Answer:
[tex]\dfrac a{b^2} + \dfrac b{a^2} = 10[/tex]
Step-by-step explanation:
[tex]\text{Given that, the roots are a,b and } ~ x^2 -4x+2 = 0\\\\\text{So,}\\\\a+b = -\dfrac{-4}1 = 4\\\\ab = \dfrac 21 = 2\\\\\text{Now,}\\\\~~~~~\dfrac a{b^2} + \dfrac b{a^2}\\\\\\=\dfrac{a^3 +b^3}{a^2b^2}\\\\\\=\dfrac{(a+b)^3 -3ab(a+b)}{(ab)^2}\\\\\\=\dfrac{4^3 -3(2)(4)}{2^2}\\\\\\=\dfrac{64-24}{4}\\\\\\=\dfrac{40}{4}\\\\\\=10[/tex]
Answer:
[tex]\dfrac{a}{b^2}+\dfrac{b}{a^2}=10[/tex]
Step-by-step explanation:
Given equation: [tex]x^2-4x+2=0[/tex]
The roots of the given quadratic equation are the values of x when [tex]y=0[/tex].
To find the roots, use the quadratic formula:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
[tex]a=1, \quad b=-4, \quad c=2[/tex]
[tex]\begin{aligned}\implies x & =\dfrac{-(-4) \pm \sqrt{(-4)^2-4(1)(2)}}{2(1)}\\& =\dfrac{4 \pm \sqrt{8}}{2}\\& =\dfrac{4 \pm 2\sqrt{2}}{2}\\& =2 \pm \sqrt{2}\end{aligned}[/tex]
[tex]\textsf{Let }a=2+\sqrt{2}[/tex]
[tex]\textsf{Let }b=2-\sqrt{2}[/tex]
Therefore:
[tex]\begin{aligned}\implies \dfrac{a}{b^2}+\dfrac{b}{a^2} & = \dfrac{2+\sqrt{2}}{(2-\sqrt{2})^2}+\dfrac{2-\sqrt{2}}{(2+\sqrt{2})^2}\\\\& = \dfrac{2+\sqrt{2}}{6-4\sqrt{2}}+\dfrac{2-\sqrt{2}}{6+4\sqrt{2}}\\\\& = \dfrac{(2+\sqrt{2})(6+4\sqrt{2})+(2-\sqrt{2})(6-4\sqrt{2})}{(6-4\sqrt{2})(6+4\sqrt{2})}\\\\& = \dfrac{12+8\sqrt{2}+6\sqrt{2}+8+12-8\sqrt{2}-6\sqrt{2}+8}{36+24\sqrt{2}-24\sqrt{2}-32}\\\\& = \dfrac{40}{4}\\\\& = 10\end{aligned}[/tex]
Paul has a spinner with 4 colors: green, yellow, blue, and orange. he spins the spinner 60 times and records each color it stops on. the results are shown in this table
Green-12
Yellow - 19
Blue - 14
orange - 15
Paul will spin the spinner an additional 450 times. how many times should he expect the spinner to stop on blue? SHOW WORK
it landed in blue 14 times in 60 spins for a 14/60 = 0.2333 probability.
450 spins x 0.2333 probability = 105 times
Answer: 105
If kinaata goes for swimming lessons every 5 days while Wayo goes every 6 days. if both kinaata and Wayo had swimming lessons together at the pool today, after how many days will both meet again at the pool for lessons?
Step-by-step explanation:
we need the least or smallest common multiple for both numbers, 5 and 6.
this is very simple for the small numbers here, but in general we look at the prime factors of both numbers :
6 has the prime factors 2 and 3.
5 has only 5.
so, the LCM is 2×3×5 = 30.
they will meet again after 30 days.
FYI -
the LCM is for larger numbers a and b not automatically a×b. if both numbers share prime factors, the LCM can be smaller than a×b, as the LCM is using every overlapping prime factor only once.
If 3x+4=133x+4=13, what is the value of x?
The value of x from the equation 3x + 4 = 31 and x + 4 = 13 is 9.
How to solve equation?3x + 4 = 31
x + 4 = 13
From equation (2)
x + 4 = 13
subtract 4 from both sides
x = 13 - 4
x = 9
Substitute x = 9 into (1)
3x + 4 = 31
3(9) + 4 = 31
27 + 4 = 31
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Question 11 (1 point)
(03.06 MC)
Braden bought a piece of commercial real estate for $101,234. The value of the real estate appreciated at a constant rate per year. The table
shows the value of the real estate after the first and second years:
Year
1
12
Value (in dollars) $104,271.02 $107,399.15
Which function best represents the value of the real estate after t years?
O a
f(t) = 101,234(1.03)
Ob
f(t) = 101,234(0.03)
f(t) = 104,271.02(1.03)
f(t) = 104,271.02(0.03)
OC
Od
Question 12 (1 point)
Answer:
f(t) = 101,234
Step-by-step explanation:
Which inequality does the graph represent?
Answer:
B
Step-by-step explanation:
The shaded area is less than the equation of the line ....it is a dashed line, so the line itelf is NOT included
the equation of the line is y = -x + 1
so the inequality is
y < -x+1
Answer:
y<-x+1
Step-by-step explanation:
by shading the left side of the dotted line x is negative, and the plus one is the point plotted on the dotted line, the dotted line is the cause of the < symbol, if it was a greater than or equals too the line would be solid.
Soon you will be doing slope which is y= mx + b
and graphing that, find some online or ask ur parents for help and get a jump on them early :) hope i helped
Convert the following equation into standard form y=10x+12
Answer:
y = 10x + 12
y + (-12) = (10x + 12) + (-12)
y - 12 = 10x + 12 -12
x = [tex]\frac{y-12}{10}[/tex]
Which values of a and b make this system of equations have infinitely many solutions?
2y + 16 = 6x
y = ax + b
a = -3, b = 8
a = -3, b = -8
a = 3, b = -8
a = 3, b = 8
Which of the following is closest to the area of the figure below, consisting of a semicircle and rectangle
2-(-9)-8 i neeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed helppppppppppppp
[tex]2 - ( - 9) - 8 \\ 2 + 9 - 8 \\ 11 - 8 \\ 3[/tex]
In the first step multiply the negative after two and the negative with 9 (negative times negative equals to positive )the according to BEDMAS from left to right do addition and subtraction
Hope it helps
Please give brainliest
What will be the output of the program? public class SqrtExample { 03 03 O NaN O Compilation fails public static void main(String [] args) { double value = -9.0; System.out.println( Math ,sqrt(value));
Answer:
216apower4 b + 512 abpower4
[tex]tanx^{2} -\frac{1}{3} =0[/tex]
These are expression written as a function of sine, cosine and tangent. The value of x from the given function is 4.29
Trigonometry expression
These are expression written as a function of sine, cosine and tangent.
Given
tanx² - 1/3 = 0
Add 1/3 to both sides
tanx² - 1/3 + 1/3 = 0 + 1/3
tanx² = 1/3
x² = arctan(1/3)
x² = 18.44
x =4.29
Hence the value of x from the given function is 4.29
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The cost of renting a bus for a field trip was split evenly among 20 students. At the last minute, 10 more students joined the trip. The cost of renting the bus was then evenly redistributed among all of the students. The cost for each of the original 20 students decreased by $1.50. What was the total cost of renting the bus, in dollars?
By solving a linear equation, we will see that the total cost for renting the bus is $90.
What was the total cost of renting the bus, in dollars?Let's say that the total cost is C.
When there are 20 students, each student should pay:
p = C/20
When the other 10 students are added (for a total of 30) each student pays:
p' = C/30.
We know that the cost for each of the original 20 students decreased by $1.50, so:
p' = p - $1.50
Then we have 3 equations to work with:
p = C/20
p' = C/30.
p' = p - $1.50
Now we can replace the first and second equations into the third one:
C/30 = C/20 - $1.50
Now we can solve this linear equation for C:
C/20 - C/30 = $1.50
C*( 1/20 - 1/30) = $1.50
C*(30/600 - 20/600) = $1.50
C*(10/600) = $1.50
C*(1/60) = $1.50
C = 60*$1.50 = $90
So the total cost for renting the bus is $90.
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The following box-and-whisker plots represent two random samples of basketball players. The first sample represents
the heights of male players in the NBA. The second sample represents the heights of female players in the WNBA.
NBA
WNBA
t
80
70
85
90
65
60
75
Height (in inches)
Using the data from these random samples, compare the heights of male and female basketball players. Write your
answer in complete sentences.
UPLOAD
The answer would be A. 1 1/5.
We have given that,
The following box-and-whisker plots represent two random samples of basketball players. The first sample represents the heights of male players in the NBA.
What is the random sample?A simple random sample is a subset of individuals chosen from a larger set in which a subset of individuals is chosen randomly, all with the same probability. Is a process of selecting a sample in a random way.
The second sample represents the heights of female players in the WNBA
Using the data from these random samples, compare the heights of male and female basketball players.
Write your answer in sentences complete
48/40 = 1 8/40
1 8/40 Simplify to 1 1/5
Therefore, The answer would be A. 1 1/5.
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Answer:
The median height for the players in the NBA is 6 inches taller than the median of the WNBA. The overlap in the data shows that the tallest players in the WNBA are around the same height as the shortest players in the NBA.
What is the product of the 2x³ and the 4x²y-3xy²?
Answer:
8x⁵y - 6x⁴y²
Step-by-step explanation:
(2x³)(4x²y - 3xy²)
= 2x³ * 4x²y + 2x³ * -3xy²
= 8x⁵y - 6x⁴y²
A researcher develops a cage for a living cell in the shape of a square-based pyramid. A scale model of the cage is shown. What is the volume of the model?
A square pyramid-shaped cage with base edge labeled “20 micrometers” and height labeled “20 micrometers”.
The total volume of this squared-base pyramid based on the information provided is 2666 micrometers.
How to calculate the volume of the pyramid?The general formula to calculate the volume of a squared-based pyramid is:
base = area x height/ 3What is the volume of the model?Base area: 20 x 20 = 400
400 micrometers x 20/ 3 = 2666 micrometers.
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Find the volume of the
triangular prism.
3.6 cm
5.4 cm
9 cm
Answer:
174.96cm2
Step-by-step explanation:
V=lbh
=3.6×5.4×9
=174.96cm2
I don't knowif you want it in milliliters or litres so here are both of them
milliliters = 174.96
litres = 0.17496
what is the following sum
Answer: D
Step-by-step explanation:
the answer is option D
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. The Osborne family and the Carey family are seeing a movie together in the theater. At the concession stand, Mr. Osborne paid $10 for 2 large popcorns and 1 large drink that his family will share. Mrs. Carey bought 4 large popcorns and 1 large drink and paid $16. How much does each item cost? A large popcorn costs $ and a large drink costs $ .
Answer:
p = 3 dollars d = 4 dollars
Step-by-step explanation:
2 p + 1 d = 10 given
4 p + 1 d = 16 given Subtract second equation from first to get:
-2p = - 6
p = 3 dollars then use this value in either of the equations to find 'd'
2(3) + d = 10
d = 4
which of these corrections represents causation
The correct option that represents Causation is; D: as a total number of family member increases the amount of money that the family spends on food increases
What is the difference between Causation and Correlation?
Correlation is used to describe the kind of relation between two variables whereas causation is a relationship between the cause and effect.
This means that in Causation, the independent variable acts like a cause to effect the dependent variable.
Thus, the correct options as seen in the brainly linked attached is Option D: as a total number of family member increases the amount of money that the family spends on food increases
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The ratio opposite/hypoenuse describes which function
A. Cosine
B. Secant
C. Sine
D. Tangent
What is the domain of the piecewise function?
A. x<0, x>4
B. -∞ 4
C. all real numbers
Answer:
C. All real numbers
I hope someone sees this!!! Can someone check my work please??
Hello there!
I will only explain the ones that do not appear correct to me. If you require further explanation, please let me know.
1] vertical
2] corresponding
-> These two angles are in corresponding places on points of the lines, so they are corresponding angles.
3] alternate interior
4] alternate exterior
-> These angles are on the "outside" of the parallel lines, and on "opposite" sides of the transversal. With this in mind, they are alternate exterior angles
5] same side interior
6] same side exterior
-> These angles are on the "outside" of the parallel lines, and on the same side of the transversal. With this in mind, they are same-side exterior angles
Solve, using the substitution method.
3m − n = 2
2m + n = − 7
(−1, −5)
(–10, –1)
(–2, –5)
(−5, 1)
Answer:
[3m - n = 2]
-3m - n + n = 2 + n
3m - n + 2
-3m/3 = n+2/3
m=1/3 n+2/3
Answer:
m=1/3n + 2/3
[2m + n = - 7]
-Let's solve for m.
2m+n=−7
Step 1: Add -n to both sides.
2m+n+−n=−7+−n
2m=−n−7
Step 2: Divide both sides by 2.
2m/2= −n−7/2
m= −1/2n + −7/2
Answer:
m= −1/2n + −7/2
Now It's Your Turn!!
Step-by-step explanation:
(Hope's it's Help)
[Keeps Safe]
Elyse is going to buy an around-the-world plane ticket. She will get to see just one city from each continent she will visit. The following table below shows the continents on her trip and how many cities she can choose from for each continent.
Elyse is going to buy an around-the-world plane ticket, the number of different combinations of cities is mathematically given as
DF=960
What is the number of different combinations of cities?Generally, the equation for different combinations is mathematically given as
DF=(one city from Europe)*a city from Asia 8city from Africa* city from Australia
Therefore
DF=10C1*8C1*4C1*2C1
DF=10*8*4*3
DF=960
In conclusion, the number of different combinations of cities
DF=960
CQ
Elyse is going to buy an around-the-world plane ticket. She will get to see just one city from each continent she will visit. The following table below shows the continents on her trip and how many cities she can choose from for each continent. Continent Number of cities Europe 10 Asia 8 Africa 4 Australia 3 = Continent How many different combinations of cities does Elyse have to choose from?
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13-3-2-1+6 = please show your work.
Answer:
the answer is going to be 13
Answer:
13
Step-by-step explanation:
Follow PEMDAS
13-3-2-1+6
13-3=10
10-2-1+6=
10-2=8
8-1+6
8-1=7
7 + 6=13
Calculate the volume of the figure below
Answer:
40 cm³Step-by-step explanation:
Calculate the volume of the figure below
find the volume of the two rectangular parallelopipeds and add the results2*2*6 + (6-2)*2*2 =
24+4*2*2=
24+16=
40cm³
Examine the diagram. It is not drawn to scale.
X
50°
3
55°
Y
75°
N
What is the m<3?
m23 =
Answer:
M3 = 105°
angles on a straight line add up to 180°
M3 = 180 - 75
= 105°
You roll a number cube. What is the probability it will land on a number greater than 5?
What is the common ratio of the geometric sequence below?
-96, 48, -24, 12, -6, ...
0-2
1
2
02
The common ratio of the geometric sequence is -1/2
How to determine the common ratio?The geometric sequence is given as: -96, 48, -24, 12, -6, ...
The common ratio is calculated using:
r = T2/T1
From the sequence, we have:
T2 = 48
T1 = -96
This means that
r = 48/-96
Evaluate the quotient
r = -1/2
Hence, the common ratio of the geometric sequence is -1/2
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Joshua’s computer loan statement said he would pay $1,244.34 in simple interest for a three-year loan at 12.4%. How much did Joshua borrow to buy the computer?
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$1244.34\\ P=\textit{original amount deposited}\\ r=rate\to 12.4\%\to \frac{12.4}{100}\dotfill &0.124\\ t=years\dotfill &3 \end{cases} \\\\\\ 1244.34=P[1+(0.124)(3)]\implies 1244.34=P(1.372) \\\\\\ \cfrac{1244.34}{1.372}=P\implies 906.95\approx P[/tex]