in the adjoining figure prove that<A+<B+<C+<D+<E is equal 180​

The value of f(1) is 81

Recursive Function is a function that repeats or uses its own previous term to calculate subsequent terms and thus forms a sequence of terms

Given:

f(n + 1) = 1/3* f(n)

f(3) = 9

let n=0

f(0+1) = 1/3 * f(0)

f(1) = 1/3 * f(0)

Let n=1

f(1+1) = 1/3 * 1/3*f(0)

f(2) = 1/9 * f(0)

let n=2

f(2+1) = 1/3 * 1/9* f(0)

f(3) = 1/27 * f(0)

Also, f(3) =9

So,

9 = 1/27 * f(0)

f(0) = 27 * 9

f(0) = 243

Now,

f(1) = 1/3 * f(0)

f(1) = 1/3/ 243

f(1) = 81

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Answer:

y= 25/3 - x/3

Step-by-step explanation:

y= 25/3 - x/3

Answer:

A

Step-by-step explanation:

:p

Polygon 3 and 4 are similar to polygon 1.

Polygons will be called similar if they are exactly in the same shape, but can be in different sizes.

Here given, Some of the images are images of the polygon 1 from similarity transformations.

So we have to find the similar polygon from the given picture.

From picture it is clear that Polygon 2 is similar to polygon 1 as the size of polygon 2 has been decreased from polygon 1 but the shape of polygon 2 is the same as polygon 1 as we can their corresponding angles are also equal.

Also, polygon 3 is similar to polygon 1 as the size of polygon 3 has been decreased from polygon 1 but the shape of polygon 2 is the same as polygon 1 and reversed of polygon 1. So polygon 3 is of the same orientation as polygon 1 as we can their corresponding angles are also equal.

So from above, it is clear that Polygon 1 is similar to polygon 3 and 4 as they have the same shape but different sizes.

Therefore Polygon 3 and Polygon 4 are similar to polygon 1.

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Answer:

D

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here (h, k ) = (3, - 2 ) , then

y = a(x - 3)² - 2

to find a substitute the point (4, 3 ) into the equation

3 = a(4 - 3)² - 2 ( add 2 to both sides )

5 = a × 1² = a

the coefficient of the squared expression is 5

Answer ya so  1 is the answer

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Given expression:

[tex]\sf \left(\dfrac{3a^{-2}b^6}{2a^{-1}b^5} \right)^2[/tex]

To find the value of the expression when a = 3 and b = -2, substitute these values into the expression:

[tex]\implies \sf \left(\dfrac{3(3)^{-2}(-2)^6}{2(3)^{-1}(-2)^5} \right)^2[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}[/tex]

[tex]\sf \implies \left(\dfrac{3\left(\dfrac{1}{3^2}\right)(-2)^6}{2\left(\dfrac{1}{3^1} \right)(-2)^5} \right)^2[/tex]

[tex]\sf \implies \left(\dfrac{3\left(\dfrac{1}{9}\right)(-2)^6}{2\left(\dfrac{1}{3} \right)(-2)^5} \right)^2[/tex]

[tex]\sf \implies \left(\dfrac{\left(\dfrac{3}{9}\right)(-2)^6}{\left(\dfrac{2}{3} \right)(-2)^5} \right)^2[/tex]

[tex]\sf \implies \left(\dfrac{\left(\dfrac{1}{3}\right)(-2)^6}{\left(\dfrac{2}{3} \right)(-2)^5} \right)^2[/tex]

[tex]\textsf{Apply exponent rule} \quad (-a)^n=a^n,\:\: \textsf{ if }n \textsf{ is even}[/tex]

[tex]\textsf{Apply exponent rule} \quad (-a)^n=-a^n,\:\: \textsf{ if }n \textsf{ is odd}[/tex]

[tex]\sf \implies \left(\dfrac{\left(\dfrac{1}{3}\right) (2^6)}{\left(\dfrac{2}{3} \right) (-(2^5))} \right)^2[/tex]

[tex]\sf \implies \left(\dfrac{\left(\dfrac{1}{3}\right) (64)}{\left(\dfrac{2}{3} \right) (-32)} \right)^2[/tex]

[tex]\sf \implies \left(\dfrac{\left(\dfrac{1 \times 64}{3}\right)}{\left(\dfrac{2 \times -32}{3} \right)} \right)^2[/tex]

[tex]\sf \implies \left(\dfrac{\dfrac{64}{3}}{\dfrac{-64}{3}} \right)^2[/tex]

When dividing fractions, flip the second fraction and multiply it by the first:

[tex]\implies \sf \left( \dfrac{64}{3} \times \dfrac {3}{-64} \right)^2[/tex]

[tex]\implies \sf \left( \dfrac{64 \times 3}{3 \times (-64)}\right)^2[/tex]

[tex]\implies \sf \left( \dfrac{192}{-192}\right)^2[/tex]

[tex]\implies \sf \left(-1\right)^2[/tex]

[tex]\textsf{Apply exponent rule} \quad (-a)^n=a^n,\:\: \textsf{ if }n \textsf{ is even}[/tex]

[tex]\sf \implies 1^2=1[/tex]

Answer:

[tex]\fbox {D. 3,200.4 mm}[/tex]

Step-by-step explanation:

Given :

[ 1 inch = 2.54 centimeters ]

Unit conversions to keep in mind :

Solving

Answer:

20 % discount

Step-by-step explanation:

Lilian got 4 dollars off of the original price    (20 - 16 = 4 )

4 / 20  * 100% = 20% off

The percentage of discount that Lillian gets because of sale is 20%.

Percentage is a measurement to find value of given number out of hundred.

Given that,

The price of phone on tag = $20.

Lillian paid for phone = $16.

To find the percent discount on phone,

First find amount of discount = 20 - 16 = $4.

The percentage of discount = (4 / 20) x 100 = 20 %

Lillian gets 20% discount on new mobile.

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Answer:

5.0×10⁷

Step-by-step explanation:

(3÷6)×(10⁴÷10^-4)

(0.5)×(10⁸)

5.0×10^-1×10⁸

5.0×10⁷

[tex] \frac{3 \times {10}^{4} }{6 \times {10}^{ - 4} } \\ \\ \frac{1 \times {10}^{4 - ( - 4)} }{2 } \\ \\ \frac{ 1 \times {10}^{4 + 4} }{2} \\ \\ \frac{1 \times {10}^{8} }{2} \\ \\ 0.5 \times {10}^{8} .[/tex]

Answer:

Step-by-step explanation:

what is the question?

Answer:

Median = A

Mean = B

Step-by-step explanation:

Khan Academy

Answer:

y = 6x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form ( linear function ) is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 3 ) and (x₂, y₂ ) = (2, 9 )

m = [tex]\frac{9-3}{2-1}[/tex] = [tex]\frac{6}{1}[/tex] = 6 , then

y = 6x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (1, 3 ) , then

3 = 6 + c ⇒ c = 3 - 6 = - 3

y = 6x - 3 ← equation of linear function

Answer:

auto correlation is the answer to the question

The value of (f/g)(-1) is 0, value of (g . f) (2) is  -3√3, the value of (g - f)(-1)  is √15, and the value of (g + f) (2) is √3 - 3

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have two functions:

f(x) = 1 - x²

g(x) = √(11 - 4x)

f(-1) = 0

g(-1) = √15

f(2) = -3

g(2) = √3

(f/g)(-1) = f(-1)/g(-1) = 0/√15  = 0

(g . f) (2) = g(2)f(2) = (√3)(-3) = -3√3

(g - f)(-1) = g(-1) - f(-1) = √15 - 0 = √15

(g + f) (2) = g(2) + f(2) = √3 + (-3) = √3 - 3

Thus, the value of (f/g)(-1) is 0, value of (g . f) (2) is  -3√3, the value of (g - f)(-1)  is √15, and the value of (g + f) (2) is √3 - 3

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Answer:

566

Step-by-step explanation:

I got it right..................

