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

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]

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

Is 3.14596387 a rational number?

Answers

no it is an irrational number

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

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:

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

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.

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

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?  

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

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

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

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

Which is bigger 6.8" or 6.52"

Answers

Answer:

6.8 is bigger than 6.52

6.8 is bigger than 6.52

Help please this is math

Answers

irrational and intergers

***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:

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

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

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

please help me solve this math problem, tryna graduate here

Answers

Answer:

141°

Step-by-step explanation:



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.

Solve
- 2 + 3x + 24 = x

Answers

Answer:

x=-1

Step-by-step explanation:

thank me later it correct did the workhope this works

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)

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)

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

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:

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]

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

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
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