I
2/5 of 2.5. = 2x2.5 / 5x1 = 5/5 = 1 pound
Find a formula for the given polynomial.
In this question, we have to identify the zeros of the polynomial, along with a point, and then we get that the formula for the polynomial is:
[tex]p(x) = -0.5(x^3 - x^2 + 6x)[/tex]
------------------------
Equation of a polynomial, according to it's zeros:
Given a polynomial f(x), this polynomial has roots such that it can be written as: , in which a is the leading coefficient.
------------------------
Identifying the zeros:
Given the graph, the zeros are the points where the graph crosses the x-axis. In this question, they are:
[tex]x_1 = -2, x_2 = 0, x_3 = 3[/tex]
Thus
[tex]p(x) = a(x - x_{1})(x - x_{2})(x-x_3)[/tex]
[tex]p(x) = a(x - (-2))(x - 0)(x-3)[/tex]
[tex]p(x) = ax(x+2)(x-3)[/tex]
[tex]p(x) = ax(x^2 - x + 6)[/tex]
[tex]p(x) = a(x^3 - x^2 + 6x)[/tex]
------------------------
Leading coefficient:
Passes through point (2,-8), that is, when [tex]x = 2, y = -8[/tex], which is used to find a. So
[tex]p(x) = a(x^3 - x^2 + 6x)[/tex]
[tex]-8 = a(2^3 - 2^2 + 6*2)[/tex]
[tex]16a = -8[/tex]
[tex]a = -\frac{8}{16} = -0.5[/tex]
------------------------
Considering the zeros and the leading coefficient, the formula is:
[tex]p(x) = -0.5(x^3 - x^2 + 6x)[/tex]
A similar problem is found at https://brainly.com/question/16078990
The formula that represents the polynomial in the figure is [tex]p(x) = x^{3}-x^{2}-6\cdot x[/tex].
Based on the Fundamental Theorem of Algebra, we understand that Polynomials with real Coefficient have at least one real Root and at most a number of Roots equal to its Grade. The Grade is the maximum exponent that Polynomial has and root is a point such that [tex]p(x) = 0[/tex]. By Algebra we understand that polynomial can be represented in this manner known as Factorized form:
[tex]p(x) = \Pi\limits_{i=0}^{n} (x-r_i)[/tex] (1)
Where:
[tex]n[/tex] - Grade of the polynomial.
[tex]i[/tex] - Index of the root binomial.
[tex]x[/tex] - Independent variable.
We notice that polynomials has three roots in [tex]x = -2[/tex], [tex]x = 0[/tex] and [tex]x = 3[/tex], having the following construction:
[tex]p(x) =(x+2)\cdot x \cdot (x-3)[/tex]
[tex]p(x) = (x^{2}+2\cdot x)\cdot (x-3)[/tex]
[tex]p(x) = x^{3}+2\cdot x^{2}-3\cdot x^{2}-6\cdot x[/tex]
[tex]p(x) = x^{3}-x^{2}-6\cdot x[/tex]
The formula that represents the polynomial in the figure is [tex]p(x) = x^{3}-x^{2}-6\cdot x[/tex].
Here is a question related to the determination polynomials: https://brainly.com/question/10241002
hi plz help ASAP tyyy ^^
Answer:
26.75 units²
Step-by-step explanation:
This shape can be split into 3 triangles and a square. Find the area of each shape then add them all up.
[tex]A(Square)=2(2)=4\\\\A(Triangle)=\frac{1}{2}(2)(2)=2\\\\A(Triangle)=\frac{1}{2}(5)(2)=5\\\\A(Triangle)=\frac{1}{2}(9)(3.5)=15.75\\\\A(Shape)=4+2+5+15.75=26.75[/tex]
Therefore, the area of the shape is 26.75 units².
Help!!
A.) show work as you evaluate the composition: (g o g) (2)
B.) show work as you find: f^-1 (x)
C.) show a composition of the two functions f and g. Are they inverse functions, explain using a complete sentence
Answer:
Hello,
Step-by-step explanation:
[tex]A)\\g(x)=\dfrac{x-5}{-3} =\dfrac{-x}{3} +\dfrac{5}{3} \\\\(gog)(x)=g(g(x))=g(\dfrac{-x}{3} +\dfrac{5}{3})\\\\=\dfrac{\dfrac{-x}{3} +\dfrac{5}{3} }{3}+\dfrac{5}{3} \\\\\\=\dfrac{-x}{9} +\dfrac{5}{9} +\dfrac{5}{3}\\\\=-\dfrac{x}{9}+\dfrac{20}{9} \\\\\\(gog)(2)=-\dfrac{2}{9}+\dfrac{20}{9} =\dfrac{18}{9}=2 \\\\[/tex]
[tex]B)\\f(x)=y=-3x-5\\exchanging\ y\ and\ x\\x=-3y-5\\3y=-x-5\\\\y=\dfrac{-x}{3} -\dfrac{5}{3} \\\\f^{-1}(x)=\dfrac{-x}{3} -\dfrac{5}{3} \\\\[/tex]
[tex]C)\\\\(fog)(x)\ must\ be\ equal\ to\ x\\\\\\(fog)(x)=g(f(x))=g(-3x-5)\\\\=\dfrac{-(-3x-5)}{3} +\dfrac{5}{3} \\\\=x+\dfrac{5}{3} +\dfrac{5}{3} \\\\\\=x+\dfrac{10}{3}\ and\ not\ x\ !!!\\[/tex]
f(x) and g(x) are not inverse functions.
Question
Find the sample variance of the following set of data:
12, 7, 6, 4, 11.
Select the correct answer below:
Answer:
Variance is 256
Step-by-step explanation:
Variance:
[tex]var = \frac{ ({ \sum x})^{2} }{n} - {( \frac{ \sum x}{n} })^{2} [/tex]
x is the number or item in the data
n is the number of terms
[tex]{ \tt{ \sum x = (12 + 7 + 6 + 4 + 11)}} \\ { \tt{ \sum x = 40}}[/tex]
Therefore:
[tex]variance = \frac{ {40}^{2} }{5} - { (\frac{40}{5}) }^{2} \\ \\ = 320 - 64 \\ variance = 256[/tex]
Please help——- Geometry problem
Thank you.
Answer:
b
Step-by-step explanation:
sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{s\sqrt{3} }{2s}[/tex] ( cancel s on numerator/ denominator ), then
sinA = [tex]\frac{\sqrt{3} }{2}[/tex] → b
prove that is here
[tex]1 - cos {2}a \div 1 - sin a{2} = tan {2} a[/tex]
[tex]\\ \sf\longmapsto \dfrac{1-cos2A}{1-sin2A}[/tex]
LHS[tex]\boxed{\sf \dfrac{cosA}{sinA}=cotA}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1-cos2A}{1-sin2A}[/tex]
[tex]\\ \sf\longmapsto 1-cot2A[/tex]
[tex]\\ \sf\longmapsto 1-\dfrac{1}{tan2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{tan2A-1}{tan2A}[/tex]
[tex]\\ \sf\longmapsto tan2A[/tex]
boat costs $54,000. you pay 10% down and amortize the rest with equal monthly payments over a 15 year period. If you must pay 4.5 % comounded monthly, what is your monthly payment?
3385.8
Step-by-step explanation:
In how many years will the population of a town be 26901 from 24400 at the growth rate of 5% per annum ?
Answer:
2 years
Step-by-step explanation:
population in 1 year= 24400*105%=25620
population in 2 year= 25620*105%=26901
The differential equation of a certain system is 20y′′+cy′+80y=0
, where c is called damping constant for what value of c critical damping hapens
Options:
110
64
50
60
Answer:
c=80
Step-by-step explanation:
Based on my reading the critical damping occurs when the discriminant of the quadratic characteristic equation is 0.
So let's see that characteristic equation:
20r^2+cr+80=0
The discriminant can be found by calculating b^2-4aC of ar^2+br+C=0.
a=20
b=c
C=80
c^2-4(20)(80)
We want this to be 0.
c^2-4(20)(80)=0
Simplify:
c^2-6400=0
Add 6400 on both sides:
c^2=6400
Take square root of both sides:
c=80 or c=-80
Based on further reading damping equations in form
ay′′+by′+Cy=0
should have positive coefficients with b also having the possibility of being zero.
The complement of set S is the set of elements in U and ___ in S
9514 1404 393
Answer:
not
Step-by-step explanation:
The complement of set S is the set of elements in U and not in S.
_____
It's a definition.
yes it's surprisingly for highschool can someone help I just can't figure it out
22
Step-by-step explanation:
For simplicity, let
x = teary smiley
y = tongue smiley
z = plain smiley
So now our system of equations is
[tex]x + x + x = 12\:\:\:\:\:\:(1)[/tex]
[tex]y + z + x = 18\:\:\:\:\:\:\:(2)[/tex]
[tex]z + z + y = 22\:\:\:\:\:\:\:(3)[/tex]
[tex]z + y + 2x= ??\:\:\:\:\:\:(4)[/tex]
From Eqn(1), we plainly see that
[tex]3x = 12 \Rightarrow x = 4[/tex]
Now subtract Eqn(2) from Eqn(3) to get
[tex](2z + y) - (y + z + x) = 22 - 18[/tex]
[tex]\Rightarrow z - x = 4[/tex]
But we know that [tex]x = 4[/tex], which then gives us [tex]z = 8.[/tex]
Using the values of [tex]x[/tex] and [tex]z[/tex] in Eqn(2), we find that [tex]y = 6.[/tex] Now that we the values of all the variables, use them in Eqn(3) and we'll get
[tex](8) + (6) + 2(4) = 22[/tex]
Solve for x using the
distributive property.
6(2 - 6x) = -24
X ?
⇛6(2 - 6x) = -24
⇛12 - 36x = -24
⇛-36x = -24 - 12
⇛-36x = -36
⇛x = -36/-36
⇛x = 1
√10 Multiple √15 is equal to
(a) 6√5
(b) √30
(c) √25
step by step
Solve :-
Answer:
Answer is 5√6 ( none of the objectives )
Step-by-step explanation:
[tex] \sqrt{10} \times \sqrt{15} \\ = \sqrt{150} \\ = \sqrt{25 \times 6} \\ = \sqrt{25} \times \sqrt{6} \\ = 5 \times \sqrt{6} \\ = 5 \sqrt{6} [/tex]
WHAT IS X³-27 SIMPLIFIED
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]
1. On the set of axes below, graph . State the roots of
Is this question complete?
Suppose that 17 inches of wire costs 68 cents.
At the same rate, how much (in cents) will 39 inches of wire cost?
cents
Х
5
?
Answer:
5
Step-by-step explanation:
17 inches is equal to 39 inches and it's answer is 5
Cost of 17 inches of wire = 68 cents
Cost of 1 inch of wire
= 68 cents/17
= 4 cents
Cost of 39 inches of wire
= 4 cents × 39
= 156 cents
= $1.56
A painter can paint 36 feet of molding per hour. How many inches of molding can he paint per hour?
Answer:
432 inches
Step-by-step explanation:
We need to convert feet to inches
1 ft = 12 inches
36 ft * 12 inches/ 1 ft = 432 inches
How many titles are in the nth figure
A rectangular window is 48 in long and 36 in wide. Lisa
would like to buy a screen for the window. The cost of
the screen is based on the number of square feet the
screen is. Use the facts to find the area of the window in
square feet.
Conversion facts for length
1 foot (ft) 12 inches (in)
1 yard (yd) = 3 feet (ft)
1 yard (yd) = 36 inches (in)
2
Х
$
?
[tex]\\ \sf\longmapsto Area=Length\times Breadth[/tex]
[tex]\\ \sf\longmapsto Area=48(36)[/tex]
[tex]\\ \sf\longmapsto Area=1728in^2[/tex]
[tex]\\ \sf\longmapsto Area=144ft^2[/tex]
[tex]\\ \sf\longmapsto Area=48yard^2[/tex]
if Albert gives 30$ to George both of them will have the same amount of money.if George give 50$ to Albert,Albert will have 5 times as much money as George. how much money do both of them have altogether
Step-by-step explanation:
let George money will be X and Albert be Y
30$+x=y
x-50$=5y
30+x=y
x=y-30
(y-30)-50=5y
y-80=5y
y-5y=80
-4y=80
y=-20
x=-50
Answer:AlBERT=150; GEORGE=90
Albert-30=George+30....(.1)eq
A=(G+60)
#2 (G-50)5=A+50......(.2)eq
substitute result of #1 for A
5G-250=(G+60)+50
4G=360
G=90
substitute $90 into equation #1
A=90+60=150
Therefore Albert has $150, George has $90, and their total is $240
How many terms of the series 2 + 5 + 8 + … must be taken if their sum is 155
9514 1404 393
Answer:
10
Step-by-step explanation:
The sum of terms of an arithmetic series is ...
