Find the inverse of f(x).

The recursive rule is f(n) = f(n - 1) * 2; f(1) = 9 and the explicit rule is f(n) = 9(2)^n-1

The recursive rule

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

The table

The table definitions imply that we simply multiply 2 to the previous term to get the current term

This means that

f(n) = f(n - 1) * 2

Where

f(1) = 9

The explicit rule

The table definitions imply that we simply multiply 2 to the previous term to get the current term

a = 9

r = 2

So we have

f(n) = a * r^n-1

This gives

f(n) = 9(2)^n-1

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The angle measures are given as follows:

First we must obtain the value of x, considering the total sum of the interior angle measures of the polygon, and then with the value of x we obtain each angel measure.

The sum of the interior angle measures of a polygon with n sides is given by the equation presented as follows:

S(n) = 180 x (n - 2).

The polygon has six vertices, hence the sum is given as follows:

S(6) = 180 x 4

S(6) = 720.

We then add all the angle measures to obtain the value of x as follows:

7x - 8 + 4x + 46 + 5x + 6x + 12 + x + 7 + 5x - 9 = 720

28x = 768

x = 768/28

x = 27.43.

Then each angle measure is rounded as follows:

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The measurement of the given angle is a 90 degree.

According to the statement

We have to find that the measurement of this angle.

So, For this purpose, we know that the

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

From the given information:

In the given figure, the measurement of the angle we have to find.

A 90-degree angle is a right angle and it is exactly half of a straight angle. It always corresponds to a quarter turn.

And from the figure it is clearly visible that the line of the angle exactly matches with the 90 degree.

Then the angle is 90 degree.

So, The measurement of the given angle is a 90 degree.

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The round off of the area of the triangle 93.725 will be 94

In the above question, it is given as

We need to round off of the area of a triangle which is given as 93.725

But first, we'll understand the rules for rounding of any number

1) When rounding of whole numbers

i) if the number if ending with digits, 5,6,7,8, or 9 then the round of that number will be up.

Ex. 18 has round of as 20 nearest 10

26 has round of as 30 nearest 10

ii)  if the number if ending with digits, 0,1,2,3 or 4 then the round of that number will be least nearest 10

Ex. 12 has round of as 10

23 has round of as 20

Similarly, the rules follow for the decimal numbers.

Ex. 7.8199 will become 7.8

1.0621 will become 1.06

Now we'll round off the given area of triangle as

93.725 will become 94

Hence, the round off of the area of the triangle 93.725 will be 94

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The expression 1 2/5 + 2 2/3 using fifteenths is 3 + 6/15 + 10/15

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

1 2/5 + 2 2/3

3 + 2/5 + 2/3

To rewrite the expression using fifteenths, we multiply the numerator and the denominator of the fractions by the same number

In this case, we use 3 and 5

So, we have

3 + 2/5 * 3/3 + 2/3 * 5/5

Evaluate the products

3 + 6/15 + 10/15

Hence, the expression using fifteenths is 3 + 6/15 + 10/15

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The equivalent equation for the given equation m = ca is a = m/c. The equivalent equation has no effect on the original equation's actual function.

An equivalent equation is one that yields the same solution as the original equation.

The equivalent equation is obtained by removing a variable from the given equation. There will be the same number of equivalent equations as there are variables in an equation.

Given that,

m = ca

Here m, c, and a are the three variables in the given equation.

We can write the equation into two more forms as follows:

W.r.t variable 'c',

m = ca

Dividing both sides by 'a'

⇒ ca/a = m/a

c = m/a

W.r.t variable 'a',

m = ca

Dividing both sides by 'c'

⇒ ca/c = m/c

a = m/c

The missing image is attached with the answer.

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Answer:

12

Step-by-step explanation:

Answer:

  angle 1 = 30°

Step-by-step explanation:

Where a transversal crosses parallel lines, consecutive interior angles are supplementary. That means angles 1 and 2 total 180°.

  (x +10)° +(5x +50)° = 180°

  6x +60 = 180 . . . . . . . . . . . divide by °, collect terms

  x +10 = 30 . . . . . . . . . . . divide by 6

The measure of angle 1 is x+10, so is 30°.

The answer is explained below.

In order to be considered a language, a system of communication must have vocabulary, grammar, syntax, and people who use and understand it. Mathematics meets this definition of a language. Linguists who don't consider math a language cite its use as a written rather than spoken form of communication.

Mathematics is pure language - the language of science. It is unique among languages in its ability to provide precise expression for every thought or concept that can be formulated in its terms. In a spoken language, there exist words, like "happiness", that defy definition.

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The inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

Inverse of a function can be calculated by following the steps mentioned below -

According to the question, the equation given is as follows

y = f(x) = 2x + 5

y = 2x + 5

Replace 'y' with 'x', we get -

x = 2y + 5

Now, solve for y -

2y = x - 5

y = (x/2) - (5/2)

Replace 'y' with f⁻¹(x) -

f⁻¹(x) = (x/2) - (5/2)

Hence, the inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

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The equation that represents a quadratic relationship is y = 4x^2. Option A.

A quadratic relationship is a mathematical relationship where the variable y is a function of the variable x raised to the power of 2. In other words, it is an equation in which the highest power of the variable is 2.

Let's analyze the given equations:

1. y = 4x^2: This equation represents a quadratic relationship because the variable x is raised to the power of 2. The term 4x^2 indicates that the relationship between x and y is quadratic.

2. y = 4x^4: This equation represents a quartic relationship, not a quadratic relationship. The variable x is raised to the power of 4, which indicates a higher degree relationship than quadratic.

3. y = 4x^3: This equation represents a cubic relationship, not a quadratic relationship. The variable x is raised to the power of 3, indicating a higher degree relationship.

4. y = 4: This equation represents a linear relationship, not a quadratic relationship. It is a constant equation where y is always equal to 4, regardless of the value of x. In a quadratic relationship, the variable x should have a power of 2. Option A.

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Answer:

I think it's D

Step-by-step explanation:

I think it's D

Answer:

D

Step-by-step explanation:

The military term most often used for retreat is withdraw. It means that some advanced position, the battle cannot be won or turned around. So you withdraw from the field.

A: advance. No you are doing the exact opposite of retreat.

B: attack. Same as A. You are leaving the field with retreat.

C: Surrender is an entirely different thing. It means that you have given up the field and are not willing to fight anymore.

D: answer

Answer:

C. 101 3/4; $1017.50

Step-by-step explanation:

Correct on E2020!

Answer:

Step-by-step explanation:

Answer:

48.49 feet

Step-by-step explanation:

The diagrammatic sketch of the details given in the question was attached in the picture below.

From the picture below, the distance between the two kites is represented by (c) and can be calculated by using the cosine angle rule which is illustrated as:

\(c^2 = a^2 + b^2 -2ab cos \ C\)

where;

a = 110

b = 104

Cos C = 26°

Then;

\(c^2 = 110^2 + 104^2 -2(110)(104) cos \ 26 \\ \\ c^2 = 12100 + 10816- 22880 ( 0.8988) \\ \\ c^2 = 22916- 20564.544 \\ \\ c^2 = 2351.456 \\ \\ c= \sqrt{2351.456} \\ \\ \mathbf{ c = 48.49 \ feet}\)

Answer:

Step-by-step explanation:

\(\sf a^{m}*a^{n} =a^{m +n}\\\\a^{\frac{1}{n}}=\sqrt[n]{a}\)

\(\sf a^{-n}=\dfrac{1}{a^{n}}\\\\\dfrac{a^{n}}{a^{m}}=a^{n-m}\\\\\\a^{0}=1\)

\(\sf (a^{n})^{m} = a^{n*m}\\\\(a^{n}*b^{m})^{p}=a^{np}b^{mp}\\\\(ab)^{n}=a^{n}b^{n}\)

Hello !

You find the GCD of 160 : 224

160

= 2 x 80

= 2 x 2 x 40

= 2 x 2 x 2 x 20

= 2 x 2 x 2 x 2 x 10

= 2 x 2 x 2 x 2 x 2 x 5

224

= 2 x 112

= 2 x 2 x 56

= 2 x 2 x 2 x 28

= 2 x 2 x 2 x 2 x 14

= 2 x 2 x 2 x 2 x 2 x 7

GDC = 2 x 2 x 2 x 2 x 2 = 32

=> 32 childrens

160/32 = 5

224/32 = 7

=> 5 apples and 7 mangoes per child

Step-by-step explanation:

in the strange US system there is suddenly a metric relationship :

1 ton = 2000 pounds.

