Answer:
[tex]-\dfrac{463}{7}[/tex]
Explanation:
Given equation: 2x² - 6x - 7 = 0
In quadratic equation: ax² + bx + c
[tex]Sum \ of \ roots : \alpha + \beta = \dfrac{-b}{a}[/tex]
[tex]product \ of \ roots : \alpha \beta = \dfrac{c}{a}[/tex]
So, here given:
[tex]Sum : \alpha + \beta = \dfrac{-(-6)}{2} = 3[/tex]
[tex]Product : \alpha \beta = \dfrac{-7}{2} = - 3.5[/tex]
For finding value:
[tex]\dfrac{\alpha^3}{\beta } + \dfrac{\beta^3 }{\alpha }[/tex]
join fractions
[tex]\dfrac{\alpha^4+ \beta^4}{\alpha \beta }[/tex]
factor out
[tex]\dfrac{(\alpha^2 + \beta ^2)^2 -2\alpha ^2 \beta ^2 }{\alpha \beta }[/tex]
when factored more
[tex]\dfrac{((\alpha + \beta)^2 -2\alpha \beta )^2 -2(\alpha \beta)^2 }{\alpha \beta }[/tex]
insert values inside
[tex]\dfrac{((3)^2 -2(-3.5) )^2 -2(-3.5)^2 }{-3.5 }[/tex]
calculate for value
[tex]-\dfrac{463}{7}[/tex]
What is the sum of the first 20 terms of the arithmetic sequence 3,9,15,21,27
Answer: 6
Step-by-step explanation: 3 + 6 = 9, 9 + 6 = 15, 15 + 6 = 21, 21 + 6 = 27
Assume that the random variable X is normally distributed with mean y = 60 and standard deviation a = 12. Find the 87th percentile for X
The 87th percentile is the value [tex]x_{0.87}[/tex] such that 87% of the distribution lies below [tex]X=x_{0.87}[/tex], i.e.
[tex]P(X \le x_{0.87}) = 0.87[/tex]
Transform [tex]X[/tex] to the standard normal random variable [tex]Z[/tex], then solve for [tex]x_{0.87}[/tex] using the inverse CDF of [tex]Z[/tex].
[tex]P(X\le x_{0.87}) = P\left(\dfrac{X-60}{12} \le \dfrac{x_{0.87}-60}{12}\right) = P\left(Z \le \dfrac{x_{0.87}-60}{12}\right) = 0.87[/tex]
[tex]\implies \dfrac{x_{0.87}-60}{12} = F_Z^{-1}(0.87) \approx 1.12369[/tex]
[tex]\implies \boxed{x_{0.87} \approx 73.5167}[/tex]
Find the measure of the exterior 1.
A. 11°
OB. 127°
O C. 85°
O D. 95°
How many significant figures does 119.3 have
Transcribed image text: In 2000, 47% of the residents in a large city regularly used newspapers for getting news and this has decreased at an average rate of approximately 1.8% per year since then. Find a linear function in slope-intercept form that models this description. The function should model the percentage of residents, P(x), who regularly used the news outlet x years after 2000 P(x)= (Use integers or decimals for any numbers in the expression.)
Answer:
/.............................../././///////////////////////////////////////
Step-by-step explanation:
.
Factorize x^2+√4x+2x+2
[tex]factorize \: {x}^{2} + \sqrt{4x} + 2x + 2 [/tex]
Answer:
x^2+4x+2
Step-by-step explanation:
√4 = 2
=x^2+2x+2x+2
add the ones that are the same (2x+2x)
x^2+4x+2
solving 3 x plus 8 equals 14
Question 9
The pOH of a solution is 5.70.
What is its hydroxide-ion concentration?
O 3.3 × 10-3
2.8 × 10-9
2.5 x 10-7
2.0 x 10-6
C
The pOH of a solution is 5.70. The correct option is C; 2.5 x 10-7 is the hydroxide ion concentration.
What is the pOH of the solution?The pOH of the solution is the negative logarithm of hydroxide ions concentration in a solution. The lower the value of pOH more alkaline will be the solution.
