An arhitect wants to draw a rectangle with a diagonal of 20 inches. The length of the rectangle is to be 8 inches more than twice the width.what dimensions should she make the rectangle

Answers

Answer 1

The diagonal of a rectangle = sqrt(w^2 + l^2)

w = width

l = length

In this problem,

The diagonal = 20 in

w = x

l = 2x + 8

Let's plug our numbers into the formula above.

20in = sqrt((x)^2 + (2x + 8)^2)

Let's simplify the inside of the sqrt

20 in = sqrt(5x^2 + 32x + 64)

Now, let's square both sides.

400 = 5x^2 + 32x + 64

Subtract 400 from both sides.

0 = 5x^2 + 32x - 336

Factor

0 = (5x - 28)(x + 12)

Set both terms equal to zero and solve.

x + 12 = 0

Subtract 12 from both sides.

x = -12

5x - 28 = 0

Add 28 to both sides.

5x = 28

Divide both sides by 5

x = 28/5

The width cant be a negative number so now we know that the only real solution is 28/5

Let's plug 28/5 into our length equation.

Length = 2(28/5) + 8 = 56/5 + 8 = 96/5

In conclusion,

Length = 96/5 inches

Width = 28/5


Related Questions

Help please this is math

Answers

irrational and intergers

6.4n-1.2+3n+8.2=19.22

What number would make the statement true

Answers

Answer:

Step-by-step explanation:

6.4n - 1.2 + 3n + 8.2 = 19.22

So we can separate the variable side on the left, and the whole numbers on the right.

6.4n + 3n = 19.22 - 8.2 + 1.2

which gives us,

9.4n = 12.22

n = 1.3

Solve and graph -4<-1-4x<-1

Answers

Answer:

x<3/4 and x>0

for graphs, refer to the images attached.

Step-by-step explanation:

-1-4x > -4 AND -1-4x <-1

-1-4x >-4-4x > -3x < 3/4

-1-4x<-1-4x<0x>0

Solve
- 2 + 3x + 24 = x

Answers

Answer:

x=-1

Step-by-step explanation:

thank me later it correct did the workhope this works

An air conditioning system can circulate 400 cubic feet of air per minute. How many cubic yards of air can it circulate per minute?

Answers

Answer:

14.814 i belive

Item 3 A snail travels 3/8 feet in 1/2 hour. How many feet does the snail travel in one hour? Express your answer in simplest form. 3/16ft 1/4ft 1/8ft 3/4ft

Answers

The answer in simplest form would be 3/4ft



Brianna is playing darts. So far, she has hit the bullseye 6 times and missed the bullseye 27
times. Considering this data, how many bullseyes would you expect Brianna to get during her
next 88 tosses?

Answers

At 111 tosses (33 + 88) she will hit the bullseye every 3.3 tosses approximately. So she would have hit the bullseye about 33.6 times. You can also rounded up to 34 times.

Courtney and Malik are buying a rug to fit in a
50-square-foot space, which rug should they
purchase? Explain.
$99 Rug Sa

Answers

where’s the rest of the problem

Set V is all the unique three-digit numbers using the digits 1, 2, 3, 4, and 5. Which set would be considered a subset of set V? Set W is all the unique three-digit numbers using the digits 1, 3, and 5. Set X is all the unique three-digit numbers using the digits 2, 4, and 6. Set Y is all the unique three-digit numbers using the digits 0, 2, and 4. Set Z is all the unique three-digit numbers using the digits 3, 5, and 7.

Answers

Answer: Choice A) Set W is all the unique three-digit numbers using the digits 1, 3, and 5

==========================================================

Explanation:

The original set uses the digits {1,2,3,4,5}. We can only use those digits. Nothing else. So that means we can't use 0, 2, 4, 6, or 7. This rules out choices B through D.

Only choice A is left. This answer choice involves 1,3 and 5 which is the correct subset of digits to use.

--------

Put another way, if set B was a subset of set A, then everything in B must also be found in A. Having B = {2,4,6} and A = {1,2,3,4,5} shows B is not a subset of A. We see a counter example has 6 in B, but not in set A.

This allows us to rule out choice B. Similar ideas apply to the answer choices C and D as well.

Answer:

A

Step-by-step explanation:

ed2020

What is the solution of the equation 16-17+ Vb=1?
b = 3
O b = 9
O b = 81
no solution

Answers

B=3 is the correct answer

Solve the equation 1/4(x+2)+5=-x

Answers

Answer: Exact Form:

x=−225

Decimal Form:

x=−4.4

Mixed Number Form:

x=−4/25

Step-by-step explanation:

***ECONOMINCS*** Which statement best summarizes the role of households in the flow of
goods?
A. Households sell products created in product markets.
B. Households provide natural resources to businesses.
C. Households trade goods between product and resource markets.
D.Households act as consumers for goods made by businesses.

Answers

The final customers of a companies' products and services are the households. They generate demand in the market dependent on their preferences, and further discussion can be defined as follows:

As per the market demand, the businesses manufactured and provided items in the market and the nation's production line is determined by its families.Households consume the commodities supplied by the companies in a circular flow diagram.It could contribute land for the production of goods, or it may offer itself as the source of employment.It also provides capital, which would be a monetary type of investment that enables businesses to generate consumer products.

Therefore, the final answer is "Choice D"

Learn more:

brainly.com/question/22097439

Answer:

D.Households act as consumers for goods made by businesses.

Step-by-step explanation:

Point N is on line segment M O ‾ MO . Given M O = 12 MO=12 and M N = 5 , MN=5, determine the length N O ‾ . NO .

Answers

Answer: NO = 7

Step-by-step explanation:

If the total length of MO is 12, and one segment, MN, is 5, the other segment, NO, must have a length so that they add up to 12.

MN + NO = MO

5 + 7 = 12

M_____ N+ N_______O= M____________O

What part of 15 is 10?

Answers

Answer:

2/3

Step-by-step explanation:

10/15=2/3

The 10 is 2/3 part of 15 by dividing common factor that is 5.

What is simplest form ?

In mathematics, the simplest form is the fraction that has the smallest equivalent value.

Here, the given fraction is :

10/15 which when converting to smallest equivalent value by dividing common factor that is 5 :

10/15 = 2/3

Therefore, the 10 is 2/3 part of 15.

Learn more about fractions on:

brainly.com/question/78672

#SPJ2

Find an equation for the line with the given properties. Express the equation in slope-intercept form.
Slope = 3; containing the point (5,-4)
What is the equation of the line?
y =

Answers

Answer:

y = 3x - 19

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Step 1: Define variables

Slope m = 3

Random point (5, -4)

Step 2: Plug in known variables

y = 3x + b

Step 3: Find b

-4 = 3(5) + b

-4 = 15 + b

b = -19

Step 4: Write linear equation

y = 3x - 19

I need help with part 2 please

Answers

Answer:

$65

Step-by-step explanation:

So we already determined that the total cost C to drive m miles is:

[tex]C=0.25m+40[/tex]

And we want to find the total cost of driving 100 miles.

So, substitute 100 for m and solve for C:

[tex]C=0.25(100)+40[/tex]

Multiply:

[tex]C=25+40[/tex]

Add:

[tex]C=\$ 65[/tex]

Therefore, it will cost $65 to drive 100 miles.

A cupcake shop earns $950 a day. The total amount of earning varies directly with the number of days. Find the total earnings the cupcake shop earns in 5 days.

Answers

The correct answer is $4750

Explanation:

If the money earned varies directly with the number of days, this means one factor makes increase the other. In other others, the more days, the higher the earnings. Moreover, the total earnings can be calculated by multiplying the amount earned in one day ($950) by the total days (5). The process is shown below.

Total earnings = Amount earned by day x days

Total earnings= 950 ×5

Total earnings= $4750

Marcus collected 5 fewer rocks than esha How many rocks did Marcus collect if esha collected 22 rocks?

Answers

Answer:

17

Step-by-step explanation:

Answer:

22-5=17 the answer is 17

I NEED HELP ANSWER ASAP. I NEED SOMEONE WHO CAN I HELP ME WITH MY OTHER QUESTIONS

Answers

Answer:

3,0

Step-by-step explanation:

hopefully this helps you

pls mark brainlest if it is correct

please help me solve this math problem, tryna graduate here

Answers

Answer:

141°

Step-by-step explanation:

Barbara has 9 stuffed animals. Trish has 3 times as many stuffed animals as Barbara. How many stuffed animals does Trish have?

Answers

Answer:

27

Step-by-step explanation:

9 + 9 + 9 = 27

I hope this helps :)

Answer:

trish has 27 because 9 times 3=27 love yall

Step-by-step explanation:

Which of the following trinomials could represent the product (x + m)(x + n) if m = 5 and n = -7? A x2 + 2x - 35 B x2 - 12x - 35 Cx2 + 35x + 2 D x2 - 2x - 35

Answers

Hey there! I'm happy to help!

Let's plug in these values.

(x+5)(x-7)

We use the FOIL method to multiply the two.

We multiply the Firsts.

x·x=x²

We multiply the Outsides.

-7·x=-7x

We multiply the Insides.

5·x=5x

And we multiply the Lasts.

-7·5=-35

We combine these all.

x²-7x+5x-35

x²-2x-35

Have a wonderful day! :D

Which is bigger 6.8" or 6.52"

Answers

Answer:

6.8 is bigger than 6.52

6.8 is bigger than 6.52

Rural and urban students are equally
likely to get admission in a college. If 100
students get admission, then the probability
that more rural students get admission than
urban students is

Answers

Answer:

The answer is below

Step-by-step explanation:

Using binomial probability:

p = probability of a rural student getting admission = 1/2

q = probability of a rural student not getting admission = 1/2

n = number of students = 100

P(x) = [tex]C(n,x) p^xq^{(n-x)[/tex]

But [tex]p^xq^{n-x}=\frac{1}{2}^x\frac{1}{2}^{n-x}=\frac{1}{2}^{n}[/tex]

P(x > 50) = P(x = 51) + P(x = 52) + P(x = 53) + . . . + P(x = 100)

P(x > 50) = [tex]\frac{1}{2} ^{100}[C(100,51)+C(100,52)+C(100,53)+\ .\ .\ .+C(100,100)]\\[/tex]

[tex]P(x>50)=\frac{1}{2}^{100} (\frac{1}{2}( 2^{100}-C(100,50)))\\\\P(x>50)=(\frac{1}{2}^{100} *\frac{1}{2}*2^{100})- (\frac{1}{2}^{100} *\frac{1}{2}*C(100,50))\\\\P(x>50)=\frac{1}{2}[(2^{-100}*2^{100})-(\frac{1}{2}^{100} *C(100,50))]\\ \\P(x>50)=\frac{1}{2}[1-\frac{1}{2}^{100} *C(100,50)][/tex]

Which of the following is equivalent to 15.45 + ( − 98.25 ) 15.45+(-98.25)

Answers

Answer:

-82.8

Step-by-step explanation:

15.45 + ( − 98.25)

15.45 - 98.25

= -82.8

Since the two terms are of opposite signs, you have to subtract and use the sign of the greater term (positive or negative)

3s – 12 = -21
Solve for s

Answers

Answer:

S= -3

Step-by-step explanation:

3s-12=-21

3s= -21+12

3s= -9

s= -9/3

s= -3

Answer:

s = -3

Step-by-step explanation:

[tex]3s - 12 = - 21[/tex]

Collect like terms

[tex]3s = - 21 + 12[/tex]

Add the numbers :

[tex] - 21 + 12 = - 9 \\ \\ 3s = - 9[/tex]

Divide both sides of the equation by 3

[tex] \frac{3s}{3} = \frac{ - 9}{3} [/tex]

Simplify

[tex]s = - 3[/tex]

2x = 8
X - 3 = 5
5x + 2 = 12
7x + 4 = 25
3x + 1 = 5x – 13
3 (2x + 1) = 2x + 11
3 (2x - 6) = 2 (2x- 1)
2 (x + 3) - 3(2x - 5) =x​

Answers

Step-by-step explanation:

2x=8

x=8÷2

x=4

x=5+3

×=8

I think you wrote the answer and the final step is x=4

Use the points H(-4,3) and K (4,3)

Answers

Y=3 can you be specific like the midpoint or ...
The midpoint is (0,3)

what is -66 2/3 - 24 1/8 + -78 3/4

Answers

Answer:

-169.541667

Step-by-step explanation:

Answer:

Step-by-step explanation:

i belive your asnwer would be -257/24 but what are u trying to find?  

Is 3.14596387 a rational number?

Answers

no it is an irrational number
Other Questions
Paleo-Indians found an abundance of wildlife in Oklahoma to support their needs. Which of the following factors led to large populations of wildlife in Oklahoma during the time of the Paleo-Indians? Express in simplest form: 12 (2 + ) (4 + ) Use the passage below to answer all parts of the question that follows. In the past, none failed to hear Confucius teachings, but few understood them. Thereafter came the vulgar Confucian scholarship of later times, which stressed memorization and literary composition, but was of no real use. Then came the deviant doctrines of Buddhism and Daoism, which had loftier goals but lacked solid substance. These teachings were mixed together in great confusion, so that rulers could no longer hear the essential teachings of Confucius, and lesser men could no longer enjoy the benefits of good government. Everything decayed until disorder and destruction reached its extreme in the Five Dynasties period*. Yet Heavens cycle continues. The virtuous power of the Song dynasty rose up, and both government and education shone with great luster. With that, the method whereby the ancients taught men was once again made brilliantly clear to the world. *an era of political chaos in China during the tenth century Zhu Xi, Chinese scholar and philosopher, preface to a commentary on The Great Learning, written in 1190. The Great Learning was a text of Confucian teachings that became a foundational text of examination for the Chinese civil service. a) Identify ONE claim made in the passage. b) Identify ONE way in which the ideas expressed in the passage illustrate the social or political development of China under the Song dynasty. What does the phrase In order to form a more perfect unionmean Whenever an object is moving at a constant rate, the value(s) that equal zero is (are): a) Speedb) Accelerationc) Velocityd) All of the above what is this from least to greatest 0.6,(9/16),2/3 Write a short argumentative essay in which you explain what factors contribute to a persons identity. What are the numerical measures of each angle? PLEASE HELP Choose the word or phrase that best completes each sentence.Charlemagne (surprised, divided, or united,) much of Western Europe by conquering other kingdoms and tribes.Charlemagne became the (king, vassal, or emperor.) of the Holy Roman Empire.Trade (grew, shrank, or stayed the same.) in Western Europe during Charlemagne's reign.Charlemagne helped (Christianity, Buddhism, or Shintoism)spread by building more churches and monasteries. Under the Declaration of Independence ordinary citizens have the right to do what and why? the Navajo people ____________ 7.What role did geographic location play in the history of Byzantium? What were its advantages and disadvantages? Why do you think toxicology is an important area of study in veterinary science? Oppositely charged parallel plates are separated by 4.49 mm. A potential difference of 600 V exists between the plates. (a) What is the magnitude of the electric field between the plates? N/C (b) What is the magnitude of the force on an electron between the plates? N (c) How much work must be done on the electron to move it to the negative plate if it is initially positioned 3.14 mm from the positive plate? 1. Sum of two numbers = 15Difference of the numbers = 3Find the numbers.What is their product? What do all of the elements in group 13 have in common? 2. How many kilometers are in 8432 meters? #2 - Simplify the expression. Type your answer with all lowercase letters and no spaces. * 3h - e + 2h - 5e Read the passage from The Farewell Speech The repetition of the word "love" is effective because it I do assure you there is no prince that loves his subjects better, or whose love can countervall our love. There is no jewel, be it or never so nich a price, which I set before this jewel I mean your love. For I do esteem it more than any treasure or nches, for that we know how to prize, but love and thanks I count invaluable. O helps the author to establish a third-person point of view O creates a romantic tone right from the beginning of the speech O emphasizes the speaker's respect and affection for the audience. provides organization so the speaker's thoughts progress logically Six times the sum of a number and 8 is 30. Find the number.