Julia has 42 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 180 square meters. List each set of possible dimensions (length and width) of the field.

Answers

Answer 1

The list of the set of dimension for fencing the building around a rectangular plot of land is 10.5 meters and 21 meters.

Area of a rectangle

area of rectangle = lw

where

l = lengthw = width

Therefore,

perimeter = 2w+ l

42 = 2w + l

l = 42  - 2w

Hence,

area = w(42 - 2w)

180 = 42w - 2w²

-2w² + 42w - 180 = 0

-w² + 21w - 90 = 0

The dimension w can be found as follows;

w = - b / 2a

where

a = -1b = 21

w = - 21 / 2 ×  -1

w = 10.5 meters

Then,

l = 42  - 2w

l = 42 - 2(10.5)

l = 21 meters

Therefore, the dimensions are 10.5 meters and 21 meters.

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Related Questions

Can someone answer theese 3 questions i will give brainliest

Answers

Answer:

#3

A

#2

D

#1

B

Hope this helps

Answer:

1.) 10/16 = 5/8  

2.) 14/16 = 2 7/8

3.) 6/16 = 1 3/8

Step-by-step explanation:

Just count the lines.

5b8c3
The degree of the monomial is?

Answers

Answer:

8

Step-by-step explanation:

The given monomial is :

5b⁸c³

The degree of the monomial is the highest power to which a variable is raised to in the monomial. The greatest power in this case belongs to b⁸, which has a power of 8.

Hence, the degree of the monomial is 8

Identify the intercepts of the graph.

Answers

Answer: X-ints = (-1,0) and Y-ints = (1,0)

Step-by-step explanation:


This is quite simple. The way to solve this problem is by visualization, if you have learned how coordinates are created, this is how you would do it.

In a 2D plane, you have an X and Y axis and coordinates are created in the form of (X,Y).


by simply looking at the graph, I can see how the line crosses the positive 1 in the Y-axis, and -1 in the X-axis.

Part A) asks to find the X-intercept(s) which as stated above, it croses -1 on the X-axis and 0 on the Y-axis. Therefore the intercept is:


(-1,0)


part B) asks the same but for the Y-intercepts. We look at the graph and see the line crosses positive 1 in the Y-axis, and 0 in the X-axis. So:


(0,1)


done :)

how do I simplify the following to "a+bi" form: (1+2i)^3

Answers

Answer:

Expand it.

(1+2i)^3 is equal to (1+2i)(1+2i)(1+2i).

Multiply everything out (being sure to multiply every term. (1+2i) * (1+2i) = 1+2i+2i+4i^2.

i is the square root of negative one, so i^2 is just -1. 1+2i+2i-4 is what you get from the first two, so now simplify that:

1-4 + 2i+2i = (-3+4i) and now multiply that by (1+2i):

(-3+4i) * (1+2i) = -3 - 6i +4i +8i^2.

Simplify again, and the answer is: -11-2i

Step-by-step explanation:

I hope this helps - really my only tip is don't spend time thinking about what i is, that just hurts your brain. Just remember that i^2 is equal to negative one, and treat it like regular multiplication and you will be fine.

HELPPPPPPPPP!!!!!!!!!!!!!!!!

Answers

Answer = (-4,1)
See picture for reason

H
3.
6x
++
For this rectangle, find x.
15
180
90
6
k

Answers

Answer:

x =15

Step-by-step explanation:

its a rectangle all interior angles must be equal to 90 so 6x=90

divide by 6 to get x on its own and you get 15

Edgar accumulated $5000 in credit card debt if the interest rate is 50% per year and he does not have to make any payments for five years how much will he go on his debt in five years by compounding continuously.

Answers

Answer:

$ 60 912.46   owed in five years

Step-by-step explanation:

FIFTY percent <====== crazy !    This is .5 in decimal form

FV = Future Value = PV e^(i*t)    

   PV = present value      i = interest in decimal form      t = years

5000 e^(.5 * 5 )  = 60912.46

Find the equation of the line of the given properties: Slope = 0 and passes through (-4,5).


Pls help me

Answers

Answer:

y = 5

Step-by-step explanation:

An equation can be written in two forms: point-slope form or slope-intercept form.

When you write an equation in point-slope form, you only need two things: a point and a slope.

Given:

point: (-4, 5)slope (m): 0

The standard point-slope equation is

y - y₁ = m(x - x₁)

Plug in what you know.

y - (5) = 0(x - (-4))

Simplify.

y - 5 = 0(x + 4)

y - 5 = 0

y = 5

This is your equation.

Let's now represent this in slope-intercept form.

The standard equation is

y = mx + b

Plug in what you know.

5 = 0(-4) + b

Simplify.

5 = 0 + b

5 = b

Therefore,

y = 0x + 5 or y = 5

Hope this helps!

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31. (05.08 MC)
What is the equation for a geometric sequence with a first term of 3 and a second term of -9?

Answers

Answer:

[tex]a_n=3(-3)^{n-1}[/tex]

Step-by-step explanation:

Geometric sequence

General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]

where:

[tex]a_n[/tex] is the nth terma is the first termr is the common ratio

Given:

[tex]a_1=3[/tex][tex]a_2=-9[/tex]

To find the common ratio r, divide consecutive terms:

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{-9}{3}=-3[/tex]

Therefore, the equation is:

[tex]a_n=3(-3)^{n-1}[/tex]

prove fermat's last theorem:no three positive integers a, b, and c satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2

Answers

The proofing of Fermat's last theorem shows that y = a² - b², z = a² + b² and x = 2ab.

How to prove fermat's last theorem?

The equation x² + y² = z². We can assume that x, y, and z are positive and relatively prime. Suppose that x is even. Then:

(z - y/2)(z + y/2) = (x/2)²

Hence,

(z - y)/2 = b²

(z + y)/2 = a²

Then, y = a² - b², z = a² + b² and x = 2ab.

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use a formula to find the surface area of the cylinder use 3.14 for pi

Answers

Answer:

376.8 cm²

Step-by-step explanation:

Given:

Radius of circular base: 4 cmHeight of cylinder: 11 cm

Surface area = 2πrh + 2πr²

[Where "r" and "h" represents the radius and the height respectively]

Let's substitute the height and the radius in the formula and simplify it.

[tex]\implies 2\pi rh + 2\pi ^{2}[/tex]

[tex]\implies 2\pi (4)(11) + 2\pi (4)^{2}[/tex]

[tex]\implies 2\pi (44) + 2\pi (16)[/tex]

[tex]\implies 88\pi + 32\pi[/tex]

We can factor π out of the expression. Therefore, we get:

[tex]\implies 88\pi + 32\pi[/tex]

[tex]\implies \pi (88 + 32)[/tex]

Now, simplify the expression inside the parentheses.

[tex]\implies \pi (88 + 32)[/tex]

[tex]\implies \pi (120)[/tex]

The value of π, we are given, is 3.14. When substituted, we get:

[tex]\implies \pi (120)[/tex]

[tex]\implies 3.14(120) = 31.4(12) = \boxed{376.8 \ \text{cm}^{2} }[/tex]

Therefore, the surface area of the cylinder is 376.8 cm².

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suppose y = sin x
what y-value corresponds to an x-value of 3pi/2

Answers

Answer: THE ANSWER ON ACELLUS IS -1

Step-by-step explanation:

I found this answer on a site used to do sin cos and tangent

The y-value corresponding to an x-value of [tex]\( \frac{3\pi}{2} \)[/tex] in the function [tex]\( y = \sin(x) \) is \( y = -1 \).[/tex]

To find the y-value corresponding to an x-value of [tex]\( \frac{3\pi}{2} \)[/tex] in the function [tex]\( y = \sin(x) \),[/tex] simply substitute [tex]\( x = \frac{3\pi}{2} \)[/tex] into the function:

[tex]\( y = \sin\left(\frac{3\pi}{2}\right) \)[/tex]

Now, let's evaluate the sine function at [tex]\( \frac{3\pi}{2} \):[/tex]

[tex]\( y = \sin\left(\frac{3\pi}{2}\right) = -1 \)[/tex]

So, the y-value corresponding to an x-value of [tex]\( \frac{3\pi}{2} \)[/tex] in the function [tex]\( y = \sin(x) \) is \( y = -1 \).[/tex]

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Which statement about the line represented by the equation y+2=(x-5) is true

A. The slope is 3 and (-2,5) is on the line
B. The slope is 2 and (3,-5) is on the line
C. The slope is 3 and (5,-2) is on the line
D. The slope is 2 and (-3,5) is on the line

Answers

Answer:

A

Step-by-step explanation:

-2+2=5-5

0=0

the correct answer is A

A student tosses a coin and then draws a card from a stack of 4 cards labeled 1 through 4

What is the sample space for this compound event?

{H, T, 1, 2, 3, 4}

{H1, T1, H4, T4}

{HT1, HT2, HT3, HT4}

{H1, T1, H2, T2, H3, T3, H4, T4}

Answers

Answer:

The answer is the longest one <3

Step-by-step explanation:

I took the test:

If the coin is tossed and a card is chosen from 1 to 4, then the total sample will be 8. Then the correct option is D.

What is a sample?

A sample is a collection of well-defined elements. A sample is represented by a capital letter symbol and the number of elements in the finite set is shown as a curly bracket {..}.

A student tosses a coin and then draws a card from a stack of 4 cards labeled 1 through 4.

Then the total number of the sample will be

Total sample = 2 × 4

Total sample = 8

Then the sample is given below.

[tex]\rm Sample = \begin{Bmatrix}(H,1) & (H,2) & (H,3) & (H,4) \\\\(T,1) & (T,2) & (T,3) & (T,4) \\\end{Bmatrix}[/tex]

More about the sample link is given below.

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In the whole number 70,819 the place value of the digit 1 is

Answers

Step-by-step explanation:

a number is a sequence of digits with every position being multiplied by increasing powers of 10.

and the whole number is then the sum of of these little multiplications.

the first position left of the decimal point is for 10⁰ (1). the second position is 10¹ (10). the third position for 10² (100). and so on.

the given number is therefore just the short version of

7×10⁴ + 0×10³ + 8×10² + 1×10¹ + 9×10⁰

and therefore, the digit 1 in this number has the value 1×10¹ = 10, which is also the place value, 10¹ = 10.

Find the square root of 169

Answers

Answer:

13

Step-by-step explanation:

Answer: 13

Verification: 13 * 13 = 169

Help with functions!! Thank you!!

Answers

Answer:

(s - t)(x) = 4x^2 - x - 5

(s + t)(x) = 4x^2 + x + 5

(s * t)(-1) = 16

Step-by-step explanation:

(s - t)(x) is simply the same as s(x) - t(x)

(s + t)(x) is simply the same as s(x) + t(x)

(s * t)(x) is simply the same as s(x) * t(x)

(s - t)(x) = s(x) - t(x) = 4x^2 - (x+5) = 4x^2 - x - 5

(s + t)(x) = s(x) + t(x) = 4x^2 + (x+5) = 4x^2 + x + 5

(s * t)(-1) = s(-1) * t(-1) = 4(-1)^2 * (-1+5) = 4 * 4 = 16

Solve for x. Round to the nearest tenth.​

Answers

Answer:

x = 25.84

Step-by-step explanation:

Secx = hyp /adj

Secx = 30/27

x = ArcSec(30/27)

x = 25.84

What is the median of the following set of numbers?

Answers

Answer: order the data from least to greatest then cross out from left to right to get to the middle and you have your number

Step-by-step explanation:

for a Saturday matinee, adult tickets cost $5.50 and kids under 12 pay only $4.00. If 70 tickets are sold for a total of $355, how many of the tickets were adult tickets and how many were sold to kids under 12?

Answers

Let x be tickets for adults
Y be tickets for kids under 12, then
5.5x + 4 y = 355 ,
x+y = 70=>(y = 70-x)
5.5x + 280-4x=355
1.5x=75
X=50
Y=20

Maths question:
5% of 40
20% of 25

Answers

5% of 40 is 2
20% of 25 is 5
Enjoy

Answer:

1. 2

2. 5

Step-by-step explanation:

1. write 5% as

[tex] \frac{5}{100} [/tex]

Then,

[tex] \frac{5}{100} \: of \: \: 40 = \frac{5}{100} \times 40[/tex]

Therefore, the answer is 2

If you are using a calculator, simply enter 5 divided by 100 times 40 which will give you 2 as the answer.

2. Write 20% as 20/100

[tex] \frac{20}{100} \: of \: 25 = \frac{20}{100} \times 25[/tex]

Therefore, the answer is 5

If you are using a calculator, simply enter 20 divided by 100 times 25 which will give you 5 as the answer.

Hayden said the expression 3(2x+1) will always be greater than 3 because when I distribute the 3 to the numbers inside the parentheses, I will multiply 3 and 1 which is 3 since I will always be adding to the first part of the expression the final answer must be greater than 3

Answers

Answer:

9x.

Step-by-step explanation:

Hayden is correct. 3(2x + 1) = 9x.

Here is explanation:

If you didn't know, 2x + 1 would simply be 3x.

So then, 3 * 3x would then be 9x.

Here is math explanation:

3(2x + 1)= 3(3x)= 3 * 3x= 9x.

You now have your answer!

9x is your answer.

Please help me out with this question

Answers

Answer:

A6n+4

Step-by-step explanation:

A wooden block is in the shape of a regular hexagonal pyramid. The lateral surface area of the pyramid is 450 square centimeters, and the pyramid has a slant height of 15 centimeters. What is the side length of the base?

Answers

Answer:

10 cm

Step-by-step explanation:

If x and y vary inversely, and y =6 when x=7, what is the constant of variation

Answers

Answer:

x alpha 1/y

: Introducing a constant k

x = k/y

where x = 7, y= 6

7 = k / 6

Cross Multiply

K ( constant) = 42

Answer: k = 42

Step-by-step explanation:

Formula = [tex]y = \frac{k}{x}[/tex]

plug in values:

6 = [tex]\frac{k}{7}[/tex]

multiply both sides by 7

k = 42

William William mowed 75% of the lawn in 33 minutes. Part A Which equation can be used to find how many minutes it will take for William to mow the whole lawn if he continues at the same rate? 75n=33 33n=75 0.33n=75 75n100=33 Part B How many minutes will it take for William to mow the whole lawn?

Answers

The equation that can be used to find out the total time it will take to William to mow the lawn is (75n) / 100=33.

What is an equation?

This is a mathematical expression that represents a situation including a value that is not known.

In this case the best equation would be 75n / 100=33 as this is the only one that includes all the factors:

75% out of a 100% that is unknown (n)100 (represents the percentage)33 (total of minutes completing 75%)

What is the result of this equation?75n / 100=33n/ 100 = 33/75n/100 =0.44n= 0.44 x 100n = 44 minutes

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A toy factory manufactures d dolls every hour.Each dolls costs e cents.How much money will the factory spend in costs for manufacturing dolls in 7 hours and 30 minutes?​

Answers

Answer:

in 7hours and 30 mn the cost will be (7.5×d×e) cents

Step-by-step explanation:

[tex]\begin{matrix}\text{Time} &1h&7.5h\\ \text{number of dolls} &d&7.5\\ \text{Cost} &d\times e&7.5\times d\times e\end{matrix}[/tex]

House numbers along a street consist of two-digit numbers. Each house number is made up of non-zero digits, and no digit in a house number is repeated. Event A is defined as choosing 8 as the first digit, and event B is defined as choosing a number less than 6 as the second digit. If a house number along this street is picked at random, with each number being equally likely and no repeated digits in a number, what is P(A and B) expressed in the simplest form? A. 1/9 B. 5/72 C. 5/8 D. 2/3

Answers

The value of the probability P(A and B) is 5/72 if the house numbers along a street consist of two-digit numbers, option (B) is correct.

What is probability?

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Total number of outcomes = 9×8  = 72

(because the total number of digits excluding 0)

Event A: choosing 8 as the first digit

Event B: choosing a number less than 6 as the second digit

Total favourable outcomes = 1×5 = 5

Because there are total 5 digits that are less than 6 {1, 2, 3, 4, 5}

Probability = 5/72

Thus, the value of the probability P(A and B) is 5/72 if the house numbers along a street consist of two-digit numbers option (B) is correct.

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Answer:

The answer is B I'm pretty sure.

Step-by-step explanation:

Time4Learning 2022 quiz

16 out of 80 baseball players are left handed.
What percent of the players are left handed?

Answers

Answer:

20% of players are left-handed

Step-by-step explanation:

First, find how much each player is worth percent-wise

100 / 80 = 1.25

Then find out how much percent of players that makes up

1.25 x 16 = 20

The answer is 20% of players are left-handed, to check it you could do

80 * 0.2 = 16

(80 = total players, 0.2 = 20%, 16 = total left handed players)

Order the following from least to greatest.

0.98, 3/5, 4, 1/2, 0.4

Answers

Answer:

.4, 1/2, 3/5, .98, 4

Step-by-step explanation:

give me brainliest please

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