A square patio has an area of 197 square feet how long is each side of the patio to the nearest 0.05

QUESTION POSTED AT 15/01/2020 - 03:10 AM

Answered by admin AT 15/01/2020 - 03:10 AM

If it is a square, all the sides are the same, i would think all the sides are 197 square feet.
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Related questions

If an exterior angle of a regular polygon is 21.2° how many sides does the polygon have?

Formula for number of sides, n =  360 / e

Where e is the exterior angle for the number of sides.

e = 21.2°

Number of sides for the regular polygon, n = 360° / 21.2°

n ≈ 16.98

The number of sides is approximately 16.98 sides..Does that make sense?

It does not. In fact, the exterior angle of a regular polygon has to be wholly divisible into 360°.

In the case 21.2° can't clearly be the exterior angle, the question is wrongly set.

The exterior can be say 20°.  

ANSWERED AT 29/01/2020 - 05:36 PM


QUESTION POSTED AT 29/01/2020 - 05:36 PM

Simplify. Cos ^-1 (square root 3/2

Hello,

As
cos(30)=sin(60)=\dfrac{\sqrt{3} }{2}\\\\

cos^{-1}(\dfrac{ \sqrt{3} }{2})


=π/6+2kπ or -π/6+2kπ

ANSWERED AT 29/01/2020 - 05:36 PM


QUESTION POSTED AT 29/01/2020 - 05:36 PM

A square field has an area of 10 square miles. What is the approximate length, to the nearest thousandth, of one side of this field? A.) 2.5 miles B.) 3 miles C.) 3.162 miles D.) 3.612 miles

Area x² = 10

x = √10 ≈ 3.16227

x ≈ 3.162 mile to the nearest thousandth.    Option C.

ANSWERED AT 29/01/2020 - 05:30 PM


QUESTION POSTED AT 29/01/2020 - 05:30 PM

Which set of values could be the side lengths of a 30-60-90 triangle. Please see picture

IT would be 6, 6√3, and 12

To find side lengths of a 30-60-90 triangle would be to use a²+b²=c². C is the hypotenuse (longest side), while a and b are the legs (short sides).

using these values we get 36(originally 6)+108(originally 6√3)=144(12), which is true.

ANSWERED AT 29/01/2020 - 05:24 PM


QUESTION POSTED AT 29/01/2020 - 05:24 PM

Jimmy has a diecast metal car that is a scale model of an actual race car. If the actual length of the car is 10 feet 6 inches and the model has a length of 7 inches, what is the scale factor of the model to the actual car?

10 feet 6 inches = 126 inches. Length of the car is 126 inches and the model length is 7 inches. 
126 : 7 = 18 
The scale factor of the model to the actual car is  1 : 18.

ANSWERED AT 29/01/2020 - 05:21 PM


QUESTION POSTED AT 29/01/2020 - 05:21 PM

15,000 feet to kilometers

4,572 is the answer.

ANSWERED AT 29/01/2020 - 05:12 PM


QUESTION POSTED AT 29/01/2020 - 05:12 PM

The combined land area of the countries a and b is 177 ,973 square kilometers. country a is larger by 773 square kilometers. determine the land area of each country.

Let b = x

a = x + 773

x + x + 773 = 177973

2x + 
773 = 177973

2x = 
177973 - 773

2x = 177200

x = 
177200/2

x = 88600

The other is x + 773,  =  8860
0 + 773 = 89373

Each country is 
88600 and 89373 square kilometers.

ANSWERED AT 29/01/2020 - 05:03 PM


QUESTION POSTED AT 29/01/2020 - 05:03 PM

Heather is training for a long-distance run. her data points listed below represent the days of practice, x, and the number of miles run, y.(1, 2.5), (2, 4.2), (4, 5.6), (6, 7), (8, 8.1), (10, 11)use the equation to interpolate the value and estimate the distance that she could have run on day 3. round to the nearest tenth of a mile.

