Help!!

why might you choose to write a recursive formula rather than an explicit formula to define a sequence

a. you need to know the 54th term in the sequence

b. the sequence is neither arithmetic or geometric

c. you need to know the value of three non-sequential terms in the sequence

d. the sequence is strictly geometric

Answers

Answer 1

We might choose to write a recursive formula rather than an explicit formula to define a sequence because (D) the sequence is strictly geometric.

What is a sequence?A sequence in mathematics is an enumerated collection of items in which repetitions are permitted and order is important. It, like a set, has members (also called elements, or terms). The length of the series is defined as the number of items (which could be infinite). Unlike a set, the same components can appear numerous times in a sequence at different points, and the order does important. Formally, a sequence can be defined as a function from natural numbers (the sequence's places) to the elements at each point. The concept of a sequence can be expanded to include an indexed family, which is defined as a function from an index set that may or may not contain integers to another set of elements.

Recursive formulas are commonly used to compute the nth term of a sequence, where a(n) is the sum of all the preceding values.

Using its position, explicit formulas can compute a(n).

Therefore, we might choose to write a recursive formula rather than an explicit formula to define a sequence because (D) the sequence is strictly geometric.

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Answer 2

Answer: (D)

Step-by-step explanation:

took quiz


Related Questions

The given figure is a solid object formed by a cylinder and a hemisphere. If the total length of that solid object is 64 cm and length of the cylinder is 50 cm, find the total surface area of the solid object.​

Answers

The total surface area of the solid object is 2660.925 square cm the answer is 2660.925 square cm.

What is a cylinder?

In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the volume of the cylinder is given by:

[tex]\rm V = \pi r^2 h[/tex]

The surface area of the

= surface area of half sphere + surface area of the cylinder - surface area

  of one circular base

The radius r = (64-50)/2 = 7 cm

= (1/2)[4π(7)²] + 2π(7)(50) + 2π(7)² - π(7)²

= (1/2)[615.75] + 2506.99 - 153.94

= 307.875 + 2506.99 - 153.94

= 2660.925 square cm

Thus, the total surface area of the solid object is 2660.925 square cm the answer is 2660.925 square cm.

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PLS HELP ITS MATH PLS

Answers

[tex] \: \: \: \: \: \: \: y = \frac{ - 7x}{8} + 4 \\ \: \: \: \: \: \: multiply \: all \: by \: 8 \\ \: \: \: \: \: \: \: \: 8y = - 7x + 32 \\ \: \: \: \: \: \: \: \: \: 7x + 8y = 32[/tex]

( 7 , 8 , 32 )

A man is 32 years older than his son. Ten years ago he was three times as old as his son was then. Find the present age of each

Answers

Answer:

Son: 26 yrs. Dad: 58 yrs.

Step-by-step explanation:

Let s equal to the present age of the son and let d equal to the present age of the dad. We can make two equations based on the information given to us. The first is about the fact that the dad is 32 yrs. older than the son:

d = s+32

the second is about the fact that 10 yrs. ago, he was triple his son's age.

d-10 = 3(s-10)

We can use the distributive property and we have:

d-10 = 3s-30

Then, let's add 10 to each side:

d = 3s-20

We can substitute the first equation into the second, resulting in:

s+32 = 3s-20

Adding 20 to both sides:

s+52 = 3s

2s = 52

s = 26

Now that we have the son's age, the dad's age is 26+32 = 58.

Son's age: 26

Dad's age: 58

Question 2(Multiple Choice Worth 2 points)
Based on the graphs of the equations y = -2x + 3 and y=x²-x + 1, the solutions are located at points?

Answers

Based on the given graphs and their equations, the solutions will be located at points (-2, 7) and (0, 1).

Where are solutions located?

To find the solution to y = -2x+ 3, assume that x is a certain number then solve for y.

Given the options, we can assume that x = -2. Solution is:

= -2(-2) + 3

= 4 + 3

y = 7

Solution point is (-2, 7)

The second equation can be solved by equating x to 0:
y = 0² - 0 + 1

y = 1

Solution point is:

= (0, 1)

In conclusion, the solution points are (-2, 7) and (0,1).

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how does math connect to animation?

Answers

Answer:

Math allows the animator to find the unknowns from a set of equations and to work out the aspects of the geometric figures when dealing with the objects that move and change.

Step-by-step explanation:

To learn more:

weusemath.org/?career=animator

Hope this helps!

Find the equation of the line using exact numbers

Answers

Answer:

y = - [tex]\frac{1}{3}[/tex] x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form 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 ) = (0, 5) and (x₂, y₂ ) = (3, 4) ← 2 points on the line

m = [tex]\frac{4-5}{3-0}[/tex] = [tex]\frac{-1}{3}[/tex] = - [tex]\frac{1}{3}[/tex]

the line crosses the y- axis at (0, 5 ) ⇒ c = 5

y = - [tex]\frac{1}{3}[/tex] x + 5 ← equation of line

A number, h, rounded to 1 d.p. is 47.2
Another number, k, rounded to 1 d.p. is 4.8
What are the lower and upper bounds of
h - k?

Answers

The lower and upper bounds of h - k are 42.31 and 42.49 respectively.

Upper and lower bounds are the maximum and minimum values that a number could have been before it was rounded. They can also be called limits of accuracy.

The upper and lower bounds can be written using error intervals

The lowest value of h is 47.15

The greatest value of h is 47.24

The greatest value of k is 4.84

The lowest value of k is 4.75

Thus upper bound of h -k = 47.24 - 4.75 = 42.49

Thus lower bound of h -k = 47.15 - 4.84 = 42.31

Thus the lower and upper bounds of h - k are 42.31 and 42.49 respectively.

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An engineer is designing an arch-shaped gate for the entrance to an amusement park. the gate must be 80 feet wide and 25 feet tall. what will be the equation of the parabolic shape of the gate? a. x2 = -16(y − 25) b. (x − 16)2 = -4(y − 25) c. x2 = -64(y − 25) d. (x − 25)2 = -16(y − 16) e. x2 = -40(y − 25)

Answers

The equation of the parabolic shape of the gate is:

(x - 40)² = -64(y - 25)

What is the equation of a parabola given it’s vertex?

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

The vertex is at the middle of the parabola, that is, a width of 80/2 = 40 meters and a height of 25 meters, hence h = 40, k = 25, and the equation is:

y = a(x - h)² + k

y = a(x - 40)² + 25

When x = 0, y = 0(start of the arc), hence the leading coefficient is found as follows:

0 = 1600a + 25

a = -25/1600

a = -1/64.

Hence the equation is:

y = -1/64(x - 40)² + 25

(x - 40)² = -64(y - 25)

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A quadrilateral must be a parallelogram if one pair of opposite sides is: a. congruent and the other pair is parallel b. congruent and parallel c. parallel d. congruent

Answers

Answer:

b

Step-by-step explanation:

the opposite sides of a parallelogram are parallel and congruent

thus option b is the correct one

Find the distance in nm between two slits that produces the first minimum for 405-nm violet light at an angle of 57. 5°

Answers

The distance between two slits is d =2.89*10^-7 m

Distance between slits,   d=2.89*10^-7 m

It is given that,

Wavelength, λ = 410nm= 410*10^-9 m

Angle, θ =45

We need to find the distance between two slits that produces first minimum. The equation for the destructive interference is given by :

dsinθ =(n+1/2) λ

For first minimum, n = 0

dsinθ =(1/2) λ

So, d is the distance between slits

d ={1/2 λ}sinθ

=2.89*10^-7 m

So, the distance between two slits is d =2.89*10^-7 m. Hence, this is the required solution.

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Solve the problems involving (HCF) highest common factor for each of the the following

B) A restaurant donated 540 pieces of fried chicken and 360 cups of drink for a gathering event. The restaurant has set the condition the every visitor will receive the portion of food equally. Find :

(1) Find the maximum number of visitors that can be invited to the event.

(2) Find the numbers of pieces of chicken to be received by the visitors who attended the event.

Answers

Step-by-step explanation:

the highest or greatest or largest common factor is the product of the prime factors the numbers have in common :

540 ÷ 2 = 270

270 ÷ 2 = 135

135 ÷ 2 no

135 ÷ 3 = 45

45 ÷ 3 = 15

15 ÷ 3 = 5

5 ÷ 3 no

5 ÷ 5 = 1

540 = 2² × 3³ × 5¹

360 ÷ 2 = 180

180 ÷ 2 = 90

90 ÷ 2 = 45

45 ÷ 2 no

45 ÷ 3 = 15

15 ÷ 3 = 5

5 ÷ 3 no

5 ÷ 5 = 1

360 = 2³ × 3² × 5¹

so, the HCF = 2² × 3² × 5¹ = 4×9×5 = 180

(1)

to satisfy the condition max. 180 visitors can be invited.

(2)

540 / 180 = 3

so, every visitor can receive 3 pieces of chicken.

and 360 / 180 = 2 cups of drink.

Hey guys please help? Trigonometry


So, the task is: find cos a, if:

1) sin a = (3√11)/10, a ∈ (0; π/2)

2) sin a = (3√11)/10, a ∈ (π/2; π)


Could someone please explain how to solve it? I can't figure out what difference a ∈ (0; π/2) and a ∈ (π/2; π) make in the way I have to solve it mmh... I'll pin my attempt to do the first one (failed for some reason)

Answers

Step-by-step explanation:

a ∈ (0; π/2) here means that our angle, a must lie between 0 and pi/2, exclusive.

So this mean our angle must be in between 0 and pi/2, but can not be neither 0 and pi/2.

Here we have

[tex] \sin( \alpha ) = \frac{3 \sqrt{11} }{10} [/tex]

We must find cos.

Using the Pythagorean theorem

[tex]( \sin( \alpha ) ) {}^{2} + ( \cos( \alpha ) ) {}^{2} = 1[/tex]

It is mostly notated as this,

[tex] \sin {}^{2} ( \alpha ) + \cos {}^{2} ( \alpha ) = 1[/tex]

But they mean the same thing, we know

[tex] \sin( \alpha ) = \frac{3 \sqrt{11} }{10} [/tex]

So we plug that in for sin a.

[tex]( \frac{3 \sqrt{11} }{10} ) {}^{2} + \cos {}^{2} ( \alpha ) = 1[/tex]

[tex] \frac{99}{100} + \cos {}^{2} ( \alpha ) = 1[/tex]

[tex] \cos {}^{2} ( \alpha ) = \frac{100}{100} - \frac{99}{100} [/tex]

[tex] \cos {}^{2} ( \alpha ) = \frac{1}{100} [/tex]

Since cos is Positve over the interval (0; π/2), we take the positive or principal square root.

[tex] \cos( \alpha ) = \frac{1}{10} [/tex]

2. We would get the same work for the second part, the only difference is that cosine is negative over the interval

(π/2, π)

So the answer for 2 is

[tex] \cos( \alpha ) = - \frac{1}{10} [/tex]

Disclaimer: Your work you did was correct, just remember for fractions like

[tex]1 - \frac{99}{100} [/tex]

Convert 1 into a fraction that has a denominator of 100.

[tex] \frac{100}{100} - \frac{99}{100} = \frac{1}{100} [/tex]

Solve this:
NO INCORRECT or report

Answers

Answer:

D

Step-by-step explanation:

Let x be the first batch

let y be the second batch

y=2x

His brothers each received 9 rolls from the second batch i.e. 9×4=36

So

2x= 36+ (10÷6)x

2x - (10÷6)x = 36

12x-10x = 216

x=108

and y= 2 × 108= 216

An architectural drawing lists the scale as 1/4" = 1'. if a bedroom measures 312" by 514" on the drawing, how large is the bedroom?

Answers

The length of the bedroom exists at x = 9 and y = 6.

How to estimate the length of the bedroom?

From the given information, we get

Then  [tex]$\frac{(1/4)}{(9/4)} = \frac{1}{x}[/tex]

Solve this for x.

simplifying the value of x we get

Equate (1/9) to 1/x.

x = 9 (feet).

Convert 1.5 inches to feet using a proportion:

[tex]$\frac{(1/4)}{(1.5)} = \frac{1}{y}[/tex]

Solve this for y.

simplifying the value of y we get

(1/4)y = 3/2

Multiply both sides of the equation by 4.

y = 6

Therefore, the length of the bedroom exists at x = 9 and y = 6.

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Solve question
6= x/4 + 2

Answers

Answer:

x=16

Step-by-step explanation:

6= x/4 + 2

Subtract 2 from both sides.

