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3 years ago

Which shows the rational expression written using the least common denominator?

Mathematics

1 answer:

aleksandr82 [10.1K]3 years ago

5 0

Answer:

(x + 1)/4x² + 4(x + 1)/4x²

Step-by-step explanation:

x+1/4x² + x+1/x²

The above can be simply as follow:

Find the least common multiple (LCM) of 4x² and x². The result is 4x²

Now Divide the LCM by the denominator of each term and multiply the result with the numerator as show below:

(4x² ÷ 4x²) × (x + 1) = x + 1

(4x² ÷ x²) × (x + 1) = 4(x + 1)

x+1/4x² + x+1/x² = [(x + 1) + 4(x + 1)]/ 4x²

= (x + 1)/4x² + 4(x + 1)/4x²

Therefore,

x+1/4x² + x+1/x² = (x + 1)/4x² + 4(x + 1)/4x²

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4 years ago

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For this spinner, what are the following probabilities? Answer in simplest fraction form using the form: x/y

luda_lava [24]

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2 years ago

Someone please help me

tester [92]

1) The scale factor for the dilation is 2/3.

2) The polygon became smaller after the dilation because you are multiplying by a scale factor less than 1.

3) The ratio of the areas is 2/5.

7 0

3 years ago

A pumpkin is launched directly upwards at 72 feet per second from a platform 24 feet high. The pumpkins height, h, at time t sec

STALIN [3.7K]

Answer: Maximum height = 105 feet

And, It takes 9/4 seconds to reach that point.

Step-by-step explanation:

Here the given function that shows the height of the pumpkin,

$h(t) = -16t^2 + 72t + 24$ --------(1)

Where t is the time in second.

Differentiating equation (1) with respect to t,

We get, $h'(t) = -32 t + 72$

Again differentiating above equation with respect to t,

We get, $h''(t) = -32$

For maximum or minimum, $h'(t) = 0$

$- 32 t + 72 = 0$

$32 t = 72$

$t = \frac{9}{4}$

At t = 9/4 , h''(t) = Negative value,

Therefore, At t = 9/4 seconds, h(t) is maximum,

And, the maximum value is,

$h(\frac{9}{4} ) = -16(\frac{9}{4})^2 + 72(\frac{9}{4}) + 24$

$h(\frac{9}{4} ) = -16(\frac{81}{16})+ 72(\frac{9}{4}) + 24$

$h(\frac{9}{4} ) = -81 + 162 + 24=105$

Therefore, the maximum height of the pumpkin is 105 feet at 9/4 seconds

8 0

3 years ago

Please answer number 14<br> I already tried but don’t understand

Rudiy27

Answer:
$< abc = < ebc \\ < acb = < ecd \\ if \: two \: angles \: in \: the \:two \: different \: triangles \: are \: equal \: then \: the \: third \: angle \: in \: the \: triangle\: must \: be \: equal. \\ using \: pythogres \: theorum \\ ab = \sqrt( ac ^{2} - bc^{2} )\\ = \sqrt (15 ^{2} - 12 ^{2}) \\ = \sqrt( 225 - 144 )\\ = \sqrt(81) \\ ab = 9 \\ sides \: of \: similar \: triangle \: are \: propotional \\ ac \div ec = dc \div bc \\ 15 \div x = 12 \div 6\\ x = 15 \times 6\div 12\\ x = 15 \div 2 \\ x = 7.5 \\ so \: ec \: = 7.5 \\ you \: can \: check \: this \: by \: applying \: pythogores \: theorum. \\ i \: hope \: this \: helps$

8 0

3 years ago