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4 years ago

Solving equations 1/2(x+3)=2/5(x+2)

Mathematics

1 answer:

katen-ka-za [31]4 years ago

7 0

Answer:

x=-7

Step-by-step explanation:

convert to decimals 0.5(x+3)=0.4(x+2)

simplify the brackets 0.5x+1.5=0.4x+0.8

isolate x to one side 0.1x=-1/7

divide both sides by 0.1 x=-7

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Solve 3-2cos²x-3sinx=0 for 0≤x≤360

crimeas [40]

3-2(Cosx)^2 - 3Sinx = 0.

Recall (Sinx)^2 + (Cosx)^2 = 1.
Therefore (Cosx)^2 = 1 - (Sinx)^2
Substitute this into the question above.

3-2(Cosx)^2 - 3Sinx = 0
3 - 2(1 - (Sinx)^2) - 3Sinx = 0 Expand
3 - 2 + 2(Sinx)^2 - 3Sinx = 0
1 + 2(Sinx)^2 - 3Sinx = 0 Rearrange
2(Sinx)^2 - 3Sinx + 1 = 0
Let p = Sinx
2p^2 - 3p + 1 = 0 Factorise the quadratic expression
2p^2 - p - 2p +1 = 0
p(2p -1) - 1(2p -1) = 0
(2p-1)(p -1) = 0

Therefore 2p-1=0 or (p-1) = 0
2p=0+1 or (p-1) = 0
2p=1 or p = 0 +1.
p=1/2 or p = 1 Recall p = Sinx

Therefore Sinx = 1/2 or 1.
For 0<x<360

Sinx =1/2, x = Sin inverse (1/2) , x = 30,
 (180-30)- 2nd Quadrant = 150 deg
Sinx = 1, x = Sin inverse (1) , x = 90

Therefore x = 30,90 & 150 degrees.

Cheers.

7 0

3 years ago

Find the 88th term of the arithmetic sequence 26, 28, 30, ...

elena-s [515]

Answer:

200

Step-by-step explanation:

The nth term of an arithmetic sequence is given as:

f(n) = a + (n - 1)d

where a = first term

d = common difference

The first term of the sequence is 26 and the common difference is 2 (28 - 26 = 2)

The 88th term of the sequence is therefore:

f(88) = 26 + (88 - 1)*2

f(88) = 26 + (87 * 2)

f(88) = 26 + 174

f(88) = 200

The 88th term is 200.

6 0

3 years ago

The tax on a $80 item is $3.20. Find the tax on a $140 item. What is the tax?

allsm [11]

Tax is 4%

Tax in the $140 item is $5.60
(0.04x140)

7 0

2 years ago

I'm marking answers as brainliest ----- One of the vertices for this linear programming problem is __________. ----- (1,2) (3.5,

Travka [436]

Answer:

(0,2.3) if only one choice expected.

(0,2.3) and (0,0) if "all that apply" expected, since (0,0) is also a vertex of the green region.

Step-by-step explanation:

From the attached diagram, the given answer optsions are shown in brown.

The red line shows the optimal combinations of the two variables, hence a maximization problem.

Out of the four answer options, two coincide with a vertice of the valid region (shown in green), namely (0,0) and (0, 2.3).

Out of the two indicated options which correspond to a vertex, the origin (0,0) is usually ignored for a maximization problem, which leaves us with (0,2.3) as the answer.

3 0

3 years ago

What is the solution of StartRoot x minus 4 EndRoot + 5 = 2?

Vlad1618 [11]

Answer:

Step-by-step explanation:

$\sqrt{x-4}+5=2 \\\\\sqrt{x-4}=-3 \\\\x-4=9 \\\\x=13$

Hope this helps!

6 0

3 years ago

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