Answer:
x = 0 and 3 other real roots. See below.
Step-by-step explanation:
This is what you wrote:
[tex] 3x + \dfrac{1}{x^2} - 1 = \dfrac{2}{x} - 2 + \dfrac{x}{x} - 1 [/tex]
I don't think that is what you meant to write.
I think you meant to write this:
[tex] 3x + \dfrac{1}{x^2 - 1} = \dfrac{2}{x - 2} + \dfrac{x}{x - 1} [/tex]
I'm going to answer the second equation because that is what I think you meant.
[tex] 3x + \dfrac{1}{(x - 1)(x + 1)} = \dfrac{2}{x - 2} + \dfrac{x}{x - 1} [/tex]
[tex] 3x(x - 1)(x + 1)(x - 2) + (x - 2) = 2(x - 1)(x + 1) + x(x + 1)(x - 2) [/tex]
[tex] (3x^2 - 6x)(x^2 - 1) + x - 2 = 2x^2 - 2 + x(x^2 - x - 2) [/tex]
[tex] 3x^4 - 3x^2 - 6x^3 + 6x + x - 2 = 2x^2 - 2 + x^3 - x^2 - 2x [/tex]
[tex] 3x^4 - 7x^3 - 4x^2 + 9x = 0 [/tex]
[tex] x(3x^3 - 7x^2 - 4x + 9) = 0 [/tex]
[tex] f(x) = 3x^3 - 7x^2 - 4x + 9 [/tex]
[tex] f(-3) = -123 [/tex]
[tex] f(-2) = -35 [/tex]
[tex] f(-1) = 3 [/tex]
[tex] f(0) = 9 [/tex]
[tex] f(1) = 1 [/tex]
[tex] f(2) = -3 [/tex]
[tex] f(3) = 15 [/tex]
One root is x = 0.
There is a root between x = -2 and x = -1.
There is a root between x = 1 and x = 2.
There is a root between x = 2 and x = 3.
Plot the graph of f(x) = 3x^3 - 7x^2 - 4x + 9 and try to read the other three roots.
Hey please help me with Math!
There’s a bicycle that runs 45km in 1 hour and 15 minutes.
1) What is the speed of this bicycle? (__km/ph)
2) How far will this bicycle get in 2 hours and 40 minutes?
Step-by-step explanation:
Hello!!!!
According to the question,
distance covered (d)= 45km.
time taken (t)= 1 hr and 15 mins.
now,
let's find answer of this question no. i).
》answer :
speed (s)= distance by time taken
= 45 /1.25
so, the speed is 36 km/hr.
now, for 2nd question,
time (t)= 2hrs and 40 mins.
speed (s)= 36km / hr
now,
distance (d)= s×t
= 36×2.6666666667
= 96km....is yourrequired answer.
Hope it helps...
Which SMART goal attribute in the table applies to each of Devon’s financial goals?
Answer:
- specific goals: describe what exactly you want to achieve by doing something and how you will do that.
- measurable: which means you need to be able to identify the goals you want to achieve. You might have to break down your goal into measurable parts.
Step-by-step explanation:
PLEASE HELP ME I WILL GIVE 5 STARS TO THE FIRST ONE WHO GETS THIS RIGHT !
Answer:
Option 1 and option 4
Step-by-step explanation:
The inverse of 12^2 is the √12 so option 4 is correct. 12^1/2 also equals √12 so option 1 is also correct.
Answer:
12 [tex]\frac{2}{1}[/tex]
Step-by-step explanation:
Mia’s house and her aunt’s house are 15.4 inches apart on the map. If every 4 inches on the map represents 10 miles, what is the actual distance from Mia’s house to her aunt’s house, to the nearest tenth of a mile? 2.6 6.2 38.5 61.6
Answer:
38.5 miles
Step-by-step explanation:
Proportions:
4 inches ⇔ 10 miles
15.4 inches ⇔ M miles
M = 15.4*10/4
M = 38.5 miles
Answer: 38.5
Step-by-step explanation: cuz im smart
The mean amount purchased by a typical customer at Churchill's Grocery Store is $23.50 with a standard deviation of $5.00. Assume the distribution of amounts purchased follows the normal distribution. For a sample of 50 customers, answer the following questions.
(a) What is the likelihood the sample mean is at least $25.00? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Probability
(b) What is the likelihood the sample mean is greater than $22.50 but less than $25.00? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Probability
(c) Within what limits will 90 percent of the sample means occur? (Round your answers to 2 decimal places.)
