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eduard
3 years ago
5

The diagram shows a square with side length 5cm.

Mathematics
1 answer:
arsen [322]3 years ago
8 0

Answer:

5sqrt2

Step-by-step explanation:

Using the pythagorean theorem, we get 5^2+5^2=c^2. C is the diagonal here. 25+25=c^2, c^2=50. c=sqrt50. Simplifying it, we get the diagonal as 5sqrt2.

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Jesse is sanding a circular wooden table that has a diameter of 6 ft. She can sand 5 square feet every hour. At this rate, appro
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The time it will take Jesse to finish sanding the table is approximately 22.61 hours.

<h3>How to find the area of a circle?</h3>

Suppose the circle has radius of 'r' units, then, its area is given as:

A  = \pi \times (r)^2 sq. units

Since radius of a circle is half of its diameter, so if diameter is of 'd' length, then r= d/2, thus, area can be rewritten as:

A = \pi \times (\dfrac{d}{2})^2 sq. units

For the given case, sanding being done needs to be equal to the area of the circular table, as it has to be done for whole table's surface, which is circular, and area of sanding done will be equal to the area of that circular table.

The area of table(diameter given as 6 ft) is: A = \pi \times (\dfrac{d}{2})^2 \approx 3.14 \times 6^2 = 113.04 \: \rm ft^2

Since Jesse does 5 sq. feet per hour, let she takes T hours time to finish sanding the table, then we have:

\rm T \times 5\:  ft^2 = A \approx 113.04 \: ft^2\\\\\text{Dividing all sides by 5, we get}\\\\T = \dfrac{113.04}{5} \approx 22.61 \: hours

(since 5 sq. feet in 1 hours, then in T hours, T times 5 sq. feet will be done which is equal to area of table, as in approx T hours, she finishes sanding the table)

Thus, it will take approx 22.61 hours for Jesse to finish sanding the table.

Learn more about area of circle here:

brainly.com/question/13056790

8 0
2 years ago
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Y=−2x+4<br> Complete the missing value in the solution to the equation.<br><br> (____,-2)
mestny [16]

(3, - 2)

given y = - 2, then

- 2x + 4 = - 2 ( solve for x )

subtract 4 from both sides

- 2x = - 6 ( divide both sides by - 2 )

x = \frac{-6}{-2} = 3


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3 years ago
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3 years ago
Please HELP! I DON'T KNOW HOW CAN I SOLVE THIS ​
Wewaii [24]

Answer:

<h2>41. x = √2</h2><h2>42. x = √5</h2><h2>43. x = 4</h2><h2>44. x = 4√3</h2>

Step-by-step explanation:

The Pythagorean Theorem:

leg^2+leg^2=hypotenuse^2\to a^2+b^2=c^2

41.\\\\a=1,\ b=1,\ c=x\\\\x^2=1^2+1^2\\\\x^2=1+1\\\\x^2=2\to x=\sqrt2

42.\\a=1, b=2,\ c=x\\\\x^2=1^2+2^2\\\\x^2=1+4\\\\x^2=5\to x=\sqrt5

43.\\a=3,\ b=x,\ c=5\\\\3^2+x^2=5^2\\\\9+x^2=25\qquad\text{subtract 9 from both sides}\\\\x^2=16\to x=\sqrt{16}\to x=4

44.\\\\a=4,\ b=x,\ c=8\\\\4^2+x^2=8^2\\\\16+x^2=64\qquad\text{subtract 16 from both sides}\\\\x^2=48\to x=\sqrt{48}\\\\x=\sqrt{16\cdot3}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\x=\sqrt{16}\cdot\sqrt3\\\\x=4\sqrt3

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