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3 years ago

Angles in circles please help

Mathematics

2 answers:

8090 [49]3 years ago

7 0

Answer:

x = 80 degrees

Step-by-step explanation:

it says right there

melamori03 [73]3 years ago

7 0

9514 1404 393

Answer:

x = 80°

Step-by-step explanation:

The measure of an arc is the same as the measure of the central angle it subtends.

x = 80°

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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

3 years ago

What is 999+999+999+23456

ohaa [14]

Your answer is 26,453

Although I don't feel as if this is a homework question, I will still show the work.

Work:

Step 1: 999 + 999 = 1,998

Step 2: 1,998 + 999 = 2,997

Step 3: 2,997 + 23,456 = 26,453

Hope I was able to help! :)

6 0

3 years ago

Read 2 more answers

Alexandra invested $800 in an account paying an interest rate3.1% compounded continuously. Assuming no deposits or withdrawals a

s2008m [1.1K]

$\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$800\\ r=rate\to 3.1\%\to \frac{3.1}{100}\dotfill &0.031\\ t=years\dotfill &20 \end{cases} \\\\\\ A=800e^{0.031\cdot 20}\implies A=800e^{0.62} \\\\\\ A\approx 1487.14\implies A=\stackrel{rounded~up}{1500}$