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3 years ago

Which equation represents the function graphed on the

Mathematics

1 answer:

puteri [66]3 years ago

6 0

Answer:

it is the third option of g(x)=|x-1|+3x-1

the way I look at this is by visualizing the translations using the parent function of f(x)=|x|

the function moved up three and to the right by one which led to my conclusion

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Hannah read a total of 798 pages over 6 hours. After a total of 36 hours of reading this week, how many pages will Hannah have r

Vika [28.1K]

Answer: 4788 pages

Step-by-step explanation:

798/6 hours

798 divided by 6 equals 133. Meaning Hannah read 133 pages in 1 hour. So divide the unit rate by 36. 133 x 36 = 4788 pages in 36 hours.

6 0

3 years ago

Use induction to prove: For every integer n > 1, the number n5 - n is a multiple of 5.

nignag [31]

Answer:

we need to prove : for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

1) check divisibility for n=1, $f(1)=(1)^{5}-1=0$ (divisible)

2) Assume that $f(k)$ is divisible by 5, $f(k)=(k)^{5}-k$

3) Induction,

$f(k+1)=(k+1)^{5}-(k+1)$

$=(k^{5}+5k^{4}+10k^{3}+10k^{2}+5k+1)-k-1$

$=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k$

Now, $f(k+1)-f(k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-(k^{5}-k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-k^{5}+k$

$f(k+1)-f(k)=5k^{4}+10k^{3}+10k^{2}+5k$

Take out the common factor,

$f(k+1)-f(k)=5(k^{4}+2k^{3}+2k^{2}+k)$ (divisible by 5)

add both the sides by f(k)

$f(k+1)=f(k)+5(k^{4}+2k^{3}+2k^{2}+k)$

We have proved that difference between $f(k+1)$ and $f(k)$ is divisible by 5.

so, our assumption in step 2 is correct.

Since $f(k)$ is divisible by 5, then $f(k+1)$ must be divisible by 5 since we are taking the sum of 2 terms that are divisible by 5.

Therefore, for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

3 0

3 years ago

In the equation c*2=22 what is the next step in the equation solving sequence?

romanna [79]

Divide 22 by 2 to get "c" isolated.

3 0

3 years ago

The sum of two numbers is at most 12, and the sum of 3 times the first number and 8 times the second number is at least 48 selec

Sever21 [200]

Answer:

(4,8)

Step-by-step explanation:

4 + 8 = 12

3(4) + 8(8)

= 12 + 64

= 76

6 0

2 years ago

If the graph of the equation y=(x+2)^2 is reflected with respect to the y-axis, what is the equation of the resulting graph?

alexandr1967 [171]

Answer:

Is important to remember that the reflection of the point (a,b) across the y-axis is the point (-a,b).

Our original equation is $y= (x+2)^2$

And after the reflection respect x we got:

$y= (-x+2)^2$

Step-by-step explanation:

Is important to remember that the reflection of the point (a,b) across the y-axis is the point (-a,b).

Our original equation is $y= (x+2)^2$

And after the reflection respect x we got:

$y= (-x+2)^2$

7 0

3 years ago