The sum of the 2 numbers is 83. The difference of the 2 numbers is 13. What is the product of the 2 numbers?

Answers

Answer 1

Answer:

  1680

Step-by-step explanation:

To find the product of the two numbers, you can work out the values of the numbers, or you can work directly with the sum and difference figures.

__

Deriving the formula

We note that the square of a sum is ...

  (a +b)² = a² +2ab +b²

and the square of a difference is ...

  (a -b)² = a² -2ab +b²

The difference of these squares is ...

  (a +b)² -(a -b)² = (a² +2ab +b²) -(a² -2ab +b²) = 4ab

__

Using the formula

That is, dividing the difference of the squares of the sum and difference by 4 will give the desired product:

  P = (83² -13²)/4 = (6889 -169)/4 = 6720/4 = 1680

The product of the two numbers is 1680.

_____

Additional comment

If we factor the formula we derived, we find ...

  P = ((a +b)² -(a -b)²)/4 = ((a +b) +(a -b))/2 × ((a +b) -(a -b))/2

This simplifies to ...

  (2a)/2 × (2b)/2 = a × b

In short:

a = ((a +b) +(a -b))/2, the average of the sum and differenceb = ((a +b) -(a -b))/2, half the difference of the sum and difference

Using this fact, we find a=(83+13)/2 = 48; b=(83-13)/2 = 35, and the product is (48)(35) = 1680, as above.


Related Questions

What is the completely factored form of x4 8x2 – 9? (x 1)(x – 1)(x 3)(x 3) (x 1) (x minus 1) (x squared 9) (x2 – 1)(x 3)(x – 3) (x 1)(x 1)(x 3)(x 3)

Answers

The complete factor of the polynomial expression is (x² + 9)(x – 1)(x + 1), then the correct option is B.

What is a factorization?

It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.

The expression is given as

x⁴ + 8x² – 9

Then by the factorization, we have

x⁴ + 8x² – 9

x⁴ + 9x² – x² – 9

x²(x² + 9) – 1(x² + 9)

(x² + 9)(x² – 1)

(x² + 9)(x – 1)(x + 1)

More about the factorization link is given below.

https://brainly.com/question/6810544

Answer:b

Step-by-step explanation:

on edg 2022

A corner of a rectangle is cut, creating a trapezoid. a right trapezoid is shown. the angles are 90 degrees, 90 degrees, 45 degrees, and x. what is the value of x? 105o 115o 125o 135o

Answers

Answer:

D) 135

Step-by-step explanation:

Add 90+90+45, which is equal to 225,

then subtract that from 360, which is the amount that every quadrilateral has in total.

The answer is 135.

Hope This Helps! :) Please Give Brainliest if this does!

Answer:

D on edge

Step-by-step explanation:

You're welcome :)

How many bars would the team need to purchase from each company in order for the total cost to be equal? 6 8 30 40

Answers

Answer:

It's 40

Step-by-step explanation: Fortunately for you I risked my test for you and ended up getting the correct answer of course^0^

Answer:

40

Step-by-step explanation:

What is the volume of the solid figure?
Enter your answer in the box.

Solid is made up of 3 cuboids. First cuboid has length as 4 ft, height as 9 ft and width as 3 ft. Remaining 2 cuboids are placed on the right and left side of the 1st cuboid whose length as 1 ft, height as 1 ft and width as 3 ft.

Answers

Answer:

Volume of the solid = 2[1 x 1 x 3] + (4 x 3 x 9) = 114 ft³

Ans: 114 ft³

Step-by-step explanation:

Miguel practiced more than 5 hours for his first soccer game. which inequality represents p, the amount of time Miguel practiced?

Answers

Answer:

P>5hours

Step-by-step explanation:

practice time is > five hours

PLEASE HELP!!!! Find the volume. Round to the nearest tenth, if necessary.

Answers

Answer:

[tex]63cm {}^{3} [/tex]

Step-by-step explanation:

the shape above is a cuboid and volume of a cuboid

= length x breath x height

=length=3cm

breath= 7cm

height= 3cm

volume= (3x7x3)cm =63 cm^3

SALE
60% OFF!
The original price of a swing set is $940. How much will Carmen pay if she buys it
during the sale?

Answers

Answer:

Carmen will pay $376.

Step-by-step explanation:

Multiply $940 by 40% because 100% - 60% = 40%:

(40%)(940) = 0.4 * 940 = $376

A graphics company charges $50 per hour to create a logo plus $250 for the ownership rights of the logo. a private contractor charges $75 per hour to develop a logo plus a $100 supply fee. which equation can be solved to determine x, the number of hours after which the costs would be the same? 50x 250 = 75x 100 50 250x = 75 100x 50x 100 = 75x 250 50 100x = 75 250x

Answers

The equation that can be solved to determine x, the number of hours after which the costs would be the same is; 50x + 250 = 75x + 100

How to create Linear Equations?

