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Alik [6]
3 years ago
9

In ΔABC, m∠ACB = 90°, CD ⊥ AB and m∠ACD = 45°. Find: a Find CD, if BC = 3 in

Mathematics
1 answer:
Elodia [21]3 years ago
6 0

Answer:

  CD = (3/2)√2

Step-by-step explanation:

All the triangles are similar isosceles right triangles, so the hypotenuse in each case is √(1²+1²) = √2 times the length of the corresponding legs. BC is the hypotenuse of ΔBCD, so leg CD is that length divided by √2.

  CD = BC/√2 = 3/√2

  CD = (3/2)√2

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The endpoints of line <img src="https://tex.z-dn.net/?f=CD" id="TexFormula1" title="CD" alt="CD" align="absmiddle" class="latex-
Juli2301 [7.4K]

\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ C(\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad D(\stackrel{x_2}{7}~,~\stackrel{y_2}{5}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{7+1}{2}~~,~~\cfrac{5-6}{2} \right)\implies \left( \cfrac{8}{2}~,~\cfrac{-1}{2} \right)\implies \stackrel{M}{\left( 4~,~-\frac{1}{2} \right)}

8 0
3 years ago
Read 2 more answers
Determine how many solutions the following equation has using quadratic formula x^2+5x=-8
Katen [24]

Answer:

I will be using differentiation method

Step-by-step explanation:

x^2+5x =-8

2×x ×x^2-1 +5x = -8

2x +5x = -8

7x = -8

divide both sides by the co-efficient of x

7x÷7=-8÷7

x =-1.5

3 0
3 years ago
4 pieces of wood each 11 and a half inches long are required to build a cabinet. If all four pieces are cut from one board and 1
mariarad [96]
Ok first we calculate the length of board without losses:
4 * 11.5 = 46 inches
then, we have 1 inch of waste allowed fir each piece, so the total waste is 4*1 = 4 inches

finally, we will add the length of the waste to the desired length to get the total length of the board as follows:
total length of board = 46+4 = 50 inches
3 0
3 years ago
Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $35 and same-day tickets $30 c
Marina CMI [18]

Answer:

The number of same-day tickets sold is 15

The number of advance ticket sold is 20

Step-by-step explanation:

Given as :

The cost of each Advance ticket = $35

The cost of each same-day ticket = $30

The total cost of the tickets sold = $1150

The total number of tickets sold = 35

Let The number of advance ticket sold = a

And The number of same-day ticket sold = s

Now, According to question

The total number of tickets sold =The number of advance ticket sold + The number of same-day ticket sold

I.e a + s = 35                   .....A

The total number of tickets sold = The cost of each Advance ticket × The number of advance ticket sold + The cost of each same-day ticket × The number of same-day ticket sold

I.e $35 a + $30 s = $1150

or, 35 a + 30 s = 1150               .......B

Now, solving eq A and B

35 × ( a + s) - ( 35 a + 30 s ) = 35 × 35 - 1150

or, ( 35 a - 35 a ) + ( 35 s - 30 s ) = 1225 - 1150

or, 0 + 5 s = 75

∴  s = \frac{75}{5}

I.e s = 15

So, The number of same-day tickets sold = s = 15

Put the value of s in Eq A

So, a + 15 = 35

∴  a = 35 - 15

I.e a = 20

So, The number of advance ticket sold = a = 20

Hence The number of same-day tickets sold is 15

And  The number of advance ticket sold is 20   Answer

7 0
3 years ago
NEED ASAP HELPPPP !!!!!!!!!!
FinnZ [79.3K]

Answer:

The answer is b

3 0
2 years ago
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