Answers
Solution:
The difference of cubes identity is
if a and b are any two real numbers, then difference of their cubes, when taken individually:
a³-b³= (a-b)(a² + ab + b²)→→→Option (D) is
true option.
I will show you, how this identity is valid.
Taking RHS
(a-b)(a² +b²+ab)
= a (a² +b²+ab)-b(a² +b²+ab)
= a³ + a b² +a²b -b a² -b³-ab² Cancelling like terms, we get
= a³-b³
= LHS
Related Questions
The correct expression for a number which is 9 times as big as the number obtained after p has been increased
by 4
Answers
Answer:
9(p + 4)
Step-by-step explanation:
One of the unknown variable is p.
First of all, we know that the number is 9 times as big (multiplication) as the new number obtained through the addition of four to p i.e (p + 4).
Translating the word problem into an algebraic expression, we have;
9 * (p + 4) = 9(p + 4)
Simplifying further, we have;
9p + 36
How many inches is in 5 1/4 feet
Answers
Answer:
63 in.
Step-by-step explanation:
Answer:
There is 63 inches in 5 1/4 feet :)
Product of 4 and x increased by 5 what's the expression
Answers
Answer:
4x+5 hope it helps :-)
Step-by-step explanation:
hdhdhch
9514 1404 393
Answer:
4x +5
Step-by-step explanation:
The product of a constant and a variable is indicated in algebra by writing them next to each other.
"the product of 4 and x" ⇒ 4x
"Increased by 5" means that 5 is added to the product.
4x +5 . . . . . . the product increased by 5
The sum of two numbers is 56. One number is 3 times as large as the other. What are the numbers?
larger number
smaller number
Answers
explanation:
x+y = 56
x = 3y
Substitute for x in the first equation:
x + y = 56
x = 3y
3y + y = 56
Combine like terms:
4y = 56
Divide both sides by 4:
y = 14
So if y = 14, and x = 3y, then x = 42.
Now substitute for both x and y in both of the original equations to prove they are the correct values.
x + y = 56
x = 42
y = 4
42 + 14 = 56
56 = 56
x = 3y
x = 42
y = 14
42 = 3*14
42 = 42
So the two numbers, x and y, are 42 and 14.
I really need help?!
Answers
Answer:
the answer is a
Step-by-step explanation:
an exponential function is graphed on the gid. which function is best represented by the graph
a) g(x)=6(1/3)^x
b)g(x)=6(3)^x
c) g(x)=6-(1/3)^x
d) g(x)=6-(3)^x
Answers
Find the area of the trapezoid. A trapezoid has a base of 8 meters, a height of 6 meters, and a top side length of 4 meters.
Answers
Answer:
36 m²Step-by-step explanation:
A = 1/2(b₁ + b₂)hA = 1/2(8 + 4)*6 = 36 m²can you please help me
Answers
1. What type of sequence is this? *
3.5, 10.5,31.5, 94.5, 283.5, ---
Arthímetic
Geornetric
Neither
Answers
Answer:
Arthimatic is the answer
write the following comparison as a ratio reduced to lowest terms.
128 hours to 6 days
Answers
Answer:
21.3:1
Step-by-step explanation:
So we have to find the unit rate, and we do that by getting that 6 down to a 1, and we do that by dividing 6 by 6 and then we gotta do that on the other side too:
6 ÷ 6 = 1
128 ÷ 6 = 21.3 (simplified)
So 128 to 6 days in simplest terms is 21.3 hours to 1 day
hope this helps:)
Ms. Huck can dig 4 holes in 5 hours. Mr Varga can dig holes 3 times as fast. What is the constant of proportionality
between the number of holes Mr. Varga can dig and the number of hours?
Answers
Answer:
yes
Step-by-step explanation:
write the following comparison as a ratio reduced to lowest terms
31 hours to 7 days
Answers
Given the length of segment EB is 12 meters. Find the length of arc EA. Round your answer to the nearest tenth.
Answers
Answer:14.9
Step-by-step explanation:
my calc 3 friend told me
What is .66666666 as a fraction?
Answers
Answer:
2/3
Step-by-step explanation:
2 divided by 3 is 0.6666666 repeated.
How do you think this data would look if it only looked at how GenZ uses mobile and online banking? Why?
Answers
Answer:
People in GenZ will definitely be using more Mobile Banking App. Because this generation is very attached to such devices. I have seen a very good amount of examples where people send money, pay bills, and even receive money through their phones. Most of the things can be done through the Mobile Banking App instead of using other methods.
Peyton is going to invest $440 and leave it in an account for 5 years. Assuming the
interest is compounded annually, what interest rate, to the nearest tenth of a percent,
would be required in order for Peyton to end up with $520?
Answers
Answer:
The required interest rate would be of 3.4% a year.
Step-by-step explanation:
The amount of money earned in compound interest, after t years, is given by:
[tex]P(t) = P(0)(1+r)^t[/tex]
In which P(0) is the initial investment and r is the interest rate, as a decimal.
Peyton is going to invest $440 and leave it in an account for 5 years.
This means that [tex]P(0) = 440, t = 5[/tex]
So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]P(t) = 440(1+r)^5[/tex]
What interest rate, to the nearest tenth of a percent, would be required in order for Peyton to end up with $520?
This is r for which P(t) = 520. So
[tex]P(t) = 440(1+r)^5[/tex]
[tex](1+r)^5 = \frac{520}{440}[/tex]
[tex]\sqrt[5]{(1+r)^5} = \sqrt[5]{\frac{52}{44}}[/tex]
[tex]1 + r = (\frac{52}{44})^{\frac{1}{5}}[/tex]
[tex]1 + r = 1.034[/tex]
Then
[tex]r = 1.034 - 1 = 0.034[/tex]
The required interest rate would be of 3.4% a year.
If the value of "y" varies directly with "ex"
and y = -8 when x = 20, find "y" if x = -4.
Enter the number that belongs in the green box.
Reduce to simplest form.
y = 2
Answers
Answer:
8/5
Step-by-step explanation:
We can use a proportion to solve this question, if we put the values of x on the left of the equal and the value of y on the right we have
20 : -4 = -8 : y
y = (-4*-8)/20
= 32/20
= 8/5
Plzzz help meeeeeeeeee!
Answers
Answer:
B
Step-by-step explanation:
More students got more than 10 than students that didnt
Lukas is trying to lose weight. He starts the year
weighing 254 pounds. If he plans to burn enough
calories to lose 2 pounds per week, which
equation can be used to find w, the number of
weeks that will pass before Lukas weights 228
pounds?
For BRAINLIST!!
Answers
Answer:
a
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
please help i need help
Answers
Answer:
78 I think
Step-by-step explanation:
simply look at the second and third wight see the pattern wich is 7.8 I think and subtract that from the first answer
Try to answer this question for me pleaseee
Answers
Answer:
H
Step-by-step explanation:
180-48=132
4. Quinn scores 275 points in 5 min on her favorite
video
game. Delilah scores 675 points in 15 min.
If they continue to play at this level, who do you
predict will score 5000 points faster? Explain.
Answers
Answer:
Quinn
For Quinn:
275 points - - > 5 min
5000 points - - > x min
--------------------------------------
275*x=5*5000-->x=90.9 minutes
For Delilah:
675 points - - > 15 min
5000 points - - > y min
--------------------------------------
675*x=15*5000-->y=111.1 minutes
90.9<111.1, so Quinn will score 5000 points faster
Find the midpoint of the segment with the following endpoints (7-6) and (4-10)
Answers
Answer:
(5.5,2)
Step-by-step explanation:
Find the midpoint of the segment with the following endpoints (7-6) and (4-10)
The formula for calculating the x and y coordinate is expressed as
X = x1+x2/2
X = 7+4/2
X = 11/2
X = 5.5
Y = y1+y2/2
Y = -6+10/2
Y = 4/2
Y = 2
Hence the required midpoint is at (5.5,2)
Answer:
(5.5, -8)
Step-by-step explanation:
Edg 2021
Help please due in 45 minutes!!
Answers
Answer:
x=4, y=5
Step-by-step explanation:
Download photo math and take a picture of it
(d) You will live for 500 years.state whether the following event is certain, impossible, even,likely or unlikely
Answers
Answer:
Impossible
Step-by-step explanation:
Please help with math asap:
Rewrite without parentheses and simplify
(y+7)^2
Answers
y * y = y^2
y * 7 = 7y
7 * y = 7y
7 * 7 = 49
So we have:
y^2 + 7y + 7y + 49
Combine like terms:
y^2 + 14y + 49
WILL NAME BRAINLIST PLEASE
Use the table to write a linear function that relates y to x . PLEASE NO HACKERS
y=
Answers
Answer:
answer: y+2/3x+5
Step-by-step explanation:
because
Solve the equation. x^x=3/4(√6)
Answers
Answer:
Hi! The answer to your question is [tex]x = 3/2[/tex]
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☁Brainliest is greatly appreciated!☁
Hope this helps!!
- Brooklynn Deka
Find the slope,
(5,0) and (0.-7)
Answers
Answer:
[tex]\frac{-7}{-5}[/tex]
-7/-5
is the slope.
or -1 -2/-2
you pick.
Step-by-step explanation:
Δy/Δx
-7-0 / 0-5
-7 / -5
-7/-5
is the slope.
change in y over change in x
y2-y1 over x2-x1
simplify if possible.
-1 -2/-2
it's negative.
Answer:
Slope = 1 2/5 or 1.4
Step-by-step explanation:
Using the y2 - y1/x2 - x1 format, you first replace the variables with the points (5 and 0 can be x1, y1, while 0 and -7 can be x2, y2)
-7 - 0/0 - 5
Now subtract: -7 - 0 = -7; 0 - 5 = -5
You would get -7/-5, which simplified: 1.4 or 1 2/5
:p
there you go!
A shoemaker claims his best product has an average lifespan of exactly 14 years. A skeptical customer asks for evidence (data) that might be used to evaluate this claim. The customer was provided data collected from a random sample of 45 people who used the product. Using the data, an average product lifespan of 15 years and a standard deviation of 6 years was calculated. Select the 95%, confidence interval for the true mean lifespan of this product.
Answers
Answer:
The 95%, confidence interval for the true mean lifespan of this product is between 13.2 and 16.8 years.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 45 - 1 = 44
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 44 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0154
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.0154\frac{6}{\sqrt{45}} = 1.8[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 15 - 1.8 = 13.2 years
The upper end of the interval is the sample mean added to M. So it is 15 + 1.8 = 16.8 years.
The 95%, confidence interval for the true mean lifespan of this product is between 13.2 and 16.8 years.