer k such that  [tex]O(n^k)[/tex] is the most restrictive polynomial-time upper bound of f(n) are as follows : (A) 9 (B) no integer exists (C)5/3(not an integer) (D)no integer exists (E) [tex]3e^{99}[/tex]

Using the Lower and Upper Bound Theory, it is possible to identify the algorithm with the lowest level of complexity. Let's quickly review what Lower and Upper bounds are before we can understand the theory.

A)[tex]2^{lg(3n+4n+5)}+lg {\spaceh} n \inO(n^k)[/tex]

or, [tex]O(2^{lgn^9}+lgn)\inO(n^k)[/tex]    since   [tex]3n^9+4n+5=O(n^9)[/tex]  

or, [tex]O(2^{lgn^9})\in O(n^k)[/tex] as [tex]2^m+lg m=O(2^m)[/tex]

Applying lg 2 on both sides we get:

[tex]lg_22^{lgn^9}=lg_2n^k[/tex]

solving we get:

k=9 × lg2 × lg n

At n=1/2

k=9

Hence the minimum integer for K is 9.

B) [tex]7lgn+13lg^5n\in O(n^k)[/tex]

Solving for k we get:

k=lgₙ(lg⁵n)

C) [tex]\sqrt[3]{7n^5+2n^3-4}\in O(n^k)[/tex]

Solving by exponent rule we get:

[tex]O(n^{5/3})\in O(n^k)[/tex]

k=5/3

D)[tex]13lg2^{3^n\inO(n^k)}[/tex]

or, [tex]k=lg_n(lg2^{3^n})[/tex]

E)[tex]7^{20!+1} \inO(n^k)[/tex]

As we don't have any term of n on the Left Hand Side, therefore no most restrictive polynomial-time upper bound exist for [tex]O(n^k)[/tex]

[tex]k=e^{99}[/tex]

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Answer:

x = 22.5

2x = 45

5x = 112.5

Step-by-step explanation:

The sum of all internal angles in a triangle is 180 degrees. This can be expressed as the following:

x + 5x + 2x = 180

Combine the like terms:

8x = 180

Divide both sides by 8 to find the value of x:

x = 180/8

Simplify:

x = 22.5

Multiply by 2 to get 2x:

2x = 22.5 * 2

2x = 45

Multiply by 5 to get 5x:

5x  = 22.5 * 5

5x = 112.5

Verify the answer is correct by taking all the obtained values and ensuring they sum to 180:

22.5 + 45 + 112.5 = 180

The translation of the graph that has the domain [−3, 6] is:

B. g(x) = |x + 3|.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, the parent function is given by:

f(x) = |x|.

The domain changed by [−6, 3] to [-3,6], meaning that 3 units was added to each bound of the domain, hence x -> x + 3 and:

g(x) = |x + 3|.

Which means that option B is correct.

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The algebraic expression from the given statement is (a+b)/ab.

Given the statement is the quotient of the sum of a and b and the product of a and b.

In mathematics, an expression is defined as a set of numbers, variables, and operations that are formed according to context-dependent rules.

In the given statement the sum of a and b means a+b.

And the product of a and b means ab.

Now, as it is given in the statement that the quotient of the sum of a and b and the product of a and b can be written as

(a+b)/ab.

Hence, the algebraic expression from the given statement "the quotient of the sum of a and b and the product of a and b" is (a+b)/ab.

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Answer:

10 x 12 x 9 cm^2

= 1080 cm^2

Answer:

105

Step-by-step explanation:

a = 1/2(bh) + 1/2(bh)

a = 1/2(12)(10) + 1/2 (9)(10)

a= 1/2 (120) + 1/2(90)

a = 60 + 45

a = 105

Answer:

x=3 and y=

Step-by-step explanation:

Answer:

x=5 and y any number

Step-by-step explanation:

Answer:

6+3+11/4[tex]\neq[/tex]5

Step-by-step explanation:

Answer:

The answer to the question is 0

Answer:

98

Step-by-step explanation:

Applying the definition of bisection, PR = RQ = 28.5 cm.

When a line segment bisects another line segment, it divides the line into two equal segments. This means the two resultant line segments formed have the same length.