Interpolation equation
Poit 1: (a,b)
Point 2: (c,d)
Intermediate point (x,y)

(d - b)/(c - a) = (y - b) / (x - a)

(a,b) = (2, 4.2)
(c,d) = (4, 5.6)

x = 3

(5.6 - 4.2) / (4 - 2)  =  (y - 4.2) / (3 -2)

y =  [1.4/2]*[1] + 4.2

y = 0.7 + 4.2 = 4.9

Answer 4.9 miles

 




ANSWERED AT 29/01/2020 - 04:51 PM


QUESTION POSTED AT 29/01/2020 - 04:51 PM

A sketch of the roosevelt room in the white house is drawn to 1/15 scale. the sketch shows a room that is 3 feet by 4.5 feet what are the actual dimensions of the room

Answer: 45 feet by 67.5 feet.

Step-by-step explanation:

Given: To draw the sketch of the Roosevelt room in the white house=\frac{1}{15}

The dimensions of the sketch is 3 feet by 4.5 feet .

To find the actual dimensions of the room multiply the dimensions of the sketch by the reciprocal of scale factor . [because to sketch we need to multiply scale factor to the actual dimensions]

The reciprocal of the scale factor = 15

3 feet → 3\times15=45 feet

4.5 feet → 4.5\times15=67.5 feet

Hence, The dimensions of the actual dimensions of the room is 45 feet by 67.5 feet.

ANSWERED AT 29/01/2020 - 04:47 PM


QUESTION POSTED AT 29/01/2020 - 04:47 PM

What are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotenuse is 15 units long? a) 9 units, 12 units b) 11 units, 10.2 units c)4.9 units, 15.8 units d)4.9 units, 14.2 units e)5.2 units, 14.1 units

The side opposite the angle 19 degrees is given by 15sin 19 = 4.9 units, while the side adjacent the angle 19 degrees is given by 15cos 19 = 14.2 units.

ANSWERED AT 29/01/2020 - 04:36 PM


QUESTION POSTED AT 29/01/2020 - 04:36 PM

A football is kicked into the air from an initial height of 4 feet. The height, in feet, of the football above the ground is given by s (t)=-16^2+50t+4, where t is time, in seconds, and t>=0. At what time will the football be 25 feet above the ground? 3.625 seconds 3.20 seconds 0.5 seconds or 3.625 seconds 0.5 seconds or 2.625 seconds

To answer the question above, substitute the given value of height. 
                                          25 = -16x²  + 50t + 4
Solving the following equation by the use of quadratic formula,
                             x = (-b +/- sqrt (b² - 4ac)) / 2a
Subsituting the known values of a, b, and c
                             x = (-50 +/- sqrt (50² - 4(-16)(-21)) / 2x-16
The values of x are 0.5 and 2.625. Therefore, the answer is the fourth choice. 

ANSWERED AT 29/01/2020 - 04:36 PM


QUESTION POSTED AT 29/01/2020 - 04:36 PM

Find the distance between the points R(0,5) and S(12,3). Round the answer to the nearest tenth. A. 10.4 B. 16 C. 12.2 D. 11.8 An airplane at T(80,20) needs to fly to both U(20,60) and V(110,85). What is the shortest possible distance for the trip? A. 165 units B. 170 units C. 97 units D. 169 units

1. The distance formula given two points is, 
                             d = sqrt ((x2 - x1)² + (y2 - y1)²)
Substituting the given values,
                            d = sqrt ((12 - 0)² + (3 - 5)²) = 12.17 or aproximately 12.2

2. Calculate the distance between points T and U and from U to V
   ( T to U)           d = sqrt ((20 - 80)² + (60 - 20)²) = 72.11
   (U to V)            d = sqrt ((110 - 20)² + (85 - 60)²) = 93.41

Adding this distances gives an answer of approximately equal to 165.52. The answer is letter A. 

ANSWERED AT 29/01/2020 - 04:35 PM


QUESTION POSTED AT 29/01/2020 - 04:35 PM

Between what two consecutive integers does the square root of 88 lie A. 7 and 8 B. 8 and 9 C. 9 and 10 D. 10 and 11

First, solve for the square root of 88. The numerical value of square root of 88 is approximately 9.38. This real number lies between the integers 9 and 10. Thus, the answer for this item is letter C. 9 and 10.

ANSWERED AT 29/01/2020 - 04:34 PM


QUESTION POSTED AT 29/01/2020 - 04:34 PM

Help!??!? How many different ways can a family of four sit at a rectangular dinner table with one person at each side? A. 4 ways B. 12 ways C. 16 ways D. 24 ways

Use the fundamental principle of counting. In the first seat, we can choose the seater from the four persons. On the next seat, only 3 people would be available. On the second, there are 2 and finally 1 to the last seat. Multiply all the possible number of seaters,
                                4 x 3 x 2 x 1 = 16
Thus, the answer is letter C. 

ANSWERED AT 29/01/2020 - 04:34 PM


QUESTION POSTED AT 29/01/2020 - 04:34 PM

What is the area of a regular 15-gon with a perimeter of 90 m ?

We are given with  a regular 15-gon with a perimeter of 90 meters. In this case, side length is equal to 90/15 or 6 m. The angle inside the center is 360/15 or 24 degrees. We determine the area of each triangle (15 of them) and just multiply by 15 to get the total area. The height of each triangle is tan (12) = 3/ h where h is equal to 14.11 meters. Hence the area is 0.5*14.11*6*15 or equal to 635.13 meters.

ANSWERED AT 29/01/2020 - 04:33 PM


QUESTION POSTED AT 29/01/2020 - 04:33 PM

A quadrilateral contains two equal sides measuring 12 cm each and an included right angle if the measure of the third side is 8 cm and the angle opposite to the right angle is 120 degrees.Find the fourth side and the area of the quadrilateral?

The fourth side of the quadrilateral can be determined by taking the sin of the difference of 120 and 90 in which the expression becomes sin 30 = x/12 where x is the extra length difference from the third side. x is equal to 6. Hence the fourth side is equal to 8+6 or 14 cm. The area of the quadrialteral is the sum of the rectangle and the area of triangle. The area of the rectangle is 8*12 equal to 96 cm2.The area of teh triangle is .5*6 \sqrt{3} *6. The sum or the total area is equal to 127.18 cm2.

ANSWERED AT 29/01/2020 - 04:33 PM


QUESTION POSTED AT 29/01/2020 - 04:33 PM

Solve for x, given the equation Square root of x plus 9 − 4 = 1. x = 16, solution is not extraneous x = 16, solution is extraneous x = 34, solution is not extraneous x = 34, solution is extraneous

Remember that an extraneous solution of an equation is a solution that emerges from the algebraic process of solving the equation but is not a valid solution of the equation.

First, we are going to solve our equation algebraically:

Step 1 simplify the equation:

 \sqrt{x} +9-4=1

 \sqrt{x}+ 5=1

Step 2 subtract 5 from both sides of the equation:

 \sqrt{x} +5-5=1-5

 \sqrt{x} =-4

Step 3 square both sides of the equation:

 \sqrt{x} ^2=(-4)^2

 x=16

Next, we are going to replace our solution in our original equation and check if it is a valid solution:

 \sqrt{x} +9-4=1

 \sqrt{16} +5=1

 4+5=1

 9\neq 1

Since 9 is not equal to 1,  x=16 is not valid solution of the equation; therefor it is an extraneous solution.

We can conclude that the correct answer is: x = 16, solution is extraneous

ANSWERED AT 29/01/2020 - 04:33 PM


QUESTION POSTED AT 29/01/2020 - 04:33 PM

A blimp provides aerial television views of a football game. The television camera sights the stadium at a 7 degree angle of depression. The altitude of the blimp is 400 m. What is the line-of-sight distance from the television camera to the case of the stadium? Round to the nearest hundred meters.

