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3 years ago

6 4/5 +3 7/10 Add and reduce to the lowest terms.

Mathematics

2 answers:

Brilliant_brown [7]3 years ago

7 0

Answer:

Step-by-step explanation:6

4/5 + 3 7/10 = 21/2 = 10 1/2 = 10.5

Elan Coil [88]3 years ago

4 0

Answer:

10 1/2 or 10.5

Step-by-step explanation:

6 4/5 + 3 7/10

= 34/5 + 3 7/10

= 34/5 + 37/10

= 21/2

= 10 1/2

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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

If i have 100 gummy vitamins and i take two a day how many months would they last me?

never [62]

100 vitamins/2 a day=50 days 50 days/30 days in a month (assumedly)= 5/3 months 1.66

4 0

3 years ago

Find the length of the line AB

sergiy2304 [10]

Answer:

the length would be 12.

Step-by-step explanation:

7 0

4 years ago

Read 2 more answers

What is the solution of this equqtion? 1w= -17

devlian [24]

Answer:

-17

Step-by-step explanation:

1w= -17

(1)(-17)=

-17

5 0

3 years ago

Read 2 more answers

Plleeaassee help it is URGENT MAATHH HELP PLEASE WILL GIVE 5 STARS ON ALL CORRECT ANSWERS, MARK AS BEST ANSWER AND SAY THANKS

lara [203]

Using Pythagoras in the first question
c= $\sqrt{16 ^{2} + 4^{2} } =16.4924$
which is approximately 16.5
for the second question
we also use Pythagoras
$b^2=c^2-a^2$
$\sqrt{13^{2}-12^2}=5$

4 0

3 years ago