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3 years ago

Find the missing side of the triangle. Round your answer to the nearest tenth if necessary.

Mathematics

2 answers:

kenny6666 [7]3 years ago

5 0

Answer:

Step-by-step explanation:

pythagoras theorem

a^2+b^2=c^2

12^2+x^2=13^2

144+x^=169

x^2=169-144

x= $\sqrt{25$

x=5 km

AleksAgata [21]3 years ago

4 0

<h3>Answer:</h3>

The missing side of the triangle is 5 km.

<h3>Step-by-step explanation:</h3>

Here we have

Perpendicular = 12 km

missing side = base = x

hypotenuse = 13 km

And since , we have given right triangle in a question . So we can use Pythagoras theorem

Pythagoras theorem

( Perpendicular ) ² + ( Base ) ² = ( hypotenuse ) ²

substitute the value

( 12 km ) ² + ( x ) ² = ( 13 km ) ²

Multiplying the values

144 km ² + x² = 169 km²

now Solve it

x ² = 169 km² - 144 km²

x ² = 25 km ²

x = √25 km²

x = 5 km.

Hence , missing Side of triangle is 5 km.

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Find the least common multiple (LCM) of 8y^6+ 144y^5+ 640y^4 and 2y^4 + 40y^3 + 200y^2.

Mice21 [21]

Answer:

LCM = $8y^{4}(y+ 10)^{2}(y + 8)$

Step-by-step explanation:

Making factors of $8y^{6}+ 144y^{5}+ 640y^{4}$

Taking $8y^{4}$ common:

$\Rightarrow 8y^{4} (y^{2}+ 18y+ 80)$

Using factorization method:

$\Rightarrow 8y^{4} (y^{2}+ 10y + 8y + 80)\\\Rightarrow 8y^{4} (y (y+ 10) + 8(y + 10))\\\Rightarrow 8y^{4} (y+ 10)(y + 8))\\\Rightarrow \underline{2y^{2}} \times 4y^{2} \underline{(y+ 10)}(y + 8)) ..... (1)$

Now, Making factors of $2y^{4} + 40y^{3} + 200y^{2}$

Taking $2y^{2}$ common:

$\Rightarrow 2y^{2} (y^{2}+ 20y+ 100)$

Using factorization method:

$\Rightarrow 2y^{2} (y^{2}+ 10y+ 10y+ 100)\\\Rightarrow 2y^{2} (y (y+ 10) + 10(y + 10))\\\Rightarrow \underline {2y^{2} (y+ 10)}(y + 10) ............ (2)$

The underlined parts show the Highest Common Factor(HCF).

i.e. HCF is $2y^{2} (y+ 10)$ .

We know the relation between LCM, HCF of the two numbers 'p' , 'q' and the numbers themselves as:

$HCF \times LCM = p \times q$

Using equations (1) and (2): $\Rightarrow 2y^{2} (y+ 10) \times LCM = 2y^{2} \times 4y^{2}(y+ 10)(y + 8) \times 2y^{2} (y+ 10)(y + 10)\\\Rightarrow LCM = 2y^{2} \times 4y^{2}(y+ 10)(y + 8) \times (y + 10)\\\Rightarrow LCM = 8y^{4}(y+ 10)^{2}(y + 8)$