Not long after he begins to study algebra he will likely meet with the "tank" problems, the "labor" problems and many other puzzle problems. He finds these problems carefully phrased in the language of practical mathematics. However, a study of the original problems and the fanciful way in which they were stated will reveal the fact that they were originally intended mostly for puzzles. The present-day student of algebra would doubtless work as industriously over the so-called practical problems if he were told they were puzzle problems that his predecessors had worked on for the past 1600 years.

The problems given below are selected from a collection made by Metrodorus about 310 A. D. found in The Greek Anthology. It is not known how much farther back they date. It will not be difficult for the reader to trace many of the problems found in the present-day algebras back to their original source. He may judge for himself as to whether the modern text-book writer has improved the problems by leaving off the little fanciful touches of rhetoric, found in the original.

The original problems were solved by rhetorical algebra as our symbols, +, -, ×, ÷, etc., were introduced many centuries later, about 1540.

Answer: The answers are 4x^2(x^2+5x+3), (x–6) (x+2), (x–9), 3(x–7)(x–4), (9x–10) (9x+10), 3(y^2+2)(x^2+4), (5x+2), 2(x–4)(6x+1), 2(x + 4)(y - 4), and the factored form is (3x–4)(x–3).

Step-by-step explanation: To solve all the factoring equations, factor using the AC method or factoring the polynomials, the 3 steps are Grouping: using the sum-product pattern, common factor from the two pairs, and

rewrite the expression in factored form.

Answer:  1 3/4 cups of apples in each batch

Step-by-step explanation:

STEP  1

Writing out the equation to represent if 7 cups of  apples make 4 batches   One batch is as a result of how many  cups of apples

LET x be number of cups of apples to make each batch

7 cups of  apples = 4 Batches

        x cups of apples = 1 Batch

STEP 2  Solving by cross multiplication

1 batch x 7 cups of apples = 4 batches  X x cups of apples

x cups of apples=1 batch x 7 cups of apples / 4batches

x   = 7 / 4 =  1 3/4

number of cups of apples to make each batch=  1 3/4

Answer:

55,32,32,19,8,3

Step-by-step explanation:

Answer:

55,32,32,19,8,3

Step-by-step explanation:

Answer:

the slope is 1/2 to this

Answer:

Each container weigh 10^3pounds

Step-by-step explanation:

The question lacks the necessary values. Let's restructure the question and include values.

Your roommate's closet is full of skeletons. There are containers full of skeletons which weigh 100,000 pounds total. If there are 100 containers, how much does each container weigh? Leave your answer in the form a^b.

From the question, we are given the following;

Weight of containers full of skeleton = 100000 pounds

Number of containers = 100

Required

Weight of each container

Let's say:

100containers = 100000pounds

1 container = xpound

Cross multiply

100×x = 100,000

Divide both sides by 100

100x/100 = 100,000/100

x = 10,000/100

x = 10^5/10^2

Using the law of indices

x = 10^{5-2}

x = 10^3

Hence the answer in form of a^b is 10^3 pounds.

Answer:

$21.25

Step-by-step explanation:

100 - 15 = 85

25 * 0.85 = 21.25

Answer:

I dont like sqaures.

Step-by-step explanation: Their pointy.

Answer:

y=1.75x + 5.00

Step-by-step explanation:

Answer:

(-2, 12)

Step-by-step explanation:

Answer:

the answer would be 20

Step-by-step explanation:

so if 18-(-2)=?

two nwgatives make a positive. So the equation would turn into 18+2=20

Im not 100% if this is right but htis is how I was taught to do it.

Answer:

Answer: B

Step-by-step explanation: y=-1/5x+1/10

Answer:

y = 9(2 - x)/4

Step-by-step explanation:

1.) Subtract 9x from both sides.

4y = 18 - 9x

2.) Divide both sides by 4.

y = 18 - 9x/4

3.) Factor out the common term 9.

y = 9(2 - x)/4

My words:

Hope this helps you and let me know if you need help again, also have a blessed day or night, also could I have brainliest for this?

The y intercept of the equation of the line  4y+9x=18 is 4.5.

