Answer:
[tex]ax^5+ by^5=241[/tex]
Step-by-step explanation:
Given:
[tex]ax + by = 1[/tex][tex]ax^2+ by^2 = 11[/tex][tex]ax^3+ by^3 = 25[/tex][tex]ax^4+ by^4 = 83[/tex]We can re-write the left sides of the given equations as follows:
[tex]ax^2+ by^2=(ax+by)(x+y)-xy(a+b)[/tex]
[tex]ax^3+ by^3=(ax^2+by^2)(x+y)-xy(ax+by)[/tex]
[tex]ax^4+ by^4=(ax^3+by^3)(x+y)-xy(ax^2+by^2)[/tex]
Therefore, following this pattern:
[tex]ax^5+ by^5=(ax^4+by^4)(x+y)-xy(ax^3+by^3)[/tex]
Use the given values and the expanded expressions to create 2 equations to help find the values of (x+y) and xy:
Equation 1
[tex]ax^3+ by^3=(ax^2+by^2)(x+y)-xy(ax+by)[/tex]
[tex]\implies 25=11(x+y)-xy(1)[/tex]
[tex]\implies 25=11(x+y)-xy[/tex]
Equation 2
[tex]ax^4+ by^4=(ax^3+by^3)(x+y)-xy(ax^2+by^2)[/tex]
[tex]\implies 83=25(x+y)-xy(11)[/tex]
[tex]\implies 83=25(x+y)-11xy[/tex]
Multiply Equation 1 by 11:
[tex]\implies 275=121(x+y)-11xy[/tex]
Then subtract Equation 2 from this to eliminate 11xy and find the value of (x+y):
[tex]\implies 192=96(x+y)[/tex]
[tex]\implies (x+y)=2[/tex]
Multiply Equation 1 by 25:
[tex]\implies 625=275(x+y)-25xy[/tex]
Multiply Equation 2 by 11:
[tex]\implies 913=275(x+y)-121xy[/tex]
Subtract the 2nd from the 1st to eliminate 275(x+y) and find the value of xy:
[tex]\implies 288=-96xy[/tex]
[tex]\implies xy=-3[/tex]
Therefore, we now have:
[tex]ax^4+ by^4 = 83[/tex][tex]ax^3+ by^3 = 25[/tex][tex](x+y)=2[/tex][tex]xy=-3[/tex]Substitute these into the equation for ax⁵ + by⁵ and solve:
[tex]\implies ax^5+ by^5=(ax^4+by^4)(x+y)-xy(ax^3+by^3)[/tex]
[tex]\implies ax^5+ by^5=(83)(2)-(-3)(25)[/tex]
[tex]\implies ax^5+ by^5=166+75[/tex]
[tex]\implies ax^5+ by^5=241[/tex]
what adds to -288 and adds to -41?
Answer: -329 sorry if i'm not right
You have one cubic mile of water. you release it at 1000 gallons per
minute. how long will it take to empty??
It will take 764664.6875 days to empty the water
How to determine the time to empty?The given parameters are:
Volume = 1 cubic mileRate = 1000 gallons per minutesThe time is calculated as:
Time = Volume/Rate
So, we have:
Time = 1 cubic mile ÷ 1000 gallons per minute
Convert gallons to cubic mile
Time = 1 cubic mile ÷ (9.0817e-13 * 1000) cubic mile per minute
Divide
Time = 1.10111715 × 10^9 minute
Convert to days
Time = 764664.6875 days
Hence, it will take 764664.6875 days to empty the water
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A cone has a height of 15 feet and a radius of 11 feet. What is its volume?
Use ≈ 3.14 and round your answer to the nearest hundredth.
cubic feet?
Answer: 1899.70 cu ft
Step-by-step explanation:
Cone volume = 1/3 TT r^2 h
V= (1/3) (3.14) (11^2) (15)
V=1899.70 cu ft
A system of two linear inequalities is graphed as shown, where the solution region is shaded. Complete the sentences below by determining whether each point is, or is not. located in the solution region.