Answer:
a. [tex]\mathtt{P(X \geq 25) =0.0170}[/tex] ( to four decimal places)
b. [tex]P(22.5<X<25) = 0.9043[/tex] ( to four decimal places )
c. The limits will be between the interval of ( 22.33,24.67 )
Step-by-step explanation:
Given that :
mean = 23.50
standard deviation = 5.00
sample size = 50
The objective is to calculate the following:
(a) What is the likelihood the sample mean is at least $25.00?
Let X be the random variable, the probability that the sample mean is at least 25.00 is:
[tex]P(X \geq 25) = 1 - P(\dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{25- 23.50}{ \dfrac{5}{\sqrt{ 50}} })[/tex]
[tex]P(X \geq 25) = 1 - P(Z< \dfrac{1.5}{ \dfrac{5}{7.07107}} })[/tex]
[tex]P(X \geq 25) = 1 - P(Z< \dfrac{1.5 \times 7.071}{ {5}})[/tex]
[tex]P(X \geq 25) = 1 - P(Z< 2.1213)[/tex]
[tex]P(X \geq 25) = 1 - P(Z< 2.12)[/tex] to two decimal places
From the normal tables :
[tex]P(X \geq 25) = 1 - 0.9830[/tex]
[tex]\mathtt{P(X \geq 25) =0.0170}[/tex] ( to four decimal places)
(b) What is the likelihood the sample mean is greater than $22.50 but less than $25.00?
[tex]P(22.5<X<25) = P(\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}} <\dfrac{25-23.5}{\dfrac{5}{\sqrt{50}}} ) - P(\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}} <\dfrac{22.5-23.5}{\dfrac{5}{\sqrt{50}}} )[/tex]
[tex]P(22.5<X<25) = P(Z<\dfrac{1.5}{\dfrac{5}{7.071}} ) - P(Z<\dfrac{-1}{\dfrac{5}{7.071}} )[/tex]
[tex]P(22.5<X<25) = P(Z<2.12) - (Z<-1.41 )[/tex]
[tex]P(22.5<X<25) = (0.9830 ) - (0.0787)[/tex]
[tex]P(22.5<X<25) = 0.9043[/tex] to four decimal places
(c) Within what limits will 90 percent of the sample means occur?
At 90 % confidence interval, level of significance = 1 - 0.90 = 0.10
The critical value for the [tex]z_{\alpha/2} = 0.05[/tex] = 1.65
Standard Error = [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]
Standard Error = [tex]\dfrac{5}{\sqrt{50}}[/tex]
Standard Error = 0.7071
Therefore, at 90 percent of the sample means, the limits will be between the intervals of : [tex](\mu \pm z_{\alpha/2} \times S.E)[/tex]
Lower limit = ( 23.5 - (1.65×0.707) )
Lower limit = ( 23.5 - 1.16655 )
Lower limit = 22.33345
Lower limit = 22.33 (to two decimal places).
Upper Limit = ( 23.5 + (1.65*0.707) )
Upper Limit = ( 23.5 + 1.16655 )
Upper Limit = 24.66655
Upper Limit = 24.67
The limits will be between the interval of ( 22.33,24.67 )
Please answer this question now
Answer:
95 degrees
Step-by-step explanation:
Measure of arc AB is 360 - (101+97+69) = 360 - 267 = 93 degrees.
Measure of arc DAB is 97+93 = 190 degrees, so measure of angle C is 190/2 = 95 degrees.
Find the sets of values of x for which x(x+2) < x.
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Hi my lil bunny!
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Let's solve your inequality step-by-step.
[tex]x(x+2)<x[/tex]
[tex]x^2 + 2x < x[/tex]
Let's find the critical points of the inequality.
[tex]x^2 + 2x = x[/tex]
[tex]x^2 + 2x - x - x[/tex] (Subtract x from both sides)
[tex]x^2 + x = 0[/tex]
[tex]x ( x + 1 ) = 0[/tex] (Factor left side of equation)
[tex]x = 0 |OR| x + 1 = 0[/tex] (Set factors equal to 0)
[tex]x = 0 |OR| x = -1[/tex]
Check intervals in between critical points. (Test values in the intervals to see if they work.)
[tex]x < - 1[/tex] (Doesn't work in original inequality)
[tex]-1 < x < 0[/tex] (Works in original inequality)
[tex]x > 0[/tex] (Doesn't work in original inequality)
So the answer is : [tex]-1 < x < 0[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
If this helped you, could you maybe give brainliest..?
❀*May*❀
Cory earns $9.50 per hour for the first 40 hours he works in a week. For any hours over 40 hours per week, his hourly rate is multiplied by 1.5. How much does he earn is he works for 43.5 hours in one week?
Answer:
429.88
Step-by-step explanation:
The first 40 hours is at 9.50
40 *9.50 =380
The remaining hours is at 9.50 * 1.5 or 14.25
43.5 -40 = 3.5
3.5 * 14.25
49.875 = 49.88 ( rounding to the nearest cent)
Add together
380+49.88 =429.88
Please answer these 3 questions for 70 points 1 thanks 5 stars and brainiest
Answer:
Step-by-step explanation:
Problem 14: Mean 5.5, Range: 5.8
Problem 15: question #1 4, mode: 63
Probelm 16: Median 63, Range: 8.3
Answer:
14: Mean is 5.5 Hours
Range is 7.9 Hours
15: 4 Numbers
Mode is 6.3
16: Median is 6.3
Range is 8.3
Step-by-step explanation:
(I'll edit in the explanations momentarily)
the function f(x)=-(x5+)(x+1) is shown. what is the range of the function
Answer:
all real numbers less than or equals to 4
Geraldo recently saw a newspaper ad for a new version of his laptop. The projected price is $400.00, and the laptop will be out on the market in about one year. Geraldo wants to purchase a new laptop but is wondering if he should wait a year. With 2.5% inflation, what amount would he pay to purchase a laptop today that is the same value as the one he saw in the ad?
Answer:
The answer would be $410.00.
Cheers,
Got an question worth 25 points, pls guys go and answer it. Find the question on my profile.
Thankssss.
The price he will have to pay now for laptop will be $390.
What is cost prize ?
The prize at which the good and services have been bought is known as cost prize.
here, the given information is :
The projected price is $400.00, and the laptop will be out on the market in about one year with 2.5% inflation.
Now, if he pay to purchase a laptop today that is the same value as the one he saw in the ad then the cost price he will have to pay will be 2.5% of $400 less that is:
cost price of laptop = $400 - 2.5& x 400
cost price of laptop = 97.5% x $400
cost price of laptop = $390
Therefore, the price he will have to pay now for laptop will be $390.
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Kelly bought a crate of floor tiles for $95.94. The crate had 6 boxes of floor tiles. Each box contained 20 floor tiles.
Write and solve an equation to determine the cost per box, b. Then write and solve a second equation to determine the cost per tile, t, to the nearest cent.
Answer:
$1.60 a crate
Step-by-step explanation:
t= 95.94/(6x20)
(6x20)= 60
95.94/60
$1.60
Answer:
Step-by-step explanation:
i) Cost per box = cost of a crate ÷ Number of boxes in the crate
b = 95.94 ÷ 6
b = $ 15.99
ii) Cost per tile = Cost per box ÷ Number of tiles in a box
t = b ÷ 20
t = 15.99 ÷20
t = $ 0.7995
Find the 6th term of the arithmetic sequence – 2 – 2,-43 +1, -72 +4, ...
Answer:
Sum = 9a + 45d = 108. Or a + 5d = 12. Hence 6th term = 12. SUFFICIENT.
What is the measure of
Answer:
60⁰ is the answer. akksjdjd
Find the number of terms of the geometric progression 81, 27, 9,....,1/81
Answer:
9
Step-by-step explanation:
r = 27/81 = 1/3
a = 81
Tn = 1/81
ar^(n-1) = 1/81
81(1/3)^(n-1) = 1/81
(1/3)^(n-1) = 1/6561
(1/3)^(n-1) = 1/3^(8)
Compare the exponents,
n-1 = 8
n = 9
write as a numeral in simplest form:(6x1000)+(4x100)+(6x1)
A bag of marbles contains 11 blue marbles, 4 green marbles, and 5 purple marbles. What is the probability of drawing a green marble, removing it, and then drawing a purple marble?
