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Lesechka [4]
3 years ago
14

The diagram shows the rectangle ABCD, where A is (3,2) and B is (1,6).

Mathematics
1 answer:
In-s [12.5K]3 years ago
6 0
(i)
A(3,2),B(1,6)
\\
\\m_{AB}= \frac{6-2}{1-3}=-2
\\
\\m_{BC}m_{AB}=-1
\\ 
\\m_{BC}= \frac{-1}{m_{AB}} = \frac{-1}{-2}= \frac{1}{2}  
\\
\\B(1,6)\Rightarrow x_1=1,y_1=6
\\
\\BC:y-y_1=m_{BC}(x-x_1)
\\
\\y-6= \frac{1}{2}(x-1)
\\
\\2y-12=x-1
\\x-2y+11=0

(ii)
AC:y=x-1
\\BC:x-2y+11=0
\\
\\C=AC\cap BC
\\
\\x-2(x-1)+11=0
\\x-2x+2+11=0
\\x=13
\\y=x-1=13-1=12
\\C(13,12)

(iii)
A(3,2)B(1,6),C(13,12)
\\P=2(d(A,B)+d(B,C))
\\
\\d(A,B)= \sqrt{(1-3)^2+(6-2)^2}= \sqrt{20}  =2 \sqrt{5} 
\\
\\d(B,C)= \sqrt{(13-1)^2+(12-6)^2}= \sqrt{180}= 6\sqrt{5}  
\\ 
\\P=2(2 \sqrt{5}+6 \sqrt{5})=2\times8 \sqrt{5} =16 \sqrt{5}
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A dress that normally costs $64.50 is on sale for 5% off. What is the sale price of the dress?
Kruka [31]
D 61.28 because you divide 64.50 by 0.05 then which is 3.23 then 64.50 - 3.23
3 0
4 years ago
I will give brainliest answer
stich3 [128]

Answer:

Left 3, down 2

Step-by-step explanation:

(6,4) --> (3,2)

-3, -2

Left 3, down 2

6 0
3 years ago
If x=6 , y=8 , and z=3<br><br> 2x+3y-z<br><br> Is the answer 33?
Oduvanchick [21]
Yes.
2x = 12
3y = 24
-z = -3

12 + 24 - 3 = 33
3 0
4 years ago
What are the roots of the equation 9x^2 + 54x +82 = 0 in simplest a + bi form?​
s344n2d4d5 [400]

Answer:

The roots are

<h3>x =  - 3 +  \frac{1}{3}  i \:  \:  \: or \:  \:  \: x =  - 3 -  \frac{1}{3} i \\</h3>

Step-by-step explanation:

9x² + 54x + 82 = 0

Using the quadratic formula

That's

<h3>x =  \frac{ - b\pm \sqrt{ {b}^{2}  - 4ac} }{2a}</h3>

From the question

a = 9 , b = 54 , c = 82

Substitute the values into the above formula and solve

That's

<h3>x =  \frac{ - 54\pm \sqrt{ {54}^{2}  - 4(9)(82)} }{2(9)}  \\ x =  \frac{ - 54\pm \sqrt{2916 - 2952} }{18}  \\ x =  \frac{ - 54\pm \sqrt{ - 36} }{18}  \\ x =  \frac{ - 54\pm 6i}{18}</h3>

Separate the real and imaginary parts

That's

<h3>x =  -  \frac{54}{18} \pm \frac{6}{18}  \: i \\ x =  - 3\pm \frac{1}{3} i</h3>

We have the final answer as

<h3>x =  - 3 +  \frac{1}{3}  i \:  \:  \: or \:  \:  \: x =  - 3 -  \frac{1}{3} i \\</h3>

Hope this helps you

5 0
3 years ago
The Ambell Company uses batteries from two different manufacturers. Historically, 70% of the batteries are from manufacturer 1,
Sunny_sXe [5.5K]

Answer:

0.625

Step-by-step explanation:

Given :

Ambell company uses or procures batteries from two manufacturers.

The life of a battery in critical tool is at = 32 hours

Ambell uses 70% of its batteries from manufacturer 1 and out of that 90% batteries lasts for about 40 hours.

Similarly, 75% of the batteries procured from the manufacturer 2 lasts for about 40 hours.

Therefore, the probability that a battery is form manufacturer 1 is :

$\frac{0.4 \times 0.25}{(0.6 \times0.1)+(0.4 \times 0.25)}$

= 0.625

5 0
3 years ago
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