Sn = (2a +d(n -1))·n/2 = (2an +dn^2 -dn)/2
For the series with first term 2 and common difference 3, the sum is 155 for n terms, where ...
155 = (3n^2 +n(2·2 -3))/2
Multiplying by 2, we have ...
3n^2 +n -310 = 0 . . . . . arranged in standard form
Using the quadratic formula, the positive solution is ...
n = (-1 +√(1 -4(3)(-310)))/(2(3)) = (-1 +√3721)/6 = (61 -1)/6 = 10
10 terms of the series will have a sum of 155.
Step-by-step explanation:
[tex]\displaystyle \ \Large \boldsymbol{} S_n=\frac{2a_1+d(n-1)}{2} \cdot n =155 \\\\ \frac{4+3(n-1)}{2} \cdot n =155 \\\\\\ 4n+3n^2-3n=310 \\\\ 3n^2+n-310=0 \\\\D=1+3720=3721=61^2\\\\n_1=\frac{61-1}{6} =\boxed{10} \\\\\\n_2=\frac{-61-1}{3} \ \ \o[/tex]
Determine whether the statement below makes sense or does not make sense. Explain clearly. Based on our sample, the 95% confidence interval for the mean amount of television watched by adults in a nation is 1.9 to 3.5 hours per day. Therefore, there is 95% chance that the mean for all adults in the nation will fall somewhere in this range and a 5% chance that it will not.
A. The statement makes sense. There is 95% probability that the confidence interval limits actually contain the true value of the population mean, so the probability it does not fall in this range is 100%−95% =5%.
B. The statement makes sense. There is 5% probability that the confidence interval limits do not contain the true value of the sample mean, so the probability it does not contain the true value of the population mean is also 5%.
C.The statement does not make sense. The probability the population mean is greater than the upper limit is 5% and the probability it is less than the lower limit is 5%, so the probability it does not is 5%+5%=10%.
D. The statement does not make sense. The population mean is a fixed constant that either falls within the confidence interval or it does not. There is no probability associated with this.
The correct option is A because
The statement makes sense. There is 95% probability that the confidence interval limits actually contain the true value of the population mean, so the probability it does not fall in this range is 100%−95% =5%.
From the question we are told that:
Confidence interval [tex]CI=95\%[/tex]
Mean [tex]\=x =1.9-3.5hours[/tex]
Level of significance (of the alternative hypothesis)
[tex]\alpha=100-95[/tex]
[tex]\alpha=5\%[/tex]
[tex]\alpha=0.05[/tex]
Generally
There is 95% probability that the confidence interval limits actually contain the true value of the population mean.
In conclusion
The it does not fall in this range is Level of significance (of the alternative hypothesis)
100%−95% =5%.
For more information on this visit
https://brainly.com/question/24131141?referrer=searchResults
What is the product of the polynomials below?
(8x2 - 4x-8)(2x +3x+2)
A. 16x4 +16x° - 12x2 - 16x-6
B. 16x4 +16x? - 12x2 - 16x-16
C. 16x4 +16x° - 12x2 – 32x-16
D. 16x4 +16 x° - 12x2 - 32x-6
Answer:
16x⁴+16x³-12x²-32x-16
Step-by-step explanation:
(8x²-4x-8)(2x²+3x+2)
= 16x⁴+24x³+16x²-8x³-12x²-8x-16x²-24x-16
= 16x⁴+16x³-12x²-32x-16
How??????????????????????
Answer:
y=-1/3x+7
Step-by-step explanation:
y=mx+c
m=-1/3, c=7
y=-1/3x+7
What is the smallest number that has both 6 and 9 as a
factor?
