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Naily [24]
3 years ago
9

What is the solution to the equation StartFraction x Over 3 EndFraction + StartFraction x Over 6 EndFraction = seven-halves? x =

Three-halves x = Seven-thirds x = 3 x = 7
Mathematics
1 answer:
Evgesh-ka [11]3 years ago
8 0

Answer:

The value of x is 7.

Step-by-step explanation:

First, you have to make both fractions into 1 fraction :

\frac{x}{3}  +  \frac{x}{6}  =  \frac{7}{2}

\frac{x \times 2}{3 \times 2}  +  \frac{x}{6}  =  \frac{7}{2}

\frac{2x}{6}  +  \frac{x}{6}  =  \frac{7}{2}

\frac{3x}{6}  =  \frac{7}{2}

Next, you have to do cross-multiplication and solve the value of x :

\frac{3x}{6}  =  \frac{7}{2}

3x(2) = 7(6)

6x = 42

x = 42 \div 6

x = 7

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If the angles of a traingle are in the ratio 2:3:4 , Find Them​
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Answer:

40°, 60°, and 80°

Step-by-step explanation:

We know that the sum of the angles of a triangle is equal to 180°.

We can use this equation to solve for these angles:

180 = 2x + 3x + 4x

180 = 9x

20 = x

Then substitute the solution in for x to solve for the angles:

2(20) = 40°

3(20) = 60°

4(20) = 80°

Therefore, the angles are 40°, 60°, and 80°.

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3 years ago
Simplify the sum. d^2-7d+12/d^2-d-6 + d^2+5d+6/d^2-2d-15
Law Incorporation [45]

Answer:

The sum is \frac{2d^2-5d+24}{d^2-3d-10}

Step-by-step explanation:

The given expression is


\frac{d^2-7d+12}{d^2-d-6}+\frac{d^2+5d+6}{d^2-2d-15}


These are all quadratic trinomials, so we split each of the middle terms to obtain,

\frac{d^2-4d-3d+12}{d^2-3d+2d-6}+\frac{d^2+2d+3d+6}{d^2-5d+3d-15}


We factor to obtain,


\frac{d(d-4)-3(d-4)}{d(d-3)+2(d-3)}+\frac{d(d+2)+3(d+2)}{d(d-5)+3(d-5)}


We factor further to obtain,

\frac{(d-4)(d-3)}{(d-3)(d+2)}+\frac{(d+2)(d+3)}{(d-5)(d+3)}


We cancel out the common factors to get,


\frac{(d-4)}{(d+2)}+\frac{(d+2)}{(d-5)}


The least common denominator is (d+2)(d-5).


We collect LCD to get


\frac{(d-4)(d-5)+(d+2)(d+2)}{(d+2)(d-5)}


We now expand to get,


\frac{d^2-5d-4d+20+d^2+2d+2d+4}{d^2-5d+2d-10}


We simplify to get,


\frac{d^2-9d+20+d^2+4d+4}{d^2-3d-10}


We simplify further to get,


\frac{2d^2-5d+24}{d^2-3d-10}










8 0
4 years ago
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