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Tems11 [23]
2 years ago
12

Which expression is equivalent to startfraction m minus 4 over m 4 endfraction divided by (m 2) ?

Mathematics
1 answer:
sertanlavr [38]2 years ago
4 0

Rational functions are written as fractions. The expression equivalent to \frac{\dfrac{m-4}{m+4} }{m+2} is \frac{m-4}{m^2+6m+8}

<h3>Rational functions</h3>

Given the rational function expressed as:

\frac{\dfrac{m-4}{m+4} }{m+2}

This can be further expressed as:

\frac{m-4}{(m+4(m+2)}


Factorize the denominator to have;

\frac{m-4}{m^2+4m+2m+8}\\ \frac{m-4}{m^2+6m+8}

Hence the expression equivalent to \frac{\dfrac{m-4}{m+4} }{m+2} is \frac{m-4}{m^2+6m+8}

Learn more on rational function here: brainly.com/question/1917026

#SPJ4


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Sum of one-half of a number and 4 is -16. find the number
Lady_Fox [76]
X is the number
sum means add

sum of half a number and 4 means
(x/2)+4
result is -16

(x/2)+4=-16
minus 4 both sides
x/2=-20
times 2 both sides
x=-40
the number is -40
5 0
4 years ago
-x(y+z) if a=2 b=-2 and c=4
egoroff_w [7]

Answer:

-4

Step-by-step explanation:

assuming xyz =abc

-x(y+z)

-2(-2+4)

(4-8)

=-4

5 0
3 years ago
Q1 A ball is thrown upwards with some initial speed. It goes up to a height of 19.6m and then returns. Find (a) The initial spee
lubasha [3.4K]

Answer:

(a)  19.6 ms⁻¹

(b)  2 s

(c)  9.8 ms⁻¹

(d)  4 s

Step-by-step explanation:

<u>Constant Acceleration Equations (SUVAT)</u>

\boxed{\begin{array}{c}\begin{aligned}v&=u+at\\\\s&=ut+\dfrac{1}{2}at^2\\\\ s&=\left(\dfrac{u+v}{2}\right)t\\\\v^2&=u^2+2as\\\\s&=vt-\dfrac{1}{2}at^2\end{aligned}\end{array}} \quad \boxed{\begin{minipage}{4.6 cm}$s$ = displacement in m\\\\$u$ = initial velocity in ms$^{-1}$\\\\$v$ = final velocity in ms$^{-1}$\\\\$a$ = acceleration in ms$^{-2}$\\\\$t$ = time in s (seconds)\end{minipage}}

When using SUVAT, assume the object is modeled as a particle and that acceleration is constant.

Acceleration due to gravity = 9.8 ms⁻².

<h3><u>Part (a)</u></h3>

When the ball reaches its maximum height, its velocity will momentarily be zero.

<u>Given values</u> (taking up as positive):

s=19.6 \quad v=0 \quad a=-9.8

\begin{aligned}\textsf{Using} \quad v^2&=u^2+2as\\\\\textsf{Substitute the given values:}\\0^2&=u^2+2(-9.8)(19.6)\\0&=u^2-384.16\\u^2&=384.16\\u&=\sqrt{384.16}\\\implies u&=19.6\; \sf ms^{-1}\end{aligned}

Therefore, the initial speed is 19.6 ms⁻¹.

<h3><u>Part (b)</u></h3>

Using the same values as for part (a):

\begin{aligned}\textsf{Using} \quad s&=vt-\dfrac{1}{2}at^2\\\\\textsf{Substitute the given values:}\\19.6&=0(t)-\dfrac{1}{2}(-9.8)t^2\\19.6&=4.9t^2\\t^2&=\dfrac{19.6}{4.9}\\t^2&=4\\t&=\sqrt{4}\\\implies t&=2\; \sf s\end{aligned}

Therefore, the time taken to reach the highest point is 2 seconds.

<h3><u>Part (c)</u></h3>

As the ball reaches its maximum height at 2 seconds, one second before this time is 1 s.

<u>Given values</u> (taking up as positive):

u=19.6 \quad a=-9.8 \quad t=1

\begin{aligned}\textsf{Using} \quad v&=u+at\\\\\textsf{Substitute the given values:}\\v&=19.6+(-9.8)(1)\\v&=19.6-9.8\\\implies v&=9.8\; \sf ms^{-1}\end{aligned}

The velocity of the ball one second before it reaches its maximum height is the <u>same</u> as the velocity one second after.

<u>Proof</u>

When the ball reaches its maximum height, its velocity is zero.

Therefore, the values for the downwards journey (from when it reaches its maximum height):

u=0 \quad a=9.8 \quad t=1

(acceleration is now positive as we are taking ↓ as positive).

\begin{aligned}\textsf{Using} \quad v&=u+at\\\\\textsf{Substitute the given values:}\\v&=0+9.8(1)\\\implies v&=9.8\; \sf ms^{-1}\end{aligned}

Therefore, the velocity of the ball one second before <u>and</u> one second after it reaches the maximum height is 9.8 ms⁻¹.

<h3><u>Part (d)</u></h3>

From part (a) we know that the time taken to reach the highest point is 2 seconds.  Therefore, the time taken by the ball to travel from the highest point to its original position will also be 2 seconds.

Therefore, the total time taken by the ball to return to its original position after it is thrown upwards is 4 seconds.

4 0
1 year ago
If the product of 4 and a number is decreased by 12 the result is twice the opposite of the number. Find the number
Darya [45]

Answer:

2 (twice the opposite i hope that's what you meant)

Step-by-step explanation:

The formula 4x - 12 = -2x

Subtract 4x to both sides

-12 = -6x

Divide X by -6

2 = x

Flip

X = 2

4 0
3 years ago
Help me plzz this is hard
san4es73 [151]

Answer:

153.9ft squared

Step-by-step explanation:

Use the calculation given

r = radius, so half the number given (14 is the diameter)

3.14 x (7 squared) = 153.9ft

3 0
3 years ago
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