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babymother [125]
1 year ago
12

Both rectangles below are similar. Find the value of x.

Mathematics
1 answer:
Margaret [11]1 year ago
3 0

The value of x is 12.15 inches when both the rectangles are similar.

According to the question,

We have the following information:

We have two figures of rectangle which are similar and measurements of their length and width is given.

We know that when two figures are similar then it means that the ratio of their corresponding sides are equal.

So, we have the following expression for these two rectangles:

40/18 = 27/x

Using the cross multiplication method:

40*x = 18*27

Dividing both the sides of the equation by 40:

x = (18*27)/40

x = 12.15 inches

Hence, the value of x is 12.15 inches when both the rectangles are similar.

To know more about rectangles here

brainly.com/question/10075733

#SPJ1

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Use the given information to find the exact value of the expression. sin α = 2129 21 29 , α lies in quadrant II, and cos β = 151
beks73 [17]
The correct question is
Use the given information to find the exact value of the expression. sin α = 21/29, α lies in quadrant II, and cos β = 15/17, β lies in quadrant I Find sin (α - β).

we know that
sin(α − β<span>) = </span>sin α cos β − cos α sin β

α lies in quadrant II
so
cos α  is negative
sin α  is positive

β lies in quadrant I
so
cos β  is positive
sin β   is positive

step 1
find sin β
cos β=15/17
sin² β+cos² β=1-----------> sin² β=1-cos² β----> sin² β=1-(15/17)²
sin² β=1-225/289-----> 64/289
sin β=8/17

step 2
find cos α
sin α = 21/29
cos² α + sin² α=1----> cos² α=1-sin² α---> cos² α=1-(21/29)²---> 1-441/841
cos² α=400/841------> cos α=-20/29  (remember cos α is negative)

step 3
find sin(α − β) 
sin α = 21/29   cos α=-20/29
sin β=8/17       cos β=15/17

sin(α − β) = [21/29]*[15/17] − [-20/29*]*[8/17]
sin(α − β) = [315/493] − [-160/493]
sin(α − β) = 475/493

the answer is
sin(α − β) = 475/493


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