Answer:

30

Step-by-step explanation:

4 cups x 60 hours a min x 2 hours of lunch ÷ 16 cups per gallon = 30 gallons

The answer is 30 gallons.

Firstly, convert the hours to minutes so you know how many minutes you're working with. 2*60=120 minutes.

Then, multiply 120 with 4 to get the number of tea (in cups) that is poured. 120*4=480 cups.

Finally, divide 480 cups with 16 cups to find out the number of gallons poured. 480/16 equals 30 gallons.

Hope this helped.

Answer:

1991.759

Step-by-step explanation:

1810.69×%10=181.069

1810.69+181.069=1991.759

The process capability index for the process is 0.1754.

The first sided specification limit will be:

= (Upper specification limit - mean)/(3 × standard deviation)

= (23.1 - 22.9)/(3 × 0.19)

= 0.2/0.57

= 0.3508

The second sided specification limit will be:

= (22.9 - 22.8)/(3 × 0.19)

= 0.1/0.57

= 0.1754

The process capability index for the process is 0.1754 wine it's the lower value.

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Answer:  [tex]\textsf{Option A, (-2, 4)}[/tex]

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Given:  [tex]\textsf{f(x) = x + 6}[/tex]

Find:  [tex]\textsf{f(-2)}[/tex]

Solution:  We need to plug in the value -2 into every variable x that we have in the expression and simplify to get the solution.

Plug in the values

Simplify

Therefore, the ordered pair that would match would have a x-coordinate of -2 and a y-coordinate of 4 producing (-2, 4) which matches option A.

By using the binary operator of addition, the result of summing f(x) = 4 · x² + 7 · x - 3 and g(x) = 6 · x³ - 7 · x² - 5 is equal to (f + g)(x) = 6 · x³ - 3 · x² + 7 · x - 8.

Binary operators is a operator that connects two functions. There are five binary operators between two functions: (i) Addition, (ii) Subtraction, (iii) Multiplication, (iv) Division, (v) Composition.

In this question we must apply the addition between two quadratic functions. In addition, we know by algebra that the sum of a quadratic function and a cubic function is equal to a cubic function. Hence, the resulting expression is:

(f + g)(x) = f(x) + g(x)

(f + g)(x) = (4 · x² + 7 · x - 3) + (6 · x³ - 7 · x² - 5)

(f + g)(x) = 6 · x³ - 3 · x² + 7 · x - 8

By using the binary operator of addition, the result of summing f(x) = 4 · x² + 7 · x - 3 and g(x) = 6 · x³ - 7 · x² - 5 is equal to (f + g)(x) = 6 · x³ - 3 · x² + 7 · x - 8.

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Answer:  [tex]\textsf{y = -2/5x}[/tex]

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Given:  [tex]\textsf{Passes through (5, -2) and slope of -2/5}[/tex]

Find:  [tex]\textsf{The equation that follows the details provided}[/tex]

Solution: We first need to plug into the point-slope form and after simplifying, distributing, and solving for y we will complete our equation.

Plug in the values

Distribute and simplify

Subtract 2 from both sides

Therefore, the final equation that follows the information that was provided is y = -2/5x.

Answer:

  85,999,999.999 999 909

Step-by-step explanation:

The expression represents the difference of a relatively large number and one that is relatively small. That difference is approximately the value of the large number. The exact value requires 17 digits for its proper expression. Most calculators and spreadsheets cannot display this many digits.

The numbers in standard form are ...

  86,000,000 = 8.6×10^7

  0.000000091 = 9.1×10^-8

Their difference is ...

  86,000,000 -0.000000091 = 85,999,999.999 999 909

In scientific notation, this is ...

  8.599 999 999 999 990 9×10^7

Step-by-step explanation:

(3+3+3*2)+(2*3-2-4*2)

The value of the addition of the two polynomials is 3x³ - x² + 1.

