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1 year ago

5

Travis converted some repeating decimals into fractions as follows based upon what he has seen so far which of the following equ

ations must be correct I'll take a pic to show you

1 answer:

ella [17]1 year ago

4 0

Answer:

$0.\bar{9}=1$

Explanation:

The fractions are formed with a 9 as a denominator and the numerator is the number that repeats. So, following the same rule, we can say that 0.999... is equivalent to:

$0.\bar{9}=\frac{9}{9}$

However, 9/9 is equal to 1, so:

$0.999\ldots=0.\bar{9}=1$

Therefore, the answer is:

$0.\bar{9}=1$

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Hi. I need help with these questions (see image)<br>Please show workings.<br>

pantera1 [17]

Answer:

see explanation

Step-by-step explanation:

Using the chain rule

Given

y = f(g(x)), then

$\frac{dy}{dx}$ = f'(g(x)) × g'(x) ← chain rule

and the standard derivatives

$\frac{d}{dx}$ ( $log_{a}$ x ) = $\frac{1}{xlna}$ , $\frac{d}{dx}$ (lnx) = $\frac{1}{x}$

(a)

Given

y = $log_{a}$ $\sqrt{(1+x)}$

$\frac{dy}{dx}$ = $\frac{1}{lna\sqrt{(1+x)} }$ × $\frac{d}{dx}$ ( $(1+x)^{\frac{1}{2} }$

= $\frac{1}{lna\sqrt{(1+x)} }$ × $\frac{1}{2}$ $(1+x)^{-\frac{1}{2} }$ × $\frac{d}{dx}$ (1 + x)

= $\frac{1}{lna\sqrt{(1+x)} }$ × $\frac{1}{2\sqrt{(1+x)} }$ × 1

= $\frac{1}{2lna(1+x)}$

= $\frac{1}{(1+x)lna^2}$

(b)

Given

y = ln sinx

$\frac{dy}{dx}$ = $\frac{1}{sinx}$ × $\frac{d}{dx}$ (sinx)

= $\frac{1}{sinx}$ × cosx

= $\frac{cosx}{sinx}$

= cotx

5 0

3 years ago

Graph the transformation y=2p(x-3)-4

nadya68 [22]

Y = 2p(x - 3) - 4
y = 2px - 6p - 4

8 0

3 years ago

(6n-7)+(8n+2)=23 HELP FAST PLEASE

nikitadnepr [17]

Answer:

n=2

Step-by-step explanation:

(6n-7)+(8n+2)=23

14n-5=23

14n=28

n=2

3 0

4 years ago

Blake has b baseball cards. His aunt gave him more cards, increasing his total number of cards by 25%. Which expression represen

Naily [24]

Answer:

Blake's total number of cards now: 1.25b

Step-by-step explanation:

Total number of cards now would be equal to 25% increase from b.

<em>This means we INCREASE b by 25% OF b.</em>

<em />

What is 25% of b???

$\frac{25}{100}*b\\=0.25b$

Now we need to ADD this to original amount, b.

So, $b+0.25b=1.25b$

6 0

3 years ago

Please help ASAP thank you.

antiseptic1488 [7]

Answer:

Q10. (1,4)

Q11. No solution

Step-by-step explanation:

Q10. To solve equations by graphing, sketch the graphs of the 2 equations. The point(s) where the two lines intersect is the solution. To sketch straight line graph, find 2 coordinates then join them.

y= -2x +6

When x=0, y= 6

When y=0,

-2x+6=0

2x=6

x=6÷2

x=3

Thus, the 2 coordinates are (0,6) and (3,0).

After plotting these 2, draw a straight line that passes these 2 points. Instead of finding the x and y coordinates, you could also find other points such as when x=5 etc.

y=4x

when y=0,

4x=0

x=0

When x=1,

y=4(1)

y=4

The 2 coordinates are (0,0) and (1,4).

Plot this graph.(1st picture) You should be able to see the point if intersection, and that is the solution.

The solution should be (1,4).

Q11. Like question 10, plot the 2 graphs and see where they intersect.(2nd picture) In this case, you would notice that the two lines does not intersect. Hence, there is no solution.

Further explanation:

This is because the first equation is y= -2x+6 and the second is y= -2(x-6). If you expand the 2nd equation, the equation is y= -2x+12.

The gradient of the two lines are the same, which means that they are parallel and therefore they do not meet.

7 0

4 years ago