Type an ordered pair: 2x-y=69 4y=x

Rectangle ABCD translates 4 units down and 2 units to the right to form rectangle A'B'C'D'. The vertices of rectangle ABCD are l

AlekseyPX

The length of B'C' in the rectangle A'B'C'D' = 9 units.

Step-by-step explanation:

step 1 :

Draw a rectangle with vertices ABCD in clockwise direction.

where, AB and DC are width of the rectangle ABCD.

AD and BC are length of the rectangle ABCD.

step 2 :

Now,

The length of the rectangle is AD = 5 units and

The width of the rectangle is AB = 3 units.

step 3 :

Draw another rectangle with vertices A'B'C'D' extended from vertices of the previous rectangle ABCD.

step 3 :

The length of the new rectangle is A'D' which is 4 units down from AD.

∴ The length of A'D' = length of AD + 4 units = 5+4 = 9 units

step 4 :

Since B'C' is also the length of the rectangle A'B'C'D', then the measure of B'C' is 9 units.

3 0

2 years ago

When Sanchez left his house this morning, his cell phone was 30% charged and it then started to lose 3% charge for each hour the

Radda [10]

Answer:

The equation that represents the battery charge in Sanchez's phone as a percentage t hours after he left his house is B(t) = 30 - 3*t.

Step-by-step explanation:

The initial state of the battery on Sanchez's phone is 30% so in time t equals zero the battery should be at that value and as time progresses the battery should lose battery charge at a rate of 3% for each hour. We can write this in an equation form by taking the initial state and subtract it by the rate multiplied by the value of time. We have:

B(t) = 30 - 3*t

The equation that represents the battery charge in Sanchez's phone as a percentage t hours after he left his house is B(t) = 30 - 3*t.

3 0

2 years ago

Find dy/dx given that y = sin x / 1 + cos x

kobusy [5.1K]

Answer:

$\frac{1}{1 + \cos(x) }$

Step-by-step explanation:

$y = \frac{ \sin(x) }{1 + \cos(x) }$

differentiating numerator wrt x :-

(sinx)' = cos x

differentiating denominator wrt x :- 

(1 + cos x)' = (cosx)' = - sinx

Let's say the denominator was "v" and the numerator was "u"

$(\frac{u}{v} )' = \frac{v. \: (u)' - u.(v)' }{ {v}^{2} }$

here,

since u is the numerator u= sinx and u = cos x
v(denominator) = 1 + cos x; v' = - sinx

$= \frac{((1 + \cos \: x) \cos \: x )- (\sin \: x. ( - \sin \: x) ) }{( {1 + \cos(x)) }^{2} }$

$= \frac{ \cos(x) + \cos {}^{2} (x) + \sin {}^{2} (x) }{(1 + \cos \: x) {}^{2} }$

since cos²x + sin²x = 1

$= \frac{ \cos \: x + 1}{(1 + \cos \: x) {}^{2} }$

diving numerator and denominator by 1 + cos x

$= \frac{1}{1 + \cos(x) }$

6 0

2 years ago

A company that manufactures video cameras produces a basic model and a deluxe model. Over the past year, 40% of the cameras sold

VikaD [51]

Answer:

(9)(9) = .013. (53). 2. A company that manufactures video cameras produces a basic model and a deluxe model. In the past, 40% of cameras sold have been the basic model. Of those basic models sold, 30% of purchasers buy the extended warranty as well. Of the deluxe models sold, 50% purchase the extended warranty,.

3 0

2 years ago

Mike took a taxi from his home to the airport. The taxi driver charged an initial fee of $6 plus $3 per mile. The total fare was

barxatty [35]

Hello! To solve this problem, we can write and solve an equation. Set it up like this:

6 + 3m = 24

This is because 6 is the one-time fixed price and you pay $3 per mile. Subtract 6 from both sides in order to get 3m = 18. Now, divide each side by 3 to isolate the “m”. 18/3 is 6. There. m = 6. Mike traveled 6 miles by taxi.

3 0

2 years ago

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