4= x/4

Multiply 4 to both sides.

x=16

Hope this helps!

need help with number 9 pls​

Answers

Answer:

i) a = 2, b = - 3, c =-6

Step-by-step explanation:

4x² - 12x + 3

4x² - 6x - 6x + 9 - 6

(2x - 3)(2x - 3) - 6

(2x - 3)² - 6

(2x + (- 3) )² - 6

In form of (ax + b)² - 6

a = 2, b = - 3, c =-6

Alina measured a distance to be 2.18 miles. what is the margin of error? 2.1 miles to 2.2 miles 2.175 miles to 2.185 miles 2.185 miles to 2.195 miles 2.2 miles to 2.3 cm

Answers

Answer:

  (b)  2.175 miles to 2.185 miles

Step-by-step explanation:

When a value is rounded, the original "exact" value is presumed to be within 1/2 of the value of one least-significant unit of the rounded number.

Application

A rounded value of 2.18 has a least-significant digit with a place value of 0.01 units. Half that value is the "margin of error". That is, the range of numbers that would be rounded to 2.18 is ...

  2.18-0.005 ≤ x < 2.18+0.005

  2.175 ≤ x < 2.185 . . . . miles

Find an equation of the line parallel to 8x − 3y = 1 and containing the point (−2, 0)

Answers

The equation of the line parallel to 8x − 3y = 1 and containing the point (−2, 0) is 8x -3y = -16

Equation of a straight line

From the question, we are to determine the equation of the line parallel to the given equation and that passes through the given point

Lines that are parallel to each other will have the same slope.

First, we will determine the slope of the line in the given equation.

The given equation of the line is

8x − 3y = 1

Express the equation in the slope-intercept form of a line, y = mx + b

Where m is the slope and

b is the y-intercept

That is,

8x − 3y = 1

8x -1 = 3y

3y = 8x - 1

y = 8/3(x) - 1/3

By comparing,

∴ The slope of the line is 8/3

Since we are to find the equation of a line parallel to this, the slope of the line will also be 8/3

Now, find the equation of a line containing the point (-2, 0) and that has  a slope of 8/3

Using the point-slope form of a line

y - y₁ = m(x - x₁)

x₁ = -2

and y₁ = 0

∴ y - 0 = 8/3(x - -2)

y = 8/3(x +2)

3y = 8(x +2)

3y = 8x + 16

8x -3y = -16

Hence, the equation of the line parallel to 8x − 3y = 1 and containing the point (−2, 0) is 8x -3y = -16

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Pick the correct answer
Please help thanks :)

Answers

Answer:

B

Step-by-step explanation:

First create the equation that has slope of -1 in the form of y=mx+b. Because the slope is -1, m=-1, so the equation is y=-x+b. Now we see that we are given the point (-3, 8) as an intersection point. Substitute x and y for -3 and 8 in our equation. With this information, our equation becomes 8=3+b. Solving, b=5. Our equation is now y=-x+5.

Simplifying all of the answer choices, we have

A. y=-x-5

B. y=-x+5

C. y=-x-5

D. and E. as what they already show

The only answer that matches is B.

x6 = 64 solve for X please

Answers

Answer:

x = 2

Step-by-step explanation:

note that 64 = [tex]2^{6}[/tex]

then

[tex]x^{6}[/tex] = [tex]2^{6}[/tex] , so x = 2

What is a fitted value for a multiple regression model and the data that is used to create it?

Answers

Fitted value is a prediction of the mean response value.

According to the statement

we have to explain the fitted value for the regression model and the data which uses to collect the value.

So, For this purpose, we know that the  

A Fitted value is a statistical model's prediction of the mean response value when you input the values of the predictors, factor levels, or components into the model.

An the fitted value used in this model is called the predicted values of response variable in the case of multiple regression model.

And data which is used to create the fitted value is the simple data by which we create the fitted value by the predict the value of given data.

So, Fitted value is a prediction of the mean response value.

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the length of the sides of a triangle are in the ratio 3:4:5. find the lengths of the sides of the triangle if its perimeter is 96cm

Answers

Answer:

let the angles be 3x,4x&5x

Now,

perimeter (p)=sum of all sides

or, 96=3x+4x+5x

or, 96=12x

or,96/12=x

or,8=x

or,x=8

Then,

3x=3*8

=24

4x=4*8

=32

5x=5*8

=45

What is the probability of selecting a male from a group of 4 male and 8 female

Answers

Answer:0.333

Step-by-step explanation:4+8=12 so there is only 4 chances it can be male so 4/12=0.333

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

probability (P) is calculated as

P = (desired result ) ÷ ( number of possible results )

here desired result is choosing a male from 4 males

number of possible results = 4 + 8 = 12 , then

P( male) = [tex]\frac{4}{12}[/tex] = [tex]\frac{1}{3}[/tex]

select the graph that correctly represents the following equation. 4x-3y=-1

Answers

The graph of the given equation is shown below

Graph of a straight line

From the question, we are to determine the graph that represents the given equation

The given equation is

4x - 3y = -1

The graph of the equation is shown below

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What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)? f(x) = 5x2 x 3

Answers

The solutions to the system of equations involving quadratic function f(x) and linear function g(x) are (-1,5) and (4/3,29/3), respectively.

What is a polynomial function?A polynomial function is a relationship in which a dependent variable equals a polynomial expression. A polynomial expression is one that has numbers and variables that are raised to non-negative powers.

To find the solution to the given system of equations:

A polynomial expression has the following generic form:a₀ + a₁x + a₂x² + a₃x³ + ... + aₙxⁿ.The degree of the polynomial expression has the greatest power on a variable.When degree = 2, the function is quadratic.When degree = one, the function is linear.

Given quadratic equation: f(x) = 3x^2 + x + 3

We must solve the linear equation g(x). Because it is a linear equation, we utilize the two-point approach to solve it.

The two point formula is: y-y₁ = ((y₂-y₁)/(x₂-x₁))*(x-x₁)

We take the points g(2) = 11, g(1) = 9

g(x) - g(1) = ((g(2)-g(1))/(2-1))*(x-1)

or, g(x) - 9 = ((11-9)/(2-1))*(x-1)

or, g(x) - 9 = 2(x-1)

or, g(x) = 2x - 2 + 9 = 2x + 7

g(x) = 2x +7, is the linear function g(x)

We are asked to solve the system of equations f(x) and g(x).

To get the solution, we must first determine what is the common solution to both f(x) and g(x).

For that, we equate f(x) and g(x).

3x² + x + 3 = 2x + 7

or, 3x² - x - 4 = 0

or, 3x² + 3x - 4x - 4 = 0

or, 3x(x+1) -4(x+1) = 0

or, (3x-4)(x+1) = 0

∴ Either 3x-4=0 ⇒ x = 4/3

or, x+1=0 ⇒ x = -1.

g(-1) = 5 (from the table)

f(-1) = 3(-1)² + (-1) + 3 = 3 - 1 + 3 = 5

g(4/3) = 2(4/3) + 7 = 8/3 + 21/3 = 29/3

f(4/3) = 3*(4/3)² + (4/3) + 3 = 16/3 + 4/3 + 9/3 = 29/3

∴ f(-1) = g(-1) and f(4/3) = g(4/3).

Therefore, the solution to the system of equations that includes quadratic function f(x) and linear function g(x) is (-1,5) and (4/3,29/3).

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The correct question is given below:

What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)?

f(x) = 3x^2 + x + 3

The function f(x) = x2 is graphed above. which of the graphs below represents the function g(x) = (x 1)2?

Answers

The graph (C) Y represents the function g(x) = (x 1`)2.

What is a graph of a function?The graph of a function f is the set of ordered pairings where display style f(x) = y in mathematics. When x and f(x) are both real values, these pairings represent Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane.

To find which of the graphs below represents the function g(x) = (x 1)2:

Parabola: It's a conic section formed by the intersection of a right circular cone with a plane parallel to one of the cone's elements.

The equation of parabola: [tex]y =x^{2}[/tex]The graph of  [tex]y=x^{2}[/tex] is given.To draw the graph of [tex]y=(x+1)^{2}[/tex], shift the graph of [tex]y=x^{2}[/tex] one unit left.The graph of [tex]y=(x+1)^{2}[/tex] is attached below.

Therefore, the graph (C) Y represents the function g(x) = (x 1)2.