Mathematically written as:
pOH = - Log[OH-]
The sum of ph and pOH is equal to 14.
pH + pOH = 14
The pOH of a solution is 5.70.
pOH = - Log[OH-]
5.70 = - Log[OH-]
[OH-] = 2.5 x 10-7 is the hydroxide ion concentration.
The solution has a pH value of more than 7 which means that it is base.
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Chana and Josiah started skating at the same time in the same direction, but Josiah had a head start 10 meters past the starting line. Chana skated 3 meters per second and Josiah skated 2 meters per second.
What does point I represent in this context?
CORRECT (SELECTED)
Chana's distance from the starting line at a time when she is behind Josiah
The point that is labeled H on this graph is that at 25th second, Josiah is 60 meter distance from the starting line.
What is the distance about?Note that At the point H, there is found to be an intersection between the distance taken by both people involve so:
Y (a)= 10 + 2x ------ Josiah
Y (0) = 3x ----- Chana
If Y (a)= Y (0)
Then:
10 + 2x = 3x
x = 10
F = x = 20
Y (o) = 60
If x = 20
= then Y(0) = 3 x 20
= 60
Therefore, The point that is labeled H on this graph is that at 25th second, Josiah is 60 meter distance from the starting line.
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1/12^-2 using positive exponents
[tex]\Large\Box\underline{\textsf{A. What is Asked}}[/tex]
Evaluate [tex]\bf{\dfrac{1}{12^{-2}}}[/tex]
[tex]\Large\Box\underline{\textsf{B. This problem has been solved!}}[/tex]
[tex]\boxed{\begin{minipage}{9cm} \text{If we have negative exponents in the denominator} \\ \text{we turn over the number,} \\ \text{leaving positive exponents only.} \end{minipage}}[/tex]
Thus,
[tex]\bf{\dfrac{1}{12^{-2}}=\dfrac{12^2}{1}}[/tex]. | see, the negative exponent turned into a positive one as soon as the fraction was turned over.
[tex]\bf{144}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=144}[/tex]
Extra information [tex]\curvearrowright[/tex][tex]\begin{tabular}{c | 1} Expression & Exponent Rule\\\cline{1-2} \\ x^m*x^n & add the powers \\ x^m\div x^n & subtract the powers \\(x^m)^n & multiply the powers \\ x^{-m} & turn over the number \\ x^0 & this equals one\end{tabular}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]
Help me please T^T
Solve for m.
m+1/3<-2 1/4
Answer:
answer is the second option m<-2 7/12
Step-by-step explanation:
process:
convert -2 1/4 into an improper fraction
m+1/3 < -9/4
m <-9/4 -1/3
calculate the difference
m<-31/12
turn into a mixed fraction
Scientists want to test a new pair of running shoes. A speed test is performed with two separate groups of participants. The treatment group will wear the new pair of running shoes, while the control group will not. It is believed that age and height may affect speed. Which of the following would be most effective in controlling the confounding variables, such as age and height, in this study?
The most effective in controlling the confounding variables is matched pairs design.
What is a matched pair design experiment?A matched pairs design is when participants are matched based on shared characteristics that is of importance to the experiment. One member of the pair is put in the control group while the other is put in the experimental group.
Here are the options:
A completely randomized design experiment
A longitudinal observational study
A retrospective observational study
A matched-pair design experiment
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x, 3x and 5x ,find the sum
x + 3x + 5x ( the variables are same you can add them immediately )
9x ( the answer is 9x for adding terms with the same variable just add the numbers and write the variable as itself)
HOPE IT HELPS
Answer: 9x
Step-by-step explanation:
As the variables are of same power (1) we can add it
x+3x+5x=9x
Billy received a raise after his first year on the job to $45,000 from his initial salary of $42,400. What was his real raise stated as a percentage? Inflation averaged 2.4 percent for the year. Round your answer to two decimal places.
Billy get 5.9% raise after completing first year.
What is PERCENTAGE?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.
Here, Billy's initial salary = $ 42,500
After raise, salary become $ 45,000
Change in salary = Raised salary - Initial salary
= 45000 - 42500
= $ 2500
% Change = change / initial salary X 100
= 2500 / 42500 X 100
= 0.0589 X 100
≈ 5.9 %
Thus, Billy get 5.9% raise after completing first year.
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10) Choose the solution for each linear system.
(3,0)
(-3,-1)
(2,-1)
(-2,1)
(x-2y=4
4x + 2y = 6
11) Choose the solution for each linear system.
(2,4)
O(-2,-4)
O (4,2)
O(-4,-2)
[6x-2y = -4
-4x+3y=-4
Answer:
10. C. (2, -1)11. B. (-2, -4)Step-by-step explanation:
10.
[tex]\left \{ {{x-2y=4} \atop {4x+2y+6}} \right.[/tex]
The y values cancel out if you add the equations
5x = 10
x = 2
plug in x
2 - 2y = 4
-2y = 2
y=-1
Answer: C. (2, -1)
11.
[tex]\left \{ {{6x-2y=-4} \atop {-4x+3y=-4}} \right.[/tex]
In order to get terms to cancel out, multiply the top by 3 and bottom by 2
[tex]\left \{ {{18x-6y=-12} \atop {-8x+6y=-8}} \right.[/tex]
The y values cancel out if you add the equations
10x = -20
x = -2
plug in x
6(-2) - 2y = -4
-12 - 2y = -4
-2y = 8
y = -4
Answer: B. (-2, -4)
(1.5 x 10^8) + ( 2.06 x 10^8) =
Answer:
356000000
Step-by-step explanation:
1. Simplify the expression
Calculate the expression inside the parentheses.
[tex](1.5*10^8)+(2.06*10^8)[/tex]
Simplify exponents and square roots
[tex](1.5*10^8)+(2.06*10^8)[/tex]
[tex](1.5*100000000)+(2.06*10^8)[/tex]
Perform any multiplication or division, from left to right:
[tex](1.5*100000000)+(2.06*10^8)\\[/tex]
[tex](150000000)+(2.06*10^8)[/tex]
Simplify exponents and square roots
[tex]150000000+(2.06*10^8)[/tex]
[tex]150000000+(2.06*100000000)[/tex]
Perform any multiplication or division, from left to right:
[tex]150000000+(2.06*100000000)[/tex]
[tex]150000000+(206000000)[/tex]
Calculate any addition or subtraction, from left to right.
[tex]150000000+206000000[/tex]
[tex]356000000[/tex]
Why learn this
Order of operations is a basic rule of algebra. It tells us what to solve first when we have an equation with multiple functions, which is something that you will likely encounter throughout your maths studies. The order is: Parentheses, Exponents, Multiplication and Division, then finally Addition and Subtraction. Remember that when you're solving within the parentheses, the Order of Operations applies!
Terms and topics
Order of operationsSolve linear equations using substitution y=-4x
y=4x+16
Answer:
(-2 , 8)
Step-by-step explanation:
[tex]\begin{cases}y=-4x&\\ y=4x+16&\end{cases}[/tex]
We substitute y by -4x in the second equation of the system:
-4x = 4x + 16
⇔ -8x = 16
⇔ x = 16/(-8)
⇔ x = -2
Now ,we substitute x by -2 in the first equation of the system:
y = -4 × (-2) = 8
then
the solution of the system is {(x = -2 , y = 8)}
point O, A, B lie on the same line. OA=12cm and OB=9cm. find the distance between the midpoints of segments OA and AB in each case
The Distance between the midpoints of segments OA and AB is 4.5cm
Lines and measuresA line is defined as the shortest distance between two points.
