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3 years ago

BD=16 and AC the perpendicular bisector of BD.

Mathematics

2 answers:

vovikov84 [41]3 years ago

7 0

Answer:

y = 5

Step-by-step explanation:

If AC is the perpendicular bisector of BD, that would mean that y+3=2y-2.

Now it's just simple algebra.

Solving for y, you get y=5.

Nady [450]3 years ago

6 0

Answer:

y=5

Step-by-step explanation:

because BD=16 you can add BC and CD together which is 3y+1 since BD and BC + CD is the same thing you can make the equation 3y+1=16

3y=15

y=5

You might be interested in

What is the sum of the first 70 consecutive odd numbers? Explain.

expeople1 [14]

The sum of the first n odd numbers is n squared! So, the short answer is that the sum of the first 70 odd numbers is 70 squared, i.e. 4900.

Allow me to prove the result: odd numbers come in the form 2n-1, because 2n is always even, and the number immediately before an even number is always odd.

So, if we sum the first N odd numbers, we have

$\displaystyle \sum_{i=1}^N 2i-1 = 2\sum_{i=1}^N i - \sum_{i=1}^N 1$

The first sum is the sum of all integers from 1 to N, which is N(N+1)/2. We want twice this sum, so we have

$\displaystyle 2\sum_{i=1}^N i = 2\cdot\dfrac{N(N+1)}{2}=N(N+1)$

The second sum is simply the sum of N ones:

$\underbrace{1+1+1\ldots+1}_{N\text{ times}}=N$

So, the final result is

$\displaystyle \sum_{i=1}^N 2i-1 = 2\sum_{i=1}^N i - \sum_{i=1}^N 1 = N(N+1)-N = N^2+N-N = N^2$

which ends the proof.

5 0

3 years ago

line y = x + 2 will be graft on the same coordinate plane to create a system of equations. what is the solution to the system of

nata0808 [166]

Answer:

Step-by-step explanation:

it’s going to be (4,-2)

4 0

3 years ago

A rectangular lot is 145 yards long and 100 yards wide.

mr_godi [17]

Answer:

150 by 100

Step-by-step explanation:

5 0

3 years ago

Please help!!!!!!!!!!!

boyakko [2]

Answer:

(7√6)/2

Step-by-step explanation:

The side ratios in these special triangles are ...

30°-60°-90° triangle: 1 : √3 : 2

45°-45°-90° triangle: 1 : 1 : √2

This tells you the length of the horizontal line is 7√3, and the value of x is ...

(7√3)/√2 = (7√6)/2

_____

<em>Additional comment</em>

Call the length of the horizontal line "y". Then the given ratios tell you ...

7 : y = 1 : √3 ⇒ y/7 = √3/1 ⇒ y = 7√3

and

x : y = 1 : √2 ⇒ x/y = 1/√2 ⇒ x = y/√2

When we rationalize the denominator, we get ...

x = (y√2)/2 = ((7√3)√2)/2 = (7√6)/2

4 0

2 years ago

Two friends sold many pieces of furniture and made $1550 during their garage sale. They had fifteen more $10 bills than $50 b

Novosadov [1.4K]

Answer:

The number of $ 10 bills is 37, the number of $ 20 is 6 and the number of $ 50 bills is 22.

Step-by-step explanation:

Let n₁ = number of $ 10 bills,

Let n₂ = number of $ 20 bills and

Let n₃ = number of $ 50 bills

Given that 10n₁ + 20n₂ + 50n₃ = 1550 (1)

Also, since we have fifteen more $10 bills than $50 bills, n₁ = n₃ + 15 (2)

and we have 4 more than three times as many $20 bills as $50 bills. n₃ = 3n₂ + 4. (3)

substituting equations (2) and (3) into (1), we have

10(n₃ + 15) + 20n₂ + 50n₃ = 1550

expanding the bracket, we have

10n₃ + 150 + 20n₂ + 50n₃ = 1550

collecting like terms, we have

60n₃ + 150 + 20n₂ = 1550

inserting equation (3), we have

60(3n₂ + 4) + 150 + 20n₂ = 1550

expanding the bracket, we have

180n₂ + 240 + 150 + 20n₂ = 1550

collecting like terms, we have

200n₂ + 390 = 1550

subtracting 390 from both sides, we have

200n₂ = 1550 - 390

200n₂ = 1160

dividing both sides by 200, we have

n₂ = 1160/200

n₂ = 5.8

n₂ ≅ 6 since it cannot be a fraction.

Substituting this into (3), we have

n₃ = 3n₂ + 4 = 3(6) + 4 = 18 + 4 = 22

substituting n₃ into (2), we have

n₁ = n₃ + 15 = 22 + 15 = 37

So, the number of $ 10 bills is 37, the number of $ 20 is 6 and the number of $ 50 bills is 22.

3 0

3 years ago