MATHEMATICS
HIGH SCHOOL

Answer: Because x,y,z form a geometric sequence, therefore the common ratio is

r = y/x = z/y

That is,

y² = xz (1)

We are given:

x + y + z = 18

Therefore

x + z = 18 - y (2)

Also,

x² + y² + z² = 612

Therefore, from (1), obtain

x² + z² + xz = 612

(x + z)² - xz = 612

From (1) and (2), obtain

(18 - y)² - y² = 612

324 - 36y + y² - y² = 612

-36y = 288

y = -8

Answer: y = -8

r = y/x = z/y

That is,

y² = xz (1)

We are given:

x + y + z = 18

Therefore

x + z = 18 - y (2)

Also,

x² + y² + z² = 612

Therefore, from (1), obtain

x² + z² + xz = 612

(x + z)² - xz = 612

From (1) and (2), obtain

(18 - y)² - y² = 612

324 - 36y + y² - y² = 612

-36y = 288

y = -8

Answer: y = -8

HIGH SCHOOL

What is the value of s – 11.5 when s = –4.6

So you put -4.6 in where s is:

-4.6-11.5

Then I see that your subtracting so its going to be an even smaller negative solution:

-4.6-11.5=-16.1

You can check by taking -16.1 and adding 11.5 you get s which is -4.6

:D

HIGH SCHOOL

An art store offers prints in two sizes. The store earns $15 on each small print sold and $25 on each large print sold. The owner needs to make a daily profit of at least $700 in order to cover costs. Due to equipment limitations, the number of small prints made must be more than three times the number of large prints. Given that x represents the number of small prints sold and y represents the number of large prints sold, determine which inequalities represent the constraints for this situation. x + y ≤ 60 15x + 25y < 700 x > 3y 15x + 25y ≥ 700 y > 3x x + 3y ≥ 60 Which combinations of small prints and large prints satisfy this system? (45,10) (35,15) (30,10) (40,5)

The inequalities are x>3y, 15x+25y≥700 (or 3x+5y≥140).

These are satisfied by (45,10) and (40,5).

These are satisfied by (45,10) and (40,5).

COLLEGE

When given Three points on a coordinate plane, you may be able to find a specific Quadratic equation that intersects all given points. true or false?

Answer:

TRUE

Step-by-step explanation:

A quadratic equation can be found that will go through any three distinct points that ...

- satisfy the requirements for a function
- are not on the same line

_____

The key word here is "may." You will not be able to find a quadratic intersecting the three points if they do not meet both requirements above.

COLLEGE

You want to place a towel bar that is 24 1⁄4 centimeters long in the center of a door that is 70 1⁄3 centimeters wide. How far should you place the bar from each edge of the door?

Answer:

You should place it 23 1/24 centimeters from each edge.

Step-by-step explanation:

The towel bar will be in the center in the door so the space between the edge of the door and each side of the bar is equal in the left and the right of the door. So lets define:

x: distance between edge of door and the towel bar edge.

We see that x is the distance left in both sides of the towel bar from the door so:

x+24 (1/4) +x = 70 (1/3)

2x + 24 (1/4) = 70 (1/3)

2x= 70 (1/3) - 24 (1/4)

To operate the fractions , we need a common denominator that can be obtained simply by multiplying both denominators 4* 3=12

We then subtract the whole numbers and fractions

2x= 70 (4/12) - 24 (3/12) = =( 46 1/12)

x= ( 46 1/12) / 2 = 23 (1/24)

Subtract the width of the towel bar from the width of the door and divide by 2.

70 1/3

- 24 1/4

--------------

You need a common denominator to subtract the fractions. The LCD is 12,so we can rewrite the subtraction using the LCD.

70 4/12

- 24 3/12

--------------

46 1/12

Now you need to divide 46 1/12 by 2.

46/2 = 23

(1/12) / 2 = 1/24

The answer is 23 1/24 cm

70 1/3

- 24 1/4

--------------

You need a common denominator to subtract the fractions. The LCD is 12,so we can rewrite the subtraction using the LCD.

70 4/12

- 24 3/12

--------------

46 1/12

Now you need to divide 46 1/12 by 2.

46/2 = 23

(1/12) / 2 = 1/24

The answer is 23 1/24 cm

HIGH SCHOOL

Susan sells computer systems. Her annual base salary is $34,000. She also earns a com- mission of 1.2% on the sale price of all computer systems that she sells. For what value of the com- puter systems sold will Susan's annual salary be at least $100,000?

Answer:

Susan needs to sell 5.5 million dollars worth

Step-by-step explanation:

In order to find that, we first need to find how much she made in commissions. We can find this by subtracting the base by the goal salary.

100,000 - 34,000 = 66,000

Since she needs to make $66,000 in commissions and gets 1.2%, we can find the amount she needs to sell by dividing the total by the percentage.

66,000/.012 = 5,500,000

MIDDLE SCHOOL

Original price - $82. Percent of discount-?? Sale price - $65.60

The original price was $82.

-- The dealer knocked ($82 - $65.60) = $16.40 off of the price because

he loves his customers so much and he wanted to make their lives easier.

-- The amount he knocked off is ( 16.40 / 82 ) = 0.2 = 20% of the original price.

==========================================

Check:

If he reduced the original price 20%, then 80% of it must have been left.

80% of the original price = 0.8 x $82 = $65.60

I hoped i help :)

-- The dealer knocked ($82 - $65.60) = $16.40 off of the price because

he loves his customers so much and he wanted to make their lives easier.

-- The amount he knocked off is ( 16.40 / 82 ) = 0.2 = 20% of the original price.

==========================================

Check:

If he reduced the original price 20%, then 80% of it must have been left.

80% of the original price = 0.8 x $82 = $65.60

I hoped i help :)

HIGH SCHOOL

All of the counting numbers (only count positive)

no fractions or decimals

Natural Numbers (counting numbers) is the answer

Answer:

Natural numbers

Step-by-step explanation:

MIDDLE SCHOOL

Division of whole numbers

You have to see if there is any common factors that can go into both.

Then you divide the smallest whole number into the bigger whole number. Finally you get your Answer

Then you divide the smallest whole number into the bigger whole number. Finally you get your Answer

Answer:

The number 24 is called the dividend ('that which is to be divided'). The number 8 is called the divisor ('that which divides'). The number 3 is called the quotient, (from the Latin quotiens meaning 'how many times'). Division without remainder can be visualized as skip-counting.

HIGH SCHOOL

Giselle works as a carpenter and as a blacksmith. She earns $ 2 0 $20dollar sign, 20 per hour as a carpenter and $ 2 5 $25dollar sign, 25 per hour as a blacksmith. Last week, Giselle worked both jobs for a total of 3 0 3030 hours, and earned a total of $ 6 9 0 $690dollar sign, 690. How long did Giselle work as a carpenter last week, and how long did she work as a blacksmith?

Answer: Carpenter:12 and Blacksmith: 18

Step-by-step explanation: Checked on khan

She worked as a carpenter for 12 hours and as a blacksmith for 18 hours.

Assuming you mean she earned $20 as a carpenter and $25 as a blacksmith per hour, with a total of 30 hours for $690,

let c represent carpenter hours and b for blacksmith hours.

20c + 25b = 690

c + b = 30

Subtract b from each side so that c = 30 - b

Plug this value into the first equation

20(30 - b) + 25b = 690

600 - 20b + 25b = 690

600 + 5b = 690

5b = 90

b = 18

To find c, plug this value of b into the other equation

c + 18 = 30

c = 12

Assuming you mean she earned $20 as a carpenter and $25 as a blacksmith per hour, with a total of 30 hours for $690,

let c represent carpenter hours and b for blacksmith hours.

20c + 25b = 690

c + b = 30

Subtract b from each side so that c = 30 - b

Plug this value into the first equation

20(30 - b) + 25b = 690

600 - 20b + 25b = 690

600 + 5b = 690

5b = 90

b = 18

To find c, plug this value of b into the other equation

c + 18 = 30

c = 12