Answer:
x = 2.579248
Step-by-step explanation:
x^2 - 9/x + 4 = 3 - (x - 3/x) + 4
a) Multiply both sides by x.
x^3 + 4x - 9/x = 6x + 3
b) Multiply both sides by x.
x^4 + 4x^2 - 9x = 6x^2 + 3x
x^4 + 4x^2 - 9x - (6x^2 + 3x) = 6x^2 + 3x - (6x^2 + 3x)
x^4 - 2x^2 - 12x = 0
x(x^3 - 2x - 12) = 0
x = 0 or x^3 - 2x - 12 = 0
x = 0 or 2.5792479999999998
this past semester, a professor had a small business calculus section. the students in the class were . suppose the professor randomly selects two people to go to the board to work problems. what is the probability that is the first person chosen to go to the board and is the second?
Given : Professor randomly selects two people to go to board to work on problems.
To find: Probability of chosen first or second person to go to the board.
Let [tex]x[/tex] be the total no. of students.
After the first student is chosen, no of students left = [tex]x[/tex] - 1
Therefore,
the required probability = 1 / total no. of students x no. of students left
⇒ 1 / [tex]x[/tex] ([tex]x[/tex]- 1 )
= 1 / ([tex]x^{2} - x[/tex])
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Amanda is driving a racecar. The table below gives the distance D (1) (in meters) she has driven at a few times t (in seconds) after she startsTimer(seconds)Distance D (1)(meters)
From the question;
we are to calculate average rate of change of distance with respect to time
The average rate of change is given as
[tex]\text{Average rate of change = }\frac{D_2-D_1}{T_2-T_1}[/tex]From the question we are given the table below
a. we are to find the average rate of change of the distance driven from 0 secons to 3 seconds
From the information
we have
[tex]undefined[/tex]What is the solution to |2x - 8| ≤ 6?
Given m\_EBC = (3x + 20)° and m \_ABC = (17x-40)° find m\_ EBC and m LABC.
Answer:
18. m<EBC = 43°, m<CBD = 47°
19. m<EBC = 50°, m<ABC = 130°
Step-by-step explanation:
18. Find m<EBC and m<CBD
m<EBC = (5x + 8) and m<CBD = (6x + 5)
these two angles add up to a right angle, therefore their sum is 90°
5x + 8 + 6x + 5 = 90
11x + 13 = 90 , 11x = 77 , x = 7
m<EBC: 5(7) + 8 = 43
m<CBD: 6(7) + 5 = 47
19. Find m<EBC and m<ABC
m<EBC = (3x + 20) and m<ABC = (17x - 40)
these two angles are supplementary, meaning that they add up to 180°
3x + 20 + 17x - 40 = 180
20x - 20 = 180, 20x = 200, x = 10
m<EBC: 3(10) + 20 = 50
m<ABC: 17(10) - 40 = 130
PLEASE help! 20 points!
There is a 6% sales tax on your clothing purchase.
You pay $1.80 in tax.
What is the total amount you pay?
well, the amount paid was "x", which oddly enough is 100%, but we also know that 6% of that is $1.80, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 1.80& 6 \end{array} \implies \cfrac{x}{1.80}~~=~~\cfrac{100}{6} \implies 6x=180\implies x=\cfrac{180}{6}\implies x=30[/tex]
Determine the rate of change of the graph (HELP PLEASE)
The 89 members of the Taft School Band spend
a total of $4,628 for tickets to Hammond's
Amusement Park. What is the cost of each
amusement park ticket?