Given the following parameters
OA = 12cm
OB = 9cm
AB = OA - OB
AB = 12 - 9 = 3cm
midpoint of OA = 12/2 = 6cm
midpoint of AB = 3/2 = 1.5cm
Distance between the midpoints of segments OA and AB in each case will be the difference between the midpoints
Difference = 6cm - 1.5
Difference = 4.5cm
Hence the Distance between the midpoints of segments OA and AB is 4.5cm
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A number generator was used to simulate the percentage of people in a town who join a health club yearly. The process simulates randomly selecting 100 people from the town and was repeated 20 times. The percentage of people who join a health club yearly is shown in the dot plot. Which statement is most likely true about the population of the town? Most likely, 50% of the people in the town join a health club yearly. Most likely, about 40% to 60% of the people in the town 0 10 20 acer 30 40 50 60 70 80 : 90 100 A number generator was used to simulate the percentage of people in a town who join a health club yearly . The process simulates randomly selecting 100 people from the town and was repeated 20 times . The percentage of people who join a health club yearly is shown in the dot plot . Which statement is most likely true about the population of the town ? Most likely , 50 % of the people in the town join a health club yearly . Most likely , about 40 % to 60 % of the people in the town 0 10 20 acer 30 40 50 60 70 80 : 90 100
The statement that's is likey true about the population of the town is that most likely about 40% to 60% of the people Jon the health club yearly.
How to illustrate the information?It should be noted that a dot plot simply gives a pictorial representation of the information given.
In this case, the population of the town is that most likely about 40% to 60% of the people Jon the health club yearly.
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Answer: Most likely, about 40% to 60 % of the people in the town join a health club yearly.
Step-by-step explanation:
Solve the following system by the substitution method. Check the solution(s)
7x + 4y = 10
x+y=1
Answer:
x = 2; y = -1
Step-by-step explanation:
We can solve (first for y, then for x) using substitution:
[tex]x+y=1\\7x+4y=10\\(x+y=1)-y\\x=1-y\\\\7(1-y)+4y=10\\7-7y+4y=10\\(7-3y=10)-7\\(-3y=3)/-3\\y=-1\\\\(x-1=1)+1\\x=2[/tex]
Suppose that the functions and are defined as follows. p(x)=-x and q(x)=2x^2-2
find the following (q°p)(2)=
and (p°q)(2)=
The two compositions for the functions are:
[tex](p\°q)(2) = -6\\\\(q\°p)(2) = 6[/tex]
How to get the compositions?
When we have two functions q(x) and p(x), the composition is:
[tex](q\°p)(x) = q(p(x))[/tex]
Here we have:
[tex]p(x) = -x\\\\q(x) = 2x^2 - 2[/tex]
The first composition is:
[tex](q\°p)(2) = q(p(2)) = 2*(p(2))^2 - 2 = 2*(-2)^2 - 2 = 6[/tex]
The other composition is:
[tex](p\°q)(2) = p(q(2)) = -(q(2)) = -(2*2^2 - 2) = -(8 - 2) = -6[/tex]
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The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is four
times the measure of the first angle. The third angle is 12 more than the second. Let x, y, and z represent the measures of
the first, second, and third angles, respectively. Find the measures of the three angles.
Answer:
x = 36°
y = 66°
z = 78°
Step-by-step explanation:
General outline:Setup equations for each sentenceSolve the resulting systemSetup equations:
Allowing the first angle to be x, the second to be y, and the third to be z, the three sentences describing the relationships between angle measures are given below:
Eq1: x + y + z = 180°Eq2: y + z = 4xEq3: z = y + 12°Solve the systemSubstituting equation 3, into equations 1 and 2
Eq1: x + y + z = 180°
x + y + (y+12°) = 180°
x + 2y + 12° = 180°
x + 2y = 168°
x = 168° - 2y
Eq2: y + z = 4x
substituting the result from equation 1, and Equation 3...
y + (y+12°) = 4*(168° - 2y)
2y + 12° = 672° - 8y
10y = 660°
y = 66°
Substituting back into Equation 3...
Eq3: z = y + 12°
z = (66°) + 12°
z = 78°
Substituting both y, and z into Equation 1...
x + y + z = 180°
x + (66°) + (78°) = 180°
x + 144° = 180°
x = 36°
So, the three angle measures are:
x = 36°
y = 66°
z = 78°
Verification"The sum of the measures of the angles of a triangle is 180."
x + y + z = 180°
36° + 66° + 78° = 180°
True
"The sum of the measures of the second and third angles is four times the measure of the first angle"
y + z = 4x
66° + 78° = 4*(36°)
144° = 144°
True
"The third angle is 12 more than the second"
z = y + 12°
78° = 66° + 12°
True
Natasha had a $922.93 balance on her credit card at the beginning of September. Her credit card has an APR of 9.89%, compounded monthly, and a minimum monthly payment of 3.08% of the total balance. The following table shows Natasha’s credit card purchases over the next two months.