FYI - an actual (metric) ton is 1000 kg, which is

2,204.6226218488 pounds.

anyway, as 1 ton = 2000 pounds, then 4 tons = 4×2000 = 8000 pounds.

8000 pounds cost $28,080.00.

1 pound costs therefore

28080/8000 = $3.51

Answer:

(1)0.0138

(2)A. If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent under water.

Nos 3-12: See Explanation

Step-by-step explanation:

Given the regression equation for the relation of dive duration (DD) to depth (D).

\(DD = 2.69 + 0.0138D\\$Where: Duration DD is measured in minutes\\epth D is in meters.\)

(1)The slope of the regression lie =0.0138

(2)

When D=1, DD = 2.69 + 0.0138(1)=2.7038

When D=2, DD = 2.69 + 0.0138(2)=2.7176

2.7176-2.7038=0.0138

Therefore, If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent under water.

(3) When depth, D =200 meters

DD = 2.69 + 0.0138(200)=5.45 Minutes

(4) When depth, D =210 meters

DD = 2.69 + 0.0138(210)=5.588 Minutes

(5) When depth, D =220 meters

DD = 2.69 + 0.0138(220)=5.726 Minutes

(6) When depth, D =230 meters

DD = 2.69 + 0.0138(230)=5.864 Minutes

(7) When depth, D =240 meters

DD = 2.69 + 0.0138(240)=6.002 Minutes

(8) When depth, D =150 meters

DD = 2.69 + 0.0138(150)=4.76 Minutes

(9) When depth, D =160 meters

DD = 2.69 + 0.0138(160)=4.898 Minutes

(10) When depth, D =170 meters

DD = 2.69 + 0.0138(170)=5.036 Minutes

(11) When depth, D =180 meters

DD = 2.69 + 0.0138(180)=5.174 Minutes

(12) When depth, D =190 meters

DD = 2.69 + 0.0138(190)=5.312 Minutes

A regression line is only a single line that fits the data the best. It tells how steep it is, whereas the intercept reveals where it intersects an axis.

For question 1):

By calculating the slope of the regression line we get the slope value that is \(= 0.0138\)

For question 2):

Describe whatever this slope means about this penguin's dives in precise terms.

The time spent under liquid increases by 0.0138 minutes whenever the diving depth is raised by one meter, which is equal to "Option A".

For question 3):

Calculated equation:

\(\to DD = 2.69 + 0.0138\times200 = 2.69+2.76 = 5.45\ minutes\)

For question 4):

Calculated equation:

\(\to DD = 2.69 + 0.0138\times210 = 2.69 + 2.898 = 5.588\ minutes\)

For question 5):

Calculated equation:

\(\to DD = 2.69 + 0.0138\times 220 = 2.69 + 3.036 = 5.726\ minutes\)

For question 6):

Calculated equation:

\(\to DD = 2.69 + 0.0138\times230 = 2.69 + 3.174 = 5.864 \ minutes\)

For question 7):

Calculated equation:

\(\to DD = 2.69 + 0.0138\times240 = 2.69 + 3.312 = 6.002\ minutes\)

For question 8):

Calculated equation:

\(\to DD = 2.69 + 0.0138\times 150 = 2.69 + 2.07 = 4.76\ minutes\)

For question 9):

Calculated equation:

\(\to DD = 2.69 + 0.0138\times 160 = 2.69 + 2.208 = 4.898\ minutes\)

For question 10):

Calculated equation:

\(\to DD = 2.69 + 0.0138\times 170 = 2.69 + 2.346 = 5.036\ minutes\)

For question 11):

Calculated equation:

\(\to DD = 2.69 + 0.0138\times 180 = 2.69 + 2.484 = 5.174 \ minutes\)

For question 12):

Calculated equation:

\(\to DD = 2.69 + 0.0138\times 190 = 2.69 + 2.622 = 5.312\ minutes\)

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Answer:

The equivalent expression is  \(8.25\cdot y -14\).

Step-by-step explanation:

Let \(4\cdot (1.75\cdot y -3.5)+1.25\cdot y\), we proceed to simplify the expression by like terms and other algebraic operations:

1)  \(4\cdot (1.75\cdot y -3.5)+1.25\cdot y\)  Given

2) \([1.75\cdot y +(-3.5)]\cdot 4 + 1.25\cdot y\) Commutative property/Definition of subtraction.

3) \((1.75\cdot 4) \cdot y +(-3.5)\cdot 4 + 1.25\cdot y\) Distributive and associative properties.

4) \(7\cdot y +(-14)+1.25\cdot y\) Definition of multiplication/\(a\cdot (-b) = - a\cdot b\)

5) \((7+1.25)\cdot y -14\) Commutative and distributive properties/Definition of subtraction.

6) \(8.25\cdot y -14\) Definition of addition/Result

The equivalent expression is  \(8.25\cdot y -14\).

Answer:

a. 3

b. 5

c. 4

d. 4

e. 10

Step-by-step explanation:

Answer:

read below

Step-by-step explanation:

a.3

b.5

c.2

d.2

6. 8p

The tangent, cosine and sine ratios of angles X & Y in the reduced faction form is 3/4, 4/5 and 3/5 respectively.

For a right angle triangle, the trigonometry ratios can be given as,

\(\rm \sin \theta=\dfrac{b}{c}\\\rm \cos \theta=\dfrac{a}{c}\\\rm \tan \theta=\dfrac{b}{a}\)

Here, a is base side, b is perpendicular side and c is the hypotenuse side of the triangle.

In the given triangle, the length of base side is 8 units, perpendicular side is 6 units and hypotenuse side is 10 units.

\(a=8\\b=6\\c=10\)

Thus, the  tangent, cosine and sine ratios of angles X & Y are,

\(\rm \sin \theta=\dfrac{6}{10}=\dfrac{3}{5}\\\rm \cos \theta=\dfrac{8}{10}=\dfrac{4}{5}\\\rm \tan \theta=\dfrac{6}{8}=\dfrac{3}{4}\)

Thus, the tangent, cosine and sine ratios of angles X & Y in the reduced faction form is 3/4, 4/5 and 3/5 respectively.

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Answer:

-3/2

Step-by-step explanation:

Parallel lines have equal slopes.

Consequently, the carpet's price is diversely correlated with its size. Then the cost of the carpet will be $647.82.

160 square feet of a certain carpet were purchased for $878.40 last week at Abe's carpet shop. The identical carpet, measuring 85 square feet, cost $466.65 at Bob's Carpet.

The cost of carpet per square foot in both cases will be

In the First case, we have

⇒ 878.40 / 160

⇒ $5.49 per square foot

In the second case, we have

⇒ 466.65 / 85

⇒ $5.49 per square foot

Consequently, the carpet's price is directly correlated with its size. Then the equation will be

Cost = 5.49 x Area

Then the cost of the carpet when the area is 118 square feet will be

Cost = 5.49 x 118

Cost = $647.82

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Answer:

Step-by-step explanation:

mean tide is (17.2 + 4.6)/ 2 = 10.9 ft

Amplitude of tide is (17.2 - 4.6)/ 2 = 6.3 ft

The full tide cycle is 2(5.8) = 11.6 hrs

As we are not told the tide condition at 12:00 noon,

I will ASSUME that the tide is high and use the cosine function

D = 10.9 + 6.3cos(2π(t/11.6)) ft

where t is in hours after noon high tide.

make sure your calculator is set to radians.

If you want to use degrees, the equation becomes

D = 10.9 + 6.3cos(360(t/11.6)) ft

Answer:

B) x + 1

Step-by-step explanation:

Consecutive integers mean continuous integers ( 1, 2 , 3 ,....). We will get the next number by adding 1 to the previous number.

Eg: 5 , 6 , 7 ,.....

6 = 5 + 1

7 = 6 + 1

So, if first number is x, then the next number will be x + 1

The sequence is will always have even numbers, is hence proved.

Given, the quadratic sequence is: 44:52:64:80

Sequences with a term are known as quadratic sequences. They can be distinguished by the fact that the first differences between terms are not equal but the second differences between terms are. Utilizing the term sum in an arithmetic progression formula, the sum of even numbers formula is achieved. The equation is Sum of Even Numbers Formula = n(n+1), where n is the total number of terms in the series.

The formula is: Tₙ = 2n² ₊ 2n  ₊ 40

take 2 common

Tₙ = 2(n² ₊ n  ₊ 20)

in other words n² ₊ n  ₊ 20  = y

therefore , Tₙ = 2y

which by definition makes Tₙ an even number at all times.

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