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2 years ago

To the Pythagorean Theorem

Mathematics

1 answer:

Aloiza [94]2 years ago

4 0

Answer:

x = 29

Step-by-step explanation:

$c^{2} = a^{2} + b^{2}$

$c^{2} = 20^{2} + 21^{2}$

$c^{2} = 400 + 441$

$c^{2} = 841$

$\sqrt{c^2} = \sqrt{841}$

$c = 29$

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Find the surface area of the cylinder use 3.14 for pi

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Answer:

351.658 square in

Step-by-step explanation:

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C = 25.13

Find area of the circle

A = 50.27

Multiply the circumference by the height

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Add 251.3 with 50.27 twice

251.13 + 50.27 + 50.27 ≈ 351.658

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3 years ago

Which congruence theorem can be used to prove △ABC ≅ △DBC?

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Step-by-step explanation:

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3 years ago

from this year to ten years later, the number of people employed as physician assistants in the country is expected to increase

wariber [46]

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Step-by-step explanation:

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2 years ago

A chemist needs 130 milliliters of a 47% solution but has only 35% and 87% solutions available. Find how many milliliters of eac

choli [55]

Answer: Amount of 35% solution required = 100 milliliters

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Step-by-step explanation:

Given: Total solution required = 130 milliliters

Let x = Amount of 35% solution (in milliliters).

Then, Amount of 87% solution required = 130 - x

As per given,

Concentration = 0.35x +0.87(130-x)=0.47(130)

$0.35x +113.1-0.87x=61.1\\\\\Rightarrow\ -0.87x+0.35x=61.1-113.1\\\\\Rightarrow\ -0.52 x= -52\\\\\Rightarrow\ x=\dfrac{52}{0.52}=100$

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3 0

2 years ago

Now there is a square city of unknown size with a gate at the center of each side. There is a tree 20 b from the north gate. Tha

Brums [2.3K]

Answer:

The length of each side of the city is 250b

Step-by-step explanation:

Given

$a = 20$ --- tree distance from north gate

$b =14$ --- movement from south gate

$c = 1775$ --- movement in west direction from (b)

See attachment for illustration

Required

Find x

To do this, we have:

$\triangle ADE \sim \triangle ACB$ --- similar triangles

So, we have the following equivalent ratios

$AE:DE = AB:CB$

Where:

$AE = 20\\ DE = x/2 \\ AB = 20 + x + 14 \\ CB = 1775$

Substitute these in the above equation

$20:x/2 = 20 + x + 14: 1775$

$20:x/2 = x + 34: 1775$

Express as fraction

$\frac{20}{x/2} = \frac{x + 34}{1775}$

$\frac{40}{x} = \frac{x + 34}{1775}$

Cross multiply

$x *(x + 34) = 1775 * 40$

Open bracket

$x^2 + 34x = 71000$

Rewrite as:

$x^2 + 34x - 71000 = 0$

Expand

$x^2 + 284x -250x - 71000 = 0$

Factorize

$x(x + 284) -250(x + 284)= 0$

Factor out x + 284

$(x - 250)(x + 284)= 0$

Split

$x - 250 = 0 \ or\ x + 284= 0$

Solve for x

$x = 250 \ or\ x =- 284$

x can't be negative;

So:

$x = 250$

6 0

3 years ago