MATHEMATICS
HIGH SCHOOL

Answer: V(t) = 2t^2 - 3t - 3

for an acceleration a(t),

a(t) = d (v(t)) / d t

a(t) = 4t - 3

at t=2

a(2) = 8 - 3

a(2) = 5 feet/s^2

for an acceleration a(t),

a(t) = d (v(t)) / d t

a(t) = 4t - 3

at t=2

a(2) = 8 - 3

a(2) = 5 feet/s^2

MIDDLE SCHOOL

Hiring the bus will cost $25 a day for the driver, $2 per mile traveled, and $3 for gas per mile traveled. The field trip will total 8 miles round trip. Mrs. Garcia needs to calculate the cost of the bus. Which expression could she write that uses the distributive property?

Answer:

65

Step-by-step explanation:

25+2x8+3x8

Answer:

25 + 8(2 + 3)

Step-by-step explanation:

HIGH SCHOOL

(2.1.4) The minimum standards for the annual firearms proficiency course of fire for __________shall be a minimum of 30 rounds of duty ammunition fired at a range of at least 50 yards, including at least one timed reload; however, an agency may, in its discretion, allow a range of less than 50 yards but not less than 10 yards if the minimum passing percentage is raised to 90. (Rule 217.21)

Answer: 50, 25

Step-by-step explanation:

MIDDLE SCHOOL

If f(x)=x-3/x and g(x)=5x-4, What is the domain of (f•g)(x)

Answer:

Step-by-step explanation: 3

(f•g)(x) has either the form ( [x - 3] /x)(5x - 4) or the form (x - ------)(5x - 4)

x

Please use parentheses to eliminate any ambiguity.

Focusing on the first possibility:

(f•g)(x) = ( [x - 3] /x)(5x - 4) is defined for all x except x = 0, as we cannot divide by 0.

HIGH SCHOOL

Use mathematical induction to prove the statement is true for all positive integers n. The integer n3 + 2n is divisible by 3 for every positive integer n.

1. prove it is true for n=1

2. assume n=k

3. prove that n=k+1 is true as well

so

1.

=

=

=1

we got a whole number, true

2.

if everything clears, then it is divisble

3.

=

=

=

we know that if z is divisble by 3, then z+3 is divisble b 3

also, 3k/3=a whole number when k= a whole number

=

=

since the k²+k+1 part cleared, it is divisble by 3

we found that it simplified back to

done

2. assume n=k

3. prove that n=k+1 is true as well

so

1.

=

=

=1

we got a whole number, true

2.

if everything clears, then it is divisble

3.

=

=

=

we know that if z is divisble by 3, then z+3 is divisble b 3

also, 3k/3=a whole number when k= a whole number

=

=

since the k²+k+1 part cleared, it is divisble by 3

we found that it simplified back to

done

Answer:

We have to use the mathematical induction to prove the statement is true for all positive integers n.

The integer is divisible by 3 for every positive integer n.

- for n=1

is divisible by 3.

Hence, the statement holds true for n=1.

- Let us assume that the statement holds true for n=k.

i.e. is divisible by 3.---------(2)

- Now we will prove that the statement is true for n=k+1.

i.e. is divisible by 3.

We know that:

and

Hence,

As we know that:

was divisible as by using the second statement.

Also:

is divisible by 3.

Hence, the addition:

is divisible by 3.

Hence, the statement holds true for n=k+1.

Hence by the mathematical induction it is proved that:

The integer is divisible by 3 for every positive integer n.