For the given question,

The equation of the line is given as;

4y+9x=18

Write the equation in slope intercept form.

y = mx + c

Where, m is the slope and c is the y intercept.

4y = -9x + 18

y = -9x/4 + 9/4

y = -9x/4 + 4.5

Comparing with the standard form, y intercept is found as 4.5.

Thus, the y intercept of the equation of the line  4y+9x=18 is 4.5.

To know more about the y-intercept, here

https://brainly.com/question/25722412

#SPJ2

Answer:

The answer is -1 + 18

Answer:

x=0

Step-by-step explanation:

-8-3x=-8(1-7x)

add 8 to both sides =( -3x=56x)

subtract 56x from both sides (-59x=0)

divide both sides by -59 = (x=0)

Answer:

false

Step-by-step explanation:

Answer:

False, it has no solution if the lines are parallel.

Answer:

38.72%

Step-by-step explanation:

Estimated attendance = 1,000

The actual value of attendance = 1,632

We need to find the percent error of Shaun's estimate. Using the formula as follows :

[tex]\%=\dfrac{|\text{actual value-estimated value}|}{\text{actual value}}\times 100[/tex]

Put all the values,

[tex]\%=\dfrac{1632-1000}{1632}\times 100\\\\=38.72\%[/tex]

So, the percent error of Shaun's estimate is 38.72%.

Answer:

c

Step-by-step explanation:

Answer:

D. -6/13

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step one:

Given data

Danica's goal is to save $1500

her pay is $180 weekly.

the duration is 6months

in a month we have 4 weeks

in 6months there are 6*4= 24 weeks

Step two:

In 24 weeks Danica's earnings will be 24*180= $4320

nevertheless, she only needs $1500 for the 24 weeks to make the down payment

So per week, she will need to save 1500/24= $62.5

Answer:

g times 15 if it's a algebraic question

g=6

Refer to the explanation for the process.

Explanation:

Solve:

9 g=15 10

Cross multiply each denominator by the opposite numerator.

9×10=15×g

Simplify.

90=15g

Divide both sides by 15

90 15=g

Simplify.

6=g

Switch sides.

g=6

Hope this helps!

Answer:

= 8

Step-by-step explanation:

y is 2 then 8y is 8×2=16

z is,8

8y - z is 16-8

=8

Answer:

$32.75 each ticket

Step-by-step explanation:

131 / 4 = $32.75 each ticket

Answer:

each ticket was $32.75

Step-by-step explanation:

You need to divide 131 by 4.

Answer:

A

Step-by-step explanation:

you were correct because you have to distribute 1st

Answer:

b because if it was c it would be 12 ft the flagpole is 10 ft so 8 ft is right because you need 10

Answer:

Please find a representation of the factor rainbow below.

The missing factors are: 4, 24, and 144

Step-by-step explanation:

The factors of a number are those numbers that can divide another number without remainder. In this case where Katya factored 288, it means she listed the numbers that can divide 288 without reminder (factors of 288). However, among the factors she listed, THREE factors are missing.

To get the missing factors, we can use a FACTOR RAINBOW, which is a display of the factors of a number in a rainbow shape. The factors are arranged from smallest to largest number in such a way that the two numbers attached to a line can be multiplied to give the original number.

From the attached factor rainbow (see attached image), it can be observed that factors:  4, 24, and 144 are missing in the list of factors Katya provided.

Answer:

Step-by-step explanation:42.50

Answer:

5 drinks: $25.00 4 candies: $18.00 Total: $43.00

inn equation form: $5d+$4.5c=?

Step-by-step explanation:

5*5=25

4.5*4=18

25+18=43

Answer:

a)

28000 + 3000·x = 36000 + 2000·x --> x = 8 years

b)

28000 + 3000·8 = $52000

Answer:

Step-by-step explanation:

company A = 28,000 + 3,000 (x)

company B = 36,000 + 2,000 (x)

where x = no. of years.

28,000 + 3,000 (x) = 36,000 + 2000 (x)

3,000 (x) - 2,000 (x) = 36,000 - 28,000

1,000 (x) = 8,000

x = 8,000

     1,000

company A = 28,000 + 3,000 (8)

company B = 36,000 + 2,000 (8)