A 54
B 12
C 36
D 18
Answer:
yep it's D
Step-by-step explanation:
plz with steps plzzzzzz
Answer: [tex]-\frac{\sqrt{2a}}{8a}[/tex]
=======================================================
Explanation:
The (x-a) in the denominator causes a problem if we tried to simply directly substitute in x = a. This is because we get a division by zero error.
The trick often used for problems like this is to rationalize the numerator as shown in the steps below.
[tex]\displaystyle \lim_{x\to a} \frac{\sqrt{3a-x}-\sqrt{x+a}}{4(x-a)}\\\\\\\lim_{x\to a} \frac{(\sqrt{3a-x}-\sqrt{x+a})(\sqrt{3a-x}+\sqrt{x+a})}{4(x-a)(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\\lim_{x\to a} \frac{(\sqrt{3a-x})^2-(\sqrt{x+a})^2}{4(x-a)(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\\lim_{x\to a} \frac{3a-x-(x+a)}{4(x-a)(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\\lim_{x\to a} \frac{3a-x-x-a}{4(x-a)(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\[/tex]
[tex]\displaystyle \lim_{x\to a} \frac{2a-2x}{4(x-a)(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\\lim_{x\to a} \frac{-2(-a+x)}{4(x-a)(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\\lim_{x\to a} \frac{-2(x-a)}{4(x-a)(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\\lim_{x\to a} \frac{-2}{4(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\[/tex]
At this point, the (x-a) in the denominator has been canceled out. We can now plug in x = a to see what happens
[tex]\displaystyle L = \lim_{x\to a} \frac{-2}{4(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\L = \frac{-2}{4(\sqrt{3a-a}+\sqrt{a+a})}\\\\\\L = \frac{-2}{4(\sqrt{2a}+\sqrt{2a})}\\\\\\L = \frac{-2}{4(2\sqrt{2a})}\\\\\\L = \frac{-2}{8\sqrt{2a}}\\\\\\L = \frac{-1}{4\sqrt{2a}}\\\\\\L = \frac{-1*\sqrt{2a}}{4\sqrt{2a}*\sqrt{2a}}\\\\\\L = \frac{-\sqrt{2a}}{4\sqrt{2a*2a}}\\\\\\L = \frac{-\sqrt{2a}}{4\sqrt{(2a)^2}}\\\\\\L = \frac{-\sqrt{2a}}{4*2a}\\\\\\L = -\frac{\sqrt{2a}}{8a}\\\\\\[/tex]
There's not much else to say from here since we don't know the value of 'a'. So we can stop here.
Therefore,
[tex]\displaystyle \lim_{x\to a} \frac{\sqrt{3a-x}-\sqrt{x+a}}{4(x-a)} = -\frac{\sqrt{2a}}{8a}\\\\\\[/tex]
Use the discriminant to
determine the number
of real solutions to the
equation.
Зm2 = -6
Answer:
m=-1 I think
Step-by-step explanation:
write the first 10 multiples of 2 and 3 and find LCM.
Answer:
multiples of 2 2,4,6,8,10,12,14,16,18,20
multiples of 3 3,6,9,12,15,,18,21,24,27,30
Step-by-step explanation:
Lcm is 6
simplify 27-{ 9+(12-5)÷4} with solution
Answer:
16.25
Step-by-step explanation:
first do 12 -5 = 7. then 7/4 = 1.75 then 9+1.75 = 10.75 and finally 27-10.75= 16.25
The mean of 5 conservative odd number is 11, find the numbers
I bet you meant "consecutive". If x is the smallest of the 5 numbers, then the other 4 are x + 1, x + 2, x + 3, and x + 4. If their mean is 11, then
(x + (x + 1) + (x + 2) + (x + 3) + (x + 4))/5
= (5x + 10)/5
= x + 2 = 11
==> x = 9
Then the five numbers are {9, 10, 11, 12, 13}.
Alternatively, since we're talking about an odd number of consecutive integers, the mean among them will always be the number in the middle. So if 11 is the mean, and there are five numbers overall, then we just take the four closest integers to 11, two on either side.