The general formula for the slope intercept form of an equation is;

y = mx + c

We are told that;

Charge per hour = $50

Ownership rights = $250

Thus, for the first company, total cost is;

y = 50x + 250

For the second company;

Total cost is;

y = 75x + 100

Thus, at same cost, we have;

50x + 250 = 75x + 100

Read more about Linear Equations at; https://brainly.com/question/1884491

Answer:

50x + 250 = 75x + 100

Step-by-step explanation:

I did the test

You roll a 6-sided die.
What is P(5)?
Write your answer as a fraction or whole number.
Submit
Work it out
Not feeling radunt? Th

Answers

Answer:

6*5=30= 30/100

Step-by-step explanation:

we will multiply 6* by 5 and after that we will do it fraction by doing that 30/100

In a triangle, a base and a corresponding height are in the ratio 3:2. The area is 108 in^2. Find the base and the corresponding height.​

Answers

base = 18

height = 12

Step-by-step explanation:

look at the photo its quick n ez

× 10^-3 is 2,000 times greater than 1. 9 × 10-6. It is also times greater than 9. 5 × 10^-4

Answers

Answer:

1.9 × 10^-6.

Step-by-step explanation:

Which expression is equivalent to side "8"?
2
d
8
3
45
1.
e
5
nv2
n3
O O OO
5
n
2n

Answers

Answer:

n

Step-by-step explanation:

Let d = n.

As both d and 8 are opposed by the same angle (45°) in the right triangle, they are equalTherefore, n = 8

Please help me I am stuck on this problem!!!!

Answers

Step-by-step explanation:

From less value to large value

30 32 33 33 35

Median is the center number = 33

Mean is (30+32+33+33+35)/5 = 32.6

The same value

Find the mean absolute deviation of the data set: 1,3,7,11,13

Answers

6 minus the abs n at at the end of 10 and 5 to amplify the 23 and 20 bring it back n out of 0 to 9

You roll a number cube one time. What is the probability that you roll a 6 or 4? Enter your answer as a fraction in simplest form.

Answers

That's two possibilities of a total of six =

2/6=1/3=33.33%

(1/3)

A bag with 12 marbles has 5 red marbles, 3 yellow marbles, and 4 blue marbles. A marble is chosen from the bag at random. What is the probability that it is red?
Write your answer as a fraction in the simplest form.

Answers

The total number of marbles is 12. Because:
5 red marbles + 3 yellow marbles + 4 blue marbles = 12 total marbles.
And there are 5 RED marbles in the special bag . . .
So the probability of a red marble would be 5/12. The reason why is because there are 5 TOTAL RED marbles and there are 12 TOTAL marbles.
Hope this helps!

what are the formula to find the vertex of hexagon​

Answers

Answer:

the answer is 6

Step-by-step explanation:

there are 6 side you times the 6 with the area of an equilateral triangle so the area of hexagon = 6

Which is the value of `3/4 + 1/2 - 1/3`?

A
`2/3`

B
`7/12`

C
`11/12`

D
`3/3`

Answers

Hey there!

3/4 + 1/2 - 1/3

= 5/4 - 1/3

≈ 15/12 - 4/12

≈ 15 - 4 / 12 - 0

= 11/12


Therefore, your answer is: 11/12


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

Nick wanted to determine the length of one blade of a windmill. He stood at a point on the ground 440 feet from the windmill's base. Using surveyor's tools, Nick measured the angle between the ground and the highest point reached by the top blade and found it was 38.8°. He measured the angle between the ground and the lowest point of the top blade and found it was 30°. Determine and state a blade's length, x, to the nearest foot.

Answers

Using the slope concept, it is found that rhe blade's length is of 90 feet.

What is a slope?

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

In this problem, the horizontal change is of 440 feet.

At the highest point, the angle is of 38º, hence:

[tex]\tan{38^\circ} = \frac{h_1}{440}[/tex]

[tex]h_1 = 440\tan{38^\circ}[/tex]

[tex]h_1 = 344[/tex]

At the lowetst point, the angle is of 30, hence:

[tex]\tan{30^\circ} = \frac{h_2}{440}[/tex]

[tex]h_2 = 440\tan{30^\circ}[/tex]

[tex]h_2 = 254[/tex]

Hence, the difference is:

[tex]h_2 - h_1 = 344 - 254 = 90[/tex]

The blade's length is of 90 feet.

More can be learned about the slope concept at https://brainly.com/question/18090623

complete this sentence
48% of __is 12.
12= 0.48xw
w=?

Answers

25

Step-by-step explanation:

hope this helps for yoir homework

what's the ans?
[tex]\bf 6(x+4)+1=x+5[/tex]

Answers

Answer:

x = -4

Step-by-step explanation:

6 (x + 4) + 1 = x + 5

6x + 24 + 1 = x + 5 (distributive property)

6x + 25 = x + 5

6x + 25 - x = 5

5x + 25 = 5

5x = 5 - 25

5x = -20

x = -20/5

x = -4

Hope it helps ⚜

Answer: x = -4

Step-by-step explanation:

[tex]6\left(x+4\right)+1=x+5[/tex]

[tex]$$Expand the parentheses[/tex]

[tex]6x+25=x+5[/tex]

[tex]\mathrm{Subtract\:}25\mathrm{\:from\:both\:sides}[/tex]

[tex]6x+25-25=x+5-25[/tex]

[tex]$$Simplify[/tex]

[tex]6x=x-20[/tex]

[tex]\mathrm{Subtract\:}x\mathrm{\:from\:both\:sides}[/tex]

[tex]6x-x=x-20-x[/tex]

[tex]$$Simplify[/tex]

[tex]5x=-20[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}5[/tex]

[tex]\frac{5x}{5}=\frac{-20}{5}[/tex]

[tex]$$Simplify[/tex]

[tex]x=-4[/tex]

in the figure below line x is parallel to line yz find the measure of angle a and the measure of angle b

Answers

Answer:

∠a = 35°  ∠b = 65°

Step-by-step explanation:

a = 35 ° ( alternate interior angles )

( the line x is parallel to line yz hence we can consider XY as a transversal)

∠b + 35° + 80° = 180 ° ( angle sum property of triangle)

∠b+ 115° = 180°

∠b= 180 - 115

∠b = 65°

The diagram shows a solid shape.
The shape is a hemisphere on top of a cylinder,

Volume of a sphere = 4/3pir^3
Pressure = force/area

The solid shape is placed on a table. The solid exerts a force of 4 Newtons on a table. The pressure on the table is 100 N/m. The height of the cylinder is 45 cm. Work out the total volume of the solid shape.
Please can someone help explain it. ​

Answers

Based on given information about pressure from table and geometry of the solid shape, the total volume of the solid shape is approximately 21073.745 cubic centimeters. [tex]\blacksquare[/tex]

How to determine the volume of the solid shape under pressure

In this question we must apply the concepts of pressure (P), in newtons per square meter, cross section area (A), in square meters, and volume (V), in cubic meters, to determine that  Let assume that the bottom experiments an uniform pressure due to a reaction force (F), in newtons, from the table, whose formula is described below:

P = F/A = 4 · F /(π · D²)     (1)

If we know that F = 4 N and P = 100 N/m², then the diameter of the cylinder is:

[tex]D = 2\cdot \sqrt{\frac{F}{\pi\cdot P} }[/tex]  

D ≈ 0.226 m²

And the volume of the solid shape is: (H = 0.45 m)

V = 0.25π · D² · H + (π/12) · D³

V = 0.25π · (0.226 m)² · (0.45 m) + (π/12) · (0.226 m)³

V ≈ 0.021 m³ (21073.745 cm³)

Based on given information about pressure from table and geometry of the solid shape, the total volume of the solid shape is approximately 21073.745 cubic centimeters. [tex]\blacksquare[/tex]

To learn more on pressure, we kindly invite to check this verified question: https://brainly.com/question/356585

What is the constant of proportionality?

Answers

Answer: y= 2x

Explanation: The constant of proportionality is the ratio between two directly proportional quantities. Two quantities are directly proportional when they increase and decrease at the same rate. The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other.

Annual sales for a fast food restaurant are 650000 and are increasing at a rate of 4% per year. Use an exponential function to find the annual sales after 5 years. What is the equation

Answers

A=P(1+r)^2
Principal as 650000
Rate = 4% or 0.04%
Time = 5 years
We are adding because as it is exponentially growth

650000(1+0.04)^5
= 790824.39

Find a real life example of an inequality and explain why it represents an inequality

Answers

Answer:

Roads have speed limits

Step-by-step explanation:

Roads have speed limits. This is an inequality because it doesn't reflect an exact number, but rather a restriction on what is permissible or possible.

How does the value of the 8 in 589,310 compare to the value of 8 in 598,301?
Options: It is 8 times as much, It is 10 times as much, It is 80 times as much, It is 100 times as much.

Answers

Answer:

It is 10 times as much.

Step-by-step explanation:

The value of 8 in 589,310 is 80,000, while the value of 8 in 598,301 in 8,000. Thus, 80,000 is 10 times as much as 8,000.

Answer:

it is 10 times as much

Step-by-step explanation:

The local store has 7 containers with 14 apples in each container. If they sell 23 apples, how many apples will they have left?

Answers

Answer: 75 apples they have left

Step-by-step explanation:

7 (14) = 98 apples total

98 - 23 = 75

Skylar made 25% of her free throws over the season. If she shot 200 free throws, how many did she make?

Answers

Answer:

50 Free Throws

Step-by-step explanation:

Answer: 50 Free Throws

25% = 0.25

0.25*200=50

skylar sucks at basketball

pls help me thank you ​

Answers

Answer:

A no. is correct one

Step-by-step explanation:

Hope it will help you. and please mark me brilliant

Answer:

A

Step-by-step explanation:

12x+6x=90deg

90deg+90deg=180deg

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