Scrat the squirrel has a few nuts. When he put them in groups of 5 nuts, two nuts were left, and
when he laid them out in groups of 3 nuts, there were no nuts left. How many nuts among the
options provided below could belong to Scrat?​

Answers

Answer 1

Answer:

The options are not shown, so i will solve this in a general way.

Let's suppose that there are N nuts

If we divide the N nuts into groups of 5, there will be a remainder of 2 nuts.

If we divide the N nuts into groups of 3, there is no remainder.

This means taht N is a multiple of 3. then we can write:

N = 3*k

where k is a random integer.

Now, we know that when we divide N by 5, there is a remainder of 2 nuts, this means that N is equal to a multiple of 5 plus 2, then we can write:

N = 5*j + 2

where j is a random integer.

Now we only need to find a pair of k and j (both positive integers) such that:

3*k = 5*j + 2

We can rewrite this as:

k = (5/3)*j + (2/3)

Now we could just input different values of j, and see if k is also an integer:

j = 2

k = (5/3)*2 + 2/3 = 10/3 + 2/3 = 12/3 = 4

Then the pair j = 2, k = 4 is a possible solution.

N = 3*k = 3*4 = 12

N = 5*j + 2 = 5*2 + 2 = 12

From this we can conclude that N = 12, so Scrat has 12 nuts.

Now with the equation

k = (5/3)*j + (2/3)

We can find other possible combinations of j and k, that will give different values for N.

for example, if j = 5:

k = (5/3)*5 + 2/3 = 25/3 + 2/3 = 27/3 = 9

Then the pair j = 5, k = 9 is also a possible solution:

N = 3*k = 3*9 =  27

N = 5*j + 2 = 5*5 + 2 = 27

In this case, Scrat has 27 nuts.


Related Questions

What is the measure of angle L?

What is the length of JL?

What is the length of KL?
Please help

Answers

Answer:

53

Step-by-step explanation:

[tex]K+J+L = 180\\90 + 37 + L = 180\\L = 53[/tex]

Name the factors in each of the following problems

Answers

Ok sure, lol.
Can’t see anything

Malik has two pencils. He has four blue pencils and 2 red pencils. What is the radio of red pencils and blue pencils?

Answers

Answer: 2:4 or 1:2

You could also write it in a fraction 1/2

Answer:

2:4

Step-by-step explanation:

We know that Malik has 4 blue pencils and 2 red pencils. Therefore, the ratio of red pencils to blue pencils is 2:4.

# of red pencils : # of blue pencils

2 red pencils : 4 blue pencils

2:4

I hope this helps!

What is 5-2(4a+1)+3a=13

Answers

Step-by-step explanation:

5-2(4a+1)+3a=13

5(4a+1)-2(4a+1)+3a=13

20a+5-8a-2+3a=13

20a-8a+3a+5-2=13

15a-3=13

15a=13+3

a=16

15

hope it helps.

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.
y=-16x^2+116x+75

Answers

Answer:

7.85

Step-by-step explanation:

the other guy is incorrect,

The 12 students in the Environmental Club represent 20% of the students in the seventh grade. How many students are in the seventh grade?

Answers

The students that are in the seventh grade is 60.

How to calculate the number of students?

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

Let the students that are in the seventh grade be x.

Since 12 students in the Environmental Club represent 20% of the students in the seventh grade. This will be:

20% × x = 12

0.2x = 12

Divide

x = 12 / 0.2

x = 60

Therefore, there are 60 students.

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what is the distance, in units, between the y-intercept of f(x) = x^2 +7x - 18 and the y-intercept of the linear function that passes through the points shown on the table below
x g(x)
-5 2
10 11
25 20
60 41

Answers

Answer:

13

Step-by-step explanation:

f(x) = x² +7x - 18

y interception: x=0  y = -18    (0 , -18)

line g(x):  --- the data of (60,47) to make a linear function

y = mx + b

m = (11-2) / (10 - -5) = 9/15 = 0.6

b = mx - y = 0.6 * (-5) - 2 = - 5  ... y intercept: (0 , -5)

distance between 2 y intercept: 18-5 = 13

y = 0.6x - 5

Answer:

23

Step-by-step explanation:

f(x) (y intercept ) = -18

g(x) (y intercept) = 5

difference so f(x)-g(x)

-18-5 = -23

the answer cannot be negative

Movie tickets cost $6 for adults and $2 for children under the age of 12. If 175 movie tickets were sold with cash receipts of $750, how many children’s tickets were sold?

Answers

Answer:

75 child tickets and 100 adult tickets were sold.

Step-by-step explanation:

Given that adult tickets cost $ 6 and children's tickets cost $ 2, knowing that 175 tickets were sold for $ 750, to determine how many child tickets were sold the following calculation must be performed:

2 x 175 = 350

750 - 350 = 400

6 - 2 = 4

400/4 = 100

175 - 100 = 75

100 x 6 = 600

75 x 2 = 150

Therefore, 75 child tickets and 100 adult tickets were sold.

Solve 3b – 8 + 6 = 2(b + 6)

Answers

Answer:

b=14

Step-by-step explanation:

3b-2=2b+12

b-2=12

b=14

What is the equation of line m

Answers

Answer:

so I dont know what you mean by that

Step-by-step explanation:

there is no way for anyone to tell sorry

Write the equation of the line that passes through the point 2,-1 and has a slope of -3

Answers

Answer:

-3

Step-by-step explanation:

-3 is your answer

What is n2+5 If n=5?

Answers

Is that cube or n just multiply to 2?

Answer:

15

Step-by-step explanation:

n is 5 so 5 times 2 equals 10 and plus 5 it equal 15

You paint four walls. Each wall is a rectangle with a length of 18 feet and a height of 12 feet. One gallon of paint covers about 320 square feet. How many gallons of paint do you need in order to cover the walls?

Answers

Answer:

you will need exactly 2.7 gallons of paint but if rounded you'll need 3 gallons

Step-by-step explanation:

A quadratic function models the graph of a parabola. The quadratic functions, y = x2 and y = x2 + 3, are modeled in the graphs of the parabolas shown below. Determine which situations best represent the scenario shown in the graph of the quadratic functions, y = x2 and y = x2 + 3. Select all that apply. From x = -2 to x = 0, the average rate of change for both functions is negative For the quadratic function, y = x2, the coordinate (2, 3) is a solution to the equation of the function. The quadratic function, y = x2 + 3, has an x-intercept at the origin The quadratic function, y = x2, has an x-intercept at the origin From x = -2 to x = 0, the average rate of change for both functions is positive For the quadratic function, y = x2 + 3, the coordinate (2, 7) is a solution to the equation of the function.

Answers

Answer:

Step-by-step explanation:

From x = -2 to x = 0, the average rate of change for both functions is negative

The quadratic function, y = x2, has an x-intercept at the origin

For the quadratic function, y = x2 + 3, the coordinate (2, 7) is a solution to the equation of the function.

those 3 are good

The quadratic function, y = x², has an x-intercept at the origin is, TRUE

And, The quadratic function, y = x² + 3, has an x-intercept at the origin is, FALSE

From x = -2 to x = 0, the average rate of change for both functions is positive is, FALSE

What is mean by Function?

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Now, We have;

When viewing a graph, you start from the left and go to right and from left to right from -2 to 0 the graph is declining.

Hence, From x = -2 to x = 0, the average rate of change for both functions is negative is true.

And, Both are declining if you read the graph from left to right.

For the quadratic function, y = x², the coordinate (2, 3) is a solution to the equation of the function is false.

y = x²

If we insert 2 into y = x² we get y = 4 but our point (2, 3) has y = 3

For the quadratic function, y = x² + 3, the coordinate (2, 7) is a solution to the equation of the function is true.

If we insert 2 for x, we see that;

⇒  y = x² + 3

⇒  y = 2² + 3

⇒  y = 7

And, our y value in the point (2, 7) is 7.

Learn more about the function visit:

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if 50% is 30 what is 75%​

Answers

the correct answer would be 45

That answer is 45 ask Siri

Can someone tell me how to do a transversal angle measurement with steps and angles

Answers

Answer:

Sorry I am not sure but when I figure it out..... I prolly won't

Step-by-step explanation:

Answer:

 

When two lines are cut by a transversal, the pairs of angles on one side of the transversal and inside the two lines are called the consecutive interior angles . If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary

Step-by-step explanation:

If you are good at math please dm me on ig 14lies, or twitt binderelluh1

Answers

Answer:

Okay

Step-by-step explanation:

Pythagorean Theorem Quiz.
1.) Find the unknown side length. Simplify answers that are radicals.
4
3
2.) Find the unknown side length. Simplify answers that are radicals.
16
12

Answers

Answer:

1.) 5              2.) 10.58

Step-by-step explanation:

For each one, you use the equation a^2 + b^2 = c^2 where c is the "hypotenuse"-- the side of the triangle opposite (facing) the right angle which is shown with a small box. The variables a and b do not matter, as long as they are the "legs", the other 2 sides.

So it is 4^2 + 3^2 = c^2 which simplifies to 16+9=25=c^2 and square root both sides and you get c=5

and 12^2 + b^2 = 16^2 which simplifies to 144+ b^2 = 256 and subtract 144 from both sides and you get b^2 = 112 and square root both sides and it is approximately 10.6 :)

Which of the following is the correct quotient identity?​

Answers

Answer:

no.c is ther your answer

3(2(8-2x4)+25divided by 5 )-(2(8 divided by 4x2)-7(7-2x3)

Answers

Answer: 3(2(8-2x4)+25divided by 5 )-(2(8 divided by 4x2)-7(7-2x3

The answer is 14

It’s in the picture please and thank you ^*

Answers

Answer:

38 degrees

Step-by-step explanation:

3x+2x+15+95+60=360

the sum of the angles of a quadrileteral=360

5x+170=360

5x=360-170

5x=190

x=190/5

x=38 degrees

find the slope thanks PLEASE ​

Answers

Answer:

37) -1/3

38) 8/5

39) 0

40) -2/3

Step-by-step explanation:

Please help.. Please. Is this a positive trend or negative trend or no trend ​

Answers

Answer:

it's a no trend cause its literally nothing but dots

please anwser this for me!!

Answers

Answer:

No

Step-by-step explanation:

The relation given as represented by the table of values is definitely not a function. This is because, 1 domain value (x-value), is having two range values (y-values), 2 and 5, that are assigned to it.

A function cannot have two y-values assigned to one x-values.

i need help with this!! i have to get my hw done quick!!

Answers

Step-by-step explanation:

221+w=274..................

.......

Answer:

53 + 221 = 274

Step-by-step explanation:

I'm pretty sure its saying

w + 221 = 274

and in this case, w = 53

because if you subtract 274 by 221 you get 53.

Best of luck to you!!!

PLEASE ANSWER ASAP!
2(h -3.5) = -11
what is h?

Answers

Answer: -2

Step-by-step explanation:

2(h -3.5) = -11 Distributive property

2h - 7 = -11. Add 7 to both sides

2h = -4. Divide both sides by 2

h = -2

Answer: The answer is -2 :)

Step-by-step explanation: 2(h -3.5) = -11  distributive propert

2h-7=-11 Add  -7 to both side

     +7  =+7

2h=-4 Divide 2 to both side

2  =  2

h=-2

Jackson has twice as many cards as his friends Alex and Chase combined. Alex has 55 Cards in his collection. Jackson Has 200 cards in his collection. How many cards does Chase have in his collection?

Answers

Answer:

45

Step-by-step explanation:

200 divided by 2 = 100-55=45

Answer:

45

Step-by-step explanation:

200-55=145

Since Jackson has twice as many as them combined, he would have 45.

Need help will give 15 points!!

Answers

Answer:cool

Step-by-step explanation:

In the 2006 season, Tom Brady threw for 3,529
yards. In the 2007 season, he threw for 2,806
yards. What is the percentage decrease

Answers

20.4873901955% decrease
3529-2806=723
(723/35290)x100= 20.4873901955

First, work out the difference (decrease) between the two numbers you are comparing. Next, divide the decrease by the original number and multiply the answer by 100. If the answer is a negative number, this is a percentage increase.

Answer:

59.02%

Step-by-step explanation:

SO SORRY THAT THIS IS LATE anyway what you is minus the biggest number by the smallest number which would be 3,529 - 2,806 = 723

BECAUSE 3,529 is the original number you would do 723 / 3,529 = 0.5902521

then you would times that number by 100

0.5902521 x 100 = 59.02%

hope this helps

What is the common ratio of the sequence?
-2, 6, -18, 54....
-3
-2
3
8

Answers

Answer:

-6/-2=-18/-6=54/-18

=3

Answer: A. -3

Step-by-step explanation: -3 is the correct answer. -2x-3=6, 6x-3=-18,

-18x-3=54

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