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 formulaWe 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 formulaThat 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 differenceUsing this fact, we find a=(83+13)/2 = 48; b=(83-13)/2 = 35, and the product is (48)(35) = 1680, as above.
Find a real life example of an inequality and explain why it represents an inequality
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.
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.
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:
Skylar made 25% of her free throws over the season. If she shot 200 free throws, how many did she make?
Answer:
50 Free Throws
Step-by-step explanation:
Answer: 50 Free Throws
25% = 0.25
0.25*200=50
skylar sucks at basketball
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
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 :)
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.
base = 18
height = 12
Step-by-step explanation:
look at the photo its quick n ez
Find the mean absolute deviation of the data set: 1,3,7,11,13
Please help me I am stuck on this problem!!!!
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
complete this sentence
48% of __is 12.
12= 0.48xw
w=?
25
Step-by-step explanation:
hope this helps for yoir homework
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.
Miguel practiced more than 5 hours for his first soccer game. which inequality represents p, the amount of time Miguel practiced?
Answer:
P>5hours
Step-by-step explanation:
practice time is > five hours
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.
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 pressureIn 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
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.
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:
× 10^-3 is 2,000 times greater than 1. 9 × 10-6. It is also times greater than 9. 5 × 10^-4
Answer:
1.9 × 10^-6.
Step-by-step explanation:
SALE
60% OFF!
The original price of a swing set is $940. How much will Carmen pay if she buys it
during the sale?
Answer:
Carmen will pay $376.
Step-by-step explanation:
Multiply $940 by 40% because 100% - 60% = 40%:
(40%)(940) = 0.4 * 940 = $376
PLEASE HELP!!!! Find the volume. Round to the nearest tenth, if necessary.
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
Which expression is equivalent to side "8"?
2
d
8
3
45
1.
e
5
nv2
n3
O O OO
5
n
2n
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 = 8What 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)
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
what are the formula to find the vertex of hexagon
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
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
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
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
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.
That's two possibilities of a total of six =
2/6=1/3=33.33%
(1/3)
what's the ans?
[tex]\bf 6(x+4)+1=x+5[/tex]
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]
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
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
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
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:
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.
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
pls help me thank you
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
What is the constant of proportionality?
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.
The local store has 7 containers with 14 apples in each container. If they sell 23 apples, how many apples will they have left?
Answer: 75 apples they have left
Step-by-step explanation:
7 (14) = 98 apples total
98 - 23 = 75
Which is the value of `3/4 + 1/2 - 1/3`?
A
`2/3`
B
`7/12`
C
`11/12`
D
`3/3`
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:)
in the figure below line x is parallel to line yz find the measure of angle a and the measure of angle b
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°