Janice puts a fence around her rectangular garden. The garden has a length that is 9 feet less than 3 times its width. What is the perimeter of Janice's fence if the area of her garden s 5,670 square feet?

Answers

Answer 1

Answer:

P = 342 ft

General Formulas and Concepts:

Pre-Algebra

Evaluations

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Distributive Property

Algebra I

Equality Properties

Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of Equality

Terms/Coefficients

Factoring/Expanding

Quadratics

Solving quadratic equationsStandard Form: ax² + bx + c = 0

Geometry

Area of a Rectangle Formula: A = lw

l is lengthw is width

Perimeter of a Rectangle Formula: P = 2w + 2l

l is lengthw is width

Step-by-step explanation:

Step 1: Define

Identify variables.

A = 5670 ft²

"Length that is 9 feet less than 3 times its width" → l = 3w - 9

Step 2: Find w

Substitute in variables [Area of a Rectangle Formula]:                                w(3w - 9) = 5670[Distributive Property] Expand:                                                                      3w² - 9w = 5670[Subtraction Property of Equality] Rewrite [Standard Form]:                      3w² - 9w - 5670 = 0[Quadratic] Factor:                                                                                          3(w - 45)(w + 42) = 0[Quadratic] Solve [Find roots]:                                                                      w = -42, 45

Since length/width cannot be negative, we know that w = 45 ft.

Step 3: Find l

Substitute in w [Length Formula]:                                                                   l = 3(45) - 9[Order of Operations] Evaluate:                                                                       l = 126 ft

Step 4: Find Perimeter

Substitute in variables [Perimeter of a Rectangle Formula]:                        P = 2(45 ft) + 2(126 ft)[Order of Operations] Evaluate:                                                                      P = 342 ft

∴ The perimeter of Janice's fence is 342 ft.

Answer 2

Let width be x ft

Length be 3x-9ft

Now

Area=Length ×Breadth5670=x(3x-9)5670=3x²-9x3x²-9x-5670=0

On solving we wI'll get x=-42,45

Take it positive

x=45width=45ftLength=3(45)-9=135-9=126ft

Now

Perimeter

2(Length+Width)2(45+126)2(171)342ft

Related Questions

Kent had $280. He spent 3/7 of his money on a present and 1/4 of his money on a meal. How much money did Kent spend altogether​

Answers

Answer:

$190

Step-by-step explanation:

he spent 3/7·(280), or $120 on a present

he spent 1/4·(280), or $70 on a meal

he spent $190 altogether

You roll one die 8 times. What is the probability of rolling exactly six fours

Please convert the fraction into a decimal

Answers

Answer:

4/8 = 1/2 = 0.5 is your answer

The difference between two numbers is 56. Five times the smaller is equal to 4 more than the larger. What are the numbers?

Answers

Answer: The numbers are 71 and 15.

Explanation:
Let x = the first number
Let y = the second number

From what they give us, we know:
x - y = 56
5y = x + 4

Either one of the equations can be rearranged and substituted into the other equation to find one variable, or number.

5y = x + 4
5y - 4 = x or x = 5y - 4

x - y = 56
5y - 4 - y = 56
4y - 4 = 56
4y = 60
y = 15

To find the other variable (number), substitute that value in either equation.

x - y = 56
x - 15 = 56
x = 71

To check the solutions, substitute both variables into each equation to make sure they work.

x - y = 56
71 - 15 = 56
56 = 56

5y = x + 4
5*15 = 71 + 4
75 = 75

Solve for x
log2(5x-4)=4
Please show steps

Answers

Answer:

x=1.2

Step-by-step explanation:

2(5x-4)=4

distribute 2 to 5x and -4

10x-8=4

add 8 to negative 8 and 4

10x=12

now divide both sides by 10

10x/10= 12/10

x=1.2

The value of x for the logarithmic expression will be x=1.2.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is log2(5x-4)=4. The value of x will be calculated as,

2(5x-4)=4

Distribute 2 to 5x and -4,

10x-8=4

Add 8 to negative 8 and 4,

10x=12

Now divide both sides by 10,

10x/10= 12/10

x=1.2

Therefore, the value of x for the logarithmic expression will be x=1.2.

To know more about an expression follow

https://brainly.com/question/28041634

#SPJ2

What is mathmatics ?​

Answers

Answer:

The abstract science of number, quantity, and space. Mathematics may be studied in its own right ( pure mathematics ), or as it is applied to other disciplines such as physics and engineering ( applied mathematics )..

Ex :- Plus , minus

I HOPE IT IS HELPFUL

Mathematics is a very important field of study in human society that can be described as the study of:

Numbers Quantities Spatial elements

Mathematics is a science and one that is constantly evolving to allow us better understand our surroundings.

There are several ways to study the subjects described above such as by applying them to things such as engineering and other sciences, or simply studying them on their own.

In conclusion, math is a science of numbers.

Find out more on mathematics at https://brainly.com/question/14473572.

Please answer this question step by step!

No links please.

Whoever gives correct answer will get a thank you aswell.

