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Citrus2011 [14]
2 years ago
13

ABC is a triangle right angled at A and D is a point on BC such that AD Ʇ BC. Show that AD2 = BD x DC. please answer fast URGENT

Mathematics
1 answer:
postnew [5]2 years ago
6 0

Answer:

The answer is below

Step-by-step explanation:

Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse side is equal to the sum of the square of the remaining sides. The hypotenuse is the longest side (that is side opposite to the 90° angle).

In right angle triangle ABD:

AB² = AD² + BD²     (1)

In right angle triangle ACD:

AC² = AD² + CD²      (2)

Also:

AC² + AB² = BC²       (3)

But BC = BD + CD

AC² + AB² = (BD + CD)²     (4)

Adding equation 1 and 2 gives:

AB² + AC² = (AD² + BD²) + (AD² + CD²)  

AB² + AC² = 2AD² + BD² + CD²

substituting AC² + AB² = (BD + CD)²:

(BD + CD)² = 2AD² + BD² + CD²

BD² + 2(BD)(CD)+ CD² = 2AD² + BD² + CD²

2AD² = 2(BD)(CD)

AD² = BD * CD

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A worker at a snack stand opened a new box of cups. The first day he used 30 cups , the second day the worker used 15 percent of
Sholpan [36]

Answer:

Step-by-step explanation:

the first day he used 30 cups

the second day he used 15% of the remaining cups...a total of 90 cups were used on second day.

so 15%of the remaining cups = 90.....so if u let x be the total cups, then the remaining cups would be x - 30

15% of (x - 30) = 90.....turn ur percent to a decimal..." of " means multiply

0.15(x - 30) = 90

0.15x - 4.5 = 90

0.15x = 90 + 4.5

0.15x = 94.5

x = 94.5 / 0.15

x = 630 total cups <==

lets check..

start with 630 cups....used 30 the first day....leaving u with 600 cups....15% of the remaining cups = 90.....so 15% of 600 = 90....lets check it

15%of 600 = 0.15(600) = 90...yep, thats correct....there were 630 cups in the new un-opened box

5 0
3 years ago
I need to borrow some money from my parents as my deficit has ____________.
MatroZZZ [7]

Answer:  Option 'D' is correct.

Step-by-step explanation:

I need to borrow some money from my parents as my deficit has <u>grown or increased.</u>

If deficit of any individual increases , means, he is short of money.

So, he needs to borrow from his parents.

Hence, Option 'D' is correct.

4 0
3 years ago
Read 2 more answers
3
Dimas [21]

Answer:

5-i

Step-by-step explanation:

Product=multiplication

Let the complex number=x

(3+2i)*x=17+7i

x=17+7i / 3+2i

x=(17-7i)*(3-2i)/(3+2i)*(3+2i)

=51-34i+21i+14i^2 / 9+6i+6i+4i^2

=51+13i+14i^2 / 9+12i+4i^2

= (51+14 - 13i) / 13

= (65 -13i) / 13

= 65 / 13 - 13 i / 13

= 5 - i.

5 0
3 years ago
Image attached pls help 40 points
lutik1710 [3]

Answer:

Jake:y

grandma:6y

cousin:y+5

the sum of all their ages:8y+5

Step-by-step explanation:

given Jake:y

His grandma is 6 times his age

so

grandma:6y

His cousin is 5 years older than

him.

so

cousin:y+5

the sum of all their ages is

y+6y+y+5

8y+5

6 0
3 years ago
Read 2 more answers
Pls someone answer because I’m not gonna be able to do this I’m going out of town pls help
Likurg_2 [28]
2 is B :::))))))))))))))))
7 0
2 years ago
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