α & β are the zeroes of 2x² - 5x + 7.
Find:polynomial whose zeroes are 2α + 3β , 2β + 3α .
Solution:On comparing with the standard form of a quadratic equation,
Let,
a = 2
b = - 5
c = 7.
We know that,
Sum of the zeroes = - b/a
⟹ α + β = - ( - 5)/2
⟹ α + β = 5/2 -- equation (1)
Product of the zeroes = c/a
⟹ αβ = 7/2 -- equation (2)
Now,
General form of a Quadratic equation is x² - (sum of the zeroes)x + product of the zeroes = 0.
★ Sum of the zeroes = 2α + 3β + 2β + 3α
⟹ Sum of the zeroes = 5α + 5β
⟹ Sum of the zeroes = 5(α + β)
Putting the value from equation (1).
⟹ Sum of the zeroes = 5(5/2)
⟹ Sum of the zeroes = 25/2
Similarly,
★ Product of the zeroes = (2α + 3β)*(2β + 3α)
⟹ Product of the zeroes = 2α( 2β + 3α) + 3β( 2β + 3α )
⟹ Product of the zeroes = 4αβ + 6α² + 6β² + 9αβ
⟹ Product of the zeroes = 13αβ + 6(α² + β²)
a² + b² = (a + b)² - 2ab → α² + β² = (α + β)² - 2αβ
⟹ Product of the zeroes = 13αβ + 6[ (α + β)² - 2αβ ]
Putting the values from equations (1) & (2) we get,
⟹ Product of the zeroes = 13(7/2) + 6 [ (5/2)² - 2(7/2) ]
⟹ Product of the zeroes = 91/2 + 6 ( 25/4 - 14/2 )
Taking LCM we get,
⟹ Product of the zeroes = ( 2 * 91 + 6 * 25 + 2 * 14 ) /2
⟹ Product of the zeroes = (182 + 150 + 28 )/2
⟹ Product of the zeroes = 180
Hence,
New quadratic equation = x² - (25/2) * x + 180 = 0
⟹ New quadratic equation = (2x² - 25x + 360)/2 = 0
⟹ New quadratic equation = 2x² - 25x + 360 = 0
∴ The required quadratic equation is 2x² - 25x + 360 = 0.
I hope it will help you.
Regards.
The dimensions of the box below are reduced by half. What is the constant of proportionality between the volume of the new box and the volume of the original box? Alternative text A.1/2 B.1/4 C.1/8 D.1/16
Answer:
C. 1/8
Step-by-step explanation:
Dimensions of the Original Box:
Length = 40 inches
Width = 20 inches
Height = 8 inches
Volume of original box = L*W*H = 40*20*8 = 6,400 in³
Dimensions of the New Box (½ of the dimensions of the original box):
Length = ½*40 = 20 in
Width = ½*20 = 10 in
Height = ½*8 = 4 in
Volume of original box = L*W*H = 20*10*4 = 800 in³
Constant of proportionality between the volume of the new box and the volume of the original box = [tex] \frac{800}{6,400} = \frac{1}{8} [/tex]
Una escalera está apoyada sobre la pared que mide 3.5m. El pie de la escalera hasta la pared mide 2.5m ¿Cuánto mide la escalera?
Responder:
Explicación paso a paso:
La configuración formará un triángulo de ángulos rectos.
Deje que el pie de la escalera a la pared sean los lados adyacentes = 2,5 m
La altura de la pared será el lado opuesto = 3,5 m
La longitud de la escalera será la hipotenusa.
Usando el teorema de Pitágoras:
hip² = opp² + adj²
hip² = 3,5² + 2,5²
hip² = 12,25 + 6,25
hip² = 6
hip = √6
hip = 2,45 m
Por tanto, la longitud de la escalera es 2,45 m.
1) A motorcycle travels 300 miles south in 3 hours. What is the average velocity?
2)If the velocity of a car is 45 kilometers per hour west, how far can it travel in 0.5 hours?
3)An airplane travels 4,425 kilometers west in 5 hours. What is its average velocity?
Answer:
you need to divide distance over time and finally you can get your answer
Step-by-step explanation:
Write a question that represents the following equation.
22-7= 15
Answer:
15 + 7= 22
Step-by-step explanation:
Tangela earns the same amount each week by babysitting. When she started this job, she had $200 in her savings account.
The table shows Tangela's savings account balance for her first month of work.
Week 0 1 2 3 4
Balance $200 $350 $500 $650 $800
Let x represent the number of weeks Tangela has been working and let y represent Tangela's account balance.
Which equation, expressed in Slope-Intercept form, represents the amount of money in Tangela's bank account over time?
