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Goryan [66]
3 years ago
9

In a right triangle, one of the legs is 5 cm smaller than the hypotenuse, and the other leg is 10 cm smaller than the hypotenuse

. Find the length of the hypotenuse
Mathematics
2 answers:
ira [324]3 years ago
5 0

Answer:

25cm

Step-by-step explanation:

the relationship between the sides of a right angle triangle was defined by Pythagoras in this theorem which states that where  a, b, and c are the lengths of the sides of a right angled triangle,

a² + b² = c²

Where c is the length of the hypotenuse side and a and b are the lengths of the other 2 sides. As such,

let the hypotenuse side in length be c,

(c - 5)² + (c - 10)² = c²

c² - 10c + 25 + c² - 20c +100 = c²

c² - 30c + 125 = 0

c² - 25c - 5c + 125 = 0

factorizing

(c - 25)(c -5) = 0

c = 25cm or 5cm

However, the length of the hypotenuse cannot be 5cm otherwise other sides would be negative.

Lostsunrise [7]3 years ago
4 0

Answer: hypotenuse = 25 cm

Step-by-step explanation:

Let h represent the length of the hypotenuse.

In a right triangle, one of the legs is 5 cm smaller than the hypotenuse. It means that the length of the leg is

(h - 5) cm

The other leg is 10 cm smaller than the hypotenuse. It means that the length of the other leg is

(h - 10) cm

We would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

h² = (h - 10)² + (h - 5)²

h² = (h - 10)(h - 10) + (h - 5)(h - 5)

h² = h² - 10h - 10h + 100 + h² - 5h - 5h + 25

h² = h² + h² - 20h - 10h + 100 + 25

h² = 2h² - 30h + 125

2h² - h² - 30h + 125 = 0

h² - 30h + 125 = 0

h² - 25h - 5h + 125 = 0

h(h - 25) - 5(h - 25) = 0

h - 25 = 0 or h - 5 = 0

h = 25 or h = 5

The hypotenuse is 25 cm since it is longer

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What is 6P4<br> permutations and combinations
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Answer:

360

Step-by-step explanation:

Here we are required to find _^{6}\textrm{P}_{4}

It is a problem of Permutation and we must understand the formula for finding permutations.

The general formula for finding the permutation is given as below:

_^{m}\textrm{P}_{n}=\frac{m!}{(m-n)!}

Hence

_^{6}\textrm{P}_{4}=\frac{6!}{(6-4)!}

_^{6}\textrm{P}_{4}=\frac{6!}{2!}

Where

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3 0
3 years ago
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natka813 [3]

Answer:

d.

Step-by-step explanation:

Left line is defined when x < 1 (x is less than 1). The point is not full and that means that x = 1 is not included.

Right line is defined when x is greater or equal to one x ≥ 1.

Options that have x < 1 and x ≥ 1 are b and d, so the answer is one of those.

Equations of the lines are in slope-intercept form y = mx + b, where m is slope and b is y-intercept.

Right line has steeper slope than left line, so the slope of right line will have bigger absolute value. That is the case with option d. (Left line has slope -1 and right one has slope -2, absolute value of right slope is bigger.)

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Answer:

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Step-by-step explanation:

Put the given value of x in the equation, and solve the resulting equation for k.

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The value of k is -1.

_____

<em>Check</em>

Use k = -1 in the original equation and solve for x.

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  2x -6 -1 -2x = -x -2 . . . . eliminate parentheses

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