MATHEMATICS
HIGH SCHOOL

Answer: 3 - 3,6,9,12,15,18,21,24,27,30,33,36,39

7 - 7,14,21,28,35

So there are17 integers

*note - 21 won't be counted twice

7 - 7,14,21,28,35

So there are17 integers

*note - 21 won't be counted twice

HIGH SCHOOL

18. Jack played three instruments in the orchestra. He played violin for two years, cello for three

years, and bass for three years. He never

played more than two instruments during the

same year. The first year, Jack played only

the violin.

What is the least number of years Jack could

have played in the orchestra?

F. 4

G. 5

H. 6

J. 7

K. 8

The least number of years Jack could have played in the orchestra is G. 5.

MIDDLE SCHOOL

Solve the following 3 × 3 system. Enter the coordinates of the solution below. 2x – 3y – 2z = 4

x + 3y + 2z = –7

–4x – 4y – 2z = 10

The system of equations is

2x - 3y - 2z = 4 (1)

x + 3y + 2z = -7 (2)

-4x - 4y - 2z = 10 (3)

There are many methods for solving the system of equations, including matrix methods. I shall use basic algebraic methods.

Subtract (3) from (1).

6x + y = -6 (4)

Add (2) and (3).

-3x - y = 3 (5)

Add (4) and (5).

3x = -3

x = -1

From (4), obtain

y = -6 - 6x

= -6 +6

= 0

From (2), obtain

2z = -7 - x - 3y

= -7 + 1

= -6

z = -3

Answer: (-1, 0, -3)

The solution is x = -1, y = 0, z = -3.

2x - 3y - 2z = 4 (1)

x + 3y + 2z = -7 (2)

-4x - 4y - 2z = 10 (3)

There are many methods for solving the system of equations, including matrix methods. I shall use basic algebraic methods.

Subtract (3) from (1).

6x + y = -6 (4)

Add (2) and (3).

-3x - y = 3 (5)

Add (4) and (5).

3x = -3

x = -1

From (4), obtain

y = -6 - 6x

= -6 +6

= 0

From (2), obtain

2z = -7 - x - 3y

= -7 + 1

= -6

z = -3

Answer: (-1, 0, -3)

The solution is x = -1, y = 0, z = -3.

Answer: -1, 0,-3

Step-by-step explanation:

MIDDLE SCHOOL

What is 5/8 divided by 4? what is that answer divided by 4?

then what is that answer divided by 4?

1. 5/32

2. 5/128

3. 5/512

2. 5/128

3. 5/512

5/8 divided by 4 is 5/32

answer divided by 4 is 5/128

answer divided by 4 is 5/512

answer divided by 4 is 5/128

answer divided by 4 is 5/512

MIDDLE SCHOOL

What’s the probability of P(T)?

Not enough to information provided

HIGH SCHOOL

Determine the truth value of the given conditional statement. Given: If 3 is an even number, then 5 + 3 = 8.

Answer:

False

Step-by-step explanation:

False, because 3 can not be an even number; it's an odd number. So the condition cannot be satisfied.

MIDDLE SCHOOL

What is (1.2 x 10^-2) x (3 x 10^5) A. 3.6 x 10^-4

B. 3.6 x 10^3

C. 3.6 x 10^4

D. 3.6 x 10^-3

Answer:

B. 3.6 x 10^3

Step-by-step explanation:

(1.2 x 10^-2) x (3 x 10^5)

When we multiply terms with powers , we multiply the factors out front and add the exponents

a * 10^b * c* 10^d = ac * 10^(b+d)

(1.2 x 10^-2) x (3 x 10^5) = (1.2* 3) * 10^(-2+5)

= 3.6 * 10 ^3

MIDDLE SCHOOL

Which of the following describes the solution set for |-4+5x|=16? A{4}. B{4, -4}. C {4, -12/5}. D{-12/5}

Answer:

C: {4, -12/5}

Step-by-step explanation:

Let's actually solve |-4+5x|=16: Divide all 3 terms by 5. Then: |-4/5 + x| = 16/5.

If we were to graph this, the center (on a number line) would be at -4/5. Now if we add 16/5 to -4/5, we get 12/5, the larger solution; if we subtract 16/5 from -4/5, we get -20/5, the smaller solution, equivalent to -4. Correct answer choice is C.

COLLEGE

Marta has $840 in her savings account. She earns $15 per hour working at a food truck and puts all of her earnings into the bank savings account. Marta is saving up for a trip to Washington DC that costs $2650. Write an inequality representing her money saved that Marta could use to determine how many hours she must work in order to afford her trip. Assume she makes no withdrawals, and only deposits money from her job. Define the variable. (3 points) Solve the inequality to determine how many hours she must work in order to go on the trip to Washington DC. Show your work. What does your answer mean? (3 points)

Let h = the number of hours Marta works

Her savings in her account can be calculated by:

840 + 15h

This needs to be at least $2650 for her trip, so an inequality to solve:

840 + 15h ≥ 2650, where h is the number of hours worked

Now solve:

15h ≥ 1810

h ≥ 1810/15

h ≥

Marta needs to work at least hours in order to have enough money for her trip.

Answer:

120 2/3 will be the answer

HIGH SCHOOL

Write the prime factorization of 2025 using exponents.

Answer:ED2

44444444444

DStep-by-step explanation: