Answer:
1,2,3,4,6,8,12,24
Step-by-step explanation:
the equation x^3 - 6x = 72 has a solution between 4 and 5.
Use a trial and improvement method to find the solution correct to one decimal place,
Answer:
4.6
Step-by-step explanation:
There are a number of "improvement" techniques that can be used to improve an estimate of a solution to a polynomial. Some of them use the polynomial itself to form the iterator function.
IteratorThere are a number of ways we can solve the given equation for x. Often, at least one of these will converge when used for improving the estimated value of x.
x₁ = (x^3 -72)/6 . . . . . . . add 6x-72, divide by 6
x₂ = 72/(x^2 -6) . . . . . . . factor out x and divide by its coefficient
x₃ = ∛(72 +6x) . . . . . . . add 6x and take the cube root
The first two of these iterators tend to diverge. For x = 4.5, they give ...
x₁ = (4.5³ -72)/6 = 3.1875
x₂ = 72/(4.5² -6) = 5.0526
Both of these stray out of the given interval of [4, 5].
However, the third one tends to converge, so can give us a useful approximation in one iteration:
x₃ = ∛(72 +6×4.5) ≈ ∛99 ≈ 4.6261
Second iterationApplying this again, we get ...
x ≈ ∛(72 +6·4.6261) ≈ 4.6378
The approximate root to 1 decimal place is 4.6.
__
Additional comment
One of the quickest converging iterators is that provided by Newton's method. For finding the solution to f(x) = 0, it uses ...
x₁ = x -f(x)/f'(x) . . . . . . . where f'(x) is the first derivative
For this problem, we can define ...
f(x) = x^3 -6x -72 ⇒ f'(x) = 3x^2 -6
x₁ = x -(x^3 -6x -72)/(3x^2 -6) = (3x^3 -6x -x^3 +6x +72)/(3x^2 -6)
x₁ = (2x^3 +72)/(3x^2 -6)
Then for x = 4.5, the "improved" solution is ...
x₁ = (2(4.5³) +72)/(3(4.5²) -6)) = 254.25/54.75 = 339/73 ≈ 4.6438
A second iteration gives ...
x ≈ 4.639026 . . . . accurate to 5 decimal places
With this iterator, the number of accurate decimal places tends to double with each iteration.
PLEASE HELP SOON I ONLY NEED HELP WITH NUMBER 18 PICTURE IS INCLUDED
Critical thinking? We're in trouble. It's hard for me to tell what grade this is.
Stem and leaf is fine but let's just write out the data.
Rich: 35 37 41 42 43 44 45 48 50 55 n=10
Will: 42 43 44 44 46 47 47 48 49 50 n=10
Use measures of center and measures of variation ...
The three measures of center typically used are the mean, the median and the mode.
Rich's sum = 440 so Rich's mean = 440/10 = 44
Rich's middle values are 43 and 44 so Rich's median = 43.5
All Rich's scores are unique so he doesn't really have a mode.
Will's sum = 460, Will's mean = 460/10 = 46
Will's middle numbers are 46 and 47 so median 46.5
Will's data has two modes tied, 44 and 47.
OK, so far these say Rich is a better golfer; he has lower mean and median scores than Will. (Low score is better in golf.)
Let's look at measures of variation. I'm guessing that they don't want to you calculate standard deviation. So we'll do range and mean absolute deviation.
The range is max-min.
Rich's range is 55-35=20
Will's range is 50-42=8
Will is more consistent.
Rich's mean is 44, his scores are here; let's calculate absolute deviation:
Score 35 37 41 42 43 44 45 48 50 55
AbsDev 9 7 3 2 1 0 1 4 6 11
Rich's deviations add to 44 so his MAD is 4.4
Will's mean is 46
Score: 42 43 44 44 46 47 47 48 49 50
AbsDev 4 3 2 2 0 1 1 2 3 4
The sum is 22, Will's MAD is 2.2
Based on the measures of variation, Will is a more consistent golfer. He's on average worse than Rich, but he always manages to stay pretty close to his average while Rich is all over the place.
Still I'd go with Rich for the tournament.
Pls help. im have such a bad day.
Solve.
2x + 1 = 3x – 4
A.x = 1
B.x = 5
C.x = –5
D.x = –1
Answer:
b
Step-by-step explanation:
Solve the equation.
9x + 5 = 113
8
12
14
15
Answer:
x=12
Step-by-step explanation:
9x+5=113 then subtract 5 from both sides
then you get 9x=108 then divide both sides by 9 to get x=12
Answer:
x = 12
Step-by-step explanation:
9x + 5 = 113
Subtract 5 from each side
9x + 5-5 = 113-5
9x = 108
Divide each side by 9
9x/9 = 108/9
x = 12
WILL GIVE BRANILIEST ANSWER!! 100 POINTS!! How important are the "special features" of a polynomial graph? When would you need to find all of the precise values of special features of the graph of a polynomial function? When would it be okay to estimate these values? Give examples in context, if possible.
Answer:
The special features of a polynomial graph are sharp corners but in these types of graphs it also has smooth curves. Polynomial graphs functions also display graphs that have no breaks.Curves with no breaks are called continuous.
Step-by-step explanation:
A math teacher gave her students two tests. On the first test, 80% of the class passed the test, but only 30% of the class passed both tests.
What is the probability that a student passes the second test, given that they passed the first one?
55% because you add 80% and 30% which is 110% and divide that by 2.
Find the slope of the line that passes through the points (-1, -2) and (-9, -2)
Slope = change in Y / change in x
Slope = (-2 - -2) / (-9 - -1)
Simplify:
Slope = 0/-8 = 0
Slope = 0
Fill in the table. To obtain each planet's distance from the sun and orbital period, click its name
Answer:
ya welcome
Step-by-step explanation:
Mercury - 0.39 and 0.242
Venus - 0.72 and 0.616
Earth - 1 and 1
Mars - 1.52 and 1.88
Uranus - 19.18 and 84.0
Neptune - 30.06 and 165
The distance between Mercury, Venus, Earth, Mars, Uranus, and Neptune from the sun is 0.39, 0.72, 1, 1.52, 19.18, and 30.06 respectively.
What is the distance?It is the measure of length between the two points is called distance.
The distance between each planet from the sun will be given as
Mercury - 0.39 and 0.242
Venus - 0.72 and 0.616
Earth - 1 and 1
Mars - 1.52 and 1.88
Uranus - 19.18 and 84.00
Neptune - 30.06 and 165.00
More about the distance link is given below.
https://brainly.com/question/26711747
Factor 4x^2-52x+160 completely
(would be great if all work was shown, please) ☺☺
Answer:
4(x - 5)(x - 8)
Step-by-step explanation:
Given
4x² - 52x + 160 ← factor out 4 from each term
= 4(x² - 13x + 40) ← factor the quadratic
Consider the factors of the constant term (+ 40) which sum to give the coefficient of the x- term (- 13)
The factors are - 5 and - 8, since
- 5 × - 8 = + 40 and - 5 - 8 = - 13, thus
x² - 13x + 40 = (x - 5)(x - 8)
Then
4x² - 52x + 160 = 4(x - 5)(x - 8)
PLZ ANSWER ASAP!!!!!!!!!!
Answer:
Step-by-step explanation:
For the first statement, we need to find the percentages of sold hats. The percentage of white hats sold was (120/200) * 100 = 60% and the percentage of black hats sold was (210/300) * 100 = 70%. The first statement is "The musical group sold 60% of the white hats and 70% of the black hats."
The second statement asks us to compare the 2 percentages, and since 70% > 60%, the statement would be "A greater percentage of black hats were sold." Hope this helps!
Which equation represent inverse variation between x and y
The equation representing the inverse relation is given by -
x = 15k/y.
What is the general equation of a Straight line?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
We have a equation that represent inverse variation between x and y.
The equation for inverse relation comes from the equation of straight line. We can write -
x = m/y
xy = m
for m = 15k -
xy = 15k
x = 15k/y
Therefore, the equation representing the inverse relation is given by -
x = 15k/y.
To solve more questions on straight lines, visit the link below-
brainly.com/question/20400984
#SPJ2
PLEASE HELP
What effect will a 90-degree clockwise rotation have on the triangle? Be sure to address how it could impact the angles, side lengths, and any congruency
between the original pre-image and the image.
Answer:
The angles and lengths should not change at all the image and pre-image should be the same just at a different place on the graph
An object in a simulation accelerates from rest to a speed of 4 meters per second in 2 seconds. It then accelerates linearly for the next 3
seconds until it reaches 10 meters per second. The object remains at that speed (acceleration = 0) for 3 seconds and then de-accelerates
linearly until it comes to rest 2 seconds later. Which graph demonstrates the speed of the object for those 10 seconds?
Answer:
Distance time graph by me
Answer:
Distance time graph is how to solve
Step-by-step explanation:
PLEASE HELP URGENT
Suppose that the functions r and s are defined for all real numbers x as follows.
r(x) = x + 5
s(x) = 3x + 1
Write the expressions for (r * s)(x) and (r + s)(x) and (r - s)(4) evaluate .
Answer:r*s = 168
Step-by-step explanation: (2x-1)(6x) = 12 x^2 - 6x
r(s(x)) = 2 (6x) - 1 = 12 x - 1
r(x) - s(x) = (2x-1) - 6x = -4x -1
r(x) = s(x) when 2x-1 = 6x or x = -1/4
r(4) = s(4) never
(r*s)(4) = 12 x^2 - 6 x = 12*16 - 24 =168
Can someone help me with this
Answer:
Step-by-step explanation:(-1.5,3) and (0,3)
A shop has the following offers
fig rolls(125g packet) normal price £1.34 buy one get 2nd half price crisps
(175g packet) normal price £1.59 three for the price of two
Work out the total price for 4 packets of fig rolls and 9 packets of crisps
CAN YOU PLEASE HELP ME !!!!!!!!!!!!!
Answer:
£13.56
Step-by-step explanation:
Fig rolls:
If you buy 4 you get 2 half price.
So, 1.34/2=0.67
So, (1.34*2)+(0.67*2)=£4.02
Crisps:
If you buy 9 crisps you get 9 for the price of 6.
So, 1.59*6=£9.54
Total:
£4.02+£9.54=£13.56
Can u help me with this pls
Answer: Angle B= 31.6
Step-by-step explanation:
Use SOH CAH TOA
TanB=14.1/22.9
A store buys a bag of chips
from a distributor for $0.50 and marks it
up 150%. How much does the store sell the
bag of chips for?
Answer:
Step-by-step explanation:
75p
Answer:
The answer is $0.75
Step-by-step explanation:
150 percent *0.50 =
(150:100)*0.50 =
(150*0.50):100 =
75:100 = 0.75
The cylinder and the sphere below have the same radius and the same volume. What is the height of the cylinder?
Answer:
Height of cylinder (h) = (4/3)R
Step-by-step explanation:
Given:
Radius of cylinder (r1) = R
Height of cylinder (h) = H
Radius of sphere (r2) = R
Volume of cylinder = volume of sphere
Find:
Height of cylinder (h) = H = ?
Computation:
[tex]Volume\ of\ cylinder = volume\ of\ sphere\\\\ \pi (r1)^2h =\frac{4}{3} \pi (r2)^3\\\\\pi (R)^2h =\frac{4}{3} \pi (R)^3\\\\ h=\frac{4}{3} (R)[/tex]
Height of cylinder (h) = (4/3)R
1
Andrea has 3 tiles.
One is a regular octagon, one is a regular pentagon
and one is a regular hexagon.
Andrea thinks the 3 tiles will fit together perfectly,
as shown in the diagram.
Show calculations to prove that she is wrong.
Andrea is incorrect. Given 3 tiles will not fit together perfectly.
Angles formed at a point: Sum of all angles around a point is 360°.
As shown in the picture,
If the tiles join perfectly at a point, sum of all angles around the joining point should be 360°.
Expression for the measure of the interior angle of a polygon,
Interior angle of a polygon = [tex]\frac{(n-2)\times 180^\circ}{n}[/tex]
Interior angle of a pentagon = [tex]\frac{(5-2)\times 180^\circ}{5}=108^\circ[/tex]
Interior angle of a hexagon = [tex]\frac{(6-2)\times 180^\circ}{6}=120^\circ[/tex]
Interior angle of an octagon = [tex]\frac{(8-2)\times 180^\circ}{8}=135^\circ[/tex]
To prove that the given tiles fit together perfectly → Sum of all the angles around the common point should be 360°
Sum of all interior angles = 108° + 120° + 135°
= 363°
Therefore, given tiles will not fit together perfectly.
Learn more about the interior angles of a polygon here,
https://brainly.com/question/12871621?referrer=searchResults
How many inches are in 3 feet?
A. 4 inches
B. 15 inches
O c. 24 inches
D. 30 inches
E. 36 inches
Answer:
e. 36 inches
Step-by-step explanation:
there are 12 inches in a foot 3 times 12 is 36
Answer:
Your correct answer is Option E. 36 inches
Step-by-step explanation:
sid and micah solve the equation below:
[tex]\frac{1}{2} (6x-10) = 2x+1[/tex]
sid's first step results in [tex]3x-5= 2x+1[/tex]
micah's first step results in [tex]6x-10 =4x+1[/tex]
a) Micah is correct
b) sid is correct
c) neither of them are correct
d) they are both correct
Which is the graph of f(x) = StartRoot x EndRoot?
Answer:
B
Step-by-step explanation:
On a coordinate plane, an exponential function increases in
quadrant 3 into quadrant 4 and approaches y = 0. It goes through
(negative 1, negative 2) and crosses the y-axis at (0, negative 0.25) ⇒ last answer
HOPE IT HELPS ....
You invest money at 6% interest compounded annually for 3 years. If the future value of your investment is $1800, how much money did you invest? Show your work.
Answer:
Step-by-step explanation:
FV = P(1+r)^t
1800 = P(1+0.06)^3
1800 = P(1.06)^3
P = 1800/(1.06)^3 = $1511
Find the mean of the following data set.
42, 45, 58, 63
52
42
47
Answer:
~49.9
Step-by-step explanation:
To get the mean, we must add all the numbers then divide by the amount of numbers there were.
42 + 45 + 58 + 63 + 52 + 42 + 47 = 349
Since we have 7 numbers we can do
349/7 ~ 49.9
Answer: 49.8 (50 if rounded to the nearest ones place)
Step-by-step explanation: First, let's put the number from greatest to least...and we also have to add all the numbers...
42 + 42 + 45 + 47 + 52 + 58 + 63 = 349
Lastly, we have to divide the total by how many numbers there are on the data set...there's 7
349 ÷ 7 = 49.8 (50 if rounded to the nearest ones place)
Therefore, the mean is 49.8 or 50, I hope this helps!
I need help with as soon a posible
Answer:
250
Step-by-step explanation:
[tex]2*5^3=2*(5*5*5)\\=2*125\\=250[/tex]
250
2*5^3
5*5*5=125
2*125=250
The graph shows the number of students who earned a score in math. Find the domain.
A) 10 < x < 100
B) {0, 5, 10, 15, 20, 25}
C) 0 ≤ x ≤ 24
D) {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
Answer:
d
Step-by-step explanation:
The domain of a graph is the possible input values the graph can take.
The domain of the graph is: [tex]\{10, 20, 30, 40, 50, 60, 70, 80, 90, 100\}[/tex]
The score (on the x-axis) represents the input values.
From the graph, we have:
Minimum score = 10Maximum score = 100This means that the domain of the graph is from 10 to 100
From the given options, (d) is correct;
Because it represents scores between 10 and 100 (inclusive)
Read more about domains at:
https://brainly.com/question/16875632
Which statement describes Axum's economy?
Axum's economy was strong due to the rich resources of the surrounding deserts
Axum had a weak economy because Axum had conquered the Kingdom of Kush
Axum's economy was strengthened by connections withyhe Roman Empire and Asia
Axum had a weak economy because Axum did not have access to water
Answer:
Its C on Edg2020
Step-by-step explanation:
The graph shows the numbers of quarts of yellow paint that must be mixed with different numbers of quarts of red paint to make a certain shade of orange paint.
Based on the graph, write an equation that shows the relationship between the number of quarts of yellow paint, y, and the number of quarts of red paint, x, needed to make the shade of orange paint.
Enter your equation in the space provided. Enter only your equation.
Answer:
[tex]y =\frac{2}{5}x[/tex]
Step-by-step explanation:
To find the equation, we need to use two points, which can be (0,0) and (5,2).
First, we find the slope
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } =\frac{2-0}{5-0}=\frac{2}{5}[/tex]
Therefore, the slope for the equation is 2/5.
Now, we use the point-slope formula to find the equation
[tex]y-y_{1} =m(x-x_{1} )\\y-0=\frac{2}{5}(x-0)\\y =\frac{2}{5}x[/tex]
Therefore, the equation that represents this situation is [tex]y =\frac{2}{5}x[/tex]
Which of the following has the larger area?
Answer:
the rectangle by 170 square inches, let me know if im right :)
Step-by-step explanation: