[tex]\begin{cases} x = -4\implies &x+4=0\\ x=-5\implies &x+5=0\\ x = 0\implies &x=0\\ x=\frac{1}{3}\implies &x -\frac{1}{3}=0\\ &3\left( x -\frac{1}{3} \right)=3(0)\\ &3x-1=0 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ (x+4)(x+5)(x)(3x-1)=\stackrel{\textit{original equation}}{0} \\\\\\ (x^2+9x+20)(x)(3x-1)=y\implies (x^3+9x^2+20x)(3x-1)=y \\\\\\ (3x^4+27x^3+60x^2)+(-x^3-9x^2-20x)=y[/tex]
[tex]3x^4+27x^3+60x^2-x^3-9x^2-20x=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill 3x^4+26x^3+51x^2-20x=y~\hfill[/tex]
no link no bot right please
9514 1404 393
Answer:
10.49
Step-by-step explanation:
Since we know 110 = 10² +10, we can make a first approximation to the root as ...
√10 ≈ 10 +10/21 . . . . . where 21 = 1 + 2×integer portion of root
This is a little outside the desired approximation accuracy, so we need to refine the estimate. There are a couple of simple ways to do this.
One of the best is to use the Babylonian method: average this value with the value obtained by dividing 110 by it.
((220/21) + (110/(220/21)))/2 = 110/21 +21/4 = 881/84 ≈ 10.49
An approximation of √110 accurate to hundredths is 10.49.
__
The other simple way to refine the root estimate is to carry the continued fraction approximation to one more level.
For n = s² +r, the first approximation is ...
√n = s +r/(2s+1)
An iterated approximation is ...
s + r/(s +(s +r/(2s+1)))
The adds 's' to the approximate root to make the new fraction denominator.
For this root, the refined approximation is ...
√110 ≈ 10 + 10/(10 +(10 +10/21)) = 10 +10/(430/21) = 10 +21/43 ≈ 10.49
_____
Additional comment
Any square root can be represented as a repeating continued fraction.
[tex]\displaystyle\sqrt{n}=\sqrt{s^2+r}\approx s+\cfrac{r}{2s+\cfrac{r}{2s+\dots}}[/tex]
If "f" represents the fractional part of the root, it can be refined by the iteration ...
[tex]f'=\dfrac{r}{2s+f}[/tex]
__
The above continued fraction iteration adds 1+ good decimal places to the root with each iteration. The Babylonian method described above doubles the number of good decimal places with each iteration. It very quickly converges to a root limited only by the precision available in your calculator.
Please can someone help me with this
Answer:
1 : 0.44.
Step-by-step explanation:
93 : 41
= (93/93) : (41/93)
= 1 : 0.44.
ramin must calculate 8.42 divided by 3.6 longhand but can't remember what to do about decimal points
Answer:
He should change 3.6 to 36
and
he should change 8.42 to 84.2
He should also move the decimal up when dividing like in the picture I posted.
Step-by-step explanation:
I other words, he should shift the decimal points to the right one
I hope that I could help!
He should also move the decimal up when dividing in the picture that is posted.
How can we interpret the division?When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.
Division, thus, can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.
We need to find 8.42 divided by 3.6 longhand.
8.42 / 3.6
= 2.33
He should change 3.6 to 36 and he should change 8.42 to 84.2
He should also move the decimal up when dividing in the picture that is posted.
Learn more about division here:
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how to add and subtracts decimals from whole nubers
Answer:
ok so to do this you line them up like normal then always remember to make sure your decimal is in the right spot if you need more help there are many easy solutions online also if you need more help you can always send me a picture of the question or tell me it and it will make things a lot easier :)
Step-by-step explanation:
You supervise the feeding of dogs at a kennel you use an average of 10 1/2 pounds of dog food each day.at the rate how many pounds of dog food will you use In 7 days
Answer:
73.5 pounds of dog food in 7 days
Step-by-step explanation:
10 1/2 x 7
10x 7 =70
1/2 x 7 = 3.5
70 + 3.5 =73.5 pounds of dog food in 7 days
Soraya earned $40 in October. She earned $50 in
November.
What is the percent increase or decrease in Soraya's monthly earnings?
A. 15% decrease
B. 30% increase
C. 25% increase
D. 20% decrease
25% increase.
Explanation: 25% of $40 is $10. You add $10 to $40 you get $50.
A parking lot has 117 spaces total. If 36 of the spaces have cars in them, what is the ratio of empty spaces to filled spaces?
Answer:
81:36
Step-by-step explanation:
117-36
= 81
Boom answer that's it
The ratio of empty spaces to filled spaces is 9 : 4.
What is proportion ?
A proportion is an equation based on the equality of two ratios.
Here it is given that :
A parking lot has total = 117 spaces
Spaces filled with cars = 36
spaces left = total spaces - space filled with cars
spaces left = 117 - 36
spaces left = 81
Now, the ratio of empty spaces to filled spaces will be :
81 : 36
cancelling common factor that is 9 :
9 : 4
Therefore, the ratio of empty spaces to filled spaces is 9 : 4.
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i need help with this word problem please! :)
Answer:
Step-by-step explanation:
ASSUMING all family members purchased ride tickets
Let n be the number of family members
148 = 8 + n(16 + 12)
140 = 28n
n = 5
Can someone plsss help me
Answer:
y = -5/3 x + 40
Step-by-step explanation:
The general form is y = ax + b, where a is the slope and b is the y intercept.
So immediately you can see that b must be 40, since the line crosses the y axis at 40.
The slope can be calculated by finding two "nice" points on the line that are also grid lines.
How about (0,40) and (6, 30).
Then, calculate the slope by dividing the y difference by the x difference:
(30-40)/(6-0) = -10/6 = -5/3
So C must be the answer.
A car travels a constant speed of 45 km/h
3.4.1 The distance travelled in 6 hours?
3.4.2 The time it takes to travel 495 km?
Answer:
1 hour
Step-by-step explanation:
because i divided
PLEASE HURRY
Todd drives 2,365 miles in a month. His average MPG is 20. How much will he pay in gas if gas is $3.12 per gallon?
$368.94
$390
$234
$208.12
Answer:
Should be $368.94
Step-by-step explanation:
hope it helps
please mark brainliest
The total cost of 118.25 gallons of gas is $368.94. Therefore, option A is the correct answer.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, Todd drives 2,365 miles in a month and the average is 20 miles per gallon
Now, number of gallons =2,365/20
= 118.25 gallons
So, total cost = 118.25×3.12
= $368.94
Therefore, the total cost of gas is $368.94.
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Which linear function represents the line given by the point-slope equation y + 1 = -3(x - 5)?
O f(x) = -3x - 6
O f(x) = -3x - 4
O f(x) = -3x + 16
O f(x) = -3x + 14
Answer:
-3x + 14
Step-by-step explanation:
Expand -3(x-5)
. -3 * x = -3x
. -3 * -5 = 15
So
. y+1 = -3x + 15
Subtract 1 from both sides so that y is the subject
. y = -3x + 14
Now you can juse replace y with f(x) since theyre basically the same thing
Need help with this quick plz??
Answer:10 or someones else’s answer this not my best
Step-by-step explanation:
Please help me due on Friday
Answer:
Galaxies are moving closer together as time progresses
Step-by-step explanation:
Let me know if this helps!
Terry and Jim have two car loans totaling $ 26,004.
One loan has an annual percentage rate (APR) of 3.1 % and the other has an APR of 7%.
If the total interest they paid after one year is $1,481.25, what is the amount owed on each car?
(1 = PRT. Note t = 1 year).
Answer needed right away!! With explanation
The annual percentage rate is the interest rate for payment for the car
loan.
The mount owed on the car with an APR of 3.1% is approximately $8,693.08.The mount owed on the car with an APR of 7% is approximately $17,310.92.The given parameters are;
The amount of loan Terry and Jim have = $26,004
The annual percentage rate (APR) on one loan = 3.1 %
The annual percentage rate (APR) on the other loan = 7 %
Total interest paid after one year = $1,481.25
Required:
The amount owed on each car
Solution:
Let X represent the loan, with 3.1% APR, we have;
The other loan with 7% APR = 26,004 - X
Therefore;
0.031·X + 0.07·(26,004 - X) = 1,481.25
0.031·X + 1,820.28 - 0.07·X = 1,481.25
1,820.28 - 1,481.25 = 0.07·X - 0.031·X = 0.039·X
339.03 = 0.039·X
[tex]X = \dfrac{339.03}{0.039} \approx 8693.08[/tex]Therefore;
The amount owed on the car with an APR of 3.1%, X ≈ $8,693.08Therefore;
The amount owed on the car with an APR of 7% ≈ 26,004 - 8693.08 =
17310.92.
The amount owed on the car with an APR of 7% ≈ $17,310.92Learn more here:
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If Brianna spent $65 on necklaces and bracelets at a crafts fair.
She spent $23 on bracelets and the rest on necklaces.
If the necklaces all cost the same and Brianna bought 3, how much did each necklace cost?
math help please :) thxx
Answer: 15 inches
Step-by-step explanation:
15 × 1 ÷ 12 = 1.25 ft
1.25 ft = 1.25 × 12 = 15 in
Seedless watermelon costs $.99 per pound. Find the cost per kilogram
please help and show the solution and answer thank uou
Answer:
$2.20/kg
Step-by-step explanation:
First, we must convert pounds to kilograms.
1 lb = 0.45 kg
If 1 lb costs $.99
then 0.45 kg costs $.99
0.45 kg = $.99
dividing both sides by 0.45
1 kg = .99 ÷ 0.45
1 kg = $2.20
Hemp help help help help help math math math
Answer:
x=25
Step-by-step explanation:
5x-5+ 2x+10 =180
2x-5x = 10+5
3x= 15
x=5
5(5)-5+ 2(5) +10 =180
According to this diagram, what is sin 23°?
67°
13
5
23°
90°
The value of sin(23°) is equivalent to 0.39.
What are trigonometric functions?There are six major trigonometric functions as -
Sine(x)Cosine(x)Tangent(x)Cotangent(x)Secant(x)Cosecant(x)We can write the relation between them as -
Sine = 1/cosecantCosine = 1/secantTangent = 1/CotangentGiven is to find the value of sin 23°.
Now, we can write the value of sin(23°) as -
sin(23°) = sin(30° - 7°)
Expanding using the compound angle formula, we can write -
sin (x - y) = sin(x) cos(y) - cos(x) sin(y)
sin(30° - 7°) = sin(30°) cos(7°) - cos(30°) sin (7°)
sin(30° - 7°) = 1/2 x 0.99 - √3/2 x 0.121
sin(30° - 7°) = 1/2 x 0.99 - √3/2 x 0.121
sin(30° - 7°) = 0.495 - 0.105
sin(30° - 7°) = 0.495 - 0.105
sin(30° - 7°) = 0.39
Therefore, the value of sin(23°) is equivalent to 0.39.
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A washer and a dryer cost $932 combined. The washer costs $82 more than the dryer. What is the cost of the dryer?
Step-by-step explanation:
Lucus had a balance of $21 in his checking account. Since then he made deposits of $187, $445 and $454 and wrote checks for $74, $137, $139, and $240. When all of the deposits are recorded and all of the checks clear, what balance will he have in his checking account?
Based on the opening balance, the amounts deposited, and the amounts for checks, the balance in the account should be $517.
The deposits into the account will increase the balance whilst the checks will do the opposite.
The balance is therefore:
= Opening balance + Deposits - Checks
= 21 + 187 + 445 + 454 - 74 - 137 - 139 - 240
= 21 + 1,086 - 590
= $517
In conclusion, the balance will be $517.
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PLEASE NO LINKS DONT WASTE YOUR TIME IM NOT GONNA CLICK. What are the zeros of this function?
Answer: C. x = 4 and x = 6
Step-by-step explanation:
Zeros of a function would be the value of x when f(x) is 0.
Based on the given graph, the parabola has 2 locations where the y-value is 0 and the graph hits the x-axis.
The graph hits the x-axis at 4 and at 6.
Answer:
I dont but want to.
Hope this helps! :) ;-;
Step-by-step explanation:
Please help me
The variables x and y are proportional. Use the values to find the constant of proportionality. Then write an equation that relates x and y. Write any fractions in the simplest form.
When y=45 , x=40 .
y=kx
20=k(12)
k= 20/12 = 5/3
y= (5/3)x
y = 5x/3 or
3y=5x
What are the coordinates of the x-intercept of the line -3x-5y=12?
well, x-intercept means for a graphed funciton where the x-axis gets touched/intercepted, Check the picture below, when that occurs, y = 0, so if we want to know what "x" is at that point we can simply set y = 0 and solve for "x".
[tex]-3x-5y=12\implies \stackrel{\textit{setting y = 0}}{-3x-5(0) =12}\implies -3x-0=12 \\\\\\ -3x=12\implies x=\cfrac{12}{-3}\implies x = -4 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{coordinates}}{(-4~~,~~0)}~\hfill[/tex]
I am having trouble with this problem. I can’t figure it out. I have tried everything but can’t figure it out. After I figure out the problem I have to check it by writing out the problem and replacing the y with the number it equals. At the end it should equal 6
The picture is a different problem but this is what the check looks like
6=-y+42+-2y
Answer:
16 = y
Step-by-step explanation:
So you have the equation 6=-y+42+-2y
Find the y first
6=-y+42+-2y
add all y's together
6=-3y+42
subtract 42 on both sides
-48 = -13y
16 = y
------------------------------------------------
Now do the check:
Plug in 16 where ever it says y in the original equation
6= -(16) + 42 + -2(16)
open the brackets
6= -16+42-32
solve
6=26-32
6 = 6
Hope this helps
An editor has a stack of k documents to review. The order in which the documents are reviewed is random with each ordering being equally likely. Of the k documents to review, two are named “Relaxation Through Mathematics” and “The Joy of Calculus.” Give an expression for each of the probabilities below as a function of k. Simplify your final expression as much as possible so that your answer does not include any expressions in the form a b . (a) What is the probability that “Relaxation Through Mathematics” is first to review?
Using the probability concept, it is found that there is a [tex]\mathbf{\frac{1}{k}}[/tex] probability that “Relaxation Through Mathematics” is first to review.
A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem:
There is a total of k documents to be reviewed, hence [tex]T = k[/tex].Of those documents, 1 is named “Relaxation Through Mathematics”, hence [tex]D = 1[/tex]The probability is:
[tex]p = \frac{D}{T} = \frac{1}{k}[/tex]
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A weather forecaster has a 60% chance of predicting the weather correctly today. If she is correct, then the probability of being correct the next day is 80%. If she is wrong, the chance of predicting incorrectly the next day is increased by 25% that she was wrong the previous day. What is the probability that the forecaster will predict the weather correctly in exactly two of the next three days?
Answer:
According to the National Weather Service, if you see a 40 percent chance of rain, "there is a 40 percent chance that rain will occur at any given point in the area."
Step-by-step explanation:
The probability that the forecaster will predict the weather correctly in exactly two of the next three days is 0.48 or 48%.
What is the chain rule in probability?For two events A and B, by chain rule, we have:
[tex]P(A \cap B) = P(B)P(A|B) = P(A)P(B|A)[/tex]
where P(A|B) is the probability of occurrence of A given that B already occurred.
A weather forecaster has a 60% chance of predicting the weather correctly today.
If she is correct, then the probability of being correct the next day is 80%.
If she is wrong, the chance of predicting incorrectly the next day is increased by 25% that she was wrong the previous day.
Let the chance of predicting the weather correctly today be A.
Let the chance of predicting the weather correctly the next day be B.
Then the probability that the forecaster will predict the weather correctly in exactly two of the next three days will be
[tex]P(A \cap B) = P(A)P(B|A) = 0.6 \times 0.8 = 0.48[/tex]
More about the chain rule of probability link is given below.
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Which job paid better 30 minutes for $10.00, 3.5 hours for $30.00, 2 hours for $30.00
Answer:
30 minutes for $10.00
Step-by-step explanation:
30min=$10
60min=$20
90min=$30
210min(3.5 hours)=$30
120min(2hours)=$30
What is the slope of the line through (-3, 3) and (-1,-1)?
2
(1-1)
O A. 2
O B.-2
O c.
OD. -