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Georgia [21]
3 years ago
15

Simplify quantity 1 over 36 minus 1 over x squared all over 1 over 6 plus 1 over x.

Mathematics
1 answer:
Ne4ueva [31]3 years ago
7 0
 <span>[ (1 / 36) - (1 / x²) ] / [ (1 / 6) + (1 / x) ] 

[ (x² - 36) / 36x² ] / [ (x + 6) / 6x ] 

</span>remember that<span>: 
x² - 36 = (x + 6)(x - 6) 

so

[ (x+6)(x-6) / 36x² ] / [ (x + 6) / 6x ] 


[ (x+6)(x-6) / 36x² ] * [ 6x / (x + 6) ] 


6x / 36x² = 1 / 6x 


[ (x+6)(x-6) / 6x ] * [ 1 / (x+6) ] -------------------- > </span>(x - 6) / 6x<span>

The answer is </span>(x - 6) / 6x<span>

</span>
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Find three consecutive EVEN integers such that the sum of the smallest number and twice the middle number is 20 more than the la
nordsb [41]

define the 3 numbers

smallest number = x

middle number = x + 2

largest number = x + 4

write the equation

sum of the smallest number and twice the middle number

\begin{gathered} x+2(x+2) \\ x+2x+4 \\ 3x+4 \end{gathered}

20 more than the largest number

\begin{gathered} x+4+20 \\ x+24 \end{gathered}

equal the expressions

\begin{gathered} 3x+4=x+24 \\ 3x-x=24-4 \\ 2x=20 \\ x=\frac{20}{2} \\ x=10 \end{gathered}

the numbers should be 10, 12 and 14

\begin{gathered} 10+2\cdot(12)=14+20 \\ 10+24=34 \\ 34=34 \end{gathered}

5 0
1 year ago
Caitlin is designing a railing for a set of stairs. The railing will begin at a height of 36 inches and follow the slant of the
ollegr [7]

The function which can represent the height, y according to the horizontal distance, x is; Choice A; y = –3/4x + 36.

Which function can represent the height, y, according to the horizontal distance x, from the top of the stairs?

According to the task content; The railing will begin at a height of 36 inches and follow the slant of the stairs. On this note, it follows that the y-intercept of the function is 36.

Additionally, since the railings decreases 9 inches for every 12 horizontal inches, it follows that the slope, m = -9/12 = -3/4.

On this note, the required function is; A.y = –3/4x + 36

Read more on linear function;

brainly.com/question/15602982

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4 0
2 years ago
Given: angle 3 and angle 5 are supplementary Prove: Line l is parallel to line m
HACTEHA [7]
Since line l and line m are cut by the transversal and angle 3 and 5 are supplementary, that means they are consecutive interior angles which proves that the two lines are parallel.
6 0
3 years ago
Plz plz plz help asap!!!
liubo4ka [24]

Answer:

Drinks= $3.50 popcorn=$4.25

Step-by-step explanation:

Let medium popcorn=m

Let drinks= d

Equation 1: m+3d=14.75

Equation 2: 2m+5d=26

Solve simultaneous equation

Multiply Equation 1 by 2 and compare to find d

Substitute d into equation 2 to find price of medium popcorn

8 0
3 years ago
Solve |1-4x| &gt; 7<br> (x-1.5 (xlx &lt; -1.5 UX&gt;1.5)<br> (xx&lt;-1.5 UX &gt; 2)
Setler [38]

If 1-4x\ge0, then by definition of absolute value

|1-4x| = 1-4x > 7 \implies 4x < -6 \implies x < -\dfrac32

On the other hand, if 1-4x, then

|1-4x| = -(1-4x) = -1 + 4x > 7 \implies 4x > 8 \implies x > 2

So, the overall solution to the inequality is interval union

\left(x < -\dfrac32\right) \cup (x > 2)

3 0
2 years ago
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