The image below shows the bisection of segment PQ by segment ST at point R, which forms two equal segments, PR and RQ.

This means that the length of segments PR and RQ will be equal to each other.

Given that, PQ = 57 centimeters, therefore:

PR = RQ = 1/2(PQ)

PR = RQ = 1/2(57)

PR = RQ = 28.5 cm

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students voted= 195

Solution :

a word problem is a problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well.

Jessica = 65 student

Sierra =  2 (Sixty-five students voted for Jessica.) = 2(65) = 130

Total number of students = NO of students voted for Jessica +NO of students voted for  Sierra

= 65+130

= 195

students voted= 195

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Answer:

the second piece of rope

Step-by-step explanation:

2.63 ≥ 2.5

2.085≤2.5

The number of meters of fence he would need is 45.72 meters

The given parameters are

Length of backyard = 150 ft

As a general rule, we have the following conversion equation

1 foot = 0.3048 meters

So, we have

Length of backyard = 150 * 0.3048 meters

Evaluate the product

So, we have

Length of backyard = 45.72 meters

Hence, the number of meters of fence he would need is 45.72 meters

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Answer:

C. two-thirds raised to the fourteenth

Step-by-step explanation:

Answer:

a. -5; b. 4; c. -2.

Step-by-step explanation:

a) f(-3)=3*(-3)+4=-5;

b) f(3)=2*3-2=4;

c) f(0)=2*0-2=-2.

Answer:

                  Equation: Y'=33.67+0.54*X'

Step-by-step explanation:

Given that

General regression line equation is:

Y'=a+b*X'

Therefore, the slope of the regression line is equal to the linear correlation coefficient times the difference between the standard deviations of y' and x'.

[tex]b = r\times\frac{S_y}{S_x}[/tex]

[tex]b = 0.5\times\frac{2.7}{2.5}[/tex]

b = 0.54

The mean of the lowered by the slope and mean of x is the intercept with axis y.

[tex]a = y'-b\times x'[/tex]

[tex]a = 68.5-0.54\times 64.5[/tex]

[tex]a = 33.67[/tex]

Now, putting the values of a and b in regression equation

So, we get

                  Y'=a+b*X'

Equation: Y'=33.67+0.54*X'

Answer:

                  Equation: Y'=33.67+0.54*X'

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By finding square numbers, we will get:

8 < √80 < 9

And we can assume that √80 is closer to 9 than to 8, so a good estimation can be 8.95

We want to approximate √80, now we need to find two consecutive square numbers such that one is smaller and the other is larger than 80.

We know that:

9*9 = 81

8*8 = 64

Then:

√81 = 9

√64 = 8

So we can see that:

√64 < √80 < √81

Then:

8 < √80 < 9

And we can assume that √80 is closer to 9 than to 8, so a good estimation can be 8.95

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Answer: y - 2 = 2(x + 7)

Step-by-step explanation:

        Point-slope form is written as y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex]) where m is the slope and ( [tex]x_{1}[/tex], [tex]y_{1}[/tex]) are points on the line.

y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])

y - 2 = 2(x + 7)

Answer: 7/39

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator GCD of 7 and 39 is 1

Divide both the numerator and denominator by the GCD 7 ÷ 1 39 ÷ 1

Reduced fraction: 7 39 Therefore, 7/39 simplified to lowest terms is 7/39.

The speed and the course of the aircraft  is 27465 km/h.

A machine or vehicle can fly by obtaining support from the air, and this is how an airplane works. It uses either static lift, dynamic lift provided by an airfoil, or, in certain rare situations, the downward thrust from jet engines to counteract the pull of gravity.

From the figure, let us use cosine formula to calculate the resultant displacement.

B^2 = C^2 + A^2 - 2(A)(C) cosØ

Where C = 580km

A = 360 km

Ø = 153 degree

Substitute all the parameters into the formula

B^2 = 580^2 + 360^2 - 2(360)(580)cos153

B^2 = 466000 - ( - 372084.32 )

B^2 = 466000 + 372084.32

B^2 = 838084.32

Square root both sides

B = 915.5 km

You are told to use a scale of 1 cm to 50 km.

Therefore, B = 915.5/50 = 18.3 cm

The time given are: 09:23 and 09:25.

The time difference = 25 - 23 = 2 minute

Convert minutes to hours

2 minute = 2/60 = 1/30 hours

Speed = distance/time

Speed = 915.5 ÷ 1/30

Speed = 915.5 × 30

Speed = 27465 km/h

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The final answer is -9, -30.75, -13

What is Quotient?

The number resulting from the division of one number by another.

In the given statement is:

What is the quotient for 81/-9

If we divide 81 by -9

The Quotient will be -9

And, come to the next :

-123 divide by -4

The quotient will be -30.75

And, 65 divided by (-5)

The Quotient will be -13

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Answer:

27

Step-by-step explanation:

just subtract 153 from 180

The interval representing the expression "82 less than a is at least −82." is given by ( -82, 82).

We are given an expression that:

82 is less than a which is at least - 82.

This expression can also be written as:

- 82 < a and a > 82

where a is any variable that can take any value according to the expression.

This can also be written as:

- 82 < a < 82

In interval form, it will be written as:

( -82, 82)

"()" brackets are used as -82 and 82 are not included in the interval.

Therefore, we get that, the interval representing the expression "82 less than a is at least −82." is given by ( -82, 82).

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Based on the fact that m represents the number of months and w is the total number of spelling words, the equation that represents the relationship between m and w is w = 8m + 3

The first thing to find is the slope of the relationship. This can be found as:

= ( 51 - 43) / (6 - 5)

= 8 / 1

= 8

The y-intercept is:

w = 8m + c

43 = 8(5) + c

c = 43 - 40

c = 3

The equation to represent the relationship between m and w is:

w = 8m + 3

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Answer:

[tex]y=\dfrac{7}{3}\left(\dfrac{1}{3}\right)^x[/tex]

Step-by-step explanation:

Given table:

[tex]\begin{array}{|c|c|}\cline{1-2} \phantom{\dfrac{1}{1}} x & y \\\cline{1-2} \phantom{\dfrac{1}{1}} -1 & 7 \\\cline{1-2} \phantom{\dfrac{1}{1}} 0 & \frac{7}{3}\\\cline{1-2} \phantom{\dfrac{1}{1}} 1 & \frac{7}{9}\\\cline{1-2} \phantom{\dfrac{1}{1}} 2 & \frac{7}{27}\\\cline{1-2} \phantom{\dfrac{1}{1}} 3 & \frac{7}{81}\\\cline{1-2}\end{array}[/tex]

Work out the first differences between the y-values:

[tex]7 \underset{-\frac{14}{3}}{\longrightarrow} \dfrac{7}{3} \underset{-\frac{14}{9}}{\longrightarrow} \dfrac{7}{9} \underset{-\frac{14}{27}}{\longrightarrow} \dfrac{7}{27} \underset{-\frac{14}{81}}{\longrightarrow} \dfrac{7}{81}[/tex]

As the first differences are not the same, it is not a linear function.

Work out the second differences:

[tex]-\dfrac{14}{3} \underset{+\frac{28}{9}}{\longrightarrow} -\dfrac{14}{9} \underset{+\frac{28}{27}}{\longrightarrow} -\dfrac{14}{27} \underset{+\frac{28}{81}}{\longrightarrow} -\dfrac{14}{81}[/tex]

As the second differences are not the same, it is not a quadratic function.

Work out if the second differences have a common ratio:

[tex]\implies \sf \dfrac{28}{27} \div \dfrac{28}{9}=\dfrac{1}{3}[/tex]

[tex]\implies \sf \dfrac{28}{81} \div \dfrac{28}{27}=\dfrac{1}{3}[/tex]

As the second differences have a common ratio of ¹/₃, the function is exponential with base ¹/₃.

General form of an exponential function:

[tex]y=a(b)^x[/tex]

where:

The y-intercept is the value of y when x = 0.

From inspection of the table, the y-intercept is ⁷/₃.

Therefore:

  [tex]a = \dfrac{7}{3}[/tex]

  [tex]b = \dfrac{1}{3}[/tex]

Substitute the found values of a and b into the formula to create an exponential function that models the given data:

[tex]\implies y=\dfrac{7}{3}\left(\dfrac{1}{3}\right)^x[/tex]

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