Answer:
y = 150x + 200
Step-by-step explanation:
Given the table :
Week (x) __ 0 ____ 1 ____ 2 ____3 _____ 4
Balance(y) :$200_ $350_ $500_ $650_ $800
Equation in slope - intercept form:
y = mx + c
Where
x and y are the independent(x) and dependent variables (y)
C = intercept, value of y, when x = 0
m = gradient change in y per change in x
Hence,
c = $200 ; y value when x = 0
m = change in x / change in y
m = (500 - 350) / ( 2 - 1)
m = $150
Hence, equation becomes :
y = 150x + 200
how do you Simplify 3^6 x 3
Answer:
3^7 or 2187
Step-by-step explanation:
Can someone please help me with these questions I don’t have much time thxxx
(x+12)23-(2x-3)+16=12+5x-1
hmmmmmmmmm
Answer:
look at the attached picture
Answer:
X = -16.75
Step-by-step explanation:
Distribute.
(x + 12)23 = 23x + 276
12 + 5x -1 = 11 + 5x
Combine like terms.
23x - 2x - 5x = 16x
11 - (276 + 3+16 ) = -284
16x = -284
x = -17.75
Mrs.Jones got a new freezer. she plugged it in, and it began to get cold. The temperature dropped 12 degrees every hour for 6 hours. What was the change in the temperature in the freezer over those 6 hours?
Answer:
-72
Step-by-step explanation:
Its pretty simple but I know that we can forget sometime, all you need to do is multiply.
12 x 6 = T
12 x 6 = 72
Is this equation linear?
y=x^2+3?
Is this equation linear?
y= x/4+7 (The x/4 is a fraction)
9514 1404 393
Answer:
noyesStep-by-step explanation:
In the equation ...
y = x² +3
the largest variable exponent is 2, which is not 1. The equation is not linear.
__
In the equation ...
y = (1/4)x +7
the largest variable exponent is 1, so the equation is linear.
Which ordered pair is on the inverse of f(x)?
O (-4,-2)
O (-2,-2)
0 (-1,-2)
f(x)
-4
-2
-2
-1
0
0
2
1
4
Answer:
(-1,-2)
Step-by-step explanation:
Inverse function is where y and x are exchanged in position of a equation of a function.
2b-4/3=b-3/6. I don’t know how to solve it :(
whatis 3 1/6 divided by 9/10
Answer:
3 14/27
Step-by-step explanation:
Answer:
3.51851851852 …95/27 or 3 14/27Step-by-step explanation:
It can be 3.518 …
or 95/27 depending
on your question. It can also be
3 14/27 ( Three and Fourteen Forward Slash Twenty Sevenths )
Hope this helps! <3
-3(m - 4) <6
Solve inequality
isolate the variable by dividing each side by factors that dont contain the variable inequality form:
M > 2
What does the arrow represent at the end of the graph
Your answer:
Goes on forever
Stops at the arrow
You didn't go over it
A public health researcher wishes to study the dietary behavior of residents in Durham County. The researcher randomly contacts 35 county residents and collects data on their daily sugar intake and obtained a sample average of 37.4 grams sugar per day and a sample standard deviation of 4.2 grams per day. The researcher would like to construct a 99% confidence interval for the mean daily sugar intake of residents in the county using the data. Which distribution should the researcher use when analyzing these data?
Answer: The researcher should use a t-distribution because they do not know the true standard deviation of daily sugar intake in Durham county
Step-by-step explanation:
Given data:
No of county residents contacted = 35
Sample average = 37.4grams
Standard deviation = 4.2.
Confidence interval.
From the given data above it is obvious that the research doesn’t know the true data for standard deviation of the daily intake of sugar in Durham. And as such the best distribution method that can be employed by the researcher to solve this problem would be the T-distribution.
Oscar received a $100 gift card from Better Buy for his birthday. He used the card to purchase 3 DVDs. The balance on the card is now $74.50. If all the DVDs cost the same amount, what was the cost, x, of 1 DVD?
Answer:
24.83
Step-by-step explanation:
74.50 divided by 3
1) Jon is standing 60 feet from the base of a cliff watching a friend, Marvin, prepare to bungee jump. The angle of elevation to the top of the cliff is 73º. How high is the cliff Marvin is jumping from?
Answer:
196 feet
Step-by-step explanation:
Let be A the point where Jon is standing, B the point at the base of the cliff and C the point where Marvin is standing, this situation resemble to a right triangle .AB us the distance from the base of the cliff, that is 60 feet.
m<BAC is 73° .We need to find BC.
Right angle is <ABC
tan73°=BC/AB
tan73°=x/60
x=tan73°*60=3.27*60=196 feet approximately.
please simplify if possible -5 1/3 × -2 2/5 AND SHOW WORK If you dont know how to show work then dont answer in really stressed and I bbh have 3 tests and 7 assignments due in a few hours
Answer:
-5 1/3 × (-2 ) 2/5
- 16/3 x (-2) 2/5
16/3 x 2 x 2/5
(calculate the product)
64/15
alternate form:
4 4/15
and
4.26
what is a negative number that has an absolute value greater than 10
Answer:
-11
Step-by-step explanation:
any number less than -10 will have an absolute value higher than 10
Mary must average at least 30 hours of work per week during each five-week cycle to keep her health benefits. During the first four weeks of the cycle, she has worked 30, 30, 28, and 28 hours. What is the lowest amount of hours she can work in the fifth week to have a weekly average of 30 hours?