The point (-3.2)
The point (-7.5)
The point (2.-5)
The point (-14,6)
All the points The point (-3.2), The point (-7.5), Point (2.-5), and The point (-14,6) is located in the solution region.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
When we plot all the points on the graph we can see that all the points The point (-3.2), The point (-7.5), Point (2.-5), and The point (-14,6) are located in the solution region.
Therefore all the points The point (-3.2), The point (-7.5), Point (2.-5), and The point (-14,6) is located in the solution region.
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The measure of an angle is 153°. What is the measure of its supplementary angle?
Answer:
27
Step-by-step explanation:
Supplementary angles add up to 180 degrees
So to find the measure of an angle supplementary to a given angle, we simply subtract the given angle from 180
The given angle here has a measure of 153 degrees
So the angle's supplement has a measure of 180 - 153 = 27 degrees.
For the function f(x) = 3x + 7, find the following:
a) f(2)=
c) f(x) = 8
b) f(-3) =
d) f(x) = 10
Answer:
a) 13
b) 1/3
c) -2
d) 1
Step-by-step explanation:
This is quite simple if you look at it from a different perspective. Imagine that when it says "f(2)" That you are plugging the number 2 in for every x on the right side of the equation:
For example:
f(x) = 3x + 7
f(2) = 3(2) + 7
f(2) = 6 + 7
f(2) = 13
________
f(-3) = 3x + 7
f(-3) = 3(-3) + 7
f(-3) = -9 + 7
f(-3) = 7 - 9 (This is just for those that hate negative values. You can rearrange the values as long as their sign is the same when you do move them. Ex: -14 + 6 - 4 + 9 == 9 + 6 - 14 - 4. I hope that makes sense.
f(-3) = -2
The other way is quite simple as well, if you look at it from a different perspective. Imagine that when it says "f(x) = 8" that you are changing the f(x) to the number 8:
For example:
f(x) = 8
f(x) = 3x + 7
8 = 3x + 7
8 - 7 = 3x
1 = 3x
x = 1/3
f(x)= 10
f(x) = 3x + 7
10 = 3x + 7
10 - 7 = 3x
3 = 3x
3/3 = x
1 = x
I hope this helps!
The total length of a road trip was 18.4 hours. If highway signs are posted every 0.08 hours, including one at the end of the road trip, how many highway signs will there be on the road trip?
There are 230 highway signs during road trip.
What is length?Length is defined as the act of measuring the length of objects in some specified units which can be standard or non-standard.
Here, The total length of a road trip = 18.4 hours.
Highway signs are posted = after every 0.08 hours.
To find: Number of highway signs.
The number of highway signs is found = 18.4 / 0.08 = 230.
Thus there are 220 highway signs available during the road trip.
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what is the volume of a sphere with an 8 cm radius
Answer:
Approx. 2140.16 cubic centimeters
Step-by-step explanation:
[tex]Volume=\frac{4}{3}\pi r^{3} \\V=\frac{4}{3}(3.14)(8)^{3} \\V=4.18(8)^{3} \\V=4.18(512) \\V=2140.16[/tex]
√34=
need some solution please
Answer:
34 1/2
Step-by-step explanation:
A rope 24m long is dividend into three pieces in the ratio 2:1:5. the length of the shortest piece is
well, let's simply divide the total of 24 by (2 + 1 + 5) and then distribute accordingly to each ratio.
[tex]2 ~~ : ~~ 1 ~~: ~~ 5\implies 2\cdot \cfrac{24}{2+1+5}~~ : ~~ 1\cdot \cfrac{24}{2+1+5} ~~: ~~ 5\cdot \cfrac{24}{2+1+5} \\\\\\ 2 \cdot \cfrac{24}{8}~~ : ~~ 1 \cdot \cfrac{24}{8}~~: ~~ 5\cdot \cfrac{24}{8}\implies 2(3)~~ : ~~ 1(3) ~~: ~~ 5(3)\implies 6:\stackrel{\stackrel{shortest}{\downarrow }}{3}:15[/tex]
find the volume to the nearest tenth
A tractor costs $20000 and depreciates in value by 15% per year. how much will the tractor be worth after 5 years?