By using division, if 89 members of the Taft school band spend a total of $4628 for tickets to Hammond's amusement park, The the cost of each amusement park ticket is $52
The total number of members of the Taft school = 89 members
The total cost for the ticket to Hammond's amusement park = $4628
The cost of each amusement park ticket = The total cost for the ticket to Hammond's amusement park ÷ The total number of members of the Taft school
Substitute the values in the equation
The cost of each amusement park ticket = 4628/89
= $52
Hence, by using division, if 89 members of the Taft school band spend a total of $4628 for tickets to Hammond's amusement park, The the cost of each amusement park ticket is $52
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which answer?
pls help
Answer:
1. C: y = 3x - 5
2. B: y = -3x - 9
Step-by-step explanation:
1.
y = 3x + 9; (2, 1) (parallel)
(x₁, y₁)
y - y₁ = m(x - x₁)
y - 1 = 3(x - 2)
y - 1 = 3x - 6
+1 +1
-------------------
y = 3x - 5
----------------------------------------------------------------------------------------------------------
2.
y = (1/3)x - 6 ; (-3, 0) (perpendicular)
(x₁, y₁)
y - y₁ = m(x - x₁)
y - 0 = -3(x - (-3))
y - 0 = -3(x + 3)
y - 0 = -3x - 9
+0 +0
----------------------
y = -3x - 9
I hope this helps!
Why is triangle DFC congruent to triangle AEB?
By Side - Angle - Side congruency (SAS) rule, ΔDFC is congruent to ΔAEB as shown below.
What are Congruent triangles?Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
Given is a geometrical diagram as shown in the image.
We can prove ΔDFC ≅ ΔAEB as follows -
AE = CF [Given]
Add length EF on both sides of the equation, we get
AE = CF ...[1]
∠ 1 = ∠ 2 [Given] ...[2]
Given is ∠ 1 = ∠ 2. Than the tangent of both angles will be same. On solving the tangent ratio, we get -
BE = FD ...[3]
From equation 1, 2 and 3, we can say that
ΔDFC ≅ ΔAEB
Therefore, by Side - Angle - Side congruency (SAS) rule, ΔDFC is congruent to ΔAEB.
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Why is diffusion considered a form of passive transport?
Responses
It requires no energy from the cell.
It requires no energy from the cell.
It's a process that occurs automatically.
It's a process that occurs automatically.
It has no effect on the health of the cell.
It has no effect on the health of the cell.
It's carried out while the cell does other things.
Answer:
It requires no energy from the cell.
Step-by-step explanation:
I dont know what im doing Help Meeee
Answer:
the x = 0 and y = 1
so start off at the zero on the x-axis, and move up to the 1 on the y- axis
100 points give me an explanation.
Dont lie or I will report you.
Answer:
Both ans are attached
professor moore forgets to set his alarm with a probability of 0.10. if he sets the alarm, it will wake him on time to make his first class with a probability of 0.95. if he forgets to set the alarm, he wakes up in time for his first class with a probability of 0.25. professor moore was late to his first class. what is the probability that professor moore set his alarm given this information?
Answer: -The probability of setting his alarm is 1-0.1=0.9
-The probability of being in time is therefore calculated as:
0.9 x 0.95 + 0.1 x 0.25
= 0.88
Hence, the probability that the professor shows up in time is 0.88
Step-by-step explanation:
Customer number two gives you a
15% off coupon. What is the new cost
of the order? 11.50
Answer:
$8.50 ? let me know if im wrong
Step-by-step explanation:
A factory adds three red drops and two blue drops of coloring to white paint to make each pint of purple paint. The factory will make 50 gallons of the purple paint.
How many drops of red and blue coloring will the factory need in the 50-gallon batch of purple paint?
Answer: 1200 red and 800 blue
Two-fifths of a number decreased by 3 is 1. Find the number.
By using the basics of the number system the calculated number from the given statement is 10.
What is number system?
In mathematics, the number system can be used to express the numbers in a way of writing to make the mathematical expression. Basically, it provide the unique representation of the number with the help of the algebraic structures and operations.
According to the question, the expression can be formed by the given statement is as follows:
Let us assume the number be 'a'
Using basics of the number system for the formation of an expression:
Therefore,
(2/5)a - 3 = 1
⇒ (2/5)a = 4
⇒ a = 10
Hence, by using the basics of the number system the calculated number from the given statement is 10.
