The value of [tex]n[/tex] such that [tex]\sqrt[3]{n+\sqrt{n^{2}+8}}+ \sqrt[3]{n-\sqrt{n^{2}+8}} = 8 [/tex] is [tex]280[/tex].
Procedure - Determination of the root of radical functionIn this question we need to find the root of the radical function [tex]\sqrt[3]{n+\sqrt{n^{2}+8}}+ \sqrt[3]{n-\sqrt{n^{2}+8}} = 8 [/tex], which must be simplified by algebraic means.
First, we need to elevate each side of the expression by third power:
[tex]\left(\sqrt[3]{n+\sqrt{n^{2}+8}} + \sqrt[3]{n+\sqrt{n^{2}+8}} \right)^{3} = 512[/tex]
[tex]2\cdot n + 3\cdot \sqrt[3]{(n+\sqrt{n^{2}+8})^{2}\cdot (n-\sqrt{n^{2}+8})} + 3\cdot \sqrt[3]{(n-\sqrt{n^{2}+8})^{2}\cdot (n+\sqrt{n^{2}+8})} = 512[/tex]
[tex]2\cdot n -6\cdot (\sqrt[3]{n+\sqrt{n^{2}+8}} + \sqrt[3]{n-\sqrt{n^{2}+8}}) = 512[/tex]
[tex]2\cdot n - 6\cdot (8) = 512[/tex]
[tex]n = 280[/tex]
The value of [tex]n[/tex] such that [tex]\sqrt[3]{n+\sqrt{n^{2}+8}}+ \sqrt[3]{n-\sqrt{n^{2}+8}} = 8 [/tex] is [tex]280[/tex]. [tex]\blacksquare[/tex]
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Find the area, in square inches, of a square with a side length 1/4 in.
Answer:1/16 squared
Step-by-step explanation:
1/4*1/4
4*4=16
1/16
There are 4 consecutive EVEN integers that have a sum of 268. What are the integers?
64 + 66 + 68 + 70
hope this helps!
5x+1=3x+y=-15, what is x?
Answer:
x= -16/5
Step-by-step explanation:
5x+1=-15
solve
5x+1=-15
-1
5x=16
16/5
x= -16/5
What is 246,588 rounded to the ten thousands place?
246,588 rounded to the nearest 10 thousands place is 250,000
Which frequency table is consistent with the histogram of weights of 86 different students, below?
Answer:
B
Step-by-step explanation:
The incorrect tables each have at least one flaw that makes it not match the histogram.
A. The relative frequency associated with 4 of 86 is about 0.047, not 0.055. The relative frequencies are incorrect.
B. this table matches the histogram
C. The "bins" are not of uniform width, nor are they centered on the same values as shown in the histogram.
D. The values in a cumulative frequency table should be non-decreasing. The table value of 24 should be 54.
Need help please if anyone one can help me now I will like that. Thanks
help please anybody Mhm
Answer:
B
Step-by-step explanation:
Answer:
Your answer would be C
Step-by-step explanation:
Because its a ratio of integers with a nonzero denominator.
Today, everything at the store is on sale. The store offers a 20% discount
If the regular price of an item is x dollars, what is the discount price in dollars?
Answer:
.8x dollars
Step-by-step explanation:
Twenty percent off means you are paying 80 percent of every dollar, and 80 percent translates to .8 to 1 as a proportion.
Answer:
$.80x
Step-by-step explanation:
0.80x
Using Pythagoras, find the lengths of the sides labelled with letters.
Answer:
Step-by-step explanation:
which of the following are equivalent
In(3x-1)+4 i don't know the answer
Answer:3x+5
Step-by-step explanation:
Answer:
In(3xe^4 - e^4)
Step-by-step explanation:
In(3x-1)+4
convert the constant to a log with base e:
In(3x-1) + In(e^4)
Simplify the expression:
In((3x-1)e^4)
Remove the parentheses:
In(3xe^4 - e^4)
Hope it help !
System practice problems
Looking at the first system of equations,
16x - 10y = 10
-8x - 6y = 6
If we multiply both sides of the second equation by 2, the coefficient of x is exactly the negative of the coefficient of x in the first equation.
-8x - 6y = 6
⇒ 2 (-8x - 6y) = 2 (6)
⇒ -16x - 12y = 12
By combining this new equation with the first one, we can eliminate x and solve for y :
(16x - 10y) + (-16x - 12y) = 10 + 12
⇒ -22y = 22
⇒ y = -1
Then we just solve for x by replacing y in either equation.
16x - 10y = 10
⇒ 16x - 10 (-1) = 10
⇒ 16x + 10 = 10
⇒ 16x = 0
⇒ x = 0
The main idea behind elimination is combining the given equations in just the right amount so that one of the variables disappears. The "right amount" involves using the LCM of the coefficients of a given variable. In this example, the x-coefficients had LCM(8, 16) = 16, so we only had to scale one of the equations (the one with -8x) to cancel all the x terms.
If we wanted to eliminate y first instead, we first note that LCM(6, 10) = 30. To get 30 as a coefficient on y, in the first equation we would have multiplied by 3:
16x - 10y = 10
⇒ 3 (16x - 10y) = 3 (10)
⇒ 48x - 30y = 30
And in the second equation, we would have multiplied by -5 (negative so that upon combining the equations, we end up with -30y + 30y = 0):
-8x - 6y = 6
⇒ -5 (-8x - 6y) = -5 (6)
⇒ 40x + 30y = -30
Now combining the two scaled equations gives
(48x - 30y) + (40x + 30y) = 30 + (-30)
⇒ 88x = 0
⇒ x = 0
We then solve for y :
16x - 10y = 10
⇒ -10y = 10
⇒ y = -1
so we end up with the same solution as before.
Today 60 students rode their bicycles to Coast Middle School. If this is 75% of the students at the school, how many students attend Coast middle School?
Answer:
i think students attend Coast middle School 80 students
Step-by-step explanation:
students attend Coast middle School x students
75%x = 60
x = 60×100/75
x = 80
Answer:
80 students attend
Step-by-step explanation:
75% is the same as 3/4 so you divide 60 by 3 to get 20 then you can multiply that by 4 to get 80
The figure below shows the number of dots in each of the first four terms of a pattern.
image 3946d177031641899e8a9055b29f185e
Which of these can be used to determine
N
, the number of dots, given
t
, the number of the term in the pattern?
N
=
4
(
t
−
1
)
N = 4 ( t − 1 )
N
=
3
t
+
1
N = 3 t + 1
N
=
3
(
t
−
1
)
+
1
N = 3 ( t − 1 ) + 1
N
=
3
t
+
2
Answer:
there is nothing just a a codding log
Step-by-step explanation:
If you put $1000 in a savings account that yields an 7% annual rate of interest that is compounded weekly, how much would that be worth in 25 weeks
Answer:
A = $1034
Step-by-step explanation:
The relevant Amount function is A = P(1 + r/n)^(n*t), where r is the annual interest rate as a decimal fraction, n is the number of compounding periods per year, and t is the number of years.
There are 52 weeks in a year. Hence, n = 52, and 25 weeks = 25/52 year, or 0.481 year.
The accumulation (value of the savings) would be
A = ($1000)(1 + 0.07/52)^(52*[25/52]), or approximately
A = ($1000)(1.0013)^25, or approximately A = $1034
The United States and Canada have the production possibilities curves shown above. It is determined that the United States has the comparative advantage in peanuts. Will both nations gain from trade if the terms of trade that are offered are 1 Peanut= 3 Corn? Why or why not? Show your work.
This is economics
It is false both nations will benefit if the terms of trade are 1 peanut = 3 corn.
What is the comparative advantage?The comparative advantage refers to the ability of one company or nation to produce something at a lower cost. In this case, the U.S. can produce peanuts at a lower cost than Canada.
Will both nations benefit if they trade 1 peanut for 3 corn?No, due to their differences in the amounts of units produced and their comparative advantage both nations will not benefit from this trade.
Canada: Canada can produce 60 corn for every 20 peanuts, this can be understood as a 1 peanut : 3 corn ratio, therefore, this country will benefit from the 1 peanut = 3 corn term.United States: The United States produces 60 corn for every 60 peanuts or 1 peanut: 1 corn. Due to this, they will not benefit from the trade because this nation does not produce enough corn to meet the demand of 1 peanut = 3 corn.Learn more about comparative advantage in: https://brainly.com/question/4461081
PLZ HELP ME!! IF YOUR A GENUIS
The equation 4.05p+14.40=4.50(p+3) represents the number of p of pounds of penuts you need to make a trail mix. How many pounds of peanuts do you need for the trail mix?
Since "p" represents the number of pounds of peanuts and:
4.05p + 14.40 = 4.50(p + 3) [then by distributing we have:
4.05p + 14.40 = 4.50p + 13.5 [then by subtracting 13.5 from both sides we have:
4.05p + 0.9 = 4.50p [then by subtracting 4.05p from both sides we have:
0.9 = 0.45p [then by dividing both sides by 0.45 we have:
2 = p
So there are 2 pounds of peanuts needed for the trail mix.
What is this expression translated into words?
2n + 1
a
one plus 2 divided by a number n
b
2 times 1 added to a number n
c
two times a number n added to one
Answer:
C. two times a number n added to one
Alejandro uses the steps below to convert StartFraction 5 over 8 EndFraction to a percent. Five-eighths right arrow 8. 0 divided by 5 = 1. 6. 1. 6 = 160 percent. Which best explains Alejandro’s error? The division was computed incorrectly. The division was completed in the incorrect order. The decimal was moved to the right too many times. The decimal was moved to the right instead of the left.
Alejandro makes an error in the first steps he divides 8 by 5 which is incorrect he has to divide 5 by 8, and in the second step, he does not multiply the term by 100 and it can be determined by using fraction or percentage.
Given that,Alejandro uses the steps below to convert 5/8 to a percent.
8 divided by 5 = 1.6.,
1.6 = 160 percent
We have to determine,Which best explains Alejandro's error?
According to the question,Alejandro uses the steps below to convert 5/8 to a percent.
8 divided by 5 = 1.6.,
1.6 = 160 percent
The division was computed incorrectly.
The division was completed in the incorrect order. The decimal was moved to the right too many times.
The decimal was moved to the right instead of the left.
Alejandro uses the steps below to convert 5/8 to a percent.
To convert 5/8 into percentages following all the steps given below.
Step1; Firstly 5 is divided by 8,[tex]= \dfrac{5}{8} \\\\ = 0.625[/tex]
Step2; To convert 0.625 into percentage multiplied by 100,[tex]\rm = 0.625 \times 100\\\\= 62.5 \ percent[/tex]
Hence, Alejandro makes an error in the first steps he divides 8 by 5 which is incorrect he has to divide 5 by 8, and in the second step, he does not multiply the term by 100.
For more details about the Equation refer to the link given below.
https://brainly.com/question/18187260
Answer:
Just tell me the letter.
Step-by-step explanation:
what is the sum of 4 and -5
Answer:
-1
Step-by-step explanation:
its like subtracting 5 and 4
There is a string of red and blue lights strung around
a window. The red lights blink every 3 seconds, and
the blue lights blink every 5
seconds. How many
times will they blink at the same time in one
minutes?
Answer:
4 times because they will have the common number of 15 and since there is 60 seconds in a minute you would divide 60 by 15, and that equals 4
Step-by-step explanation:
.RP.1.3 | JoAnn bought 2 shirts for $13.50 each and a purse for $8.
The sales tax was 6%. What is the total she paid for her
purchase, including tax?
Answer:
The answer is $22.79. Hope this helped! If the answer is wrong i'm super sorry!
Step-by-step explanation:
$13.50 + $8 = $21.50
0.06 x 21.50 = $1.29
$1.29 + $21.50 = $22.79
A T-shirt company charges $4 per T-shirt, plus a
flat shipping fee of $5. Terry bought some
T-shirts. How can you write an algebraic
expression to represent the total cost of Terry's
order including shipping?
Plz help plz
Answer:
y = 4x + 5
Step-by-step explanation:
4 times the number of shirts, which is unknown, +$5 no matter how many.
Answer:
4x + 5
Step-by-step explanation:
Four multiplied by the number of shirts purchased (x) plus five dollars for shipping.
I hope this helps!!
Sasha drinks 2.5 liters of water each
weekday. She drinks a total of 3 liters of
water on the weekend. What is the total
volume of water, in milliliters, Sasha drinks
each week?
Answer:
17000
Step-by-step explanation:
2.5
.5
11.0
3*2=6
11
+6
17
convert 3x-y=-5 to slope intercept form
Answer:
y=3x+5
Step-by-step explanation:
y=mx+b
-y=-5-3x
divide each term
y=5+3x
reorder 5 and 3x
answer:y=3x+5
- is dilated to be ' ' ' '. The original is the center of dilation.
What scale factor is used to create the dilation?
Find the slope of the line segment shown.
A) -1/2
B -1
C 1/3
D 1
Answer:
D)
Step-by-step explanation:
The answer would be D. The slope of a line is how fast it climbs. Height divided by base. Up divided by over. Thus, if it goes across 3 and up 1, its slope would be 1/3. If it goes across 1 and up 2, the slope is 2. If it goes across 1 and up -1, the slope is -1.
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Y=x2+3x+1
when х= 5, y=?
Answer:
y = 41
Step-by-step explanation:
Substitute x = 5 into the equation
y = 5² + 3(5) + 1 = 25 + 15 + 1 = 41
There are 81 calories in a 0.75 cup serving of chicken noodle soup. How many calories are in a 2 cup serving?
Answer:
162Step-by-step explanation:
There are 81 calories in a 0.75 cup serving of chicken noodle soup. How many calories are in a 2 cup serving?
0.75*2=2 cups
81*2=162
Answer:
x = 216
Step-by-step explanation:
[tex]\frac{81}{0.75}[/tex] = [tex]\frac{?}{2}[/tex]
I hope this helps!!
A total of 11 trucks was used to carry 126 tonnes of iron. Some of the trucks carry
16 tonnes each, and the rest carry 6 tonnes each. Form an equation and solve it to
find the number of 16 tonne trucks.
Step-by-step explanation:
x = number of trucks with 16 tonnes capacity
y = number of trucks with 6 tonnes capacity
x + y = 11
16x + 6y = 126
the first equation gives us
x = -y + 11
and we use that in equation 2 :
16(-y + 11) + 6y = 126
-16y + 176 + 6y = 126
-10y = -50
10y = 50
y = 5
x = -y + 11 = -5 + 11 = 6
the number of 16 tonne trucks was 6.