Answer:
$ 8874.11 after 5 years
Step-by-step explanation:
Each year it is worth 85 % of its value
20 000 ( .85)^5 = 8874.11
*TIMID* The spinner is divided into 8 equal sections.
A spinner divided into 8 equal sections labeled gray, green, red, purple, gray, green, yellow, blue.
Which two events have the same probability?
options:
P(gray), P(green)
P(red), P(gray)
P(gray), P(purple)
P(yellow), P(gray)
Use the given information to determine which of the following relationships
can be proved and why.
ZL= 20
ZME P
M
Answer:
C. ∆LMN ~ ∆OPQ, because of AA
Step-by-step explanation:
All of the triangle congruence postulates require at least one pair of corresponding sides be congruent (in addition to other requirements). Triangle similarity can be proved if there are two pairs of congruent corresponding angles.
__
congruenceNo sides are given as congruent, so no congruences can be proved.
similarityTwo pairs of corresponding angles are said to be congruent, so we can say ...
∆LMN ~ ∆OPQ, because of AA
Simplify 4 + (-3) - 2 times (-6)
Step-by-step explanation:
[tex] = 4 + ( - 3) - 2 ( - 6)[/tex]
here ( + ) × ( - ) = ( - )
[tex] = 4 - 3 + 12[/tex]
[tex] = 4 + 12 - 3[/tex]
[tex] = 16 - 3[/tex]
[tex] = 13[/tex]
The correct result of this simplification is 13
To solve this question, we'll just apply the rule of signs - and then we'll calculate the operations.
- In the sign rule - when both signs are equal, the result will be positive. If the signs are different, the result is negative.
- ( - ) = ++ ( + ) = +- ( + ) = -+ ( - ) = -Resolution4 + ( - 3 ) - 2 · ( - 6 )
4 - 3 - ( - 12 )
4 - 3 + 12
1 + 12
13
Therefore, the alternative value will be 13
Wren is at the grocery store buying fruit. She buys x pounds of apples for $1.68 per pound. She buys 2 fewer pounds of grapes for $2.48 per pound. The cost of the fruit, before tax, is $13.76. How many pounds of each fruit is she buying?
A.
2.8 pounds of apples and 4.8 pounds of grapes
B.
3.3 pounds of apples and 1.3 pounds of grapes
C.
3.8 pounds of apples and 1.8 pounds of grapes
D.
4.5 pounds of apples and 2.5 pounds of grapes
Answer:
A.
Step-by-step explanation:
Wren is at the grocery store buying fruit. She buys x pounds of apples for $1.68 per pound. She buys 2 fewer pounds of grapes for $2.48 per pound. The cost of the fruit, before tax, is $13.76. How many pounds of each fruit is she buying?
A.
2.8 pounds of apples and 4.8 pounds of grapes
B.
3.3 pounds of apples and 1.3 pounds of grapes
C.
3.8 pounds of apples and 1.8 pounds of grapes
D.
4.5 pounds of apples and 2.5 pounds of grapes
If f(x)=2(3x-5) when f(x) =74,what is the value of x??
Answer:
x = 14
Step-by-step explanation:
given f(x) = 2(3x - 5) and f(x) = 74 , then equating gives
2(3x - 5) = 74 ( divide both sides by 2 )
3x - 5 = 37 ( add 5 to both sides )
3x = 42 ( divide both sides by 3 )
x = 14
Windborn company has 20,000 shares of cumulative preferred 2% stock, $150 par and 50,000 shares of $25 par common stock. the following amounts were distributed as dividends:
20y1 $120,000
20y2 24,000
20y3 180,000
determine the dividends per share for preferred and common stock for each year. round all answers to two decimal places. if an answer is zero, enter '0'.
preferred stock common stock
(dividends per share) (dividends per share)
20y1
20y2
20y3
Based on the preferred dividends, the dividends for preferred and common stock in each year are:
Preferred stock dividends:
20y1 - $3.00 per share.20y2 - $1.20 per share.20y3 - $4.80 per share.Common stock dividends:
20y1 - $1.20 per share.20y2 - $0 per share.20y3 - $1.68 per share.What are the preferred dividends?Preferred shares have a specific dividend, and as these are cumulative shares, the dividends that are not paid in one year, will be paid in the next.
Dividends per year:
= 20,000 x 2% x 150
= $60,000
20y1 dividend per share:
= 60,000 / 20,000
= $3.00 per share
20y2 dividend per share:
= 24,000 / 20,000
= $1.20 per share
20y3 dividend per share:
The remaining dividend from 20y2 will have to be paid here:
= (60,000 + (60,000 - 24,000)) / 20,000
= 96,000 / 20,000
= $4.80 per share
What are the common dividends?Preferred dividends are paid first:
Common dividends are:
= (Amount distributed as dividends - Preferred dividends) / Number of common shares
In 20y1:
= (120,000 - 60,000) / 50,000
= $1.20
In 20y2:
= (45,000 - 45,000) / 50,000
= $0 per share
In 20y3:
= (180,000 - 96,000) / 50,000
= $1.68 per share.
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What is 12x³ – 9x² − 4x + 3 in factored form?
Pls hurry
Answer:
[tex]\bold{\green{(4x-3)(3x^{2}-1) }}[/tex]
Step-by-step explanation:
[tex]\sf{12x^{3}-9x^{2}-4x+3 }[/tex][tex]\sf{3x^{2}(4x-3)-1(4x-3) }[/tex][tex]\sf{(4x-3)(3x^{2}-1) }[/tex]Answer:
(3x^2 - 1)(4x - 3)
Step-by-step explanation:
We can use grouping to factor this
12x^3 – 9x^2 − 4x + 3
group into: (12x^3 – 9x^2)(− 4x + 3)
Solve one side at a time:
(12x^3 – 9x^2)
3x^2(4x - 3) factor out a 3x^2
(− 4x + 3)
- 1 (4x - 3) factor out a -1
put the two equations togeth
(3x^2 - 1)(4x + 3)
The average vehicle releases 1.39 grams of nox per mile driven. if a vehicle is driven 22,000 miles per year for 15 years, how much nox does that vehicle release
In 15 years, the average car releases 458.7 kilograms of nox.
How much nox does that vehicle release?
We know that the average vehicle releases 1.39 grams per mile driven.
And, in average, that car drives 22,000 miles per year.
So in a year, a car releases:
M = (22,000)*1.39 g = 30,580 g = 30.58 kg
In one year, the average car releases around 30.58 kilograms of nox.
Then in 15 years, the car releases 15 times that amount, then we have the product:
T = 15*30.58 kg = 458.7 kg
In 15 years, the average car releases 458.7 kilograms of nox.
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The table represents the function f(x).
The value of f(3) is 9
How to determine the value of f(3)?The table that completes the question is added as an attachment.
From the complete table, we have:
When x = 3, the value of the function is 9
This means that:
f(3) = 9
Hence, the value of f(3) is 9
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What must be a factor of the polynomial function f(x) graphed on the coordinate plane below? on a coordinate plane, a parabola opens up. it goes through (0, 3), has a vertex at (3.5, 3), and goes through (6, 0). x – 3 x – 1 x 1 x 3
The factor of the polynomial function f(x) graphed on the coordinate plane below is x - 1 , Option B is the right answer.
What is a Polynomial Function ?A function in which there is only positive exponents to the variables are called polynomial function.
The missing image is attached with the answer.
It is given in the question
on a coordinate plane, a parabola opens up. it goes through (0, 3), has a vertex at (3.5, 3), and goes through (6, 0)
The zeroes of the polynomial function are the points at which the curve will cut x axis
For the given graph,
the curve cuts the x-axis at x = 1 and x = 6
the factors will be x - 1 and x - 6
Therefore, a factor of the polynomial function f(x) graphed on the coordinate plane below is x - 1 , Option B is the right answer.
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Answer:
B
Step-by-step explanation:
B
When Famke charges her phone, it gains 2 percentage points each minute. When Famke uses her phone, it loses 5 percentage points each minute. Once, Famke used her phone for some time, and then charged it for twice the amount of time she used it. In the end, her phone lost 10 percentage points. How long did Famke use her phone and how long did she charge it?
For a science project, billy observed a chipmunk and a squirrel stashing acorns in trees. the chipmunk hid 3 acorns in each tree. the squirrel hid 4 acorns in each tree. they each hid the same number of acorns, although the squirrel needed 2 fewer trees. you are going to investigate the number of acorns that each animal hid.
The number of acorns that each animal hid is 48
What is an Equation ?An equation is formed when two algebraic expressions are equated by an equal sign.
It is asked to calculate the number of acorns that each animal hid.
Total number of acorns hid = number of acorns hid per tree * number of trees
Let T be the number of trees chipmunk used
For chipmunk: = 3*T
For squirrel: = 4*(T-4)
As both the animals hid same number of acorns.
3T = 4(T-4)
3T = 4T - 16
16 = T
Therefore the chipmunk hid 16 * 3 = 48 acorns
and the squirrel hid 4(16-4) = 48 acorns.
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True or false? The graph represents a function
Answer:
true
Step-by-step explanation:
The statement is true because every graph associated a unique x-value for each y - value
In the given figure, if y = 30, find (i) x (ii) z and (iii) u
Answer:
u=30
x=150
z=150
y=30
Step-by-step explanation:
u=y [ being vertically opposite angle]
x+u=180[ being linear pair]
x+30=180
x=180-30
x=150
z=x[being vertically opposite angle]
z=150
y=u[ being voa]
Answer:
=40°
Step-by-step explanation:
Sorry that's all I know
^keep safe^
John believes that the amount of sleep he gets the night before a test and his score on that test are inversely related. On his first exam, he got eight hours of sleep and scored 70 on the exam. To the nearest tenth, how many hours does John believe he must sleep the night before his second exam so that the average of his two exam scores is an 80?
Answer:
Step-by-step explanation:
ohn will need to sleep for 10.3 hours before his second exam so that the
he average of his two exam scores is an 80.
We were given
8 hours of sleep = 70
To get an average of 80
70+ x = 80
2
Cross multiply:
70+x = 160
x= 160-70
= 90.
If 8 hours of sleep = 70
x hours of sleep = 90
Cross multiply
8× 90 = 70 × x
720 = 70x
x = 720/70
x = 10.2857
≈ 10.3 hours of sleep
Simplify..
Please show work
I give Brainliest
Answer:
[tex]\frac{4}{n^{2} }[/tex]
Step-by-step explanation:
(2nm⁻³) * 2m³n⁻³
First, focus on the coefficients, 2*2 = 4.
Now the n, n * n⁻³ = n⁻²
Now the m, m⁻³ * m³ = m⁰ = 1
Now multiply altogether, 4n⁻²(1) = [tex]\frac{4}{n^{2} }[/tex]
Christian owns a small business selling bagels. He knows that in the last week 10 customers paid cash, 14 customers used a debit card, and 38 customers used a credit card. Based on these results, express the probability that the next customer will pay with a credit card as a decimal to the nearest hundredth.
The probability that the next customer will pay with a credit card is 0.61.
What is probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it.
Given that Cristian's customers pay using, cash, debit cards and credit cards,
He knows that in the last week 10 customers paid cash, 14 customers used a debit card, and 38 customers used a credit card.
We need to find the probability that the next customer will pay with a credit card,
Therefore,
The favorable outcomes = 38
Total outcomes = 38+10+14 = 62
Therefore,
P(credit cards) = 38/62 = 0.61
Hence the probability that the next customer will pay with a credit card is 0.61.
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Could someone help me on this
Answer:
13.) 314.2 in²
15.) 181.5 ft²
Step-by-step explanation:
The area of a circle is found using the equation:
A = πr²
In this equation, "π" represents the number pi (3.14....) and "r" represents the radius (half the diameter).
For 13.), you have been given the radius. Thus, you can substitute it into the equation and solve for "A".
A = πr²
A = π(10)²
A = π x (100)
A = 314.2 in²
For 15.), you have been given the diameter. To find the radius, you need to divide this value by 2. Once you find the radius, you can plug it into the equation and simplify like above.
diameter = 15.2 ft
radius = 7.6 ft
A = πr²
A = π(7.6)²
A = π x (57.76)
A = 181.5 ft²