Answer:
It is (x - 3)³ - 9x(3 - x)
Step-by-step explanation:
Express 27 in terms of cubes, 27 = 3³:
[tex] = {x}^{3} - {3}^{3} [/tex]
From trinomial expansion:
[tex] {(x - y)}^{3} = (x - y)(x - y)(x - y) \\ [/tex]
open first two brackets to get a quadratic equation:
[tex] {(x - y)}^{3} = ( {x}^{2} - 2xy + {y}^{2} )(x - y)[/tex]
expand further:
[tex] {(x - y)}^{3} = {x}^{3} - y {x}^{2} - 2y {x}^{2} + 2x {y}^{2} + x {y}^{2} - {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3x {y}^{2} - 3y {x}^{2} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3xy(y - x) \\ \\ { \boxed{( {x}^{3} - {y}^{3} ) = {(x - y)}^{3} - 3xy(y - x)}}[/tex]
take y to be 3, then substitute:
[tex]( {x}^{3} - 3^3) = {(x - 3)}^{3} - 9x(3 - x)[/tex]
x+9=13352643-2x answer get brainliest
Answer:
4450878
Step-by-step explanation:
What statement is not true? A) a square is a rhombus C) a rhombus is a rectangle D) a square is a rectangle
B) a rhombus is a parallelogram
Answer:
A square is a retangle
Step-by-step explanation:
Because a squre is a rectangle
PLEASE HELP IM SO LOST
1. Ted is working on his financial plan and lists all of his income and expenses in the spreadsheet below.
А
B
Net Pay
$5,000
2
Interest on Deposits $0
3 Income from Investments $225
4 Rent
$3,000
5 Utilities
$250
6 Satellite Dish
$175
7 Cell Phone Plan
$135
8 Car Payment
$385
9 Groceries
$200
10 Insurance
$380
11 Recreation
$400
What is Ted's net cash flow?
2. Tamara earns $8 an hour at her job working 25 hours per week. If her net pay is 78% of her paycheck
and she has no other sources of income, what is Tamara's monthly cash inflow? (Assume there are 4
pays per month.)
Answer: 1) $300 2) $624
Step-by-step explanation:
[tex]\begin{array}{l||l|l}\underline{\quad \text{Item}\qquad \qquad \qquad \qquad}&\underline{\text{Income} }&\underline{\text{Expense}}\\\text{Net Pay}&5000&\\\text{Interest on Deposits}&0&\\\text{Income from Investments}&225&\\\text{Rent}&&3000\\\text{Utilities}&&250\\\text{Satellite Dish}&&175\\\text{Cell Phone Plan}&&135\\\text{Car Payment}&&385\\\text{Groceries}&&200\\\text{Insurance}&&380\\\underline{\text{Recreation}\qquad \qquad \qquad}&\underline{\qquad \quad }&\underline{400\qquad}\\\end{array}[/tex]
TOTALS 5225 4925
Net Cash Flow = Income - Expenses
= 5225 - 4925
= 300
*************************************************************************************
[tex]\dfrac{25\ hours}{week}\times \dfrac{\$8}{hour}\times 4\ weeks\times 78\%\\\\\\=25\times \$8 \times 0.78\\\\= \$624[/tex]
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!
1. How can a matrix be used to solve a system of equations? Demonstrate by solving the following system. Show your work. In other words, use a problem of system of equations problem as an example.
Answer:
Step-by-step explanation:
Assuming the system is solvable in the first place, create an augmented matrix of coefficients from the equations. Then put the matrix into reduced row echelon form.
Example is attached.
"Demonstrate by solving the following system."
You need to provide the system of equations.
convert 407 in base 8 to decimal
[tex]4\cdot8^2+0\cdot8^1+7\cdot8^0=256+7=263[/tex]
[tex]407_8=263_{10}[/tex]
Help please!!! Thank you
Answer:
5/7
Step-by-step explanation:
There are a couple ways to solve this. One would be by finding the least common denominator for each one with 2/3, subtracting, and seeing what is left over. Another way is converting to decimals.
2/3=0.666666
————————-
7/8=0.875
8/9=0.88888
4/5=0.8
5/7=0.7143
They are all greater than 2/3 (0.6666666), but 5/7 is the closest, so would have the least waste.
=
Graphing an integer function and finding its range for a given...
The function h is defined as follows for the domain given.
h(x) = 2 -2x, domain = {-3, -2, 1, 5}
Write the range of h using set notation. Then graph h.
Answer:
Step-by-step explanation:
● h(x) = 2-2x
The domain is {-3,-2,1,5}
● h(-3) = 2-2×(-3) = 2+6 = 8
● h(-2) = 2 -2×(-2) = 2+4 = 6
● h(1) = 2-2×1 = 2-2 = 0
● h(5) = 2-2×5 = 2-10 = -8
The range is {-8,0,6,8}
if sin150=1/2 then find sin75
Sin75° = Sin(30° + 45°)
= Sin30°.Cos45° + Sin45°.Cos30°
= 1/2 . √2/2 + √2/2.√3/2
= √2/2 ( 1/2 + √3/2 )
= √2/2 ((1+√3 ) /2 )
= (√2 + √6 )/ 4
What is the mulitplicative rate of change for the exponential function f(x) = 2 (5over2) to the negative x power ?
Answer:
2/5
Step-by-step explanation:
f(x) = 2(5/2)^-x = 2(2/5)^x
The multiplicative rate of change is the base of the positive exponent, 2/5.
(x-2) is a factor of x^2-3x^2+kx+14. The value of k is?
Answer:
k = 5
Step-by-step explanation:
I will assume that your polynomial is
x^2 - 3x^2 + kx + 14
If x - a is a factor of this polynomial, then a is a root.
Use synthetic division to divide (x - 2) into x^2 - 3x^2 + kx + 14:
2 / 1 -3 k 14
2 -2 2k - 4
-------------------------------------
1 -1 (k - 2) 2k - 10
If 2 is a root (if x - 2 is a factor), then the remainder must be zero.
Setting 2k - 10 = to zero, we get k = 5.
The value of k is 5 and the polynomial is x^2 - 3x^2 + 5x + 14
A cardboard box without a lid is to be made with a volume of 4 ft 3 . Find the dimensions of the box that requires the least amount of cardboard.
Answer:
2ft by 2ft by 1 ftStep-by-step explanation:
Total surface of the cardboard box is expressed as S = 2LW + 2WH + 2LH where L is the length of the box, W is the width and H is the height of the box. Since the cardboard box is without a lid, then the total surface area will be expressed as;
S = lw+2wh+2lh ... 1
Given the volume V = lwh = 4ft³ ... 2
From equation 2;
h = 4/lw
Substituting into r[equation 1;
S = lw + 2w(4/lw)+ 2l(4/lw)
S = lw+8/l+8/w
Differentiating the resulting equation with respect to w and l will give;
dS/dw = l + (-8w⁻²)
dS/dw = l - 8/w²
Similarly,
dS/dl = w + (-8l⁻²)
dS/dw = w - 8/l²
At turning point, ds/dw = 0 and ds/dl = 0
l - 8/w² = 0 and w - 8/l² = 0
l = 8/w² and w =8/l²
l = 8/(8/l² )²
l = 8/(64/I⁴)
l = 8*l⁴/64
l = l⁴/8
8l = l⁴
l³ = 8
l = ∛8
l = 2
Hence the length of the box is 2 feet
Substituting l = 2 into the function l = 8/w² to get the eidth w
2 = 8/w²
1 = 4/w²
w² = 4
w = 2 ft
width of the cardboard is 2 ft
Since Volume = lwh
4 = 2(2)h
4 = 4h
h = 1 ft
Height of the cardboard is 1 ft
The dimensions of the box that requires the least amount of cardboard is 2ft by 2ft by 1 ft
What is the circumference of the following circle?
Answer:
The answer is 157 inStep-by-step explanation:
Circumference of a circle = 2πr
where
r is the radius
From the above question
radius = 25 in.
Substitute this value into the above formula
That's
Circumference = 2(25)π
= 50π
= 157.079
We have the final answer as
Circumference = 157 inHope this helps you
NEED HELP ASAP!!!!!!!!!!
Answer:
Hey there!
