Ask question

Ask question

All categories

4 years ago

11

Helena lost her marbles. But then she found them and put them in 4 bags with m marbles in each bag. She had 3 marbles left over

that didn't fit in the bags.
How many marbles does Helena have in all?

2 answers:

madreJ [45]4 years ago

6 0

She had 4m marbles in the 4 bags

So number of marbles that Helena has = 4m + 3.

arlik [135]4 years ago

6 0

Answer:

Helena has $4m+3$ marbles in all.

Step-by-step explanation:

Let the total number of marbles be denoted by 'm'.

Helena found them and put them in 4 bags with m marbles in each bag.

Total marbles in 4 bags become = $4\times m=4m$

Now, she had 3 marbles left over that didn't fit in the bags.

That gives total marbles as = $4m+3$

<u>We can solve this using an example.</u>

Suppose Helena had 15 marbles in total.

She divides these in 4 bags, $\frac{15}{4}=3$ plus 3 extra.

Now, m = 3

So, putting the value of m as 3 in equation we get,

$4(3)+3$

= $12+3$

= 15

Therefore, we can say that Helena has

$4m+3$ marbles in all.

You might be interested in

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

Katherine went to Hibbet sports and spent $125.50 on a pair of shoes and $12.25

Sergio039 [100]

Answer:

1. $137.75

3. $149.15

Step-by-step explanation:

1.

12.25+125.50=137.75

3. 8.25% of 137.75= 11.4

137.75+11.4=149.15

3 0

3 years ago

Read 2 more answers

What are the solutions of the quadratic equation? 4x^2+34x+60=0

insens350 [35]

Answer:

Option 3) -6,-5/2

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$4x^{2} +34x+60=0$

so

$a=4\\b=34\\c=60$

substitute in the formula

$x=\frac{-34(+/-)\sqrt{34^{2}-4(4)(60)}} {2(4)}$

$x=\frac{-34(+/-)\sqrt{196}} {8}$

$x=\frac{-34(+/-)14} {8}$

$x_1=\frac{-34(+)14} {8}=-\frac{20}{8}=-\frac{5}{2}$

$x_2=\frac{-34(-)14} {8}=-6$

6 0

3 years ago

Pls help! Include the unit.

Bezzdna [24]

She swim 0.85 kilometers

4 0

3 years ago

There are 3,280.84 feet in a kilometer. There are 5,280 feet in a mile. To the nearest hundredth, how many kilometers are in a m

just olya [345]

Answer:

1.609344 kilometers

Step-by-step explanation:

8 0

3 years ago