[tex]\left( x+\frac{1}{x}\right)^{8} =\sum _{k=0}^{8}\binom{8}{k} \cdotp x^{8-k} \cdotp \left(\frac{1}{x}\right)^{k}\\\\\\ \begin{array}{l}\text{We\ wish\ to\ find\ } x^{0} :\\\\x^{8-k} \cdotp \left(\frac{1}{x}\right)^{k} =x^{0}\\\\\Longrightarrow x^{8-k} \cdotp x^{-k} =x^{0}\\\\\Longrightarrow \cancel{x}^{8-2k} =\cancel{x}^{0}\\\\\Longrightarrow 2k=8\\\\\Longrightarrow k=4\end{array}\\\\\therefore \binom{8}{4} \cdotp x^{4} \cdotp \left(\frac{1}{x}\right)^{4} =\frac{8!}{( 8-4) !\cdotp 4!}[/tex]
[tex]\binom{8}{4} \cdotp x^{4} \cdotp \left(\frac{1}{x}\right)^{4} =\frac{8\cdotp 7\cdotp 6\cdotp 5\cdotp \cancel{4!}}{\cancel{4!} \cdotp 4\cdotp 3\cdotp 2\cdotp 1}\\\\\binom{8}{4} \cdotp x^{4} \cdotp \left(\frac{1}{x}\right)^{4}=70\\\\\therefore \boxed{\boxed{\text{The\ constant\ term\ is\ } 70}}[/tex]
Solve the equation below
x/7 = 6
9514 1404 393
Answer:
x = 42
Step-by-step explanation:
You know from your multiplication tables that ...
42/7 = 6
x = 42
__
If you like, you can solve this by multiplying both sides of the equation by 7.
(x/7)(7) = 6(7)
x = 42
Answer: The correct answer is: " x = 42 . "
_____________________
Step-by-step explanation:
------------------------------------------
Given:
x/7 = 6 ; Solve for "x" ;
_____________________
"x" divided by "7" equals "6" ;
to solve for "x"
______________________
Multiply Each Side of the equation by "7" :
______________________
→ " 7 * [tex](\frac{x}{7}) = 6 * (7)[/tex] ;
______________________
On the "left-hand side" of the equation; the "7's" cancel out;
→ {since: " 7 / 7 = 1 " } ;
___________________
and on the "right-hand side" of the equestion:
→ 6 * 7 = 42 ;
___________________
So; we have: " x = 42 " ; which is our answer.
___________________
Hope this is helpful!
Best of luck to you!
___________________
Can someone help me (Geometry)
Step-by-step explanation:
I think these is your correct answer .
0.3546875 Rounded to the nearest tenth
Answer:
0.4
Step-by-step explanation:
0.35 is hundredth, and since you always round 5 up, it makes 0.4
Answer:
0.4
Step-by-step explanation:
To figure out the answer, first we need to know how to round. Find the tenths place. That's the first 3 you come upon. Look at the number beside it. It is a five which means you would round up (this is because of the 5 or more raise the floor, four or less let it rest rule) The 3 would then turn into a 4.
what is the Answer to this?
Find the distance between the points ( - 5, 5) and (-2, 3). Round your answer to the nearest tenth
Answer:
D=√13(Decimal: 3.605551)
3.6
Step-by-step explanation:
Let's find the distance between your two points.
(−5,5);(−2,3)
(x1,y1)=(−5,5)
(x2,y2)=(−2,3)
Use the distance formula:
D=√(x2−x1[tex])^{2}[/tex]+(y2−y1[tex])^{2}[/tex]
=√(−2−−5[tex])^{2}[/tex]+(3−5[tex])^{2}[/tex]
=√(3[tex])^{2}[/tex]+(−2[tex])^{2}[/tex]
=√9+4
=√13
D=√13(Decimal: 3.605551)
solve square root equation.
2x^2-2=-12
Answer:
x=+/- root 5..................
Answer:
[tex]2 {x}^{2} - 2 = 12 \\ 2 {x}^{2} = 12 + 2 \\2 {x}^{2} = 14 \\ {x}^{2} = \frac{14}{2} = 7 \\ {x}^{2} = 7 \\ x = \sqrt{7} \\ thank \: ou[/tex]
If f(x)=5x-11 what is f(1)? f(3)?
Answer:
jhbgjbfvjbdfkvbdkbnxkhfb kxvnxkvbfvkbchbfcnccfkxkhvchjjj
Step-by-step explanation:
dywfrfvyetwfkfgffyffusofgsjfdgsdlcgslvgsivsfgfisfgisfdyfdic
Step-by-step explanation:
Hi there!
Given;
f(x) = 5x-1
Now; Simply keep the value of x in the given function.
f(1) = 5*1-11
= -6
Again;
f(3) = 5*3-11
= 15-11
= 4
Therefore, f(1) = -6 and f(3) = 4.
Hope it helps!
if 2x + 5 = 1 then x =
1. -2
2. -1.5
3. 0
4. 2
5. none of these
Answer:
1. x = -2
Step-by-step explanation:
2x + 5 = 1
2x + 5 - 5 = 1 - 5
2x = -4
2x/2 = -4/2
x = -2
Can someone help me ASAP
Answer:
8. thousands, 5,000
9. millions 6,000,000
Step-by-step explanation:
Answer:
8: thousands place, 5,000
9: millions place, 6 million
Step-by-step explanation:
Place value is quite confusing at first, but it gets to be much easier. Basically, every time you add a place on a number, you are increasing its place value! Lets use number 9 for example. The one in this number is in the ones place. You know this because it is the last digit. The 4, is the tens place, since it is directly to the left of the ones place. You are increasing the place value to the left. The order of place value is:
Ones
Tens
Hundreds
Thousands
Ten thousands
Hundred thousands
Millions
Ten Millions
Hundred Millions
Billions
and so on. I hope this was helpful!
If (5^4)m = 5^12, what is the value of m? (4 points)
A. 2
B. 3
C. 5
D. 8
Answer:
The value of m is 3
Step-by-step explanation:
(5^4)m =5^12
M = 3
(5^4)3 =5^4*3=12
(5^4)3 = 5^12
Answer:
(5 ^4)^m = (5)^12
625^m = (5)^12
Taking logs of both sides
log(625) *m = log (5) *12
m = log (5) *12 / log(625)
m = 0.69897000434 * 12 / log (625)
m = 0.69897000434 * 12 / 2.7958800173
m = 0.69897000434 * 12 / 2.7958800173
m = 3 answer is B
Here's a handy logarithm calculator: https://www.1728.org/logrithm.htm
Step-by-step explanation:
NEED HELP NOW WILL MARK BRANLIEST
Show all work to multiply quantity 3 plus the square root of negative 16 end quantity times quantity 6 minus the square root of negative 64 end quantity (10 points)
Answer:
50Step-by-step explanation:
Quantity 3 plus the square root of negative 16 end quantity:
3 + √-16Quantity 6 minus the square root of negative 64 end quantity:
6 - √-64Multiply the two above:
(3 + √-16)(6 - √-64) = (3 + 4√-1)(6 - 8√-1) = (3 + 4i)(6 - 8i) = 3*6 - 3*8i + 6*4i - 4i*8i = 18 - 24i + 24i - 32i² = 18 - 32(-1) = 18 + 32 = 50please help me, if you help then thanks!
Answer:
The last one is the answer.
Step-by-step explanation:
Inverses are like opposites so [tex]\sqrt{x}[/tex] would be the inverse of [tex]x^{2}[/tex]. However don't be fooled by the second option because that is not the same although it seems like it. The true inverses are [tex]\sqrt[3]{27}[/tex] and [tex]3^{3}[/tex]. 3 cubed is 27 and the cube root of 27 is 3.
The sum of 6 times a number and 6 is the same as the difference of the number and 9. Find the number.
Answer:
x = -3Step-by-step explanation:
Let x= the missing number6x + 6 = x - 96x - x = -9 - 65x ÷ 5 = -15 ÷ 5x = -3Checking:
6(-3) + 6 = (-3) - 9-18 + 6 = -12-12 = -12Solve 5x - 7y = 16 for y.
y =
(Use integers or fractions for any numbers in the expression.)
(Answer quickly)
Answer:
y=5x/7-16/7
Step-by-step explanation:
make y the subject formulae
7y=5x-16
divide by 7 both sides
y=5x/7-16/7
What is the approximate value of 159 to the nearest tenth?
Select the dot to plot your answer on the number line ASAP!!!!! WILL GIVE BRAINLEST TO CORRECT PERSON!!!!
Answer:
12.6
Step-by-step explanation:
The square root on 159 is 12.6095202129. Rounding to the nearest tenth should be 12.6.
Problems like this require a calculator for most people.
The approximate value of [tex]\sqrt{159}[/tex] to the nearest tenth is 12.61
Here,
We have to find the approximate value of [tex]\sqrt{159}[/tex] to the nearest tenth.
What is Rounding number?
Rounding is a method of approximating a number to its nearest place value.
Now,
The value of [tex]\sqrt{159}[/tex] = [tex]12.6095202129.[/tex]
To find Rounding number of 12.6095202129 nearest tenth look at the hundredth number. The number is 9 which is greater than 5, then add 1 in tenth place and remove all the number after tenth place.
Hence,
Rounding number of 12.6095202129 nearest tenth is 12.61
Learn more about the rounding number visit:
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Translate the word phrase into an algebraic expression: 6 divided into 12x.
Answer:
12x/6
Step-by-step explanation:
6 is being divided into 12x so you ask yourself what is 12x divided by 6 and that is your algebraic expression.
The radius of a monocycle wheel is 35 cm. How many revolutions will the wheel make in travelling 440m?
Answer:
200
Step-by-step explanation:
circumference of wheel =2πr = 219.91cm = 2.19m
total revolutions= total distance/circumference of wheel
= 440/2.19= 200.080
Referring to the figure, is the transformation a
rotation about the origin?
a. yes
b. no
Answer:
yes.
Step-by-step explanation:
90 Degree Rotation. When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x).
Anybody know the awnser to number 4 and 5 please awnser fast if you know it
Answer:
the final answer of 4 should be 24 7/12.
Step-by-step explanation:
I need to know [35 - (8 + 2) x 3]
Q) [35 - (8 + 2) × 3] = ?
→ 35 - {(8 + 2) × 3}
→ 35 - {10 × 3}
→ 35 - 30
→ 5 is the correct answer.
Order the numbers from least to
greatest.
1.5, 1.27, 1.4, 1.05 , 1.07 , 1.44
Answer:
1.05, 1.07, 1.27, 1.4, 1.44, and 1.5
Step-by-step explanation:
Answer:
1.05, 1.07, 1.27, 1.4, 1.44, 1.5
Step-by-step explanation:
The value of a car dropped from $23,600 to $21,900 over the last year. Determine the actual and relative change in this situation.
Actual Change: ? This car's value decreased by $
last year.
Round your answer to the nearest dollar.
Relative Change: ? This car's value decreased by
% last year.
Round your answer to the nearest tenth of a percent.
Answer:
The actual change in the car's value is $[tex]1700[/tex] and the relative change is [tex]7.20[/tex]%.
Step-by-step explanation:
It is given that the value of a car is dropped from $[tex]23600[/tex] to $[tex]21900[/tex].
So, the change in the value is the drop in the value of car, which is, [tex]23600-21900=1700[/tex].
So, the actual change in this car's value is $[tex]1700[/tex].
The relative change can be given by the expression,
[tex]\dfrac{\:\rm{Actual Change}}{\:\rm{Original Value}}\times100[/tex]
Substituting values, the relative change can be given by,
[tex]\begin{aligned}\dfrac{1700}{23600} \times 100&=\dfrac{1700}{236}\\&=7.20\end{aligned}[/tex]
1. How many times larger is 6 x 10^8 than 2 x 10^2?
2. How many times larger is 9 x 10-4 than 3 x 10-11?
Answer:
18
Step-by-step explanation:
suppose the manager of a shoe store wants to determine the current percentage of customers who are males. How many customers should the manager survey in order to be 92% confident that the estimated (sample) proportion is within 7 percentage points of the true population proportion of customers who are males?
z0.10 z0.05 z0.04 z0.025 z0.01 z0.005
1.282 1.645 1.751 1.960 2.326 2.576
Use the table of values above.
Answer:
There are 8 percent of customers who are males
Step-by-step explanation:
if 92 percent are females that would mean that the rest of that 8 percent are males
Help will give Brainly points
Answer:
They are similar.
Step-by-step explanation:
123 + 36 + x = 180
159 + x = 180
(159 - 159) + x = 180 - 159
x = 21
36 + 21 + x = 180
57 + x = 180
(57 - 57) + x = 180 - 57
x = 123
CDE = 123 + 36 + 21
ABC = 123 + 36 + 21
Fill in the blank by choosing the most appropriate word.
Regression equations are usually used to predict values of unavailable data. If the data do not closely model a particular type of function, then that type of function is not appropriate to use in statistical regression. The more closely data fit a model, the more _______________ predicted values will be.
a.
accurate
b.
quadratic
c.
scattered
d.
variable
The correct option is (a) i.e. Regression equations are usually used to predict values of unavailable data. If the data do not closely model a particular type of function, then that type of function is not appropriate to use in statistical regression. The more closely data fit a model, the more accurate predicted values will be.
What is Regression analysis?
A collection of statistical techniques known as regression analysis is used to estimate the associations between a dependent variable and one or more independent variables. It can be used to simulate the long-term link between variables and gauge how strongly the relationships between them are related.
Although there are non-linear regression techniques for more complex data and analysis, simple linear regression and multiple linear regression are the two fundamental types of regression. While multiple linear regression employs two or more independent factors to predict the outcome, simple linear regression just uses one independent variable to explain or predict the outcome of the dependent variable Y. (while holding all others constant).
Professionals in other industries, including banking and investment, might benefit from regression. Regression can also aid in predicting sales for a business based on external factors like the weather, past sales, GDP growth, and other variables. A popular regression model in finance for valuing assets and calculating capital expenses is the capital asset pricing model (CAPM).
To learn more about Regression analysis, visit the link :
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I need help look at the attached image
Which equation represents a line that passes through the points (5,-2) and (8,4)?
A. y= -2x*8
B. y= 1/2x-9/2
C. y=x-6
D. y=2x-12
Answer:
The correct choice is option D. y = 2x -12
Step-by-step explanation:
slope of the points (5,-2) and (8,4) is m = 2
y — intercept of the points (5,-2) and (8,4) is b = -12
Now, put it all together, and you'll get : y = 2x -12
Jazmine worked 58 hours last week. She gets time and a half for overtime. If her hourly rate is
$16, ;what will she get for the week? *
a.1072
b.928
c.946
d.964
Answer:
answer is A. 1072
Step-by-step explanation:
$16 x 40 hours = $640.00
$24 (time & Half) x 18 over time beyond 40 hours (40+18 = 58)) = $432.00
$432.00 + $640.00 = $1,072.00
1 a Copy and complete to begin to solve the
equation.
4x - 3=2x+7
4x - 3-0=2x + 7-O
Ox - 3=0
Answer:
0
Step-by-step explanation:
