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3 years ago

Observe the following pattern and find the missing digits.

Mathematics

1 answer:

madam [21]3 years ago

7 0

Answer:

Step-by-step explanation:

I don't know the pattern but 1010101² is 1020304030201.

I'm always happy to help :)

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In right △ABC, the altitude CH to the hypotenuse AB intersects angle bisector AL in point D. Find the sides of △ABC if AD = 8 cm

tangare [24]

Answer:

$AC=8\sqrt{3}\ cm\\ \\AB=16\sqrt{3}\ cm\\ \\BC=24\ cm$

Step-by-step explanation:

Consider right triangle ADH ( it is right triangle, because CH is the altitude). In this triangle, the hypotenuse AD = 8 cm and the leg DH = 4 cm. If the leg is half of the hypotenuse, then the opposite to this leg angle is equal to 30°.

By the Pythagorean theorem,

$AD^2=AH^2+DH^2\\ \\8^2=AH^2+4^2\\ \\AH^2=64-16=48\\ \\AH=\sqrt{48}=4\sqrt{3}\ cm$

AL is angle A bisector, then angle A is 60°. Use the angle's bisector property:

$\dfrac{CA}{CD}=\dfrac{AH}{HD}\\ \\\dfrac{CA}{CD}=\dfrac{4\sqrt{3}}{4}=\sqrt{3}\Rightarrow CA=\sqrt{3}CD$

Consider right triangle CAH.By the Pythagorean theorem,

$CA^2=CH^2+AH^2\\ \\(\sqrt{3}CD)^2=(CD+4)^2+(4\sqrt{3})^2\\ \\3CD^2=CD^2+8CD+16+48\\ \\2CD^2-8CD-64=0\\ \\CD^2-4CD-32=0\\ \\D=(-4)^2-4\cdot 1\cdot (-32)=16+128=144\\ \\CD_{1,2}=\dfrac{-(-4)\pm\sqrt{144}}{2\cdot 1}=\dfrac{4\pm 12}{2}=-4,\ 8$

The length cannot be negative, so CD=8 cm and

$CA=\sqrt{3}CD=8\sqrt{3}\ cm$

In right triangle ABC, angle B = 90° - 60° = 30°, leg AC is opposite to 30°, and the hypotenuse AB is twice the leg AC. Hence,

$AB=2CA=16\sqrt{3}\ cm$

By the Pythagorean theorem,

$BC^2=AB^2-AC^2\\ \\BC^2=(16\sqrt{3})^2-(8\sqrt{3})^2=256\cdot 3-64\cdot 3=576\\ \\BC=24\ cm$

3 0

3 years ago

HELP ME PLEASE!!!!

horsena [70]

$2\sqrt5+3\sqrt5-\sqrt5=(2+3-1)\sqrt5=4\sqrt5\\\\\text{Answer:}\ 4\sqrt5$
Look at the square root like "x", then
$2\sqrt5+3\sqrt5-\sqrt5=/2x+3x-x=4x/=4\sqrt5$

3 0

3 years ago

The sum of twice a number and seven is twenty five

Mama L [17]

9

Because 9x2 is 18+7=25

3 0

3 years ago

John has $20.43 dollars in his pocket. He buys a tv for $15.39 dollars. How many dollars does John have left?

AleksAgata [21]

All you do is subtract what John is spending from the amount he has. 20.43-15.39= $5.04

4 0

4 years ago