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2 years ago

Assuming that $3u + 12v\neq0$, simplify $\dfrac{12u^3 + 48u^2v}{3u+12v}$.

Mathematics

1 answer:

Kay [80]2 years ago

5 0

Answer:

4u²

Step-by-step explanation:

$\dfrac{12u^3 + 48u^2v}{3u+12v}=\dfrac{12u^2(u+4v)}{3(u+4v)}=\boxed{4u^2}$

Common factors cancel from numerator and denominator. The one factor that might make the expression undefined is given as non-zero, so no additional restrictions apply.

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WORTH 20 POINTS HELP

vfiekz [6]

Below represents the proof that the quadrilateral QRST is a parallelogram

<h3>How to prove that QRST is a parallelogram?</h3>

The coordinates are given as:

Q = (-1,-1)

R = (2,9)

S = (-4,5)

T = (-7,-5)

Calculate the length of each side using:

$d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}$

So, we have:

$QR = \sqrt{(-1 - 2)^2 + (-1 -9)^2} = \sqrt{109}$

$RS = \sqrt{(-4 - 2)^2 + (5 - 9)^2} = \sqrt{52}$

$ST = \sqrt{(-7 + 4)^2 + (-5 - 5)^2} = \sqrt{109}$

$TQ = \sqrt{(-7 + 1)^2 + (-5 + 1)^2} = \sqrt{52}$

The above computations show that opposite sides are equal.

Next, we determine the slope of each side using:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$QR = \frac{9 + 1}{2 + 3} = \frac{10}3$

$RS = \frac{5-9}{-4 - 2} = \frac{2}3$

$ST = \frac{5+5}{-4 + 7} = \frac{10}3$

$TQ = \frac{-5+1}{-7 + 1} = \frac{2}3$

The above computations show that opposite sides are parallel, because they have equal slope

Hence, the quadrilateral QRST is a parallelogram

Read more about parallelograms at:

brainly.com/question/3050890

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6 0

2 years ago

A<br> (Triangle)ABC is isosceles.<br> AB= 88 and CB = 12x + 4.<br> B<br> x= [?]

CaHeK987 [17]

Answer:

X=7 because 88=12x+4. Simple math gives you x=7

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Write the equation of the line that passes through the given points. Include your work in your final answer. Type your answer in

Harman [31]

The equation you use for the slope of this kind of problem is (y2-y1)/(x2-x1). x1 is the first X coordinate, x2 is the second, y1 is the first y coordinate, y2 is the second.

(5-3)/(2-2)
2/0
This equation has an UNDEFINED SLOPE, as it is just a vertical line.

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