(a - b)(a 2 + ab + b 2) HELP
Answers
( a - b )( a² + ab + b² )
Let us distribute ( a - b ) into the other
a ( a² ) + a ( ab ) + a ( b² ) - b ( a² ) - b ( ab ) - b ( b² )
a³ + a²b + ab² - a²b - ab² - b³
We can further simplify
a²b - ab² = 0
ab² - ab² = 0
a³ - b³
You can see in the picture which I have attached. It is the 8th formula
(a - b)(a^2 + ab + b^2)
a^3 + a^2b + b^2a - a^2b - b^2a - b^3
a^3 - b^3 <----------Answer
Related Questions
Trey wants to plant grass in his backyard. His backyard is in the shape of a rectangle. Its length is 31
feet and its width is 24
feet. Suppose each pack of seed covers 12
square feet. How many packs of seed will he need to cover the backyard?
Answers
The first step to solve this problem is to compute for the area of the rectangular backyard. The formula in computing the area of a rectangle is:
A = LW
Substituting the given measurement to the formula:
A = 31 (24)
A = 744 square feet
The area of the backyard is 744 square feet.
Since each pack of seed covers 12 square feet, you need to divide this to the total area of the backyard.
Therefore, you need 62 (744 / 12) packs of seed to cover the backyard.
Trey will need 62 packs of seed to cover his backyard.
Explanation:To find the number of packs of seed Trey will need to cover his backyard, we need to calculate the total area of the backyard and then divide it by the area covered by each pack of seed.
The formula to find the area of a rectangle is length x width. For Trey's backyard, the length is 31 feet and the width is 24 feet, so the area is 31 x 24 = 744 square feet.
Each pack of seed covers 12 square feet, so we divide the total area of the backyard by the area covered by each pack of seed: 744 / 12 = 62 packs of seed.
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39 is 75% of what number
Answers
IF 39 is 75%, divide 39 by 3.
39/3= 13
Multiply that by 4.
13*4= 52
39 is 75% of 52.
Have a nice day!
What is the measure of angle x, help
Answers
x = 180 - 73 - 72 = 35
x = 35 degrees
=73
x=180-72-73
=35°
Which function has a domain of all real numbers except x=π/2 ±nπ?
A. y=secx
B. y=cosx
C. y=1/sinx
D. y=cotx,
Answers
Answer:
y=cos x
Step-by-step explanation:
A P E X
The mean weight of five complete computer stations is 167.2 pounds. The weights of four of the computer stations are 158.4 pounds, 162.8 pounds, 165 pounds, and 178.2 pounds respectively. What is the fifth computer station?
Answers
The mean weight of five complete computer stations is 167.2 pounds.
The weights of four of the computer stations are 158.4 pounds, 162.8 pounds, 165 pounds, and 178.2 pounds.
We have to determine the weight of fifth computer station.
Let the weight of fifth computer station be 'x' pounds.
Mean is calculated by sum of all the observations divided by the total number of observations.
So, [tex] \frac{158.4+162.8+165+178.2+x}{5}=167.2 [/tex]
[tex] \frac{664.4+x}{5}=167.2 [/tex]
[tex] {664.4+x}=167.2 \times 5 [/tex]
[tex] {664.4+x}=836 [/tex]
x= 171.6 pounds
The weight of fifth computer station is 171.6 pounds.
To find the weight of the fifth computer station, subtract the sum of the weights of the four given stations from the mean weight.
Explanation:The mean weight of five complete computer stations is 167.2 pounds. To find the weight of the fifth computer station, we can calculate the sum of the weights of all five stations and then subtract the sum of the weights of the four given stations. The weight of the fifth station can be found by subtracting the sum of the weights of the four given stations from the mean weight.
Sum of the weights of all five stations = 5 * 167.2 pounds
Sum of the weights of the four given stations = 158.4 pounds + 162.8 pounds + 165 pounds + 178.2 pounds
Weight of the fifth station = Sum of the weights of all five stations - Sum of the weights of the four given stations
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helppppppppppppppppp
Answers
14.1 in
Explanation:
The equation relating the length of arc, radius of circle and angle is:
S = rθ
where:
S is the length of the arc
r is the radius of the circle = 6 in
θ is the angle in radians = 135 degrees = (135*π) / 180 = 0.75 π radian
Substitute with the givens in the above equation to get the length of the arc as follows:
S = rθ
S = 6 * 0.75π
S = (9/2) π which is approximately 14.1in
Hope this helps :)
A bakery bakes 10 cakes per hour & had 3 from the day before. What equation represents this?
A.y = 10x + 3
B.y = 3x + 10
C.y = x + 13
D.y = 13x
Answers
x represents the number of hours spent
y = 10x + 3
-----------------------------
Answer: 10x + 3
-----------------------------
For a school group, a skating rink charges a flat fee of $50 for skates for the students to use the skating rink.
•For 40 Students the skating rink charges 180.
•For 75 students, the skating rink charges 293.75
Which question represents the amount the skating rink charges for x students?
A)y=3.25x+35
B)y=3.25x+ 50
C)y=4.50x+ 35
D) y=4.50x+ 50
Answers
That fixed part is given by the fee for skates, which is $50.
The variable part depends on the quantity of students which is called 'x'. For this part, you are provided with a couple of points where the linear function passes by, they are: A(40,180) and B(75,293.75).
So, first thing to do is getting the slope:
[tex]m= \dfrac{293.75-180}{75-40} = \dfrac{113.75}{35} \\ \\ m=3.25[/tex]
Linear function structure is:
[tex]y=mx+b[/tex]
Where b is the y-intercept, which in this case is the fixed part, 50.
Finally, the function is:
[tex]y=3.25x+50[/tex]
Attached picture shows its graph.
Emily’s pet snake is 5 feet long. Kristen’s snake is 50 inches long. Kristen says her snake is much longer because 50 is so much bigger than 5. Is Kristen right? Why or why not?
Answers
Which equation finds the value of x in the triangle below?
Answers
1) cot 70=x/12
Cot 70=[opposite side]/[adyacent side]=x/12
The option 1 is correct
2) cot 70=12/x
Cot 70=[opposite side]/[adyacent side]=x/12
The option 2 is not correct
3)sec 20=x/12
Sec 20 =1/cos20
Cos 20==[opposite side]/[hypotenuse]=12/z
1/(1/cos20)-------> 1/(12/z)------> z/12
The option 3 is not correct
4) sec 20=12/x
Sec 20 =1/cos20
Cos 20==[opposite side]/[hypotenuse]=12/z
1/(1/cos20)-------> 1/(12/z)------> z/12
The option 4 is not correct
the correct value is
1) cot 70=x/12
Answer:
A: cot 70 degrees = x/12
Step-by-step explanation:
on edg... Good Luck!!!
Ivan earns $8 each time he walks his neighbors dog.he already walked his neighbors dog 5 times.how many more times does he need to walk the dog to earn enough money to buy a game that costs $88
Answers
Answer:
6 more times
Step-by-step explanation:
△ABC∼△DEF , △ABC has a height of 20 inches, and △DEF has a height of 24 inches. What is the ratio of the area of △ABC to the area of △DEF ? Enter your answer, in simplest form, in the boxes. :
Answers
h1---------------> height of △ABC
b1---------------> base of △ABC
h2--------------->height of △DEF
b2---------------> base of △DEF
we know that
h1=20 in
h2=24 in
Since they are similar, their bases must be in the same proportion:
h1/b1=h2/b2------> 20/b1=24/b2-----------> 24b1=20b2
b1=20b2/24-------------> equation 1
Area of △ABC=b1*h1/2
Area of △DEF=b2*h2/2
Let
r------>[the ratio of the area of △ABC to the area of △DEF]
r=[b1*h1/2]/[b2*h2/2]------> [b1*h1]/[b2*h2]
r=[20b1]/[24b2]---------------> equation 2
I substitute 1 in 2
r=[20(20b2/24)]/[24b2]--------> r=20²/24²-------> r=0.6944
the answer is
the ratio of the area of △ABC to the area of △DEF is 0.69
Help please been stuck on this for a week.
Answers
Surface Area = (2 • π • r²) + (2 • π • r • height)
However the 2*PI*r^2 part of the formula is used to calculate the 2 "ends" of a cylinder. Since the problem states that you are NOT to count any of surface area of the "ends" then you only need the (2 • π • r • height) part of the formula.
So, r = 3 inches and height = 8 * 3 inches, the side area equals
2 * PI * r * height
2 * 3.14159 * 3 * 24 =
452.39 cubic inches which is the lateral area.
Tim predicts he will get 98 points on the next exam. If Tim actually earned 62 points, what was Tim's percent error? Round your answer to the nearest tenth of a percent.
Answers
original #= 98
new #= 62
% change= (62-98)/98 x 100
= -36/98 x 100
= -0.36734 x 100
= -36.73%
Rounded to nearest 10th of %= -36.7%
CHECK:
= 98 - (98 * 36.73%)
= 98 - (98 * 0.3673)
= 98 - 36
= 62 new #
ANSWER:
Her percent error was 36.7% (rounded to the nearest tenth of a percent). The negative indicates a decrease.
Hope this helps! :)
Answer: 58.1
Step-by-step explanation:
98 - 62 / 62 = rounds to 58.1 Thank me Later..
Lines AB and CD are parallel. If the measure of W equals 129°, what is the measure of X?
Answers
Given f(x) =10x-2x find f(7)
Answers
10(7) -2(7)
70 - 14
56
f(7) = 56
what’s the inverse of y=4x^2-2
Answers
x = 4y^2 - 2
(x + 2) = 4y^2
(x + 2)/4 = y^2
+/- sqrt(x + 2)/2 = y
The graph of these two is below.
The original is in red
The inverse is in blue and green
Guys please help me
this is a system of equation word problem
Answers
.. w = 185 -3d . . . . . . d is the number of days, w is the weight in pounds
Evaluating this for d=7, we have
.. w = 185 -3*7 = 164
The point is represented by the ordered pair (7, 164).
The value on day 7 corresponds to the weight loss due to rejection. We might conclude the reaction to rejection was the cause of death.
find the approximate surface area of a bowling ball with a raius of 5 inches
Answers
Formula for the surface area of a sphere: SA = 4·π·r2
Formula for the volume of a sphere: V = (4/3)·π·r3
Surface area to volume ratio: ( 4·π·r2 ) / ( (4/3)·π·r3 ) = 3 / r
Radius = 5 ---> 3/5
The dollar value v(t) of a certain car model that is t years old is given by the following exponential function.
V(t)=24,500(0.95^t)
Find the initial value of the car and the value after 13 years.
Round answers to the nearest dollar as necessary.
Answers
24,500*(0.95^0) =
24,500*1 = 24,500
Hence, the initial value is £24,500
The value after 13 years means t equals 13. Therefore
24,500*(0.95^13) =
12,576.88
Hence, the value after 13 years is about £12,577
Which expression shows a sum of three terms? (1 point)
3x
3 + x
x^3
x + 3 + x
Answers
The answer is x + 3 + x
Answer:
x + 3 + x
Step-by-step explanation:
3x :
This is a product of two terms, where x is any variable.
3 + x :
This is sum of two terms,where x is any variable.
x^3 :
This expresses x to the power of three. It can also be written as (x times x times x ). Thus it is the product of three terms, where x is any variable.
x + 3 + x :
This is the sum of three terms, where x is any variable.
Thus answer is x + 3 + x
Triangle ABC was dilated and translated to form similar triangle A'B'C'.
What is the scale factor of the dilation?
A. 1/5
B. 2/5
C. 5/2
D. 5/1
Answers
On this exercise is asked to find the scale factor by which the triangle ABC was
dilated to produce the triangle A'B'C'.
Dilation is define by the rule (x,y)-- (kx, ky) where k represents the scale factor.
As can be see on the picture the dilation produce was an enlargement meaning that the image is larger that the preimage.
Of this form you can discard the choices A and B as possible solutions.
Lets try 5/2 as the possible scale factor:
(x,y)-- (kx, ky)
A(0,2)--(5/2(0),5/2(2))=A'(0,5)
B(2,2)--(5/2(2),5/2(2))=B'(5,5)
C(2,0)--(5/2(2),5/2(0))=C'(5,0)
Lets try 5/1 or 5 as the scale factor:
A(0,2)--(5(0),5(2))=A'(0,10)
B(2,2)--(5(2),5(2))=B'(10,10)
C(2,0)--(5(2),5(0))=C'(10,0)
As said at the beginning of the question the triangle was not only dilated.
After a dilation and a translation, the scale factor of the dilation is letter C or 5/2.
correct answer is 5/2
What is the ratio of CDs & DVDs
Answers
B. 1:4
C. 1:2
D. 1:5
Convert -1.2 repeating as a mixed number
Answers
Can someone help me please, how to add this? Thank you!
Answers
Choice B) [tex]9.9 \angle \underline{76.10^{\circ}}[/tex]
============================================
Explanation:
The given vectors in polar form are
(17,60)
(8,220)
by polar form I mean (r,theta) where
r = magnitude
theta = angle
Convert the polar form (r,theta) = (17,60) to component form
x = r*cos(theta)
x = 17*cos(60)
x = 8.5
y = r*sin(theta)
y = 17*sin(60)
y = 14.72243186
The component form of the first vector is (x,y) = (8.5, 14.72243186)
Do the same for the second vector
x = r*cos(theta)
x = 8*cos(220)
x = -6.1283555
y = r*sin(theta)
y = 8*sin(220)
y = -5.1423009
The component form of the second vector is (x,y) = (-6.1283555, -5.1423009)
Now we add the vectors. Add up the corresponding components
(8.5, 14.72243186)+(-6.1283555, -5.1423009)
(8.5+(-6.1283555) , 14.72243186+(-5.1423009))
(2.3716445, 9.58013096)
So,
(x,y) = (2.3716445, 9.58013096)
is the component form of the resultant vector. Its the vector we get after adding the two original vectors
The last step is to convert this back to polar form
r = sqrt(x^2+y^2)
r = sqrt(2.3716445^2+9.58013096^2)
r = 9.869326564
which is roughly 9.9
theta = arctan(y/x)
theta = arctan(9.58013096/2.3716445)
theta = 76.09548164
which rounds to 76.10
So we end up with (r,theta) = (9.9, 76.10) pointing to choice B as the answer
There are 18 animals and 40 legs in all so lets see how many cows could be born. 4,8,16,12,24,28,32,36,40. so there could be 9 cows and now lets see on chickens 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40. so the could be 20 chickens so if u think. i think the ancewer is 30 chickens and 10 cowws thx!!!!
Answers
Given information
--------------------------------------
Total animals = 18
Total legs = 40
--------------------------------------
Assumed all are chickens
--------------------------------------
Total legs = 18 x 2 = 36
--------------------------------------
Calculate extra legs
--------------------------------------
40 - 36 = 4
--------------------------------------
Difference in legs between the cow and chicken
--------------------------------------
4 - 2 = 2
--------------------------------------
Find the number of cows
--------------------------------------
4 ÷ 2 = 2
--------------------------------------
Find the number of chickens
--------------------------------------
18 - 2 = 16
--------------------------------------
Answer: 16 chickens and 2 cows
--------------------------------------
I WILL GIVE BRAINLIEST FOR Correct Answer
A plane is located at C on the diagram. There are two towers located at A and B. The distance between the towers is 7,600 feet, and the angles of elevation are given.
EXPLAIN YOUR ANSWER
a. Find BC, the distance from Tower 2 to the plane, to the nearest foot.
b. Find CD, the height of the plane from the ground, to the nearest foot.
Answers
Answer:
a. 15052.1ft b. 6122ft
Step-by-step explanation:
A high school student working part-time as a pizza delivery man had a gross income of 6324 last year. If his federal tax rate was 10% and his state tax rate was 4.2% what was the amount withheld from his pay last year in fenderal tax, state tax, and FICA combined
Answers
Answer:
$1381.79 withheld from his pay last year.
Step-by-step explanation:
A student working as a pizza delivery man and earned = $6324.00
first we calculate all the taxes at the given tax rates
Federal Tax Rate = 10% of 6324.00
= 0.10 × 6324 = $632.40
State Tax Rate = 4.2% of 6324.00
= 0.042 × 6324 = $265.608
FICA is comprised of taxes for social security and medicare. For social security tax rate is 6.2% and for medicare tax rate is 1.45% which add up to 7.65%.
FICA combined Tax Rate = 7.65% of 6324.00
= 0.0765 × 6324 = $483.786
Now we add all the taxes to get what amount withheld from his pay
= 632.40 + 265.608 + 483.786 = $1381.79
$1381.79 withheld from his pay last year.
How to find the equation of a circle
Answers
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{5}{ h},\stackrel{3}{ k})\qquad \qquad radius=\stackrel{2}{ r} \\\\\\ (x-5)^2+(y-3)^2=2^2\implies (x-5)^2+(y-3)^2=4[/tex]
Final answer:
To find the equation of a circle, use the formula (x - h)² + (y - k)² = r², where (h,k) is the center of the circle and r is its radius. You apply this knowledge to other circular calculations, such as the angular velocity or the position and velocity of a moving point on the perimeter of the circle.
Explanation:
Finding the Equation of a Circle
To find the equation of a circle, you need to know the circle's radius (r) and the coordinates of its center (h,k). The general form of the equation is (x - h)² + (y - k)² = r². The values of h and k are the x and y coordinates of the center of the circle, respectively. If you recall the formula for the circumference of a circle, which is 2πr, and the area, which is πr², you can see that these both incorporate the radius of the circle in their calculations, similar to how the radius is used in the equation of the circle. When given certain dimensions or related motion problems, you can substitute known values into the equation to solve for the unknowns.
For example, if a circle has a radius of 5 units and its center is at the point (3,4), the equation would be (x - 3)² + (y - 4)² = 25. To find equations related to circular motion, like in the scenario of a student on a merry-go-round, knowing the radius also allows for determining the angular velocity and the velocity of a shadow or any point moving in circular motion.
PLEASE HELP PLEASE HURRY!!!!!!!!!
BRAINLIEST AVAILABLE
Answers
The second one is is also exponential and the rule is 32 times .25^x and the last one is is linear and the rule is 5x+-4
1]
y = 14 * (7/2)^x This is never going to linear.
2]
y = 32/(4)^x This also is not linear.
3]
y = 5x - 4 This one is linear
If you have a graphing calculator, you might think about graphing these three. The questions are a bit of by guess and by golly. You just have to keep on trying things until you get it. Look at 0 as an x value first.