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Radda [10]
3 years ago
12

A square rug covers 79 square feet of floor. What is the approximate length of one side of the rug? (Approximate to the nearest

hundredth foot.) (4 points) 8.86 feet 8.87 feet 8.88 feet 8.89 feet
Mathematics
1 answer:
GaryK [48]3 years ago
6 0

Answer:

8.88 feet

Step-by-step explanation: Since it is a square all the sides equal the same number. You may not know how to use square roots yet but, I will show you how they are helpful. The square root of a number is when the 2 numbers being multiplied together are the same. For example, 3*3 is 9. The square root of 9 is 3 because when you multiply 3 and 3 together you get 9. For your problem since all the problems start with 8.8 we know it is bigger than 8 and less than 9 because the square root of 8 is 64 and the square root of 9 is 81. Since 79 is closer to 81 then it is to 64 we know 8.86 and 8.87 won't work because they are too small. From here the best way to figure it out is by trial and error if you are not allowed to use a calculator. So try 8.88 times 8.88 and 8.89 times 8.89. But if you are allowed to use a calculator (a scientific calculator) type in 79. There should be a button that looks like \sqrt{x\\. If you press it it will give you the square root of 79 (which is what you are looking for).

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marta [7]

Answer:

-\frac{5}{4x}

Step-by-step explanation:

<h2>\left(-5x^3\right)^3\div \left(10x^5\right)^2</h2><h2>\frac{-5^3x^9}{\left(10x^5\right)^2}</h2><h2>\frac{-5^3x^9}{10^2x^{10}}</h2><h2>\frac{-5^3x^9}{5^2\cdot \:2^2x^{10}}</h2><h2>\frac{-5x^9}{2^2x^{10}}</h2><h2>\frac{-5}{2^2x}</h2>

-\frac{5}{4x}

- hope it helps! -

<h2 />

3 0
2 years ago
Focus Question: How do you determine whether a real-world context should be
Yakvenalex [24]

Answer:

Simplify the equation as closely as possible to the form of y = mx + b. Check to see if your equation has exponents. If it has exponents, it is nonlinear (exponential). If your equation has no exponents, it is linear.

3 0
3 years ago
When a water-cooled nuclear power plant is in operation, oxygen in the water is transmuted to nitrogen-17. After the reactor is
wolverine [178]

Answer:

The differential equation is \frac{dR}{dt} = -kR

Step-by-step explanation:

Differential equation for the rate of change in radiation level:

Radiation level is R.

Rate of change indicates that the radiation level R varies in function of time t, which mathematically means that we have:

\frac{dR}{dt}

After the reactor is shut down, the radiation from the nitrogen-17 decreases in such a way that the rate of change in the radiation level is directly proportional to the radiation level.

Rate of change is k. Decreases means that k is negative. Proportional to the radiation level of R means that -k multiplies R. So the differential equation is:

\frac{dR}{dt} = -kR

7 0
3 years ago
The product (x) of two numbers is 24 and their sum (+) is 10. What is the value of the largest of the two numbers?
RideAnS [48]

let the two numbers be x and y

From the first sentence,

xy=24

x+y=10

Then make y in equation 2 the subject of the formular and substitute in equation 1

x+y=10

y=10-x

substituting in equation 2

x(10-x)=24

open the bracket

10x-x^2=24

=-x^2+10x=24

Transfer the constant to the left hand side

=-x^2+10x-24=0

Then factorise completely

Look at the photo above

4 0
3 years ago
The top and bottom margins of a poster 66 cm each, and the side margins are 44 cm each. If the area of the printed material on t
jasenka [17]

Answer:

  • width: 24 cm
  • height: 36 cm

Step-by-step explanation:

When margins are involved, the smallest area will be the one that has its dimensions in the same proportion as the margins. If x is the "multiplier", the dimensions of the printed area are ...

  (4x)(6x) = 384 cm^2

  x^2 = 16 cm^2 . . . . . divide by 24

  x = 4 cm

The printed area is 4x by 6x, so is 16 cm by 24 cm. With the margins added, the smallest poster will be ...

  24 cm by 36 cm

_____

<em>Comment on margins</em>

It should be obvious that if both side margins are 4 cm, then the width of the poster is 8 cm more than the printed width. Similarly, the 6 cm top and bottom margins make the height of the poster 12 cm more than the height of the printed area.

_____

<em>Alternate solution</em>

Let w represent the width of the printed area. Then the printed height is 384/w, and the total poster area is ...

  A = (w+8)(384/w +12) = 384 +12w +3072/w +96

Differentiating with respect to w gives ...

  A' = 12 -3072/w^2

Setting this to zero and solving for w gives ...

  w = √(3072/12) = 16 . . . . matches above solution.

__

<em>Generic solution</em>

If we let s and t represent the side and top margins, and we use "a" for the printed area, then the above equation becomes the symbolic equation ...

  A = (w +s)(a/w +t)

  A' = t - sa/w^2

For A' = 0, ...

  w = √(sa/t)

and the height is ...

  a/w = a/√(sa/t) = √(ta/s)

Then the ratio of width to height is ...

  w/(a/w) = w^2/a = (sa/t)/a

  width/height = s/t . . . . . . the premise we started with, above

6 0
3 years ago
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