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3 years ago

I am stuck on these last four questions please help if possible.

Mathematics

1 answer:

zloy xaker [14]3 years ago

4 0

Answer:

Step-by-step explanation:

9). -2.2(4 - 1.9x) = 3.3(0.2x - 0.8)

-8.8 + 2.2(1.9x) = 0.66x - 2.64

-8.8 + 4.18x = 0.66x - 2.64

4.18x - 0.66x = 8.8 - 2.64

3.52x = 6.16

x = 1.75

10). 3.2(1 + 2.6x) = 2.4(x - 3.6)

3.2 + 8.32x = 2.4x - 8.64

8.32x - 2.4x = -3.2 - 8.64

5.92x = -11.84

x = 2

11). 4.6(2x - 5.5) = 3.9 + 0.8(1 + 5.5x)

9.2x - 25.3 = 3.9 + 0.8 + 4.4x

9.2x - 25.3 = 4.7 + 4.4x

9.2x - 4.4x = 25.3 + 4.7

4.8x = 30

x = 6.25

12). 0.2(3x + 2.5) - 4.9 = 3.8 - 2.2(x - 5.5)

0.6x + 0.5 - 4.9 = 3.8 - 2.2x + 12.10

0.6x - 4.4 = -2.2x + 15.90

0.6x + 2.2x = 15.90 + 4.4

2.8x = 20.30

x = 7.25

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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) = 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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