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Alexxandr [17]
3 years ago
8

Solve for x (1/x) -2/3 = (4x)

Mathematics
1 answer:
Vadim26 [7]3 years ago
4 0

The value of x is x=\frac{-1+\sqrt{37}}{12} and x=\frac{-1-\sqrt{37}}{12}

Step-by-step explanation:

The equation is \frac{1}{x}-\frac{2}{3}=4 x

Subtracting by 4x on both sides,

\frac{1}{x}-\frac{2}{3}-4 x=0

Taking LCM,

\frac{3-12 x^{2}-2 x}{3 x}=0

Multiplying by 3x on both sides,

-12 x^{2}-2 x+3=0

Dividing by (-) on both sides,

12 x^{2}+2 x-3=0

Using quadratic formula, we can solve for x.

\begin{aligned}x &=\frac{-2 \pm \sqrt{2^{2}-4 \cdot 12 \cdot(-3)}}{2 \cdot 12} \\&=\frac{-2 \pm \sqrt{4+144}}{2 \cdot 144} \\&=\frac{-2 \pm \sqrt{148}}{24} \\&=\frac{-2 \pm 2 \sqrt{37}}{24}\end{aligned}

Taking out common term 2, we get,

\begin{array}{l}{x=\frac{-2(1 \pm \sqrt{37})}{24}} \\{x=\frac{-1 \pm \sqrt{37}}{12}}\end{array}

Thus, the value of x is  x=\frac{-1+\sqrt{37}}{12} and x=\frac{-1-\sqrt{37}}{12}

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Degger [83]

Answer:

A=73.8\°

B=8.2\°

c=76.3\ units

Step-by-step explanation:

step 1

Find the measure of side c

Applying the law of cosines

c^{2}= a^{2}+b^{2}-2(a)(b)cos(C)

substitute the given values

c^{2}= 74^{2}+11^{2}-2(74)(11)cos(98\°)

c^{2}=5,823.5738

c=76.3\ units

step 2

Find the measure of angle A

Applying the law of sine

\frac{a}{sin(A)}=\frac{c}{sin(C)}

substitute the given values

\frac{74}{sin(A)}=\frac{76.3}{sin(98\°)}

sin(A)=(74)sin(98\°)/76.3

A=arcsin((74)sin(98\°)/76.3)

A=73.8\°

step 3

Find the measure of angle B

we know that

The sum of the internal angles of a triangle must be equal to 180 degrees

so

A+B+C=180\°

substitute the given values

73.8\°+B+98\°=180\°

171.8\°+B=180\°

B=180\°-171.8\°=8.2\°

5 0
3 years ago
The sum of twice a number and five is 13. Find the number.
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4

let the number be x

so by the question , 2x+5=13

solving this we get ,

2x=13-5

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Answer:

The correct answer is option C. y = 31x + 154.

Step-by-step explanation:

Since x represents the days and she learns 31 words per day you would need to multiply 31 and the number of days (x).

This would look like 31x.

We also know she already knew 154 from the beginning which means we just have to add 154.

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