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Rainbow [258]
3 years ago
14

Can anyone please help. this is my last question!!!!

Mathematics
1 answer:
Andrej [43]3 years ago
8 0

9514 1404 393

Answer:

  x = 3.6

Step-by-step explanation:

The angle bisector divides the triangle proportionally.

The base segment to the right of the bisector is 6-x, so we can write the proportion ...

  x/6 = (6-x)/4

Multiplying by 12, we get ...

  2x = 3(6 -x)

  5x = 18 . . . . . add 3x

  x = 18/5 . . . .  divide by 5

  x = 3.6

_____

<em>Alternate solution</em>

Since the base of the triangle is given as a left-part and a sum-of-both-parts, we can write the proportion the same way:

  left-part / sum-of-both-parts = x/6 = 6/(6+4)

Then the solution is x = 6(6/10) = 36/10 = 3.6.

Doing it this way avoids having x on both sides of the equation, so makes solving the equation be "one step."

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d =  \frac{t - 7c}{ - 2}

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3 years ago
What two rational expressions sum to 2x+3/x^2-5x+4
Anni [7]

Answer:

\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}

Step-by-step explanation:

Given the rational expression: \frac{2x + 3}{x^2 - 5x + 4}, to express this in simplified form, we would need to apply the concept of partial fraction.

Step 1: factorise the denominator

x^2 - 5x + 4

x^2 - 4x - x + 4

(x^2 - 4x) - (x + 4)

x(x - 4) - 1(x - 4)

(x- 1)(x - 4)

Thus, we now have: \frac{2x + 3}{(x- 1)(x - 4)}

Step 2: Apply the concept of Partial Fraction

Let,

\frac{2x + 3}{(x- 1)(x - 4)} = \frac{A}{x- 1} + \frac{B}{x - 4}

Multiply both sides by (x - 1)(x - 4)

\frac{2x + 3}{(x- 1)(x - 4)} * (x - 1)(x - 4) = (\frac{A}{x- 1} + \frac{B}{x - 4}) * (x - 1)(x - 4)

2x + 3 = A(x - 4) + B(x - 1)

Step 3:

Substituting x = 4 in 2x + 3 = A(x - 4) + B(x - 1)

2(4) + 3 = A(4 - 4) + B(4 - 1)

8 + 3 = A(0) + B(3)

11 = 3B

\frac{11}{3} = B

B = \frac{11}{3}

Substituting x = 1 in 2x + 3 = A(x - 4) + B(x - 1)

2(1) + 3 = A(1 - 4) + B(1 - 1)

2 + 3 = A(-3) + B(0)

5 = -3A

\frac{5}{-3} = \frac{-3A}{-3}

A = -\frac{5}{3}

Step 4: Plug in the values of A and B into the original equation in step 2

\frac{2x + 3}{(x- 1)(x - 4)} = \frac{A}{x- 1} + \frac{B}{x - 4}

\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}

7 0
3 years ago
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3 0
3 years ago
Can somebody help me please
Veseljchak [2.6K]

Step-by-step explanation:

yes its ans is (3,3) fast you have see in x axis then y axis .so according to this we write 3 which lies in x- axis and then another 3 which lies in y-axis.

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