Answer:
1/19
Step-by-step explanation:
11 blue marbles, 4 green marbles, and 5 purple marbles = 20 marbles
P( green) = green / total = 4/20 = 1/5
Now keep the green
11 blue marbles, 3 green marbles, and 5 purple marbles = 19 marbles
P(purple) = purple/ total = 5/19
P(green, keep,purple) = 1/5 * 5/19 = 1/19
(x^2-4x)^2+7x^2-28x+12=0
Answer:
[tex]x^4-9x^2-28x=-12[/tex]
Step-by-step explanation:
[tex](x^2-4x)^2+7x^2-28x+12=0[/tex]
[tex](x^4-16x^2)+7x^2-28x=-12[/tex]
[tex]x^4-9x^2-28x=-12[/tex]
2. If Bill has an apple, an orange, a pear, a grapefruit, a banana, and a kiwi at home and he wants to bring three pieces of fruit to school, how many combinations of fruit can he bring?
Answer:
6 choose 3 = 20
Step-by-step explanation:
[tex]=\frac{n!}{r!\left(n-r\right)!}[/tex]
6 choose 3 = 20
The total combinations of fruit he can bring is 20 if Bill has an apple, an orange, a pear, a grapefruit, a banana, and a kiwi at home and he wants to bring three pieces of fruit to school the answer is 20.
What are permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
We have:
Bill has an apple, an orange, a pear, a grapefruit, a banana, and a kiwi at home and he wants to bring three pieces of fruit to school
Total number of fruits = 1+1+1+1+1+1
Total number of fruits = 6
n = 6
He wants to bring three pieces of fruit to school,
r = 3
Total combination:
= C(6, 3)
= 6!/(6-3)!3!
= 720/(6)(6)
= 720/36
= 20 combination
Thus, the total combinations of fruit he can bring is 20 if Bill has an apple, an orange, a pear, a grapefruit, a banana, and a kiwi at home and he wants to bring three pieces of fruit to school the answer is 20.
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Work out an estimate for the value of 89.3X0.51divided by 4.8
Answer:
It is 9.5
Step-by-step explanation:
[tex] = (89.3 \times 0.51 )\div 4.8[/tex]
first solve the bracket:
[tex] = (45.543) \div 4.8 \\ = 9.488[/tex]
find square root of: 91+9, 47+2, 19+125, 9+0
Answer:
√(91+9)=√100
= 10
√(47+2)=√49
= 7
√(19+125)=√144
= 12
√(9+0)=√9
=3
Find: 499 decreased by 100%
Answer:
0,
If you want, I can explain more into it.
Mr. Wilkerson bought frozen treats for 34 children. Each child picked either a popsicle or an ice cream bar. Each popsicle cost $2 and each ice cream bar cost $5. If Mr. Wilkerson spent a total of $128, how many of each type of treat did he buy?
Answer: He bought 20 ice cream bars and 14 popsicle
Step-by-step explanation:
To solve this I used the elimination method, you could use substitution as well
Here are our two equations
x+y=34 Because the total number of ice creams bought must be given to 34 children and no more
2x+5y=128 because that is the cost for each ice cream and the amount he spent
For the elimination method we have to cancel out one of the variables, I decided to cancel out the x, so I multiplied the top equation by -2. So i got -2x-2y=-68
2x+5y=128 Then we get
3y=60 so
y=20
Now we can go back to the first equation and plug in y.
x+20=34
-20 -20
x=14
So he bought 14 popsicles and 20 ice cream bars.
Help please quick for c and d
Answer:
6.82 cm
Step-by-step explanation:
1000=V=pi*r^2*h. 1000=pi*r^3, r=6.82 cm
need help pls will give you 5 stars
Answer:
f(x + k)
Step-by-step explanation:
A horizontal shift moves to the left or right
y = f(x + k) k > 0 moves it left
k < 0 moves it right
Please help, 50 points! :)
PDF attached below
Answer:
See below
Step-by-step explanation:
Attachment 1 : (a) Remember that it mentions x is the years since 1900. That would mean that the table is a bit different. To create this " new table " simply subtract 1900 from the years provided, and substitute.
To create this equation we will need a regression calculator. The equation will be as follows.
y = 0.125873x - 7.11916 ( note that you can double check this equation be substituting points from the table in the attachment )
(b) 2025 - 1900 = 126 years,
y = 0.125873(125) - 7.11916 = $ 8.614965
Minimum Wage : $ 8.614965
Attachment 2 : The rest of the problems can be solved similarly...
(a) Quadratic Regression Equation : - 0.49311x² + 23.2798x + 996.029
(b) - 0.49311(20)² + 23.2798(20) + 996.029 = 1264.381 mg/cm³
Attachment 3 : (a) Exponential Regression : 9.08292(1.09965)ˣ
(b) 9.08292(1.09965)⁶⁰ = [tex]2713.27743\dots[/tex] ( About 2713 recommendations )
Simultaneous equation 2x-y=-1,x-2y=4 solve graphically
Answer:
y= - 1.4
x= 0.2
Step-by-step explanation:
2x-Y= -1
x-2y=4
A pair of opposite vertices of a square is (1, 2) and (3,4). Find the coordinates of the remaining
vertices of the square.
Answer:
(3, 2) and (1, 4)
Step-by-step explanation:
Plot the two points on a graph.
The other two points are (3, 2) and (1, 4).
To do this with algebra, it takes a few steps.
The diagonals of a square are perpendicular and bisect each other. You are given opposite vertices, so first, find the midpoint of that diagonal.
((1 + 3)/2, (2 + 4)/2) = (2, 3)
The midpoint of the diagonal is (2, 3).
This diagonal has slope 1 and y-intercept 1, so its equation is
y = x + 1
The perpendicular bisector has equation
y = -x + 5
The two vertices we are looking for, lie in a circle whose center is the midpoint of the diagonals, (2, 3), and whose radius is half of the diagonal.
Use Pythagoras to find the diagonal's length.
2^2 + 2^2 = c^2
c^2 = 8
c = sqrt(8) = 2sqrt(2)
Half of the diagonal is sqrt(2). This is the radius if the circle.
The equation of the circle is
(x - 2)^2 + (y - 3)^2 = (sqrt(2))^2
(x - 2)^2 + (y - 3)^2 = 2
The points of intersection of this circle and the second diagonal are the two vertices you are looking for.
System of equations:
(x - 2)^2 + (y - 3)^2 = 2
y = -x + 5
Use substitution and substitute y with -x + 5 in the equation of the circle.
(x - 2)^2 + (-x + 5 - 3)^2 = 2
(x - 2)^2 + (-x + 2)^2 - 2 = 0
x^2 - 4x + 4 + x^2 - 4x + 4 - 2= 0
2x^2 - 8x + 6 = 0
x^2 - 4x + 3 = 0
(x - 3)(x - 1) = 0
x - 3 = 0 or x - 1 = 0
x = 3 or x = 1
Now we find corresponding y values.
y = -x + 5
x = 3
y = -3 + 5 = 2
This gives us (3, 2).
y = -x + 5
x = 1
y = -1 + 5 = 4
This gives us (1, 4).
Answer: (1, 4) and (3, 2)
fill in the table with whole numbers to make 2.8 in three different ways i do not get this qestion can you help me
Answer: what table? u need to add an attachment
Step-by-step explanation:
The table containing whole number express 2.8 as the sum or difference.
To express 2.8 as the sum or difference of whole numbers.
There are three different ways to do it:
1. As a sum of whole numbers:
2 + 0.8 = 2.8
2. As a difference of whole numbers:
4 - 1.2 = 2.8
3. Another way as a sum of whole numbers:
1 + 1.8 = 2.8
The table will be:
Representation Whole Number 1 Whole Number 2 Result
1 2 0.8 2.8
2 4 1.2 2.8
3 1 1.8 2.8
As each row represents a different way to represent the number 2.8 using whole numbers.
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a polynomial has been factored below but some constants are missing. 2x^3-8x^2-24x=ax(x+b)(x+c)
Answer:
The polynomial is 2x^3 - 8x^2 - 24x
And we can factor out a 2x from each of the three terms:
2x(x^2 - 4x - 12)
Lastly, factor the remaining quadratic:
2x(x+(-2))(x+6)
And we have our answer:
a=2
b=-2
c=6
Let me know if this helps!
Answer:
a =2, b =2, and c = -6
Step-by-step explanation:
We factor the polynomial and then see which value corresponds to what.
2x^3-8x^2-24x
As we see it, all terms are factorable by 2x. So if we take out 2x from every term, we get
2x(x^2 - 4x - 12)
Now we factor the quadratic, which we can do mentally to get
2x(x+2)(x-6)
ax(x+b)(x+c)
Comparing that to ax(x+b)(x+c), we can tell that a =2, b =2, and c = -6.