Sergei buys a rectangular rug for his living room. He measures the diagonal of the rug to be 18 feet. The length of the rug is 3 feet longer than the width. What are the approximate dimensions of the rug? Round each dimension to the nearest tenth of a foot. 10. 4 feet by 7. 4 feet 11. 1 feet by 8. 1 feet 13. 4 feet by 10. 4 feet 14. 1 feet by 11. 1 feet.

Answers

Answer 1

A rectangular rug divided by its diagonal becomes a right angle triangle

The length and width of the rug is 14.1 feet by 11.1 feet

A right angle triangle has the longest side as the hypotenus which is also the diagonal.

Diagonal = 18 feet

width = x

length = x + 3

diagonal ² = length ² + width ²

18² = x² + (x + 3)²

18² = x² + x² + 6x + 9

324 = 2x² + 6x + 9

2x² + 6x + 9 - 324 = 0

2x² + 6x - 315 = 0

solve using quadratic formula

x = - b ± √b² - 4ac / 2a

= - 6 ± √6² - 4×2×-315 / 2×2

= -6 ± √36 - (-2520) / 4

= -6 ± √36 + 2520/4

= -6 ± √2556 / 4

= - 6 ± 6√71 / 4

= -6/4 ± 6√71 / 4

= -3/2 ± 3√71/2

x = 11.1392 or -14.1392

The value of x can't be negative

So,

x = 11.1 to the nearest tenth

Therefore, the value of width and length is

width = x

= 11.1 feet

length = x + 3

= 11.1 + 3

= 14.1 feet

Learn more about Pythagoras theorem:

https://brainly.com/question/20545047


Related Questions

Mr. Smith charged Jill $320 for parts and $150 per hour for labor to repair her bicycle. If he spent 3 hours repairing her bike, how much does Jill owe him? Write an expression and show your work and answer.

Answers

Answer:A repair bill for a car is $648.45. The parts cost $265.95. The labor cost is $85 per hour.

Step-by-step explanation:

had this question

PARALLEL PERPENDICULAR OR NEITHER OR SAME slope

Answers

Answer:

21. Same Line

22. Same Line

23. Perpendicular

24. Neither

25. Parallel

26. Neither

27. Neither

28. Neither

29. Perpendicular

30. Perpendicular

31. Neither

32. Perpendicular

33. Parallel

34. Perpendicular

35. Perpendicular (?)

36. Neither

37. Neither

38. Parallel

39. Neither

40. Parallel

Please translate each algebraic expression to English phrase
1. x - 8

2. 13 + 2y

3. 4 ( x+ 5)

4. 7x

5. m + 6

Answers


1. x - 8

2. 13 + 2y

3. 4 ( x+ 5)

4. 7x

5. m + 6
1. Eight less than some number

2. Thirteen plus two times some number (I think)

3. Four times the sum of a number and five

4. Seven times some number or the product of a number and seven (not sure)

5. Six more than a number

What is the slope of the line?

Answers

Step-by-step explanation:

the slope of the line is expressed as the ratio

y coordinate change / x coordinate change

when going from one point to the other.

the trick in such a situation is to find good points on the chart that are crossed by the line. and by "good" I mean points with round integer coordinates.

I see 2 such points :

(-3, 4) and (1, -3)

x changes by +4 (from -3 to 1)

y changes by -7 (from 4 to -3)

the slope is therefore -7/+4 = -7/4

plss help i'll give 80 points!! no links please

Answers

Answer:

domain [-1, ∞)

range [ -3, ∞)

Step-by-step explanation:

Brainliest?

A curve has the equation y = x^3 – 3x + 2

Find the coordinates of the two turning points. Please help ❤️

Answers

Answer:

PLEASE MARK ME BRAINLIEST!!!

Step-by-step explanation:

moddedcraftxdepic

02/28/2021

Mathematics

High School

answered

Y= x^3 + 8x^2 +5x

work out the coordinates of the two turning points 1  

what are the values of each variable

Answers

Answer:

Step-by-step explanation:

Pls help will give 10 pts

Answers

Answer:

276 guests

Step-by-step explanation:

Let the number of guests be n.  We are to find the value of n.

Then (1/3)n + (5/12)n + 69 = n, or

                (9/12)n + 69 = n or (12/12)n

Solving for n, we get    (3/12)n = 69, or (1/12)n = 23, or n = 12(23) = 276

There were 276 guests at the wedding.