Answer:
34 hours
Step-by-step explanation:
given the figures for the work are
30, 30, 28, and 28
we know that average
A= sum of values/number of values
let the fifth value be x
the number of values is now 5
given that A=30
30=30+30+28+28+x/5
cross multiply
150=116+x
x=150-116
x=34 hours
Please Please answer this! I will be so thankful and will mark brainliest.
If angle 1 and angle 3 are vertical angles, and m<1= (5x + 14) degrees and m<3= (7x - 4) degrees, what is the value of x, and the measure for angle 1?
Answer:
x = 9
[tex] m\angle 1= 59\degree [/tex]
Step-by-step explanation:
Since, [tex] \angle 1 \:and \:\angle 3[/tex] are vertical angles.
[tex]\therefore m\angle 1 = m\angle 3\\
\therefore (5x + 14) \degree= (7x - 4) \degree\\
\therefore (5x + 14) = (7x - 4) \\
\therefore 5x - 7x = - 4 - 14\\
\therefore -2 x = - 18\\\\
\therefore x =\frac{-18}{-2}\\\\
\huge \orange {\boxed {\therefore x = 9}} \\\\
m\angle 1 = (5x + 14) \degree\\
m\angle 1 = (5\times 9+ 14) \degree\\
m\angle 1 = (45+ 14) \degree\\
\huge \purple{ \boxed{m\angle 1 =59\degree}}[/tex]
Slope intercept equation
A16 ounce bottle of orange juice says it could take 200 mg of vitamin C which is 250% of the daily recommended allowance of vitamin C for adults what is 100% of the daily recommended
Answer:
100% of the daily recommended allowance of vitamin C for adults is 80 milligrams.
Step-by-step explanation:
Cary is having a party and can only afford to spend no more than $40 on food. She wants to order at least 3 pizzas which cost $6 a pie, and at least 2 orders of wings that cost $8 per order. Select all the inequalities she would have to graph to determine how many pizzas and wings she could order. Let x stand for the number of pizzas and y stand for the number of wings.
do you want us to show how we solved it too?
Answer:
y ≥ 2
x ≥ 3
6x + 8y ≤ 40
Step-by-step explanation:
Isaac read that 32% of people owned dogs. What decimal represents the portion of people who
do not own dogs?
The 0.68 decimal represents the part of humans who do not own dogs.
What is proportionality?the property of having suitable proportions in terms of size, number, degree, harshness, etc. If a defensive action against an unfair attack results in destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.
Given, Isaac read that 32% of people owned dogs.
Thus,
We can say the portion of people who owned dogs = is 32% of * the total number of people
the portion of people who owned dogs = 0.32* total people
So,
The portion of people who Do not own dogs will be = 1 - 0.32* total people
The portion of people who Do not own dogs will be = 0.68 total people
therefore, the 0.68 decimal represents the portion of people who
do not own dogs.
Learn more about proportionalities here:
https://brainly.com/question/3254974
#SPJ2
Which statement about the ordered pairs (2, −9) and (3, −6) is true for the equation 5x−y/3=13?
Answer:
(2,-9)
Step-by-step explanation:
5.2+9/3=13(?)
10+3=13
or
5.3+6/3=13(?)
15+2=17
what is the perimeter and area for 6m and 4m rectangle floor
Answer:
perimeter = 20 area = 24
Step-by-step explanation:
add all the sides to find the perimeter and multiply two sides to find the area
Answer:
perimeter: 20
area: 24
Step-by-step explanation:
To do perimeter add all the sides together. so 6+4=10 then times 2 because there are 4 sides to a rectangle. not just 6 and 4(2 sides.)
Area: Multply them together. 6*4=24
PLZ HELP LAST QUESTION given the piecewise function given below select all statements that are true f(x)=-x+1,x<0 -2,x=0 x^2-1,x>0 All in brackets A.F(4)=7 Bf(-1)=2 c.F(-2)=0 d.F(1)=0
Answer:
Step-by-step explanation:
Given the function f(x)=-x+1,x<0 and f(x) = x^2-1,x>0
when x = 4
f(4) = -4+1
f(4) = -3
Also f(4) = 4^2 -1
f(4) = 8-1
f(4) = 7
when x = -1
f(-1) = -(-1)+1
f(-1) = 2
Also f(-1) = (-1)^2 -1
f(-1) = 1-1
f(-1) = 0
when x = -2
f(-2) = -(-2)+1
f(-2) = 3
Also f(-2) = (-2)^2 -1
f(-2) = 4-1
f(-2) = 3
when x = 1
f(1) = -1)+1
f(1) = -2
Also f(1) = (1)^2 -1
f(1) = 1-1
f(1) = 0
From the calculation above, the correct statements are
A. F(4)=7
B f(-1)=2
d. F(1)=0
12,851 rounded to the nearest ten thousand?
Answer:
13000
Step-by-step explanation:
because 851 is above 500 you add 1 to the 2 then put 000 for the other numbers