The addition of polynomials involves combining like terms of two or more polynomials to create a new polynomial. A polynomial is an expression consisting of variables, coefficients, and exponents, connected by addition and subtraction operations.

To add the given polynomials:

(3 + x³ + 3x²) + (2x³ - 2 - 4x²)

First, let's group the like terms:

(x³ + 2x³) + (3x² - 4x²) + (3 - 2)

Combine the coefficients of the like terms:

3x³ + 3x² - 4x² + 3 - 2

Simplify the expression:

3x³ - x² + 1

Therefore, the sum of the given polynomials is: 3x³ - x² + 1.

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There's a fixed difference of 6 between terms (9 - 3 = 6, 15 - 9 = 6, and so on). The first term of the sequence is 3, so the [tex]n[/tex]-th term is

[tex]3 + 6(n-1) = 6n - 3[/tex]

If there are 24 terms in the sum, then the last term is 6×23 - 3 = 135.

Let [tex]S[/tex] be the sum,

[tex]S = 3 + 9 + 15 + \cdots + 123 + 129 + 135[/tex]

Reverse the order of terms:

[tex]S = 135 + 129 + 123 + \cdots + 15 + 9 + 3[/tex]

If we add up the terms in the same positions, we get twice [tex]S[/tex] on the left side, while on the right side we observe that each pair of terms will sum to 138.

[tex]S + S = (3 + 135) + (9 + 129) + (15 + 123) + \cdots + (135 + 3)[/tex]

[tex]2S = 138 + 138 + 138 + \cdots + 138[/tex]

and since there are 24 terms in the sum, the right side is the sum of 24 copies of 138. In other words,

[tex]2S = 24 \times 138[/tex]

and solving for [tex]S[/tex] gives

[tex]S = \dfrac{24\times138}2 = \boxed{1656}[/tex]

Answer:

VQU =58°

Step-by-step explanation:

angle QUV is 61 because of F angles (I don't know what they call them in ur country)

triangle QUV is an isosceles triangles so base angles are the same

61+61=122

180-122=58

Answer:

a

Step-by-step explanation:

we know that g(x) means y therefore in this case let's suppose we have the coordinate (5;y) so we must find the corresponding y value

*DO THE TRIAL AND ERROR METHOD*

take any equation above and substitute the value of x of which is 5 and the corresponding value should be 1.

[tex]g(x) = (\frac{1}{5} x) {}^{2} [/tex]

Answer:

Can you give exanation

I don't understand

The parts that are missing in the proof are:

It is given

∠2 ≅ ∠3

converse alternate exterior angles theorem

The theorem states that, if two exterior alternate angles are congruent, then the lines cut by the transversal are parallel.

∠1 ≅ ∠3 and l║m because we are: given

By the transitive property,

∠2 and ∠3 are alternate interior angles, therefore, they are congruent to each other by the alternate interior angles theorem.

Based on the converse alternate exterior angles theorem, lines p and q are proven to be parallel.

Therefore, the missing parts pf the paragraph proof are:

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Answer:

it is given

angle 2

angle 3

converse alternate exterior angles theorem

Step-by-step explanation:

Answer:

18x + 14

Step-by-step explanation:

First, we need to distribute the 5:

 5(4x + 7) - 2x = __ + 21

 20x + 35 - 2x = __ + 21

Now, we can combine like terms:

 20x + 35 - 2x  = ___ + 21

  18x + 35 = ___ + 21

> subtract 21 from both sides to isolate "___"

 18x + 35 = __ + 21

          -21             -21

18x + 14 = ___

now that we have a solution, we should check that it works:

5(4x + 7) - 2x = ____ + 21

5(4x + 7) - 2x = 18x + 14 + 21  

{simplify both sides:}

20x + 35 -2x = 18x + 35

18x + 35 = 18x + 35

(TRUE)

So, we know our solution is 18x + 14

hope this helps!!