The outside edges of the walkway form a rectangle whose length and width are proportional to the sides of the garden, increased by a scale factor of 3. the sides of the garden are (2x+4) and (3x+2). determine the lengths of the outside edges of the garden. write your answer in
simplest form.

Answers

Answer 1

The length and the width of the outside edge of the garden will be ( 6x + 12 ) and ( 9x + 6 ) respectively.

What is the scale factor?

In mathematics, a scale factor is the proportion of related dimensions of an object to a description of that object.

Given that:-

The outside edges of the walkway form a rectangle whose length and width are proportional to the sides of the garden, increased by a scale factor of 3. the sides of the garden are (2x+4) and (3x+2)

The length and width of the outside edge will be:-

The sides are Dilated by factor 3 so the edges of the rectangle will be calculated as;-

Length = 3 ( 2x+4 ) = 6x + 12

Width = 3 ( 3x+2 ) = 9x + 6

Therefore the length and the width of the outside edge of the garden will be ( 6x + 12 ) and ( 9x + 6 ) respectively.

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The Outside Edges Of The Walkway Form A Rectangle Whose Length And Width Are Proportional To The Sides

Related Questions

Kamaria opens a bank account with $300. Five weeks later, her account balance is $500. What was the average rate of change of her account balance in dollars per week?

Answers

Answer:

$40 average

Step-by-step explanation:

500-300=200

200/5=40

Nick wants to write a 1,260 page science-fiction novel.
How many pages will Nick need to write each month to finish his novel in 1 year?

Answers

105 pages a month

Divide 1,260 by 12 cuz there’s 12 months in a year and you get 105

1 year = 12 months

Pages to write in 12 months = 1260

Pages to write in 1 month = 1260/12

= 105 pages per month

What is the difference between the highest and lowest points in a data set?the mean the median the mode the range

Answers

Answer:

Range

Step-by-step explanation:

Range is found by subtracting the highest and lowest point in the dataset

Mode is the number that occurs most frequently in the set

Median is the central number in the dataset when arranged from lowest to highest

Mean is the sum of all the numbers in the dataset divided by how many numbers there are.

For example, take this list of numbers: 10, 10, 20, 40, 70.

The mean (also known as average) is found by: 10 + 10 + 20 + 40 + 70 / 5 = 30.

The median is found by ordering the set from lowest to highest and finding the exact middle. The median is just the middle number: 20.

four students are trying to determine what number must replace the question (x^2)^7=x^4*x^8 in order to make it true
Joe said the answer is 6. Sam said it is impossible to answer.
Peter said the answer is 32. Alex said the answer is 16.
Who is correct? Explain why.

Answers

Let's solve ourselves instead of believing anyone

[tex]\\ \rm\Rrightarrow (x^2)^7=x^4x^8[/tex]

a^m+a^n=a^m+n

[tex]\\ \rm\Rrightarrow x^{14}=x^{4+8}[/tex]

[tex]\\ \rm\Rrightarrow x^{14}=x^{12}[/tex]

[tex]\\ \rm\Rrightarrow x^{14}-x^{12}=0[/tex]

[tex]\\ \rm\Rrightarrow x^{12}(x^2-1)=0[/tex]

[tex]\\ \rm\Rrightarrow x^2-1=0[/tex]

[tex]\\ \rm\Rrightarrow x^2=1[/tex]

[tex]\\ \rm\Rrightarrow x=\pm 1[/tex]

0 is also a solution

Answer:

Joe is correct

Step-by-step explanation:

Given equation:

[tex](x^2)^?=x^4 \cdot x^8[/tex]

The exponent outside the bracket is a question mark and the students are trying to determine the value of the question mark.

For ease of answering, let y be the unknown number (question mark):

[tex]\implies (x^2)^y=x^4 \cdot x^8[/tex]

First, simplify the equation by applying exponent rules to either side of the equation:

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}\quad\textsf{to the left side}:[/tex]

[tex]\implies (x^2)^y=x^4 \cdot x^8[/tex]

[tex]\implies x^{2y}=x^4 \cdot x^8[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c} \quad \textsf{to the right side}:[/tex]

[tex]\implies x^{2y}=x^4 \cdot x^8[/tex]

[tex]\implies x^{2y}=x^{4+8}[/tex]

[tex]\implies x^{2y}=x^{12}[/tex]

Now, apply the exponent rule:

[tex]x^{f(x)}=x^{g(x)} \implies f(x)=g(x)[/tex]

Therefore,

[tex]x^{2y}=x^{12}\implies 2y=12[/tex]

Finally, solve for y:

[tex]\implies 2y=12[/tex]

[tex]\implies 2y \div 2 = 12 \div 2[/tex]

[tex]\implies y=6[/tex]

Therefore, Joe is correct as the unknown number is 6.

What expression represents this description? Twice the quantity m plus n

Answers

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find which expression represents the description "twice the quantity m plus n".

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Translate this phrase into an algebraic expression.

First, add m and n:

[tex]\star~\large\pmb{m+n}[/tex]

Now, multiply two times this sum:

[tex]\star~\large\pmb{2(m+n)}[/tex]

See, the parentheses around the sum show that we multiply two times both m and n.

Hope it helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

Answer:

2(m + n)

Step-by-step explanation:

The words describe a quantity. "Twice" means two-times the previous amount. m and n are the unknown numbers that are being added, so you must put them in parentheses to indicate that they should be added first.

Through aregular hexagonal prism whose base edge is 8cm whose height 12 cm ahole in the shape of aright prism with its end being arhombus with diagonals 6cm and 8cm is drilled find total surface area of remaining solid and the volume

Answers

Answer:

96 cm2, 48 cm2

Step-by-step explanation:

Basically you times the first two questions and then the other 2, that leads you with the answer

hello people, can anybody solve it

Answers

[tex]\\ \rm\Rrightarrow \left(\dfrac{x^a}{x^{-b}}\right)^{a^2-ab+b^2}\times \left(\dfrac{x^b}{x^{-c}}\right)^{b^2-bc+c^2}\times \left(\dfrac{x^c}{x^{-a}}\right)^{c^2-ca+a^2}=1[/tex]

[tex]\\ \rm\Rrightarrow (x^{a+b})^{a^2-ab+b^2}\times (x^{b+c})^{b^2-bc+c^2}\times (x^{c+a})^{c^2-ac+a^2}=1[/tex]

[tex]\\ \rm\Rrightarrow x^{(a+b)(a^2-ab+b^2)}\times x^{(b+c)(b^2-bc+c^2)}\times x^{(c+a)(c^2-ca+a^2)}=1[/tex]

a³+b³=(a+b)(a²-ab+b²)

[tex]\\ \rm\Rrightarrow x^{a^3+b^3}\times x^{b^3+c^3}\times x^{c^3+a^3}=1[/tex]

[tex]\\ \rm\Rrightarrow x^{a^3+b^3+b^3+c^3+c^3+a^3}=1[/tex]

[tex]\\ \rm\Rrightarrow x^{2a^3+2b^3+2c^3}=x^0[/tex]

[tex]\\ \rm\Rrightarrow 2(a^3+b^3+c^3)=0[/tex]

[tex]\\ \rm\Rrightarrow a^3+b^3+c^3=0[/tex]

If lines Joined each given point on the graph to the origin, which points would be on lines that represent a unit rate greater than the one
represented in the table?
x y
5 11
10 22
15 33
10
9
3
022 Edmentum. All rights reserved.

Answers

The points (2, 8), (3, 9) and (4, 10) have a greater slope than the table

How to determine the points?

The table and the graph that complete the question are added as an attachment

Start by calculating the slope of the table using:

m = (y2 - y1)/(x2 - x1)

This gives

m = (22 - 11)/(10 - 5)

m = 2.2

Next, we calculate the slope of each point on the graph when connected to the origin using:

m = y/x

So, we have:

(2,8) ⇒ m = 8/2 = 4

(3,9) ⇒ m = 9/2 = 3

(4,10) ⇒ m = 10/4 = 2.5

(5,8) ⇒ m = 8/5 = 1.6

(6,7) ⇒ m = 7/6 = 1.2

(7,6) ⇒ m = 6/7 = 0.9

By comparing the slopes with 2.2, we can see that only points (2, 8), (3, 9) and (4, 10) have a greater slope than the table

Hence, the points are (2, 8), (3, 9) and (4, 10).

Answers

Answer: Hope this helps if this is what you want.

$14.25

Step-by-step explanation:

$1.50 = 1 ticket

1.50 * 10 = 15

$15 = 10 tickets

100% - 5% = 95% (0.95)

15 * 0.95 = 14.25

$14.25

MATH!!! 15 points;))) find the surface area of the composite figure
please answer correctly and check over your work...

Answers

The area of a 2D form is the amount of space within its perimeter. The surface area of the composite figure is 76.8 ft².

What is an area?

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The surface area of the composite figure,

Surface area = 2(3.6×2) + (4×2) + 3(3.6×4) + 2(5.6)

= 14.4 + 8 + 43.2 + 11.2

= 76.8

Hence, the surface area of the composite figure is 76.8 ft².

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Justin did push-ups for the past 555 days.The following data points are the number of push-ups he did each day.
21,24,24,27,29
Find the standard deviation of the data set.
Round your answer to the nearest hundredth.
push-ups

Answers

Answer: σ: 2.76

Step-by-step explanation:

Count, N: 5

Sum, Σx: 125

Mean, μ: 25

Variance, σ2: 7.6

Steps

look at attached pic for formula

σ^2 = [tex]\frac{Σ(xi - μ)^{2} }{N}[/tex]

[tex]\frac{(21 - 25)2 + ... + (29 - 25)2}{5}[/tex]

⇒ [tex]\frac{38}{5}[/tex]

⇒ 7.6

σ = [tex]\sqrt{7.6}[/tex]

⇒ 2.756809750418

⇒ or 2.76

HELP MEE ,20 POINTS !!!!
Celina says that each of the following expressions is actually a binomial in disguise:
5abc-2a^2+6abc
5x^3∙2x^2-10x^4+3x^5+3x∙(-2) x^4
(t+2)^2-4t
5(a-1)-10(a-1)+100(a-1)
(2πr-πr^2 )r-(2πr-πr^2)∙2r

Answers

Celina says true that each of the following expressions is actually a binomial expression.

What is binomial?

The binomial is a polynomial of two-term only. For example, x + 5 where x and 5 are the two separate terms.

Celina says that each of the following expressions is actually a binomial in disguise:

a. 5abc - 2a² + 6abc = 11abc - 2a²