Month
Cost ($)
September
33.70
October
61.70
October
27.80
If Natasha makes only the minimum payments, what will her balance at the beginning of November? (Assume that the interest accrues before the monthly payment, and that the monthly payment occurs at the end of the month. Round all dollar values to the nearest cent.)
Answer:
Her balance at the beginning of November=$973.76
Step-by-step explanation:
What is Natasha's credit balance at the beginning of November?(i.e. at the end of October)
The balance at the end of each month is the beginning balance plus the current month's purchases minus the minimum payment for the month.
Sept =$922.93+$33.70+9.89%/12*($922.93+$33.70)
Sept=$964.51
payment= 964.51*3.08%
balance at the end of Sept=$964.51-($964.51*3.08%)
balance at the end of Sept=$934.80
Oct=$934.80+$61.70+9.89%/12*($934.80+$61.70)
Oct=$ 1,004.71
payment=$1,004.71*3.08%
balance at the end of Oct(at beginning of Nov)=$ 1,004.71-($1,004.71*3.08%)
balance at the end of Oct(at beginning of Nov)=$973.76
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Answer:
The answer is C.$1,000.93 just did it om edge
Step-by-step explanation:
Kate is the captain of a large cruise ship. As she
drives the ship, she sits 50 meters above the sea.
Paul is the captain of a boat. He sits 15 meters
above the sea. If the radius of the earth is
6,371,000 meters, how much further can Kate see
across the horizon than Paul?
here are the first few questions the rest are in the picture.
1.Show me that you understand the problem. restate it in your own words and identify the important information.
2. what is your prior knowledge and what tools do you have to solve this problem?
a. Draw two diagrams, one for Kate and one for Paul. Include important numbers. Insert your diagrams into your answer.
The amount further by which Kate can see across the horizon than Paul is; 3.33 times farther
How to use volume of a cone in applications?Formula for volume of a cone is;
V = ¹/₃πr²h
For Kate:
Height (h) = 50 m
Radius (r) = 6,371,000 m
Thus;
V = ¹/₃ * π * (6,371,000)² * 50
V = 2.12526863 × 10¹⁵ m³
To determine how much further can kate see across the horizon than Paul, we have:
⇒ (2.12526863 × 10¹⁵ m³)/6.3758059 × 10¹⁴ m³
= 3.33 times further.
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Please help me....trying to get my HS diploma, i did not graduate :(
A ball is thrown in air and it's height, h(t) in feet, at any time, t in seconds, is represented by the equation h(t)=−t2+7t. When is the ball higher than 10 feet off the ground?
Answer:
A.
Step-by-step explanation:
so, the equation is
h(t) = -t² + 7t
so, we need to find the solutions for t (the time when the ball is exactly 10 ft in the air). there had to be 2 solutions, as the ball first goes up passing the 10 ft height, and then comes back down again, passing the 10 ft mark a second time. and between these 2 times the ball is higher (but not equal, so, we can only use < or > as inequality signs) than 10 ft.
10 = -t² + 7t
-t² + 7t - 10 = 0
the generation solution to a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = t
a = -1
b = 7
c = -10
t = (-7 ± sqrt(7² - 4×-1×-10))/(2×-1) =
= (-7 ± sqrt(49 - 40))/-2 = (-7 ± sqrt(9))/-2
t1 = (-7 + 3)/-2 = -4/-2 = 2 seconds
t2 = (-7 - 3)/-2 = -10/-2 = 5 seconds
so, between 2 and 5 seconds airtime the ball is higher than 10 ft.
and remember : HIGHER THAN.
so, we cannot use any equality (like <= or >=).
t must be higher than 2 and lower than 5 :
2 < t < 5
Solve algebraically
X+4=-2
Answer:
x=-6
Step-by-step explanation:
-6+4=-2
Give brainliest please
what is the z score of x=12 if it is two standard deviations to the right of the mean?
