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.

Answers

Answer 1

Answer:

wow thats some good information there!

Step-by-step explanation:


Related Questions

Secant and Tangent Angles in circles.
Solve for x.

Answers

Answer:

x = 1

Step-by-step explanation:

5x + 17 = 1/2[(73x + 5) - (23x - 5)]

5x + 17 = 1/2[37x + 5 - 23x + 5]

5x + 17 = 1/2[14x + 10]

5x + 17 = 1/2 * 2(7x + 5)

5x + 17 = 7x + 5

5x - 17x = 5 - 17

-12x = - 12

x = - 12/-12

x = 1

A circle is a curve sketched out by a point moving in a plane. The value of x that will make the Secant and Tangent Angles true for the circle is 17/25.

What is a circle?

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

For the given circle, as per the Secant and Tangent Angles theorem, the measure of the angle formed by two tangents can be written as,

∠WVU = (arc WU + arc WU)/2

5x + 17 = [(37x + 5) + (23x - 5)]/2

2(5x + 17) = (37x + 5) + (23x - 5)

10x + 34 = 37x + 5 + 23x - 5

10x - 37x - 23x = 5 - 5 - 34

-50x = -34

x = 34/50

x = 17/25

Hence, the value of x is 17/25.

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For the inequality y < 8 which statement best describes the graph?
There would be a horizontal dotted line on (0,8) and shading would occur below the line.
There would be a horizontal solid line on (0,8) and shading would occur above the line.
There would be a vertical dotted line on (8,0) and shading would occur to the right of the line
There would be a vertical solid line on (8,0) and shading would occur to the left of the line.

Answers

Answer:

There would be a horizontal dotted line on (0,8) and shading would occur below the line.

I just took the test and got it right :) hope this helps!

For the given inequality, the best describes the graph is that there would be a horizontal-dotted line on the point (0, 8) and shading occurred below the line. Hence, option A is correct.

What is a graph?

In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.

Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.

When the is made, there is the shaded area provided that is made due to intersection of lines and the area below the both the lines and the common that is said to be the shaded area.

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can someone please simplify this? :)
9x(8 * 9y) + 4

Answers

Answer:

648xy+4

Step-by-step explanation:

9x*72y + 4 = 648xy+4

The last time Aiden played baseball, he hit the ball 35% of the times he was at bat. Based on this information, how many times will Aiden hit the ball the next time he plays baseball if he is at bat 20 times?

Answers

Answer:

the number of times  will Aiden hit the ball is 7

Step-by-step explanation:

The computation of the number of times will Aiden hit the ball is shown below:

She hit 35% of the times

i.e.

= Given percentage of number of times

= 35% of 20

= 35 ÷ 100 × 20

= 0.35 × 20

= 7

Hence, the number of times  will Aiden hit the ball is 7

We simply applied the above formula so that the correct value could come

The same is to be considered

if g(x)=3x-1 and if g(x)=7, then which of the following is the value of x

Answers

Answer:

g(x)=3x-1=7<=> 3x=8<=> x=8/3

Answer:

The value of x will be 8/3

Step-by-step explanation:

g(x) = 3x-1

3x-1 = 7

3x = 7+1  

3x = 8

x = 8/3

Hope that helped :)

4m-3(m +2) what is the answer step by step​

Answers

Answer:

-1m-6

Step-by-step explanation:

1. Multiply -3*m = -3m

2. Multiply -3* 2 = -6

3. Combine like terms : 4m + -3m = -1m

4. -1m - 6


M is the midpoint of AD.
Triangles A B M and D C M are connected at point M. Sides A B and C D are congruent. The length of side B M is 3 x + 6 and the length of corresponding side M C is 4 x minus 1.
What value of x will make triangles ABM and DCM congruent?
3
5
7
9

Answers

Answer:

7

Step-by-step explanation:

ΔABM and ΔDCM

4x - 1 = 3x + 6

4x - 3x = 6 + 1

x = 7

Answer:

C. 7

Step-by-step explanation:

Find the diagram to the question attached. Two congruent triangles has all its sides to be equal. This means that the sides of ΔABM will be equal to that of ΔDCM (SSS rule).

Given

BM = 3x+6

MC =4x-1

Since both triangles are congruent, then BM = MC

Next is to get x;

3x+6 = 4x-1

collect like terms'

3x-4x = -1-6

-x = -7

multiply through by -1

-(-x) = -(-7)

x = 7

Hence the value of x that will make triangles ABM and DCM congruent is 7

PLZ ANSWER WILL GIVE BRAINLIST 15 POINTS AND PLUS THREE FOR CORRECT ANSWER!!!!!!

Answers

Answer:

22

Step-by-step explanation:

just simple deduction

i think 22 i’m not positive

Your Turn (Activity 3): Calculate the LCM of 54 and 90​

Answers

Answer:

270

Step-by-step explanation:

Same factory has supplies expenses of $1135.78 a day, in addition to the wages above and makes $60,128.72 in one week, what is the factory's total profit or loss in one week?

Answers

Given :

Factory has supplies expenses of $1135.78 a day.

Company earns $60,128.72 in one week.

To Find :

The factory's total profit or loss in one week.

Solution :

Expenses of factory of a week :

E =$( 1135.78 × 7 ) = $7950.46 .

Now, profit is given by :

P = $60,128.72 - $7950.46

P = $52178.26

Therefore, total profit of factory in one week is $52178.26 .

Hence, this is the required solution.

Kyle missed 3 questions on the math exam. If he missed 15% of the questions, how many questions were on the exam all together?

Answers

Step-by-step explanation:

consider the number of Q = X

then 15% × X = 3

then (15 ÷100) X = 3

X = 3 × ( 100÷ 15 ) = 20 Q ( :

Neil bought 4 baseballs for a total of $15.25. If the baseball were the same cost, about how much did each baseball cost?
$3.00
$64.00
$4.00
$3.81

Answers

Answer: your answer is $74.81  and you are welcome

Step-by-step explanation:

$3.00 +$64.00 + $4.00 +$3.81 = $74.81

ASAP answer it please.!!!!!!!!!!!!!!!!!!! thank uuu

Answers

Answer:

X=120 and y=10,z=120

Step-by-step explanation:

corresponding angles

thus 120=(13y-10)=x

is 0.25 greater than 3/8

Answers

Answer:

no 0.250 is not greater than 3/8

Step-by-step explanation:

because when you make 3/8 into a decimal it becomes 0.375 so no

Answer:

No. 0.25 is not greater than 3/8

Step-by-step explanation:

Convert 3/8 to a decimal.

1/8 = 0.125 in decimal form.

Multiply this by 3.

3/8 = 0.375.

0.375 > 0.250

Your answer will be 0.25 < 3/8

Calculate the shortest distance between P and Q.

Answers

Answer:

10.6 cm

Step-by-step explanation:

Shortest distance between P(3, -1) and Q(-5, 6) using [tex] PQ = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

Plug in the values

[tex] PQ = \sqrt{(-5 - 3)^2 + (6 -(-1))^2} [/tex]

[tex] PQ = \sqrt{(-8)^2 + (7)^2} [/tex]

[tex] PQ = \sqrt{64 + 49} [/tex]

[tex] PQ = \sqrt{113} = 10.6 [/tex] (1 d.p)

(-4,4)(4,-2) slope the points

Answers

Slope (y2-y1)/(x2-x1)
(-2-4)/(4+4) = -6/8 = -3/4

When asked to write the domain for the equation y= |x - 6| + 3, Mary wrote the Domain is y < 3. What mistake(s) did Mary make? Write the correct domain for Mary using inequality notation. Explain to Mary how you found your answer.

Answers

Answer:

Ok, the domain is the set of values that we can input in a function.

In this case, we have:

y = Ix - 6I + 3.

Notice that there is no restriction here, x can actually take any value, then the domain will be the set of all real numbers.

The correct domain is x, x ∈ R

Now, if we had (for example) something like:

y = Ix - 6I < 3

Now we have a restriction in the domain because we can not have y equal or larger than 3.

To find the domain, we can break the absolute value:

Ix - 6I < 3

is equivalent to:

-3 < x - 6 < 3

now let's add 6 in each side.

-3 + 6 < x - 6 + 6 < 3 + 6

3 < x < 9

That will be the domain in that case.

bruh if you can help with algebra 2 please help

Answers

Answer:

what do you need?

Step-by-step explanation:

pictures would be nice

Answer:

yea sure whats the problem

Zachary purchased a computer for $1200 on a payment plan three months after he purchased a computer his balance was $795. six months after he purchased a computer his balance was $390 what is the equation that models the balance y after X months

Answers

Money man gets to it 100000

6- 4(2r - 5) < 26 - 8r
This is algebra

Answers

Answer:

r>1

Step-by-step explanation:

6-4(2r-5)<26-8r do () first

6-8r+20<26-8r subtract 6 from both sides

-8r+20<20-8r Since this is the same on both sides, r>1 to make the equation not come out as 0

On Dan's eReader 2/3 of the books are fiction. Of the fiction books, 4/5 are mysteries. What fraction of the books on Dan's eReader are mysteries?
1 point
A. 4/5
B. 8/15
C. 2/3
D. 4/6

Answers

Answer:

4/6

Step-by-step explanation:

hope this helps you

How to solve 25= 4+ 7x

Answers

Answer: x =3

Step-by-step explanation:

What value of x makes the equation 0.25(10x-3)= 1.5(x+2) - 0.75 true?
x= 3
x= 4
x= 3.75
x= 4.25

Answers

Answer:

Value of x = 3

Step-by-step explanation:

Given:

0.25 (10 x - 3) = 1.5(x + 2) - 0.75

Find:

Value of x

Computation:

0.25 (10 x - 3) = 1.5(x + 2) - 0.75

2.5 x - 0.75 = 1.5 x + 3 - 0.75

x = 3

Value of x = 3

Answer:

x=3

Step-by-step explanation:

When completing an online shopping transaction, a typical shopper takes 5 seconds to select each product and another 28 seconds to complete the check-out process. If it takes 48 seconds to complete a transaction, how many products are being purchased? If it takes 80 seconds to complete a transaction, how many products are being purchased?​If it takes 80 seconds to complete a transaction, how many products are being purchased? If it takes 80 seconds to complete a transaction, how many products are being purchased?​ If it takes 80 seconds to complete a transaction, how many products are being purchased? If it takes 48 seconds to complete a transaction, how many products are being purchased?​

Answers

Answer:

a) 4 products

b) 10 products

Step-by-step explanation:

When completing an online shopping transaction, a typical shopper takes 5 seconds to select each product and another 28 seconds to complete the check-out process.

For 1 product, the total time =

5 seconds + 28 seconds = 33 second.

We can derive an equation

Total time of transaction = 5x + 28

Where x is the number of products you are selecting

a) If it takes 48 seconds to complete a transaction, how many products are being purchased?

Total time = 5x + 28

48s = 5x + 28

5x = 48 - 28

5x = 20

x = 20/5

x = 4 items

b) If it takes 80 seconds to complete a transaction, how many products are being purchased?

Total time = 5x + 28

80s = 5x + 28

5x = 80 - 28

5x = 52

x = 52/5

x = 10 items

In whole number = 10 items

I have to order it from least to greatest in absolute value, and i dont get it can anyone help?

Answers

Answer:

ight A on top since it's the cmallest followed by B,C,D,E

Step-by-step explanation:

What's the answer of 7/10×4​

Answers

Answer:

2.8 in decimal form

Step-by-step explanation:

Answer:

Im pretty sure its 2.8

Step-by-step explanation:

Seventeen out of 20 teens said they eat breakfast every morning. What is the reasonable prediction for the number of teens out of 1,280 who eat breakfast every morning?

A.
340

B.
940

C.
1088

D.
1260

Answers

Answer:

The correct answer is C. 1088

If x varies directly as y. Find x when y = 1 if x= 12 when y= 4

Answers

Step-by-step explanation:

x/y=constant

12/4=3

x/1=3

x=3

Here, if x varies directly as y. When y=1, then x=3.

Given that, x varies directly as y.

What are proportions?

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

If x= 12 when y= 4

Here, x varies directly as y is x∝y

⇒ x=ky

⇒ 12=k(4)

⇒ k=3

So, x=3y

When y=1, we have

x=3(1)

⇒ x=3

Here, if x varies directly as y. When y=1, then x=3.

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1. If g(x)= 4(3)* then g(-2)= ?


Help please

Answers

Answer:

-8

Step-by-step explanation:

Assuming that the in parentheses is what we are supposed to change (3)..We would replace the three with the negative two this means that we will solve for four times -2 which equals -8.Hope this helps!

What makes math word problems challenging for you? If word problems are not hard for you, explain what you do to solve them.​

Answers

Well.

Step-by-step explanation:

For me, typically I dont read the question properly and do the math wrong. Other moments I cant even figure out what exactly the question is even asking.

Step-by-step explanation:

You can try to read the word problem once first (no need to be really through just need to get an idea of what's really happening), and then read again, now a little more through, where you need to understand what the question wants of you. Once you understood the question, relate it to the topic you have learnt and see if there's any formula in this topic that you have been taught. If there is, keep all of these formulas in mind. If there isn't then it's good just search for all the numbers given in the question and form and equation in it or just solve. If there may be formulas involved, try relate the question/info given to the formulas you have in your head and yeah

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