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2 years ago

If a 30-60-90 right triangle has a hypotenuse 6, what is the length of the short leg?

Mathematics

1 answer:

Anton [14]2 years ago

6 0

Answer:

$\sqrt[3]{3}$

Step-by-step explanation:

use the Pythagoras Theorem

Since you have the hypotenuse (6"), just go backwards. 62 = 36 = a2 + b2.

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2 years ago

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1 year ago

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Step 3: 2x > 10 Step 4: x > 5 What property justifies the work between step 3 and step 4? A. division property of inequali

BigorU [14]

Answer:

A. Division property of inequality.

Step-by-step explanation:

Let be $2\cdot x > 10$ , we proceed to show the appropriate procedure to step 4:

1) $2\cdot x >10$ Given

2) $x > 5$ Compatibility with multiplication/Existence of multiplicative inverse/Associative property/Modulative property/Result. (Division property of inequality)

In consequence, the division property of inequality which states that:

$\forall\, a, b, c \in \mathbb{R}$ . If $c > 0$ , then:

$a> b\,\longrightarrow a\cdot c > b\cdot c \,\lor\, a$

But if $c < 0$ , then:

$a> b\,\longrightarrow a\cdot c < b\cdot c \,\lor\, a b\cdot c$

Hence, correct answer is A.

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2 years ago

What is the radius of a circle whose equation is x2 + y2 + 8x – 6y + 21 = 0?

s344n2d4d5 [400]

Answer:

2 units

Step-by-step explanation:

The given equation of the circle is:

$x^{2} + y^{2}+8x-6y+21=0$

The general equation of the circle is:

$x^{2} + y^{2}+2gx+2fy+c=0$

Comparing the given equation with the general equation we can say:

g = 4

f = -3

c = 21

The formula for radius of the circle is:

$radius=\sqrt{g^{2} +f^{2} -c }$

Using these values of the given circle, we get:

$radius=\sqrt{(4)^{2}+(-3)^{2}-21}\\\\radius=\sqrt{4}\\\\radius=2$

Therefore, the length of radius of the given circle is 2.

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2 years ago