A is correct. The +2 means shifted up two units, 1/2 means compressed by a factor of 1/2, and the -3 means to the left of three units.
Let me know if this helps :)
Let REPEAT TM = { | M is a TM, and for all s ∈ L(M), s = uv where u = v }. Show that REPEATTM is undecidable. Do not use Rice’s Theorem.
Answer:
Step-by-step explanation:
Let REPEAT [tex]_{TM[/tex]= { | M is a TM, and for all s ∈ L(M), s = uv where u = v }
To prove that REPEAT [tex]_{TM[/tex] is undecidable.
Let REPEAT [tex]_{TM[/tex] {| M is a TM that does not accept M}
Then, we form a TM u for L by applying TM v as a subroutine.
Assume Repeat is decidable
Let M be the algorithm that TM which decides the REPEATU = on input "s" simulate the M
Accept; if M ever enters the accept state
Reject; if M ever enters the reject state
U does not decide the REPEAT as it may loop over s
so REPEAT is undecidable
When f(x) = -3, what is x?
-29
-10
-3
-1
Answer:
The correct choice is option D. -1
Step-by-step explanation:
Find f(x) = - 3 on the table. When y = -3, what is the x value? Look on the right side, you can see it's -1, correct? So, f(x) = - 3 when x = - 1.
A car dealer's markup on every car they sell is 20%. For what price did the dealership buy a car that they sold for $18,600?
Answer:
buying price = $15,500
Step-by-step explanation:
selling price 20% more than the buying price
let the buying price be 100% then;
selling price = 120%
120% = $18,600
100% = ?
(100 × 18600) ÷ 120
= $15,500
How many solutions does the following equation have ?
−3x+9−2x=−12−5x
[tex]\text{Solve for x:}\\\\-3x+9-2x=-12-5x\\\\\text{Combine like terms}\\\\-5x+9=-12-5x\\\\\text{Add 5x to both sides}\\\\9=-12\\\\\text{Since that's not valid, there would be no solutions}\\\\\boxed{\text{No solutions}}[/tex]
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. (If the quantity diverges, enter DIVERGES.) an = 1/sqrt(n)
This sequence converges to 0.
Proof: Recall that
[tex]\displaystyle\lim_{n\to\infty}\frac1{\sqrt n}=0[/tex]
is to say that for any given [tex]\varepsilon>0[/tex], there is some [tex]N[/tex] for which [tex]\left|\frac1{\sqrt n}-0\right|=\frac1{\sqrt n}<\varepsilon[/tex] for all [tex]n>N[/tex].
Let [tex]N=\left\lceil\frac1{\varepsilon^2}\right\rceil[/tex]. Then
[tex]n>\left\lceil\dfrac1{\varepsilon^2}\right\rceil\ge\dfrac1{\varepsilon^2}[/tex]
[tex]\implies\dfrac1n<\varepsilon^2[/tex]
[tex]\implies\dfrac1{\sqrt n}<\varepsilon[/tex]
as required.
Please answer this correctly without making mistakes
Answer:
[tex]\large \boxed{\mathrm{4/5 \ cups}}[/tex]
Step-by-step explanation:
Subtract 1/10 from 9/10 to find out how much is left.
9/10 - 1/10
8/10 = 4/5
Answer:
4/5 cupsStep-by-step explanation:
[tex]Volume\:of \: syrup \:in \:cup\:from\:jug = \frac{9}{10}\\\\ She \:took\: \frac{1}{10} from \:the\:cup\:into\:the \:jug \\\\Volume \:of syrup\:in\:cup=?\\\\\frac{9}{10} -\frac{1}{10} \\\\= \frac{4}{5} cups[/tex]
Calculate how many different sequences can be formed that use the letters of the given word. Leave your answer as a product of terms of the form C(n, r). HINT [Decide where, for example, all the s's will go, rather than what will go in each position.]
georgianna
A) C(10, 7)
B) C(2, 10)C(1, 8)C(1, 7)C(1, 6)C(1, 5)C(2, 4)C(2, 2)
C) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 1)C(3, 1)C(2, 1)C(1, 1)
D) 10 · C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)
E) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)
Answer: E) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)
Step-by-step explanation:
According to the combinations: Number of ways to choose r things out of n things = C(n,r)
Given word: "georgianna"
It is a sequence of 10 letters with 2 a's , 2 g's , 2 n's , and one of each e, o,r, i.
If we think 10 blank spaces, then in a sequence we need 2 spaces for each of g.
Number of ways = C(10,2)
Similarly,
1 space for 'e' → C(8,1)
1 space for 'o' → C(7,1)
1 space for 'r' → C(6,1)
1 space for 'i' → C(5,1)
1 space for 'a' → C(4,2)
1 space for 'n' → C(2,2)
Required number of different sequences = C(10,2) ×C(8,1)× C(7,1)× C(6,1)×C(5,1)×C(2,2).
Hence, the correct option is E) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)
Researchers recorded that a certain bacteria population declined from 120,000 to 200 in 36 hours. At this rate of decay, how many bacteria will there be in 31 hours? Round to the nearest whole number.
Answer: There will 486 bacteria in 31 hours.
Step-by-step explanation:
The population decay in bacteria is exponential.
Exponential function : [tex]y=Ab^x[/tex], where A = initial population, b multiplication decay factor, t= time:
As per given:
Initial population: [tex]A=120,000[/tex]
After 36 hours, population = [tex]120000(b^{36})=200[/tex]
Divide both sides by 120,000 we get
[tex]b^{36}= 0.00167[/tex]
Taking natural log on both sides , we get
[tex]36\ln b=\ln 0.00167\\\\\Rightarrow\ b=e^{\left(\frac{\ln0.00167}{36}\right)}=0.83724629\approx0.8372[/tex]
At x= 31,
[tex]y=120000(0.8372)^{31}=120000\times0.00405234\approx486[/tex]
Hence, there will 486 bacteria in 31 hours.
Find the distance between the points. Give an exact answer and an approximation to three decimal places.
(3.1,0.3) and (2.7. - 4.9)
The exact distance is
(Simplify your answer. Type an exact ans
Answer: sqrt(27.2) =approx 5.215
Step-by-step explanation:
The distance between 2 points can be calculated using Phitagor theorem
L= sqrt( (x1-x2)²+(y1-y2)²)
Where x1, y1 are the coordinates of the first point and x2, y2 are the coordinates of the 2-nd point.
L=sqrt((3.1-2.7)²+(0.3-(-4.9))²)= sqrt(0.4²+5.2²)=sqrt(27.2) - this is exact answer.
sqrt(27.2)=5.21536...=approx 5.215
The solutions to the equation $(x+1)(x+2) = x+3$ can be written in the form $m+\sqrt n$ and $m-\sqrt n$, where $m$ and $n$ are integers. What is $m+n$?
Answer:
1
Step-by-step explanation:
Hello, please consider the following.
First, we develop and move everything to the left side, then we solve the equation, using the discriminant.
Finally, we get the expression of the two solutions and we can conclude.
[tex](x+1)(x+2)=(x+3)\\\\<=> x^2+3x+2-x-3=0\\\\<=>x^2+2x-1=0\\\\\Delta=b^2-4ac=4+4=8\\\\x_1=\dfrac{-2-\sqrt{8}}{2}=\dfrac{-2-2\sqrt{2}}{2}=-1-\sqrt{2}\\\\x_2=\dfrac{-2+\sqrt{8}}{2}=-1+\sqrt{2}[/tex]
So, m=-1 and n = 2
m+n = -1 + 2 = 1
Thank you
The value of m + n is 1.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 - 9 is an equation.
We have,
(x + 1)(x + 2) = x + 3
x² + 2x + x + 2 = x + 3
x² + 3x + 2 - x - 3 = 0
x² + 2x - 1 = 0
This is in the form of ax² + bx + c = 0
a = 1, b = 2, and c = -1
Now,
Using the determinant.
x = -b ± √(b² - 4ac) / 2a
x = -2 ± √(4 + 4) / 2
x = (-2 ± 2√2) / 2
x = (-1 ± √2)
x = -1 + √2
x = -1 - √2
Now,
The solutions can be written in the form of (m + √n) and (m - √n).