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an ecologist wishes to mark off a circular sampling region having radius 13 m. however, the radius of the resulting region is actually a random variable r with the following pdf.
The expected area of a circular sampling region is 531.56 m²
Given,
The radius of the circular sampling region = 13m
f(r) = [tex]\left \{ {\frac{3}{4} } \atop {0}} \right.[/tex] [1 - (13 - r)²] 12 ≤ r ≤ 14
We have to find the area of the circular sampling region = E (π r²)
E (π r²) = π E (r²)
Lets find E (r²)
E (r²) =₁₂ [tex]\int\limits^[/tex]¹⁴ r² f(r) dr
= ₁₂∫¹⁴ (3r²/4) (1 - (13 -r)²) dr
= 3/4 ₁₂∫¹⁴ r² (1 - 169 - r² + 26r) dr
= 3/4 ₁₂∫¹⁴ r² (26r³ - r⁴ - 168r²) dr
= 3/4 [ 26r⁴/4 - r⁵/5 - 168r³/3]₁₂¹⁴
= 3/4 [ (26 × 14⁴)/4 - 14⁵/5 - (168 × 14³)/3] - [ (26 × 12⁴)/4 - 12⁵/5 (168 × 12³)/3]
= 3/4 [ (26 × 38416)/4 - 537824/5 - (168 × 2744)/3] - [ (26 × 20736)/4 - 248832/5 - (168 × 1728)/3]
= 3/4 [ 249704 - 107564.8 - 153664] - [ 134784 - 49766.4 - 96768]
= 3/4 [-11524.8] - [-11750.4]
= 3/4 [225.6]
= 169.2
∴ E(r²) = 169.2
Now lets find the expected area of the circular sampling region:
Area = E(π r²) = π E (r²)
Here, E(r²) = 169.2
So, area = π × 169.2 = 531.56 m²
That is, the expected area of a circular sampling region is 531.56 m²
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The graph of y = f(x) is shown below. Find all values of x where f(x) = 0
The values of x when f(x) = 0 are 2 and 8
Graphs are used mostly to show the relationship between two variables (usually x and y).
The graph of y = f(x) is attached
To get the values of x when f(x) = 0 , we consider where the line of the graph crosses the x-axis.
The graph crosses the x-axis at:
x = 2
x = 8
This means that the values of x when f(x) = 0 are 2 and 8
Therefore, in the graph of y = f(x), the values of x where f(x) = 0 are 2 and 8
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Disclaimer : The question mentined is not provided with a graph, the above solution is done as per the graph attached.
A company takes 16 minutes to wash 24 cars. How many cars can be
washed in 1 minute?
Answer:1.5 cars can be washed in 1 minute but realistically only 1 car can be washed
Step-by-step explanation: 24/16 =1.5 and that get you your answer of 1.5 but the correct answer is 1.5 or 1 depending on if they are asking you to round down or not.
what is 10.88+10.88+10.88
Answer:
32.64
Step-by-step explanation:
Round 0.699 to the nearest hundredth.
Answer: 0.700
0.699 is the closest to 0.700, the hundredth would go up by one creating 0.700 hope this helps
select the correct answer. a 500-gallon water tank drains at a rate of 50 gallons per minute. the amount of water left in the tank depends on the number of minutes it has been draining. what is the range of this relation? 0 ≤ y ≤ 500 0 ≤ y ≤ 10 y ≤ 500 y ≥ 0
Our range is 0 x 10, We could also graph this with x along with the x-axis and w along the y-axis then every minute 50x gallons are gone
We have 500 gallons of the water tank and it drains at the rate of 50 gallons per minute,
.Let's suppose after 5 minutes,
W = 500 - 50 * 5W = 500 - 250W = 250
After 5 minutes, 250 gallons are left in the water tank.
Here the lowest value is 0 so our maximum time is once the tank emptied, or when w is equal to 0.
0 = 500 - 50x
50x = 500X = 500/50X = 10
So, our range is 0 x 10
We could also graph this with x along with x-axis and w along the y-axis, in the graph the x- intercept where the tank is empty
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HELP
What is the slope of the line?
Answer:
y= 1/2x+3.5
Step-by-step explanation:
Answer:
y= 1/2x+3.5
I took the test this is right
Step-by-step explanation:
Read through the solution below. Then, answer
the questions that follow.
16
6 + d =
[box]*
d
ad=b(de-c)
b
=
ad
de
=e
-C
= b
In the line marked *, what strategy was used?
The expression
fills in the orange box.
The population of a city decreases by 1.7% per year. If this year's population is 366,000, what will next year's population be, to the nearest individual?
The population of the city next year, after decreasing, will be 359,778
Here, we are given that the population of a city decreases by 1.7% per year.
This, means that the city's population will decrease by 1.7% in 1 year, (1.7 × 1.7)% in 2 years and so on.
The population of the city this year is given to be 366,000.
Thus, next year, the population will decrease by-
1.7% of 366,000
= 1.7/100 × 366,000
= 17/10 × 3,660
= 17 × 366
= 6,222
Thus, the city's total population next year will be-
366,000 - 6,222
= 3,59,778
Hence, the city's population to the nearest individual comes out to be 359,778.
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Lisa spent $27 on fruit at the grocery store. She spent a total of $30 at the store. What percentage of the total did she spend on fruit?
Lisa spent 90% of the total money on the fruits.
What is Percentage?In mathematics, a percentage is a number or ratio expressed as a fraction of 100.
Given is Lisa spent $27 on fruits at the grocery store. She spent a total of $30 at the same store.
Money spent by Lisa on fruits = $27
Total money spent by Lisa = $30
Therefore, percentage of the total money she spend on fruits will be -
(27/30) x 100 = 90%
Hence, Lisa spent 90% of the total money on the fruits.
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[5*(54-:6-3)]+6*2-60
i need help?
Answer:
177
Step-by-step explanation:
5(54 − 6 − 3) + (6)(2) − 60
= 177
A cat can jump eight times as high as it is tall. How high could a cat jump if it is 5.6 inches tall?
Answer:
44.8 inches
Step-by-step explanation:
5.6x8
need to write something to let me answer
Answer:
44.8 inches
Step-by-step explanation:
Hope this helps
A seafood market sells Maryland crabs for $10.50 per Ib and Alaskan crabs for $8.50 per lb. The owner can bring 500 lbs of crabs to sell at a weekend seafood festival. How much
money can the owner earn at the festival? Show your work and explain your reasoning.
Provided the owner can bring 500 lbs of crabs to sell at the weekend seafood festival, they can earn between $4,250 and $5,250, depending on which type of crabs or their different combinations.
How are the total earnings determined?The total earnings can be determined using mathematical operations of multiplication, division, addition, and subtraction.
The total earnings are the products (multiplication results) of the units of each type of crab and their selling prices.
The selling price of Maryland crabs per Ib = $10.50
The selling price of Alaskan crabs per lb = $8.50
The total quantity of crabs the owner can bring to the seafood festival = 500 lbs
If the owner decides to bring in Maryland crabs, they can earn $5,250 ($10.50 x 500)
If the owner decides to bring in Alaskan crabs, they can earn $4,250 ($8.50 x 500)
If the owner decides to bring a combination of Maryland and Alaskan in the ratio of 50:50, they can earn $4,750 ($10.50 x 250) + $8.50 x 250)
Thus, if the owner sells Maryland crabs, the total earnings are $5,250, but if they sell Alaskan crabs, they earn $4,250.
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One pound of apples costs $3.25. Five pounds of apples costs $16.25.
Answer:
what do you mean?
Step-by-step explanation: