MATHEMATICS
HIGH SCHOOL

Answer: Scale factor = 9.5 / 7

the ratio of the volumes will be 9.5^3 / 7^3

= 2.5 to nearest thousandth

So the volume the regulation ball is 2.5 times the volume of the junior one.

the ratio of the volumes will be 9.5^3 / 7^3

= 2.5 to nearest thousandth

So the volume the regulation ball is 2.5 times the volume of the junior one.

MIDDLE SCHOOL

what must be subtracted from 4x4 - 2x3 - 6x2 + x - 5 so that the answer is exactly divisible by x + x - 2

To solve this problem, what we have to do is to divide the whole equation 4 x^4 – 2 x^3 – 6 x^2 + x – 5 with the equation 2 x^2 + x – 1. Whatever remainder we get must be the value that we have to subtract from the main equation 4 x^4 – 2 x^3 – 6 x^2 + x – 5 for it to be exactly divisible by 2 x^2 + x – 1.

By using any method, I used long division we get a remainder of -6.

Therefore we have to subtract -6 from the main equation which results in:

4 x^4 – 2 x^3 – 6 x^2 + x – 5 – (-6) = 4 x^4 – 2 x^3 – 6 x^2 + x + 1

MIDDLE SCHOOL

What is y-2=-2.5(x-1) in STANDARD FORM? (It has to be in Ax+By=C form)

Y-2=-2.5(x-1)

Y-2=-2.5x+2.5

2.5x+y=4.5

Y-2=-2.5x+2.5

2.5x+y=4.5

COLLEGE

Make a conjecture about the sum of the first 15 positive even number

I conclude that the sum will be even because any even number can be represented by 2n where n is a whole number

and even numbers are 2 apart, so

the sum of the first 15 are

2n+2(n+1)+2(n+2) etc until we get to 2(n+14)

we can undistribute the 2 from all of them and get

2(n+n+1+n+2...n+14)

and we are sure that whatever is in the parenthasees is a whole number because whole+whole=whole

therefor, the sum is even

if you did want to find the sum then

an=2n

the 15th even number is 30

the first is 2

S15=15(2+30)/2=15(32)/2=15(16)=240

which is even

and even numbers are 2 apart, so

the sum of the first 15 are

2n+2(n+1)+2(n+2) etc until we get to 2(n+14)

we can undistribute the 2 from all of them and get

2(n+n+1+n+2...n+14)

and we are sure that whatever is in the parenthasees is a whole number because whole+whole=whole

therefor, the sum is even

if you did want to find the sum then

an=2n

the 15th even number is 30

the first is 2

S15=15(2+30)/2=15(32)/2=15(16)=240

which is even

HIGH SCHOOL

Two arcades have different pricing structures. Arcade A costs $5 to enter and $0.60 per game. Arcade B costs $7 to enter and $0.40 per game. How many games do you have to play in order for the two arcades to be the same price?

Answer:

you would have to play 10 games

Answer:

10 games

Step-by-step explanation:

Let C be cost and x be number of games

Arcade A: C = 5 + 0.6x

Arcade B: C = 7 + 0.4x

for both arcades to be the same price, Both C's must be equal, hence we equate the right side of both equations:

5 + 0.6x = 7 + 0.4x (subtract 5 fromboth sides)

0.6x = 7 + 0.4x - 5

0.6x = 2 + 0.4x (subtract 0.4x from both sides)

0.6x - 0.4x = 2

0.2x = 2 (divide both sides by 0.2)

x = 2 / (0.2)

x = 10