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What is the radius of the sector of the circle below, if the area is 30.39 m^2 and the central angle < AOB measures 43 °. (round answer to the nearest whole meter)

Answers

Answer:

a. 9m

Step-by-step explanation:

Pi = 3.14 = 22/7

formula :

Area of a Sector of a Circle = (central angle)/360 * πr² =

(central angle)/360 * πr² = Area of a Sector of a Circle

43/360 * Pi * r^2 = 30.39

r^2 = (30.39 * 360) / (Pi * 43)

r^2 = (30.39 * 360) / (22/7 * 43)

r = √ (30.39 * 360 * 7) / (22 * 43)

r = √76582.8/946

r = √80.9543340381

8.99746264444 which is roughly

9

The radius of the sector will be 9m. The correct option is A.

What is the arc length of the circle?

The distance between two places along a segment of a curve is known as the arc length. Curve rectification is the process of measuring the length of an irregular arc segment by simulating it as a network of connected line segments.

The radius will be calculated as below:-

Area of a Sector of a Circle = (central angle)/360 * πr² =

(Ф)/360 * πr² = Area of a Sector of a Circle

43/360 * Pi * r²= 30.39

r² = (30.39 * 360) / (Pi x 43)

r²= (30.39 x 360) / (22/7 x 43)

r = √ (30.39 x 360 x 7) / (22 x 43)

r = √76582.8/946

r = √80.9543340381

r = 9

Therefore, the radius of the sector will be 9m. The correct option is A.

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Helpppppppppp show your steps to the answer

Answers

Answer:

9

Step-by-step explanation:

you have to plug in the numbers and solve it, so it would go as follows:

-(-3^2)- 2(-5)(2) - /2/

-9 + 20 - 2 =

9

i hope this helps

There are an average of 45 buffalos for every 125 acres in the Canadian wilderness. How many buffalos are there in 150 acres?

Answers

Answer:

there are 54 buffalos in 150 acres

Step-by-step explanation:

1. determine the rate of buffalos per acres

45 buffalos per 125 acres =

45 / 125 =

0.36 buffalos per 1 acre

now we know the rate of buffalos per 1 acre, we can multiply it by the required amount of acres (in this case 150)

buffalos per 1 acre x total acres = total buffalos per total acres

0.36 x 150 = 54 buffalos

therefore, there are 54 buffalos per 150 acres.

hope this helps :)

The rectangles below have the same perimeter.

Rectangle:A Base=3 height=9
Rectangle B:base=4

Answers

Answer:

32 mm²

Step-by-step explanation:

perimeter of left rectangle = 2(9 mm + 3 mm) = 24 mm

length of right rectangle = L

perimeter of right rectangle = 2(L + 4 mm) = 2L + 8

perimeter of right rectangle = 24 mm

The perimeter of the right triangle is 2L + 8 and also 24, so 2L + 8 must equal 24. We can solve for L and find the length of the right rectangle.

2L + 8 = 24

2L = 16

L = 8

area of right triangle = length × width

area = 8 mm × 4 mm

area = 32 mm²

**Disclaimer** Hi there! I assumed the purple triangle to be the one on the right. The following answer will be according to this understanding. If I am wrong, please let me know and I will modify my answer.

Answer: [tex]\Large\boxed{Area=32~mm^2}[/tex]

Step-by-step explanation:

Given information

Rectangle A:

Base (b) = 3 mmHeight (h) = 9 mm

Rectangle B:

Base (b) = 4 mmHeight (h) = ?

Both rectangles have the same perimeter

Given formula

1) P = 2 (b + h)

P = Perimeterb = baseh = height

2) A = b × h

A = Perimeterb = baseh = height

Find the height of rectangle B

Substitute values into 1) formula to find the perimeter of rectangle A

P = 2 (b + h)

P = 2 (3 + 9)

Simplify by addition

P = 2 × 12

Simplify by multiplication

P = 24 mm

Substitute values into 1) formula to find the perimeter of rectangle B

P = 2 (b + h)

24 = 2 (4 + h)

Divide 2 on both sides

24 / 2 = 2 (4 + h) / 2

12 = 4 + h

Subtract 4 on both sides

12 - 4 = 4 + h - 4

h = 8 mm

Find the area of rectangle B (Purple)

Substitute values into 2) formula

A = b × h

A = 4 × 8

Simplify by multiplication

[tex]\Large\boxed{Area=32~mm^2}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

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