Answers

Answer:

[tex]x = \frac{3}{2} [/tex]

Step-by-step explanation:

first distribute

[tex] \frac{36x - 9}{2x} = 15[/tex]

next multiply both sides by 2x

[tex]36x - 9 = 15(2x) \\ 36x - 9 = 30x[/tex]

simplify

[tex] - 9 = - 6x[/tex]

divide both sides by -6

[tex] \frac{ - 9}{ - 6} = x \\ \frac{3}{2} = x[/tex]

help please!
i can't figure it out.

Answers

Answer:

35

Step-by-step explanation:

8 + 27 would give us 35

We add the negative since it starts from there and works it's way up.

Find the equation of a line whose graph passes through the two points (2,-3) and (4,-8).

Answers

Answer:

y=-5/2x+2

y+3= -5/2. (x-2)

Step-by-step explanation:

Answer:

y=-5/2x+2

Step-by-step explanation:

y=mx+b, where m is slope, b is y-int and y and x are variables.

Step 1: plot your points

Step 2: draw a line thru them

Step 3: find the slope. -5/2. And your y-int. +2

Hope that helps! Brainliest is appreciated :)

combine k/4 and 5k


pls pls pls pls

Answers

[tex]\dfrac k4 + 5k = \dfrac{k + 20k}4 = \dfrac{21k}4[/tex]

Your answer is 21k/4

Find the LCM of 14 and 18 using prime factorizations.

Answers

Answer:

126

Step-by-step explanation:

2 decreased by the sum of m and 8

Answers

Answer:

(m+8) - 2

Step-by-step explanation:

Help me pleaseeee with this

Answers

Ok done. Thank to me :>

Translate this phrase into an algebraic expression.
7 increased by twice Goran's savings
Use the variable g to represent Goran's savings.

Answers

Answer: 2g + 7 or 7 + 2g

Step-by-step explanation:

7 increased by twice g can be represented as 2g + 7 or 7 + 2g

Blake has xx dimes and yy nickels. He has a minimum of 13 coins worth at most $1 combined. Solve this system of inequalities graphically and determine one possible solution.

Answers

Blake has 5 dimes and 10 nickels.

Let x represent the number of dimes and y represent the number of nickels.

Each dime is worth 10 cent ($0.1) and each nickel is worth 5 cents ($0.05).

Since he has a minimum of 13 coins, hence:

x + y ≥ 13     (1)

It is worth at most $1 combined, hence:

0.1x + 0.05y ≤ 1     (2)

From the graph, a possible solution is (5, 10).

Blake has 5 dimes and 10 nickels.

Find out more about inequalities at: https://brainly.com/question/241541

A forest covers 73,000 acres. A survey finds that 0.4% of the forest is old-growth trees. How man acres of old-growth trees are there?

There are__?__ acres of old-grown trees.

Answers

Answer:

292 acres.

Step-by-step explanation:

OK so if there are 73,000 acres of trees in total and 0.4% are old we would simply calculate what 0.4% of 73,000 which is 292. So of those 73,000 acres of trees 292 acres of them would be "old-growth trees".

Greg has only nickels and dimes in his money box. He knows that he has more than $10 in the box. Let x represent the number of nickels in the box and y represent the number of dimes in the box. Which of the following statements best describes the steps to graph the solution to the inequality in x and y? (5 points)

a
Draw a dashed line to represent the graph of 5x + 10y = 1000, and shade the portion below the line for positive values of x and y.

b
Draw a dashed line to represent the graph of 5x + 10y = 1000, and shade the portion above the line for positive values of x and y.

c
Draw a dashed line to represent the graph of 10x + 5y = 1000, and shade the portion above the line for positive values of x and y.

d
Draw a dashed line to represent the graph of 10x + 5y = 1000, and shade the portion below the line for positive values of x and y.

Answers

Answer: Draw a dashed line to represent the graph of , and shade the portion above the line for positive values of x and y

Step-by-step explanation: Let

x------> the number of nickels in the box

y------->the number of dimes in the box

we know that

so

Multiply by  both sides

-----> inequality that represent the situation

The solution of the inequality is the shaded area above the dashed line for positive values of x and y

The equation of the dashed line is

therefore

the answer is

Draw a dashed line to represent the graph of , and shade the portion above the line for positive values of x and y

The sum of 3 and m
A.x-3
B.1/2y
C.3+m
D.14+3x
E.x+5
F.14+4x

Answers

Answer:

C

Step-by-step explanation:

Answer:

the answer is C

Step-by-step explanation:

first of all thank you for reading this

it's addition which 3 + m

MAS CARDS
5. Determine if the equation has one solution, no solution, or infinite
solutions.
-2(x – 3) + 5 = -6(x + 1) + 4x

One solution
No solution
Infinite solutions

Answers

No solution

-2(x-3)+5=-6(x+1)+4x

Multiply to get rid of the parentheses

-2 x X = -2x
-2x-3=6

6 x X = 6x
6x1=6

New equation = -2x+6+5=-6x+6+4x

Add same

6+5=11
-6x + 4x = -2x

New equation = -2x+11=-2x+6

That just doesn’t work

Answer:

No solution

Step-by-step explanation:

-2(x-3)+5= -6(x+1)+4x

First Distribute:

-2x+6+5= -6x-6+4x

Then transfer all variables to one side and the rest to other side:*when transfer u turn to opposite number for example: -6x will transfer to 6x

6+5+6= -6x+4x+2x

Last solve

17=0

no solution

2(5 - 8x) -13 = 9(1 - x) -12 ​

Answers

2 (5 - 8x) - 13 = 9 (1 - x) - 12

10 - 16x - 13 = 9 - 9x - 12

10 - 13 - 16x = 9 - 12 - 9x

- 3 - 16x = - 3 - 9x

- 3 + 3 = - 9x + 16x

0 = 7x

0/7 = x

0 = x

_____

Hope it helps ⚜

Answer:

x = 0

Step-by-step explanation:

2(5 - 8x) - 13 = 9(1 - x) -12 ​=> 10 - 16x - 13 = 9 - 9x - 12=> -3 - 16x = -3 - 9x=> 0 = 16x - 9x=> 0 = 7x => x = 0

Conclusion:

Therefore, the answer is 'x = 0'

!! Hoped this helped !!

[tex]BrainiacUser1357[/tex]

Archie and Michael are helping their friend George move the washers and dryers from his laundromat to a larger building. Archie's truck is carrying three washers and four dryers that have a combined mass of 1260 kg Michael's truck is carrying two washers and three dryers that have a combined mass of 880 kg.
How much does one of George's washers weigh?​

Answers

Answer:

A

Step-by-step explanation:

Yes

please help me asap, i suck at math tbh :)

ty!

Answers

x intercepts: (9,0)
y intercepts: (0,-6)

Answer:

Y intercept = (0,-6)

X intercept = (9,0)

Step-by-step explanation:

To find the y-intercept of an equation, let x = 0 and then solve for y

6(0) - 9y = 54 (6 times 0 gives us 0)

0 - 9y = 54 (subtract 9y from 0 gives you -9)

-9y = 54 (divide both sides by -9, the left side cancels out and the right side gives you -6)

y = -6 and x = 0

To find the x-intercept of the equation just let y = 0 and then solve for x

6x - 9(0) = 54 (9 times 0 gives us 0)

6x - 0 = 54 (subtract 0 from 6x gives us 6x)

6x = 54 (divide both sides by 6, left side cancels, right side gives 9)

x = 9 and y = 0

1) -64÷16+[12x{6÷(16÷10-2)}] ​

Answers

Answer:

= -30[tex]x^{6}[/tex]-4

i hope that helps and is right

If that is a multiplication sign then it is -184

if that is an x then it would be -4 -180x

Suppose you know the area of the yard is 7,500 square feet. How can you find the value of a?


—help and it comes with a picture

Answers

Answer:

a = 50

Step-by-step explanation:

From the introduction, you know that the area is 3a^2

You also know that it is 7500 square feet. \

So the two must be equal

3a^2 = 7500                    Divide by 3

a^2 = 7500/3

a^2 = 2500

The square root of 2500 is 50

sqrt(a^2) = sqrt(2500)

a = 50

A car travels 32 miles for each gallon of gas. How many gallons of gas does it need to travel 192 miles?

Answers

You need 6 gallons of gas to travel 192 miles ..

Please help I’ll love u forever

Answers

Answer:

3. non linear

4. weak

Step-by-step explanation:

3. it doesn't go in a line

4. it's a weak association.

The length of a rectangular hall exceeds its breadth by 7 m. If the breadth is decreased by 1 m and the length increased by 2 m, the area remains the same. Find the length and breadth of the hall.​

Answers

Answer:

Step-by-step explanation:

Let the length be :x+7

Let the breadth be:x

After addition and subtraction

Length:x+7+2=x+9

Breadth:x-1

A.T.Q

x(x+7) = (x+9)(x-1)

x²+7x = x(x-1)+9(x-1)

x²+7x = x²-x+9x-9

x²+7x-x²+8x = 9

8x-7x = 9

So, Breadth: 9m

So, Length :16m

What percent of 80 is 10?

Carrie is driving to a friend’s house for the weekend. The friend lives in a town 160 mi. away. So far, Carrie has driven 64 mi. What percent of the drive does she have left?

Answers

Answer:

12.5% and 60%

Step-by-step explanation:

0.125 x 80 = 10

160-64 = 96

96/160 = 0.6

0.6 x 100 = 60%

Solve for h. (h − 8)(h + 2) = 0

Answers

Answer:

donwload the gautmaht this is very powerful calculator to math problems

Step-by-step explanation:

make this is helpful too you

Plzzzzz help meeee plzzzzzzz plzzz

Answers

Answer:

try 20%

Step-by-step explanation:

Pls due tmr pls pls fast I need it like rn

Answers

Answer:

Step-by-step explanation:

50 of 100

= 50%

120 of 1

= 1.2%

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