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Shkiper50 [21]
3 years ago
7

Let $\overline{AB}$ and $\overline{CD}$ be chords of a circle, that meet at point $Q$ inside the circle. If $AQ = 6,$ $BQ = 12$,

and $CD = 38$, then find the minimum length of $CQ$.
Mathematics
1 answer:
Cloud [144]3 years ago
3 0

9514 1404 393

Answer:

  2

Step-by-step explanation:

The products of chord lengths are the same for the intersecting chords:

  AQ×BQ = CQ×DQ

  6×12 = CQ×(38 -CQ)

This gives a quadratic in CQ:

  CQ² -38CQ +72 = 0 . . . . . write in standard form

  (CQ -2)(CQ -36) = 0 . . . . . factor the quadratic

  CQ = 2 or 36 . . . . . . . values of CQ that make the factors zero

The minimum length of CQ is 2 units. (DQ will be 36.)

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Sarah began the week with $2.60 in her lunch account. She deposited $20 on Monday, and then spent $4.75 each day that week for l
GuDViN [60]

Answer:

The balance in her lunch account at the end of the day on Friday is -$1.15.

Step-by-step explanation:

The balance at the end of the week will be the result of adding up the initial balance with the amount deposited on Monday minus the total amount spent that week.

Initial balance=$2.60

Amount deposited on Monday=$20

Total amount spent that week=$4.75*5=$23.75

Balance=$2.60+$20-$23.75

Balance=$22.60-$23.75

Balance=-$1.15

According to this, the answer is that the balance in her lunch account at the end of the day on Friday is -$1.15.

8 0
3 years ago
Alexis washes 10 1/2 windows in 3/4 hours. At this rate, how many windows can she wash in one hour?
Zepler [3.9K]

Alexis can wash a total of 14 windows in 1 hour

<h3><u>Solution:</u></h3>

Given that Alexis washes 10\frac{1}{2} windows in \frac{3}{4} hours

<u><em>To find: </em></u>number of windows washed in one hour

To simplify the calculations we will convert the given mixed fraction to improper fraction

\begin{array}{l}{=10 \frac{1}{2}} \\\\ {=\frac{2 \times 10+1}{2}} \\\\ {=\frac{21}{2}=10.5}\end{array}

Hence, to wash 10.5 windows, Alexis takes 0.75 hours

Let "n" be the number of windows washed in 1 hour

10.5 windows ⇒ 0.75 hours

"n" windows ⇒ 1 hour

By cross-multiplication we get,

n \times 0.75 = 10.5 \times 1

n = \frac{10.5}{0.75} \\\\n = 14

Thus Alexis can wash 14 windows in one hour

4 0
3 years ago
Simplify 19 - 1.67 + (2.4)
natali 33 [55]
The answer is 19.73 because 19 minus 1.67 is 17.33 and 17.33 plus 2.4 is 19.73
3 0
2 years ago
Read 2 more answers
Olive Oil costs $8.70 per liter. A restaurant owner buys 5.6 liter of olive oil. How much does the owner pay?
hammer [34]

Answer:

$48.72

Step-by-step explanation:

5.6 liters x $8.70 per liter= $48.72 total cost

7 0
3 years ago
If U = {x: X € N, 1 &lt; × &lt; 15)
Inessa05 [86]

Answer:

Step-by-step explanation:

Given:

U = {x: X € N, 1 < × < 15) = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}

A = {2,4,6,8,10,12,14}

B = {3,6,9,12,15}

C = {5,10,15}

(a) Verify A(BnB)=(AUB)(AUB)

A U (B n B)

=  {2,4,6,8,10,12,14} U (  {3,6,9,12,15} n  {3,6,9,12,15} )

=  {2,4,6,8,10,12,14} U {3,6,9,12,15}

=  {2,3,4,6,8,9,10,12,14,15}

( A U B) n (A U B)

= {2,3,4,6,8,9,10,12,14,15} n {2,3,4,6,8,9,10,12,14,15}

= {2,3,4,6,8,9,10,12,14,15}

Therefore

A U (B n B)  =  ( A U B) n (A U B)

verifies

(b) Verify An(BUC)=(AnB)u(AnC)

A n ( B U C)

=  {2,4,6,8,10,12,14} n ( {3,6,9,12,15} U {5,10,15} )

=  {2,4,6,8,10,12,14} n {3,5,6,9,10,12,15}

= {6,10,12}

( A n B ) U ( A n C )

= ( {2,4,6,8,10,12,14} n {3,6,9,12,15} ) U ( {2,4,6,8,10,12,14} n {5,10,15} )

= {6,12} U {10}

= {6,10,12}

Therefore

A n ( B U C) = ( A n B ) U ( A n C )

verifies

(c) Verify AU(BUC)=(AUB)U(AUC)​

AU(BUC)

=  {2,4,6,8,10,12,14}U{3,6,9,12,15}U{5,10,15}

= {2,3,4,5,6,8,9,10,12,14,15}

(AUB)U(AUC)​

=  ({2,4,6,8,10,12,14}{3,6,9,12,15})U({2,4,6,8,10,12,14}U{5,10,15})

= {2,3,4,6,8,9,10,12,14,15}U{2,4,5,6,8,10,12,14,15}

= {2,3,4,5,6,8,9,10,12,14,15}

Therefore

AU(BUC)=(AUB)U(AUC)​

verifies

5 0
3 years ago
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