Looks like sin is best here

sin (7) = opp / hyp
sin (7) = 400 / x
x sin (7) = 400
x = 400 / sin (7)

So we need to get the value of x.

x = 400 / sin (7)
x = 400 / 0.1218
x = 3284.07

Roughly, the correct answer is 3284.1 meters

ANSWERED AT 29/01/2020 - 04:32 PM


QUESTION POSTED AT 29/01/2020 - 04:32 PM

One liter of paint covers 100 square feet. a wall that measures 32 feet by 16 feet is going to be painted. a. about how many gallons of paint will it take to paint the whole wall? b. if the paint can only be bought in gallons containers,how many containers will be purchased? c. how many liters of paint will be remaining in the container?

Find the area (A) of the rectangular wall by multiplying the dimensions,
                                       A = L x W
Substituting,
                                       A = (32 ft) x (16 ft) = 512 ft²
a.  (512 ft²) x (1 L / 100 ft²) x (1 gal/ 3.79 L) = 1.35 gal
b. The nearest whole number that is greater than 1.35 is 2. So, 2 containers should be bought.
c. There will remain an amount of 0.65 gallon which is equal to 2.4635 L. 

ANSWERED AT 29/01/2020 - 04:32 PM


QUESTION POSTED AT 29/01/2020 - 04:32 PM

Please Help!!! I give a medal to anyone to tries!!! 3 party-goers are in the corner of the ballroom having an intense argument. You walk over to settle the debate. They are discussing a function g(x). You take out your notepad and jot down their statements. • Professor McCoy: She says that 2 is a zero of g(x) because long division with (x + 2) results in a remainder of 0. • Ms. Guerra: She says that 2 is a zero of g(x) because g(2) = 0. • Mr. Romano: He says that 2 is a zero of g(x) because synthetic division with 2 results in a remainder of 0.

Well, the way I see it is that both Mr. Romano, and Ms. Guerra are correct but Professor McCoy is incorrect because he said (x+2) when it should be (x-2).


The factor theorem states that:
If f(a)=0, then (x-a) is a factor


The remainder theorem states that:
If (x-a) is a factor of f(x), then f(x) / (x-a)  = 0


So if 2 is indeed a zero of f(x), then a factor must be (x-2) according to the fist which supports Ms. Guerra and also if (x-2) is indeed a factor as Ms. Guerra says then we know that f(x) / (x-a) = 0 which supports Mr. Romano

Professor McCoy is wrong because he used (x + 2) when it should be (x-2). I know this because according to the factor theorem if f(a)=0, then (x-a) is a factor. And the remainder theorem says if (x-a) is a factor of f(x), then f(x)/x-a =0.

ANSWERED AT 29/01/2020 - 04:30 PM


QUESTION POSTED AT 29/01/2020 - 04:30 PM

Round 9.0285 to the nearest hundredth

9.0285 rounded to the nearest hundredth is 9.03

ANSWERED AT 29/01/2020 - 04:27 PM


QUESTION POSTED AT 29/01/2020 - 04:27 PM

A football is kicked into the air from an initial height of 3 feet. the height, in feet, of the football above the ground is given by s(t)=-16t^2+35t+3. Where t is time in seconds and t>=0. which is closest to the time when the football will be 20ft above the ground?? A) 2.72 seconds B) 0.73 seconds or 1.46 seconds C) 0.53 seconds D) 0.53 seconds or 2.72 seconds

 For this case we have the following quadratic equation:
 s (t) = - 16t ^ 2 + 35t + 3

 Where,
 t: time
 s: height of the ball
 By the time the height is 20 feet we have:
 -16t ^ 2 + 35t + 3 = 20

 Rewriting the polynomial we have:
 -16t ^ 2 + 35t + 3-20 = 0

-16t ^ 2 + 35t-17 = 0
 Using the quadratic formula we have:
 t =  \frac{-b+/- \sqrt{b^2 - 4ac}}{2a}
 Substituting values we have:
 t = \frac{-35+/- \sqrt{35^2 - 4(-16)(-17)}}{2(-16)}
 Doing the calculations we have the roots are:
 t1 = 0.728

t2 = 1.46
 Answer:
 
the time when the football will be 20ft above the ground is:
 
B) 0.73 seconds or 1.46 seconds

ANSWERED AT 29/01/2020 - 04:24 PM


QUESTION POSTED AT 29/01/2020 - 04:24 PM