The value of the Z-score will be equal to 2.
What is Z-score?The z score indicates how many standard deviations your score is from the mean.
At the mean position, the standard deviation is 0 now the z score is the measure of the data which is how far from the mean. So the given data is at two standard deviations to the right of the mean so the Z-Score will be 2.
Therefore the value of the Z-score will be equal to 2.
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I need the correct answer for questions 1
The truth values of the propositions are false, true and false
How to determine the true values?The Boolean variables are given as:
p = false
r = false
q = true
s = true
The truth values of the propositions are as follows:
1. (s → (p ∧ ¬ r)) ∧ ((p → (r ∨ q)) ∧ s)
As a general rule:
∧ means and
¬ not
∨ or
So, we have:
(true → (false ∧ ¬ false)) ∧ ((false → (false ∨ true)) ∧ true)
¬ false= true.
So, we have:
(true → (false ∧ true)) ∧ ((false → (false ∨ true)) ∧ true)
false ∧ true = false and false ∨ true = true
So, we have:
(true → false) ∧ ((false → true) ∧ true)
false → true = true and true → false = false
So, we have:
(false) ∧ (true ∧ true)
true ∧ true = true
So, we have:
false ∧ true
Lastly
false ∧ true = false
Hence, the truth value of (s → (p ∧ ¬ r)) ∧ ((p → (r ∨ q)) ∧ s) is false
2. ((p ∧ ¬ q) → (q ∧ r)) → (s ∨ ¬q)
This means
((false ∧ ¬ true) → (true ∧ false)) → (true ∨ ¬true)
Using the established rules in (1), we have:
((false ∧ false) → (true ∧ false)) → (true ∨ false)
This gives
((false → false)) → true
This gives
true → true
Lastly, we have:
true
Hence, the truth value of ((false ∧ ¬ true) → (true ∧ false)) → (true ∨ ¬true) is true
3. (p → q) ∧ (q → r)
This gives
(false → true) ∧ (true → false)
Using the established rules in (1), we have:
true ∧ false
This gives
false
Hence, the truth value of (p → q) ∧ (q → r) is false
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Two gymnasts are running toward each other in a floor routine, and they plan to precisely time a flip to stay synchronized for the audience. The path of the gymnasts is parabolic and modeled by the following equations, where y is the height of the flip and x is the time in seconds.
= – (x – 5)2 + 3
y = –3(x –6)2 + x + 1
2seconds
3seconds
4seconds
5seconds
To make sure the flip is in unison after 4 seconds should the flip occur, as given by option C: 4 seconds.
We have given that,
Two gymnasts are running toward each other in a floor routine, and they plan to precisely time a flip to stay synchronized for the audience.
What does synchronized motion mean?Synchronized motion is a motion of two or more system which goes in synchronization with each other.
For this case, the flip will occur such that both gymnasts are synchronized and the flip is in unison (simultaneous).
For that, we need the time(x) and the height (y) same.
Since the motion paths are:
[tex]y=-(x-5)^2+3[/tex]
[tex]y=-3(x-3)^2+x+1[/tex]
Therefore, we need to find the values of x for which the same y comes as output.
Let x = t be the time for which the height y is the same, then:
[tex]-(t-5)^2+3=-3(t-3)^2+t+1[/tex] = height achieved by both gymnasts.
Solving it further:
[tex]-(t-5)^2+3=-3(t-3)^2+t+1[/tex]
t=4,t=1/2
Assuming they planned to do a flip after an integral number of time in seconds, the correct option is t = 4 seconds.
Thus, to make sure the flip is in unison after 4 seconds should the flip occur, as given by the option C: 4 seconds.
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A $15 credit to revenue was posted as a $150 credit by what amount is the revenue account in error?
Answer: Multiple Choice $15 understated. $135 overstated. $135 understated. $150 understated. $150 overstated. 2.The numbering system used in a company's chart of accounts: Typically begins with income statement accounts.
Step-by-step explanation: