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3 years ago

What is an efficient way to compute 47^2–37^2 without using raw calculations?

Mathematics

1 answer:

e-lub [12.9K]3 years ago

6 0

Answer:

(47+37)(47-37)

Step-by-step explanation:

47^2-37^2 is a difference of two squares. a^2-b^2 = (a+b)(a-b) so this expression can be factored to (47+37)(47-37) = (84)(10) = 840

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Can anyone explain how to do this? The answer isn't as important as the explanation. My teacher gave us a video w/o an example l

solong [7]

Answer:

x = 182.53

Step-by-step explanation:

Use trigonometric ratios to find the whole side length (a) adjacent to 20° and the side length (b) adjacent to 57° respectively. Then find the difference. That would give you the value of x. That is: a - b = x

Let's solve.

✍️Finding the whole side length adjacent to 20°:

Opp = 87

Adjacent length = ? = a

$\theta = 20$

Thus,

$tan(\theta) = \frac{opposite}{adjacent}$

Plug in the values

$tan(20) = \frac{87}{a}$

Multiply both sides by a

$tan(20) \times a = \frac{87}{a} \times a$

$tan(20) \times a = 87$

Divide both sides by tan(20)

$\frac{tan(20) \times a}{tan(20)} = \frac{87}{tan(20)}$

$a = \frac{87}{tan(20)}$

$a = 239.03$

Finding the side length adjacent to 57°:

Opp = 87

Adjacent length = ? = b

$\theta = 57$

Thus,

$tan(\theta) = \frac{opposite}{adjacent}$

Plug in the values

$tan(57) = \frac{87}{b}$

Multiply both sides by b

$tan(57) \times b = \frac{87}{b} \times b$

$tan(57) \times b = 87$

Divide both sides by tan(57)

$\frac{tan(57) \times b}{tan(57)} = \frac{87}{tan(57)}$

$b = \frac{87}{tan(57)}$

$b = 56.50$

Therefore:

x = a - b

x = 239.03 - 56.50

x = 182.53

4 0

3 years ago

Write a division problem in words include the solution and equation

Marta_Voda [28]

Fifteen divided by five equals three

6 0

4 years ago

Read 2 more answers

Help me answer this!!!

miss Akunina [59]

Answer/Step-by-step explanation:

Year = x

Weight (kg) = y

Rate of change between 2010 and 2011 = $\frac{y_2 - y_1}{x_2 - x_1}$

Where,

$(2010, 35) = (x_1, y_1)$

$(2011, 30) = (x_2, y_2)$

Plug in the values

$= \frac{30 - 35}{2011 - 2010}$

$= \frac{-5}{1} = -5$

Rate of change = -5kg per year

This means that there was a decrease in the weight of the winning dog form 2010 to 2011 by 5 kilograms

3 0

3 years ago

The perimeter of a square is 28 feet, what is the area

Nastasia [14]

Squares have equal sides, so 28 divided by 4 equals 7, and then base times height, which are both 7. So the area will be 7*7= 49.

3 0

4 years ago

Read 2 more answers

A rectangle is twice as long as it is wide. If its area is 50 sq. yd., find the length.

sertanlavr [38]

A = L * W
A = 50
L = 2W

50 = W(2W)
50 = 2W^2
50/2 = W^2
25 = W^2
sqrt 25 = W
5 = W

L = 2W
L = 2(5)
L = 10 <==length is 10 yd

5 0

3 years ago