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Amiraneli [1.4K]

2 years ago

6

Simplify the following radicals. 1. √16 2. √17 3. √18 4. √19 5. √20

1 answer:

Pavel [41]2 years ago

3 0

Answer:

Step-by-step explanation:

$1) \sqrt{16}= \sqrt{4*4}=4\\\\\\2) \sqrt{17}$

This is the simplest form as 17 is a prime number.

$3) \sqrt{18}= \sqrt{2*3*3} = 3 \sqrt{2}\\\\\\4) \sqrt{19}$

19 is a prime number. so it is the simplest form.

$5) \sqrt{20}= \sqrt{2*2*5}=2 \sqrt{5}$

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Find the missing lengths: LK=15 and KH=9, find KI and HI.

Luda [366]

Answer:

KI=11.25 and HI=6.75

Step-by-step explanation:

Consider the below figure attached with this question.

According to Pythagoras Theorem:

$base^2+perpendicular^2=hypotenuse^2$

Use Pythagoras in triangle HKL

$LH^2+KH^2=LK^2$

$(LH)^2+9^2=15^2$

$(LH)^2+81=225$

$(LH)^2=144$

Taking square root on both sides.

$LH=12$

Let length of HI be x.

LI = 12+x

Use Pythagoras theorem in ΔKLI,

$(KI)^2+15^2=(12+x)^2$

$(KI)^2+225=x^2+24x+144$

$(KI)^2=x^2+24x+144-225$

$(KI)^2=x^2+24x-81...(1)$

Use Pythagoras theorem in ΔHKI,

$(KI)^2=x^2+9^2$

$(KI)^2=x^2+81...(2)$

From (1) and (2) we get

$x^2+81=x^2+24x-81$

$24x=162$

$x=\dfrac{162}{24}=6.75$

Hence, the measure of HI is 6.75 units.

Substitute x=6.75 in equation (2).

$(KI)^2=(6.75)^2+81$

$(KI)^2=126.5625$

Taking square root on both sides.

$KI=\sqrt{126.5625}$

$KI=11.25$

Hence, the measure of KI is 11.25 units.

3 0

2 years ago

3 square root of 2 in radical form

Stolb23 [73]

Answer:

v

Step-by-step explanation:

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2 years ago

Hello Pleasa help ASAP !!!!

cricket20 [7]

Would have to go with A.

Most of us have to invest in study time for recall at test time.

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2 years ago

Write the equation of the graph shown below in factored form.

nika2105 [10]

Answer:

(x+2)2(x+1)(x+4)

Because

x=-4. x=2. x=-1

(x+4). (x+2). (x+1)

6 0

2 years ago

If a chord of a circle is 6 and is twice as far from the center chord of length 12, how long is the radius of the circle?

Ad libitum [116K]

Answer and explanation:

A center chord in a circle is the diameter of that circle. Therefore a center chord of a circle is different from other chords that touch two points on the circle but not in the center of the circle. A diameter of a circle is the chord that runs the length of the center of the circle touching two points at the edge of the circle. A diameter is twice the radius of the circle. So if the diameter of the circle is 12cm then the radius of the circle is 6cm

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2 years ago