Check:  Does (1/3)(276) + (5/12)(276) + 69 work out to 276?  yes

Select all the options that have the same value as 3 1/2% of 20

Answers

Answer:

0.7, 7/10

Step-by-step explanation:

3.5% of 20 would be 3.5/100x20 = 3.5/5 = 0.7. Also, 0.7 = 7/10.

can anyone help me with this?
Find the missing angle measure.

Answers

Answer:

116

Step-by-step explanation:

Given shape has 6 angles and the sum of interior angles for this shape is calculated as following:

180*(6-2) = 720 now to find x we need to find the sum of given angles first:

144 + 163 + 50 + 131 + 126 x = 720

614 + x = 720 subtract 614 from both sides

x = 116

You are solving 5 – 8/3

=y/3
. Which equation will you get if you multiply both sides by 3?

Answers

Answer:

y=0.76

Step-by-step explanation:

5-8/3 = 3y

(5-8/3) x 3 = 3y x 3

6.9=9y

9y=6.9

y=6.9/9

y=0.76

find the area of each of the following polygons. aj 1 cm b) 1 cm c 1 cm 1 cm​

Answers

Answer:

1 cm

Step-by-step explanation:

help me please!!!!!!!!!!!

Answers

Answer:

I did mostly everything for you bestiieee on the pictureee :3

Step-by-step explanation:

hope this helped :3

:3 byeeeeeeeeeee

7⋅5+(4^2−2^3)÷4 answers: 49 41 34 9

Answers

It’s 9.25 :))))))))))))

On evaluating the given expression 7.5 + (4² − 2³) ÷ 4, we get 9.5 as the result.

What is Expression?

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. For example -

5x + 7 = 6

7r + π = 4

Given is the following expression -

7.5 + (4² − 2³) ÷ 4

The given expression is -

7.5 + (4² − 2³) ÷ 4

Using the BODMAS rule, we can solve -

7.5 + (16 - 8) ÷ 4

7.5 + 8 ÷ 4

7.5 + 2

9.5

Therefore, on evaluating the given expression 7.5 + (4² − 2³) ÷ 4, we get 9.5 as the result.

To solve more questions on evaluating expressions, visit the link below-

https://brainly.com/question/13589173

#SPJ5

which of the following is not a true dilation?

A. The image and preimage have congruent angles

B. The image and preimage have proportional sides

C. The image and preimage are congruent

D. The image and preimage are similar

Answers

Answer:

umm i think it is B.

Step-by-step explanation:

What is the scale factor from ABC to XYZ?
A 1/5
B 1/6
C 5
D 6​

Answers

The scale factor is 6

Answer:

Is 6

Step-by-step explanation:

5X6=30

3X6=18

4X6=24

Evaluate the expression below.

​5^{0}5
0

Answers

The 5-0-5 Agility Test is one of the most commonly recognised agility tests, despite its inability to actually measure agility. Instead, this is a change of direction speed test, which contrary to common belief, may not be capable of distinguishing between dominant and non-dominant leg performances.

Graph the equation.

Answers

Y=10x Dats what I got sorry if wrong

use the long division method to divide 120÷24​

Answers

Step-by-step explanation:

120÷24

    

    0   24⟌120

    0   24⟌120   0  

    0   24⟌120   -0      1

    00  24⟌120   -0      12 

   0   24⟌120   -0      12 

    00  24⟌120   -0      12    - 0     12 

   00  24⟌120   -0      12    - 0     120

I’m not sure since you can only come up with one digit

How to do the 9 multiplication trick.

Answers

Answer:

0123456789

9876543210

Step-by-step explanation:

09

18

27

36

45

54

63

72

81

90

Answer:

Step-by-step explanation:

for each 9 you add, take away 1 from the first number and add 10, like

81

72

63

52

41

32

23

18

9

A rectangular prism is 7.1 millimeters long and 10 millimeters high. Its volume is 213.0 cubic millimeters . What is the width of the rectangular prism?

Answers

Answer:

5 milimeters

Step-by-step explanation:

PLEASE HELP ME OUT!!!

Convert the following

0.005 kg = _____ dag

0.075 m = ______ cm

Answers

Answer:  0.5 dag and 7.5 cm

Step-by-step explanation:

1 Decagram (dag) =10^-2 kg

We can change this into a conversion factor by dividing either side into the other. Since we want to change Kg into dag, I'll divide both sides by 10^-2kg:

1 Decagram (dag)/10^-2 kg = 1

Now we can multiply this times 0.005 kg:

(0.005 kg)*(1 Decagram (dag)/10^-2 kg)

this equals 0.5 dag

------------

100 cm = 1 meter

(100 cm/1 meter):  Conversion factor

(0.075 m)*((100 cm/1 meter) = 7.5 cm

0.005 kg = 0.5 dag
0.075 m = 7.5 cm

How do you do the elimination method on these equations: 3x = y+5 and 2x+y=5

Answers

Answer:

[tex](2,1)[/tex]

Step-by-step explanation:

Let's first write down the first in traditional form:

[tex]\left \{3x-y=5} \atop {2x+y=5}} \right.[/tex]

At this point, let's choose the order we want to do it.

Eliminating x: Let's multiply the first by 2, the second by 3, and subtract one from the other. Rest is simple algebra

[tex]2I-3II: 6x-2y -6x-3y = 10-15\\-5y=-5 \rightarrow y=1[/tex]

Eliminating y: Let's simply add the two equations together. Rest is simple algebra

[tex]I+II:3x-y+2x+y = 10\\5x=10 \rightarrow x = 2[/tex]

Jon ate 1/3 of a bag of candies and Monica ate 1/4 of the bag. What fraction of the bag of candies did they eat?

Answers

Answer:

13 AND 14

Step-by-step explanation:

THERE IS NO PICTURE OR ANY ANSWERS

1/3+1/4=4/12+3/12
=7/12

-----------------------------------------------------------
Standard form / Slope intercept form

_____________1. 3x -y = 7
_____________2. y = 5x - 2
_____________3. 2x + y = -4
_____________4. y = - ¾ x + 1
_____________5. 4 x - y = -8
_____________6. y= -x + 9
_____________7. 3x + 6y = 12
_____________8.y = ⅔x + 5
-----------------------------------------------------------


Answers

Answer:

1.) y=3x-7

2.) 2=5x-y

3.) y=-4-2x

4.) 1=3/4x+y

5.) y=4x+8

6.) 9=3/4x+8

7.) 9=y+x

8.) y=-2/6x+2

9.) 5=-2/3x+y

Step-by-step explanation:

Standard form is Ax=By=C and Slope form is y-mx+b

for all of the equations fiqure out which is standard and which is slope, 3x-y=7 is standard and just switch it to slope ie:

3x-y=7

+7 -7

3x-7=y

then switch around so y is in the front and vice versa, also divde any y or C by negative 1 if the answer is negative or if there is a number in front of it like in 9, and 8

How to multiply mixed fractions with same denominators.

Answers

Answer:

  multiply the numerators; express that product over the product of the denominators

Step-by-step explanation:

Multiplication of fractions is done the same way regardless of whether the denominators are the same or different.

  [tex]\dfrac{a}{b}\times\dfrac{c}{d}=\dfrac{ac}{bd}[/tex]

The numerator of the product is the product of the numerators.

The denominator of the product is the product of the denominators.

If you have one quarter, nine pennies, six dimes, and one nickle, how much money would you have?

Answers

Answer:

99 cents

Step-by-step explanation:

one quarter=25 cents

nine pennies= 9 cents

six dimes= 60 cents

one nickle= 5 cents

25+9+60+5=85+14=99

Answer:

99 cents

Step-by-step explanation:

quarter = 25 cents

pennie = 1 cent

dime = 10 cents

nickle = 5 cents

1 quarter = 25 cents

9 pennies = 9 cents

6 dimes = 60 cents

1 nickle = 5 cents

25 + 9 + 60 + 5 = 99 cents


How many of the following statements are true?
19)
a
d Any set of ordered pairs is a function.
d The domain of a relation is the set containing the first
member of its ordered pairs.
d The independent variable in a relation is the variable
used for the range.
d A function is a relation in which each domain value is
paired with exactly one range value.
A) 1
B) 2
C) 3
D) 4

Answers

Answer:

A) 1

Step-by-step explanation:

yeah-ya,.................. right?

A)1
Step by step explanation:yeah…….right

9i⋅(−4−7i) Your answer should be a complex number in the form a+bi where a and b are real numbers.

Answers

Answer:

see below

Step-by-step explanation:

here we are using the distributive property and noting that i^2=-1 so the answer is -36i-(63i^2) or -36i+63

Describe if the function is linear, exponential, or neither. Explain how you can tell

Answers

Answer: neither
It is not linear because it does not follow a set pattern and it is not exponential because there are no exponents present.
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