This means,
m + √n = -1 + √2
m - √n = -1 - √2
m = -1 and n = 2
Now,
m + n
= -1 + 2
= 1
Thus,
m + n is 1.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ2
Consider the quadratic equation 4x2 - 11x - 3 = 0. Which of the following shows
this equation rewritten and ready to solve using factoring by grouping?
A) 4x2 - 9x - 2x - 3 = 0
B) 4x2 - 6x - 5x - 3 = 0
C) 4x2 - 12x + x - 3 = 0
D) 4x2 + 12x - x-3 = 0
Answer:
C
Step-by-step explanation:
The required equation that is rewritten and ready to solve is 4x² - 12x + x - 3 = 0. Option C is correct.
Given that,
The quadratic equation 4x² - 11x - 3 = 0 The equations is rewritten and ready to solve using factoring by grouping is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
4x² - 11x - 3 = 0
4x² - 12x + x - 3 = 0
4x[x - 3] + 1[x - 3] = 0
[4x + 1][x - 3] = 0
Thus, the required equation that is rewritten and ready to solve is 4x² - 12x + x - 3 = 0. Option C is correct.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ2
4. Two unbiased coins are tossed. Calculate the probability that
(a) Two heads are obtained.
(b) One head and one tail is obtained.
A professional soccer player kicked a ball across the field. The ball’s height, in meters, is modeled by the function graphed below. What's the average rate of change between the point when the ball reached its maximum height and the point where it hit the ground?
Answer:
Hey there!
You can think of the rate of change as the slope of a quadratic function- here we see that it is 9/-3, or - 3.
Let me know if this helps :)
Answer:
–3 meters per second
Step-by-step explanation:
If I get paid $100 a week but my car cost $4, 990 how long will I have to save to officially buy my car?
Answer:
50 weeks.
Step-by-step explanation:
Did the math like u should've
write a thirdthird-degree polynomial expression that has only two terms with a leading term that has a coefficient of five and a constant of negative two
Answer:
5x^3-2
[tex]ax^{3} +bx^{2} +cx+d\\5x^{3}-given\\ d=-2-given\\5x^{3} -2[/tex]
Explanation:
The two terms are [tex]5x^3[/tex] and [tex]2[/tex]. Terms are separated by either a plus or minus.
We can write it as [tex]5x^3+(-2)[/tex] which is an equivalent form. Here the two terms are [tex]5x^3[/tex] and [tex]-2[/tex]. This is because adding a negative is the same as subtracting.
The coefficient is the number to the left of the variable.
The degree is the largest exponent, which helps form the leading term.
The third degree polynomial written above is considered a cubic binomial. "Cubic" refers to the third degree, while "binomial" means there are 2 terms.
We can write something like [tex]5x^3[/tex] as 5x^3 when it comes to computer settings.
identify the decimals labeled with the letters A, B, and C on the scale below. Letter A represents the decimal Letter B represents the decimal Letter C represents the decimal
[tex]10[/tex] divisions between $20$ and $20.1$ so each division is $\frac{20.1-20.0}{10}=0.01$
A is 2nd division from $20.0$, so, A is $20.0+2\times 0.01=20.02$
similarly, C is one division behind $20.0$ so it is 19.99
and B is $20.14$
A 95% confidence interval for the mean number of television per American household is (1.15, 4.20). For each of the following statements about the above confidence interval, choose true or false.
a. The probability that u is between 1.15 and 4.20 is .95.
b. We are 95% confident that the true mean number of televisions per American household is between 1.15 and 4.20.
c. 95% of all samples should have x-bars between 1.15 and 4.20 televisions.
d. 95% of all American households have between 1.15 and 4.20 televisions
e. Of 100 intervals calculated the same way (95%), we expect 95 of them to capture the population mean.
f. Of 100 intervals calculated the same way (95%), we expect 100 of them to capture the sample mean.
Answer:
a. False
b. True
c. False
d. False
e.True
f. True
Step-by-step explanation:
The 95% is confidence interval its not a probability estimate. The probability will be different from the confidence interval. Confidence interval is about the population mean and is not calculated based on sample mean. Every confidence interval contains the sample mean. There is 95% confidence that the number of televisions per American household is between 1.15 to 4.20.