Given:
The expression is:
[tex]\left(\dfrac{1}{7}-4\sqrt{3}\right)^3+\left(\dfrac{1}{7}+4\sqrt{3}\right)^3 [/tex]
To find:
The simplified form of the given expression.
Solution:
Formulae used:
[tex](a-b)^3=a^3-3a^2b+3ab^2-b^3[/tex]
[tex](a-b)^3=a^3+3a^2b+3ab^2+b^3[/tex]
Adding this formulae, we get
[tex](a-b)^3+(a+b)^3=2a^3+6ab^2[/tex] ...(i)
We have,
[tex]\left(\dfrac{1}{7}-4\sqrt{3}\right)^3+\left(\dfrac{1}{7}+4\sqrt{3}\right)^3 [/tex]
Using formula (i), the given expression can be written as:
[tex]=2\left(\dfrac{1}{7}\right)^3+6\left(\dfrac{1}{7}\right)\left(4\sqrt{3}\right)^2[/tex]
[tex]=2\times \dfrac{1}{343}+6\left(\dfrac{1}{7}\right)48[/tex]
[tex]=\dfrac{2}{343}+\dfrac{288}{7}[/tex]
[tex]=\dfrac{2+14112}{343}[/tex]
[tex]=\dfrac{14114}{343}[/tex]
Therefore, the simplified form of the given expression is [tex]\dfrac{14114}{343}[/tex].
help ?? Anyone ?? Pls
Find the volume of a pyramid with a square base, where the perimeter of the base is 16\text{ m}16 m and the height of the pyramid is 16.2\text{ m}16.2 m. Round your answer to the nearest tenth of a cubic meter.
Answer:
86.4 M
Step-by-step explanation:
(4 * 4 * 16.2) / 3
Find the slope of the line passing through the points (-2, -8) and (9,-8).
slope:
To get that answer, apply the slope formula
m = (y2 - y1)/(x2 - x1)
m = (-8 - (-8))/(9 - (-2))
m = (-8 + 8)/(9 + 2)
m = 0/11
m = 0
Any line with slope 0 is completely horizontal.
As a quick rule of thumb: if the y coordinates of the two points are the same, then the slope is 0 on this horizontal line.
The diagonals of a quadrilateral must be bisect each other and be perpendicular to gurarantee that the quadrilateral is a parrelogram
Answer:
False
Step-by-step explanation:
A quadrilateral is a closed geometrical figure that have four sides and four vertices. Thus the following includes in a quadrilateral : parallelogram, square, rhombus, rectangle and trapezium.
If the diagonals of the quadrilateral bisects each other and are perpendicular to each other, then the quadrilateral forms a rhombus.
Hence the answer is FALSE.
Need help on this please!!! 10 points!!!
Answer:
I think the answer is the first one ... am i right...
Which expressions are equivalent to 2^5•2^4? Check all that apply.
Answer:
2⁵×2⁴=2⁹
2⁵×2⁴=2×2×2×2×2×2×2×2×2
2⁵×2⁴=4⁵
2⁵×2⁴=8³×2
Answer:
[see below]
Step-by-step explanation:
Recall the product rule: [tex]a^x+a^y=a^{x+y}[/tex]
[tex]2^5 + 2^4 = 2^{5 + 4} = \boxed{2^9}[/tex]
Other expressions could be:
[tex]2^{-2} *2^{11}=2^{-2+11} = \boxed{2^9}[/tex]
[tex](2*2*2*2*2)(2*2*2*2) = 2^5 + 2^4 = \boxed{2^9}[/tex]
Hope this helps.
Question 7(Multiple Choice Worth 1 points) (08.02 LC) Eva conducted a survey to find out the amount of time high schoolers spend surfing the Internet. From the data collected, the range of time spent was 3 hours. What does this range say about the data? The quotient between the greatest amount of time and the least amount of time spent surfing the Internet is 3 hours. The difference between the greatest amount of time and the least amount of time spent surfing the Internet is 3 hours. All the students surveyed spend exactly 3 hours surfing the Internet. All the students surveyed spend an average of 3 hours surfing the Internet.
Answer:
The answer is "Option B".
Step-by-step explanation:
The difference between most time and also the least spending time on Internet surfing is 3 hours. Since we do not have charts for tables etc., only 3 can be used we need. A range is defined as the difference between the largest and the smallest amounts. The range between both the largest as well as the smallest is unique. In this reply, it tells us that the gap between most time and the fewer hours invested surfing the web is 3 hours.
In option A, it is wrong since the range has nothing to do with formulas. (Of course, the dividend with a divisor results in a quotient). Only subtraction and not division may be achieved.In option C, when all surf for exactly one hour, it could take the largest time of 3 hours and 3 hours, the last time. Add it into the equation and the range of the data present would've been 0.In option D, It is erroneous even as the range is not the mean, and the mean seems to be the average. We search for both the range, not the mean.The answer is B
The difference between the greatest amount of time and the least amount of time spent surfing the Internet is 3 hours.
This answer is proven 100% correct.
Hope this helps!
help plz, thanks!
2x + 6 = 4x - 2
Step-by-step explanation:
here's the answer to your question about
Answer:
2x + 6 = 4x + -2
6 + 2x = 4x + -2
6 + 2x = -2 + 4x
Add -4x to both sides
6 + 2x + -4x = -2 + 4x + -4x
Combine like terms
6 + -2x = -2 + 4x + -4x
6 + -2x = -2 + 0
6 + -2x = -2
add -6 to both sides
6 + -6 + -2x = -2 + -6
0 + -2x = -2 + -6
-2x = -2 + -6
-2x = -8
Divide each side by -2
x = 4
OAmalOHopeO
What’s the answer? Help
Answer:
$14
Step-by-step explanation:
x = price of scarf 1
y = price of scarf 2
together they cost $25
x + y = 25
one scarf costs $3 more than the other
x = y + 3
now we use that in the first equation again
y+3 + y = 25
2y +3 = 25
2y = 22
y = $11
=> x = y +3 = 11 + 3 = $14
Evaluate the expression 10 + 3(5 - 2) using order of operations.
Answer:
31
Step-by-step explanation:
PEMDAS
5-2=7
3 times 7 is 21
21+10
31
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{10 + 3 (5 - 2)}[/tex]
[tex]\large\textsf{5 - 2 = \bf 3}[/tex]
[tex]\large\textsf{= 10 + 3(3)}[/tex]
[tex]\large\textsf{3(3) = \bf 9}[/tex]
[tex]\large\textsf{= 10 + 9}[/tex]
[tex]\large\textsf{= \bf 19}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \bf 19}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Can someone help me with this math homework please!
Answer:
Meh
Step-by-step explanation:
2 tablespoons =
A) 3 teaspoons
B) 2 fluid ounces
C) 1 fluid Ounce
D) 1 teaspoon
Answer:
C) 1 fluid Once
Step-by-step explanation:
Can someone help me out
answer is
4ft* 5ft
= 20ft^2
If AABC is reflected across the y-axis, what are the coordinates of A'?
Answer:
-2,-4
Step-by-step explanation:
**HELP**
find the angle measures given the figure is a rhombus.
Answer:
m<1=74
m<2=37
Step-by-step explanation:
m<2 is the same as the other angle, 37 degrees. So now we need to find the other angle in the triangle.
37+37+x=180.
The total degree of a triangle is 180.
x=106
Subtract that from 180 to get m<1.
180-106=74
I hope this helps!
Good luck!
Find x,cb, and do, in the image below AB is the angle bisector of
**Fill in the blanks !!
x = 9
CB = DB = 61
Step-by-step explanation:
∠CAB = ∠DAB
So, DB = CB {Sides opposite to equal angles are equal}
6x +7 = 3x+ 34
Subtract 7 from both sides.
6x = 3x + 34 - 7
6x = 3x + 27
Subtract 3x from both sides.
6x - 3x = 27
3x = 27
Divide both sides by 3
x = 27/3
x = 9
DB = 6x +7
= 6*9 + 7
= 54 + 7
DB = 61
CB = 3x + 34
= 3*9 + 34
= 27 + 34
CB = 61
The equation of line a is y=−14x+3. If line b runs perpendicular to line a and passes through (2, 6), what would be the equation of line b?
Hint : The product of the slopes of two lines perpendicular to each other is - 1 .
______________________________
In slope-intercept ( y = ax + b ) from of the linear equations the coefficient of x is the slope of the line.
Thus :
Slope of line a = - 14
______________________________
Suppose that the slope of line b is x according to the Hint we have :
- 14 × x = - 1
negatives simplify
14x = 1
Divide both side by 14
14x ÷ 14 = 1 ÷ 14
x = 1/14
So the slope of line b is 1/14
_____________________________
Now let's find the equation of line b by point-slope formula using the point question have us ( 2 , 6 ) :
y - y( given point ) = Slope × ( x - x ( g p ) )
y - 6 = 1/14 × ( x - 2 )
y - 6 = 1/14 x - 2/14
y - 6 = 1/14 x - 1/7
Add both sides 6
y - 6 + 6 = 1/14 x - 1/7 + 6
y = 1/14 x - 1/7 + 42/7
y = 1/14 x + 41/7
And we're done ...
Answer:
more info needed
Step-by-step explanation:
HELP PLEASE!!! The readings on the thermometers are normally distributed with a mean of
0° and a standard deviation of 1º. The value of PIX greater than - 1.96) is
A. 0.9750 B. 0.9970 C. 0.9950 D. 0.9850
Explanation:
You can use a calculator or a Z table here. I'll go with the table option.
Using a Z table, you should find that P(Z < -1.96) = 0.0250
So the remaining area must be 1 - 0.0250 = 0.9750 which represents P(Z > -1.96). This is the same as P(X > -1.96) because X is distributed identical to the Z distribution (mean = 0, std dev = 1).
If you go the calculator route, then it depends on which calculator or computer software you use. If you prefer this route, then let me know which calculator you're using and I'll try to find the correct input to type in for that calculator.
Si Martha retira de su cuenta el 10% para los transportes del mes. ¿Cuál es el nuevo saldo de la cuenta?
Respuesta:
0,9 veces
Explicación paso a paso:
Deje que la cantidad en la cuenta de Martha se denote como x, que es la cantidad en la cuenta = x
Porcentaje retirado para transporte = 10%
El porcentaje total siempre será del 100%
Por lo tanto, si se retira el 10%, entonces; el porcentaje restante es:
Porcentaje total: porcentaje gastado en transporte
(100% - 10%) * monto en cuenta
90% * x = 0,9 * x = 0,9x
Saldo de cuenta nueva = 0.9x
By converting to an exponential expression, solve log3 (x + 9) = 5.
Answer:
[tex]{ \tt{ log_{3}(x + 9) = 5 }} \\ { \tt{x + 9 = {3}^{5} }} \\ { \tt{x + {3}^{2} = {3}^{5} }} \\ { \tt{x = {3}^{5} - {3}^{2} }} \\ { \tt{x = 234}}[/tex]
mary stated that 2.01 x 10⁶ is less than 4.8 x 10⁴ because 2.01 is less than 4.8. what was mary's mistake ?
SOMEONE HELP PLEASE
Answer:
Mary's mistake was that she didn't take into account of the power that 10 is raised to; since 2.01 is multiplied by 10 to the 6, it makes 2.01 bigger. You can also expand the number to check:
2 010 000 vs. 4800
Jane , peter and mary each have some cards of 3:5:6 . Peter has 40 cards . How many fewer cards did mary has then peter?
Answer:
Mary has 8 more card than Peter
Step-by-step explanation:
Jane: peter: mary
3 5 6
Peter has 40
40/5 = 8
Multiply each by 8
Jane: peter: mary
3*8 5*8 6*8
24 40 48
We want Mary - Peter
48-40
8
Mary has 8 more card than Peter
Rhombus LMNO is shown with its diagonals. Rhombus L M N O is shown. Diagonals are drawn from point M to point O and from point L to point N and intersect at point P. All sides are congruent. The length of LN is 28 centimeters. What is the length of LP?
In a Rhombus the diagonals intersect and divides it in two equal halves.
Therefore LP = 28/2
LP = 14cm
Answered by GauthMath if you like please click thanks and comment thanks
Answer:
Answer: 14 cm
Step-by-step explanation:
E2020
Find the equation of the line parallel to y = -3x + 4 with a y-intercept of -10
Answer:
y=-3x-10
Step-by-step explanation:
Hi there!
We need to find the equation of the line parallel to y=-3x+4 that has the y intercept of -10 (the point (0, -10))
Parallel lines have the same slope
The slope of y=-3x+4 is -3 (it is in the placement of where m (slope) is in y=mx+b)
So the slope of the new line parallel to y=-3x+4 is also -3
Here is the equation of that line so far:
y=-3x+b
b is a placeholder for the y intercept
However, we are given the y intercept as -10, so substitute -10 as b into the equation
y=-3x-10
There's the equation of the line parallel to y=-3x+4 with a y intercept of -10
Hope this helps!
which expression is equivalent to (4 square root 5 to the power of 3) to the power of 1/2
Rex buries 6 bones in the backyard on Monday then he buries more on Tuesday he buried a total of 10 bones how many did he bury Tuesday?
Answer:
Rex buried 4 bones on Tuesday
Step-by-step explanation:
10 - 6 = 4. Simple as that
The slope of MN is -3 which segment is parallel to MN
Answer:
B and D
Step-by-step explanation:
What is the product?
43 .4-3
0)
1)
4)
6)
Answer:
1
Step-by-step explanation:
So we can actually simplify the exponents here. The power rule for exponents is that when multiplying, you add the exponents. So,
3 + (-3) = 0
so the number is now 4^0.
Everything by the power of 0 is equal to 1, so the answer is 1.
Hope this helps !!
-Ketifa
tìm x,y nguyên tố thỏa mãn:y^2-2x^2=1
Answer:
dx/dy = y/2x
Step-by-step explanation:
-4x × dx/dy = -2y..... that's all
what type of polynomial is p(x)=4x−2x2+3
a. quadratic
b. quartic
c. quintic
d. cubic
Answer:
a. quadratic.
The given polynomial p(x)=4x−2x²+3 is a quadratic polynomial. The correct option is A.
What is a polynomial?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
In algebra, a polynomial function with one or more variables in which the highest-degree term is of the second degree is known as a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic.
In the given polynomial p(x)=4x−2x²+3 it can be observed that the degree of the polynomial is 2 or the highest power of the variable is 2.
Therefore, the given polynomial p(x)=4x−2x²+3 is a quadratic polynomial. The correct option is A.
To know more about quadratic polynomials follow
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