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3 years ago

Does 10,15,20 form a right triangle

1 answer:

5 0

A right triangle can only be formed when you use the 3/4/5 rule.
The 3/4/5 rule is a^2 + b^2 = c^2.

We will use 10 for a, 15 for b, and 20 for c.

a^2 + b^2 = c^2

Plug in 10 for a, 15 for b, and 20 for c.

10^2 + 15^2 = 20^2

10^2 = 100

15^2 = 225

20^2 = 400

100 + 225 = 400
This is not applicable, as 100 + 225 = 325.

Your answer is:

No, 10,15,20 does not form a right triangle.

I hope this helps!

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Find the complex fourth roots \[-\sqrt{3}+\iota \] in polar form.

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Let $z=-\sqrt3+i$ . Then

$|z|=\sqrt{(-\sqrt3)^2+1^2}=2$

$z$ lies in the second quadrant, so

$\arg z=\pi+\tan^{-1}\left(-\dfrac1{\sqrt3}\right)=\dfrac{5\pi}6$

So we have

$z=2e^{i5\pi/6}$

and the fourth roots of $z$ are

$2^{1/4}e^{i(5\pi/6+k\pi)/4}$

where $k\in\{0,1,2,3\}$ . In particular, they are

$2^{1/4}e^{i(5\pi/6)/4}=2^{1/4}e^{i5\pi/24}$

$2^{1/4}e^{i(5\pi/6+2\pi)/4}=2^{1/4}e^{i17\pi/24}$

$2^{1/4}e^{i(5\pi/6+4\pi)/4}=2^{1/4}e^{i29\pi/24}$

$2^{1/4}e^{i(5\pi/6+6\pi)/4}=2^{1/4}e^{i41\pi/24}$

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2 years ago

A woman is 10 times as old as her daughter. In 8 years she will be 4 times as old as her daughter. How old is the mother now?

jeka57 [31]

Answer:

Mom is 40 and her daughter is 4; in eight years, mom will be 48 and her daughter will be 12.

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

If point P is 4/7 of the distnace frm M to N, what ratio does the point P partiion the directed line segment from M to N

vredina [299]

Answer: 4:3.

Step-by-step explanation:

Given: Point P is $\dfrac{4}{7}$ of the distance from M to N.

To find: The ratio in which the point P partition the directed line segment from M to N.

If Point P is between points M and N, then the ratio can be written as

$\dfrac{MP}{MN}=\dfrac{MP}{MP+PN}$

As per given,

$\dfrac{MP}{MP+PN}=\dfrac{4}{7}\\\\\Rightarrow\ \dfrac{MP+PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ \dfrac{MP}{MP}+\dfrac{PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ -1+\dfrac{PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ \dfrac{PN}{MP}=\dfrac{7}{4}-1=\dfrac{7-4}{4}=\dfrac{3}{4}\\\\\Rightarrow\ \dfrac{PN}{MP}=\dfrac{3}{4}\ \ \or\ \dfrac{MP}{PN}=\dfrac{4}{3}$

Hence, P partition the directed line segment from M to N in 4:3.

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3 years ago

!!!!!!!!!!! Help (Measuring Angles)

lana [24]

Answer:

Angle DGF = DEF

Step-by-step explanation:

Since all the angles are congruent in the diagram and the hypothenuses are both congruent, it makes the other triangle, DEF congruent to DGF.

In other words, sense all 3 angles are congruent and they share a side, DEF is congruent to DGF.

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2 years ago

10.5 equal or less than 10.005

maksim [4K]

10.5 is more than 10.005

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3 years ago