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3 years ago

6

Fiona's car has 8.5 gallons of gas in a tank her car can travel about 21 miles per gallon does she have enough gas to travel 158

miles

2 answers:

Juliette [100K]3 years ago

6 0

Answer:

yes

Step-by-step explanation:

tamaranim1 [39]3 years ago

3 0

(65 mi/hr)(45 min)(1 hr/60 min) = 48.75 mi (the hours and minutes cancel out)

(48.75 mi / 25 mi/gal) = 1.95 gal

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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.

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A right triangle has a hypotenuse of length 9 inches. If one angle is 35 degrees, find the length of each leg.

Montano1993 [528]

<span>90 + 35 = 125.
180 -125 = 55 degrees.

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3 years ago

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MrRissso [65]

Answer:

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If 2.5cm → 15 km, then

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x= (15km*17.5cm)/(2.5cm)=105 km

Step-by-step explanation:

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