Answer:
42
Step-by-step explanation:
HELLPP. ITS URGENT.50 PTS
Please show working.
Question : If α and β are roots of the quadratic equation : 4x²-5x-1=0, find the quadratic equation whose roots are :
(See image for full question . No (IV) and (v))
Answer:
I replaced alpha by A and bitta by B. Sorry for this mistake
Answer:
4x² - 13x + 8 = 04x² - 11x + 5 = 016x² - 41x + 1 = 0x² + 5x + 4 = 0x² - 66x + 64 = 0Step-by-step explanation:
Given
α and β are roots of 4x²-5x-1=0Then the sum and product of the roots are:
α+b = -(-5)/4 = 5/4αβ = -1/4(i) Roots are α + 1 and β + 1, then we have:
(x - (α + 1))(x - (β + 1)) = 0(x - α - 1)(x - β - 1) = 0x² - (α+β+2)x + α+β+ αβ + 1 = 0x² - (5/4+2)x +5/4 - 1/4 + 1 = 0x² - 13/4x + 2= 04x² - 13x + 8 = 0(ii) Roots are 2 - α and 2 - β, then we have:
(x + α - 2)(x + β - 2) = 0x² + (a + β - 4)x - 2(α + β) + αβ + 4 = 0x² + (5/4 - 4)x - 2(5/4) - 1/4 + 4 = 0x² - 11/4x - 10/4 - 1/4 + 16/4 = 0x² - 11/4x + 5/4x = 04x² - 11x + 5 = 0(iii) Roots are α² and β², then:
(x - α²)(x-β²) = 0x² -(α²+β²)x + (αβ)² = 0x² - ((α+β)² - 2αβ)x + (-1/4)² = 0x² - ((5/4)² -2(-1/4))x + 1/16 = 0x² - ( 25/16 + 1/2)x + 1/16 = 0x² - 33/16x + 1/16 = 016x² - 33x + 1 = 0(iv) Roots are 1/α and 1/β, then:
(x - 1/α)(x - 1/β) = 0x² - (1/α+1/β)x + 1/αβ = 0x² - ((α+β)/αβ)x + 1/αβ = 0x² - (5/4)/(-1/4)x - 1/(-1/4) = 0x² + 5x + 4 = 0(v) Roots are 2/α² and 2/β², then:
(x - 2/α²)(x - 2/β²) = 0x² - (2/α² + 2/β²)x + 4/(αβ)² = 0x² - 2((α+β)² - 2αβ)/(αβ)²)x + 4/(αβ)² = 0x² - 2((5/4)² - 2(-1/4))/(-1/4)²x + 4/(-1/4)² = 0x² - 2(25/16 + 8/16)/(1/16)x + 4(16) = 0x² - 2(33)x + 64 = 0x² - 66x + 64 = 0y-2 = -3(x + 6), write the equation of the line in slope intercept form.
Answer:
y = -3x - 16
Step-by-step explanation:
Point-slope form: y - y1 = m(x - x1)
Given: y - 2 = -3(x + 6)
Slope-intercept form: y = mx + b
To write the equation in slope-intercept form, we need to know the slope(m) and the y-intercept(b). By looking at the given equation, we can see that the slope is -3. We are also given the value of one point: (-6, 2).
To find the y-intercept, input the given values of the slope and the point into the equation format and solve for b:
y = mx + b
2 = -3(-6) + b
2 = 18 + b
Subtract 18 from both sides of the equation to isolate b:
2 - 18 = 18 - 18 + b
-16 = b
The y-intercept is -16.
Now that we know the slope and the y-intercept, we can write the equation:
y = -3x - 16
The nth term of a sequence is 3−2n
Work out the 8th term of the sequence
Answer:
-13
Step-by-step explanation:
3-2n
3-2×8
3-16
-13
PLEASE HELP!!!!! 2.) What is the perimeter of a polygon with vertices at (-3, 1), (5, 1), (-3, 4), (5, 4)? 30 points if you can help
Answer:
22 units.
Step-by-step explanation:
We want to find the perimeter of the polygon with vertices at: (-3, 1); (5, 1); (-3, 4); and (5, 4).
Let’s first plot the points and see what polygon we acquire. Please refer to the graph below.
As we can see, when plotting the points and connecting them, we get a rectangle.
So, we can use the perimeter formula for a rectangle, given by:
[tex]P=2(\ell+w)[/tex]
Where [tex]\ell[/tex] Is the length and [tex]w[/tex] is width.
Remember that the perimeter is simply the distance around the figure.
So, let’s find the length. We can do so by counting or by subtracting.
By counting, we can see that the length (longer side) is 8 units.
And by subtracting, we get the same length of |5-(-3)| or 8 units.
We use absolute value because distance is always positive.
Using the same process, we find the width to be 3 units.
Using subtract, we can see that this is indeed true as |1-4|=3.
So, we can now substitute the values into our formula:
[tex]P=2(8+3)[/tex]
Evaluate:
[tex]P=2(8+3)=2(11)=22\text{ units}[/tex]
So, the perimeter of the polygon is 22 units.
I'm more than 9 dozen and less than the number of days in 4 months. The sum of my digits is 11.
Answer: 92 or 119
in 4 months, 2 months with 30 days per month, 2 months with 31 days per month
suppose: the number to find is X
have: 90 < X < 30.2 + 31. 2 ⇔ 90 < X < 122
if X is a number has 2 digits => X is xy
=> [tex]\left \{ {{x+y=11} \atop {90<x\leq 100}} \right.[/tex]
=> xy = 92
if X is a number has 3 digits => X is abc
we have: [tex]\left \{ {{a+b+c=11} \atop {100\leq abc<122}} \right.[/tex]
because 100 ≤ abc < 122 => a = 1; b = 0 or 1
+) if a =1 ,b = 0 but a+ b +c = 11 => c = 10 (removed because c is a 1-digit number)
+) if a = 1, b = 1 => c = 9
=> abc = 119
=> X is 92 or 119
Step-by-step explanation:
working on a song for someone I used to love
I'll go through all of the realities to find you
(If I need you)
Just so I can hold your hand...
Even if they think it's fake...
I want you to understand
that there's a certain miss
and a certain love
and a heartache in my chest
every time i hear your name
and im still lying in my bed
without you....
Answer:
wowww!! it's very sad and wonderfull
If you leave your house at 1:00 and get to your friends house at 5:00, what was your average speed
Explain in your own words why you would use division to change a smaller unit to a bigger one . What would happen if you multiplied instead ? TOPIC IS MEASUREMENT
Answer:
you would use division to change bigger units into smaller ones as a form of cancellation
Please help me! Im making the first correct answer brainliest!
Answer:
The answer is most likely c.)
Step-by-step explanation:
It says that they sold 40 scarves and hats at the Winter Festival, but it never told us exactly how many hats total and how many scarves total that they sold. So we leave it as "s+h=40" Next we have the price of the scarves and hats, not the numbers sold. Since the scarves cost $18 and the hats cost $14, we know that a certain amount of each equals $700. Since we don't know the exact number of each that were sold, we leave it at "18s+14h=700." Sorry if you got a bit lost.
Kayla has a older sister and a younger sister. her older sister is one year more than twice Kayla's age. Kayla's younger sister is three years younger than she is. the sum of their ages is 26. find Kayla's age
Answer:
x= kaylas age
older sister: 2x+1
younger sister: x-3
x+2x+1+x-3=26
4x-2=26
4x=28
x=7 years old
Step-by-step explanation:
Which equation best describes a relationship between x and y in the table below?
Answer:
y = [tex]\frac{1}{3}[/tex] x + 5
Step-by-step explanation:
Slope m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
y = mx + b , "b" is y-intercept with coordinates (0, b)
(0, 5)
(6, 7)
m = [tex]\frac{7-5}{6-0}[/tex] = [tex]\frac{1}{3}[/tex]
y = [tex]\frac{1}{3}[/tex] x + 5
what is 7-(2x+1)+4x simpilist form
y-2=-(x-7) slope intercept form
Answer:
y= -x+9
Step-by-step explanation:
PLEASE MARK BRAINLIESTThe 4th term of a sequence is 108. Each term after the first is three times the previous term. Write an expression that represents all 4 terms. Write an equation that represents the 4th term. What are the 4 numbers?
Answer:
First 4 terms are a, 3a, 3^2 a and 3^3 a.
The numbers are:
4, 12, 36, 108.
Step-by-step explanation:
This is a geometric sequence and we can write it as:
a, ar, ar^2, ar^3 <---- the first 4 terms.
Here the common ratio r = 3 and the 4th term is 108 so:
a(3)^3 = 108
So the first term a = 108 / 3^3
= 108/27
= 4.
So the second number = 3*4 = 12 and 3rd is 12*3 = 36.
Date
Page
A rectangular meadow has an area of 28 square
meter and perimeter 22 m, find the length and breadth.
Answer:
perimeter =22m
area=28square meter
perimeter of rectangle=4l
22m=4l
22÷4=l
5.5=l
l=5.5m
area of rectangle =l×b
28=5.5×b
28÷5.5=b
5.09=b
b=5.09m
length =5.5m and breadth =5.09m answer !!!!
A rectangular lawn 4m by 10m has a garden of uniform width added to one end. Then, along the combined side length of the lawn and garden , another garden is added, whose width is twice that of garden . The total area of the lawn and both gardens is 72 m2
Answer and explanation:
A rectangle's width is longer than the length
And so given a rectangular lawn 4m by 10m,
the width of the lawn= 10m
the length of the lawn= 4m
If a garden of uniform width is added, then garden's width = 10m
The garden of uniform width is added to the width side of the rectangular lawn( since along the combined side length of the lawn and garden, another garden is added)
The garden added to the combined side length of the lawn and garden has width twice that of the garden = 2*10= 20m
Given that total area of the lawn and two gardens = 72m²
Total area of lawn and 2 gardens(Area of rectangle(lawn+2 garden's)) is length * width
= 4*10+ 10*x+ 20*y=72
Therefore equation for total area of lawn and both gardens is 40+10x+20y=72
Where x is length of second garden attached to the width side of the lawn and y is length of the garden attached to the combined length side of the lawn and first garden
x can be solved
40+10x+20y=72
10x+20y=72-40
10x+20y=32
10x=32-20y
x=32-20y/10
Y can be solved
40+10x+20y=72
10x+20y=72-40
10x+20y=32
20y=32-10x
y=32-10x/20
After being exposed to an incredible shrinking machine, Halley's height decreased by 108 cm over 6 seco
by the same amount each second. How much did Halley's height change each second?
18 cm
B
108 cm
-18 cm
D
-108 cm
Answer:
it would be -18
Step-by-step explanation:
because you would divide 108 by 6 and you will get -18 each second
Joseph recently noticed that this time next year he will be twice as old as Jasmine. I couldn't help noticing that when I am 66 at this time of the year the combined future ages of Joseph and Jasmine will also be 66. Also, 6 years from now my future age will be a multiple of the sum of Joseph and Jasmine's future ages. Of course, all ages are non-negative integers. How old. are Joseph Jasmine, and I now?
The vertex of a parabola that opens downward is at (0, 4). The vertex of a second parabola is at (0, –4). If the parabolas intersect at two points, which statement must be true?
Answer:
D
Step-by-step explanation:
Edge 2021 ;))
Write the word sentence as an equation. Then solve. The sum of a number y and −3 is −8.
need asap
Answer:
y + (-3) = -8
Step-by-step explanation:
i just know
pls mark branliest
h - 15 = -22
Help please
Answer:
-7
Step-by-step explanation:
H - 15 = -22
H= -22+15
H= -7
Value of H is -7
Answer:
- 7
Step-by-step explanation:
h - 15 = - 22
h = 15 - 22
h = - 7
Thus, The value of h is - 7
-TheUnknownScientist
A sociologist polled a random sample of people and asked them their age and annual income. The two-way frequency table below shows the results. Annual income vs. age group Less than $50,000 At least $50,000 Total Ages 44 and under 148 68 216 Ages 45 and above 38 94 132 Total 186 162 348 Which of the following statements is true of those polled? Choose 1 answer: А A person with an annual income of less than $50,000 is more likely to be 45 years old or above. B A person in the 44 and under age group is more likely to to have an annual income of at least $50,000
Answer:
C A person with an annual income of at least \$50{,}000$50,000dollar sign, 50, comma, 000 is more likely to be 454545 years old or above
A person in the 44 and under age group is more likely to have an annual income of at least $50,000 is a correct statement.
We have given that,
A sociologist polled a random sample of people and asked them their age and annual income.
What is the annual income?
annual income is the amount of money you receive during the year into your bank account, before any deductions.
The two-way frequency table below shows the results.
Annual income vs. age group Less than $50,000 At least $50,000
Total Ages 44 and under 148 68 216 Ages 45 and above 38 94 132
Total 186 162 348
A person with an annual income of at least
[tex]=\$50000\\=$50,000dollar[/tex]
Therefore statement b is true.
A person in the 44 and under age group is more likely to have an annual income of at least $50,000.
To learn more about the annual income visit:
https://brainly.com/question/6070671
#SPJ2
i need help on this please
Describe the products made by the process of cellular respiration.
Step-by-step explanation:
The product is carbon dioxide and water
Plz help me with this question
10 points
9514 1404 393
Answer:
The sequence 18
Step-by-step explanation:
After Nolan brings down a zero, the dividend Nolan will be 20, the same one he started with. So, he will get the same result he has gotten so far: the first quotient digit is 1 and the second quotient digit is 8, resulting in a new dividend of 20 (after the 0 is brought down).
The digits 18 will repeat until Nolan gets tired.
The number 1,134 is divisible by all of the following except
A.3
B. 6
C. 9
D. 12
E. 14
Answer:
1,134 is not divisible by 12
Answer:
I think is: D. 12
Step-by-step explanation:
The gross domestic product (GDP) of France is about $2.00 × 10 12 12 , and the GDP of Tuvalu is about $4.00 × 10 7 7 . How many times larger is the GDP of France than the GDP of Tuvalu?
Answer:
France's GDP is 50 000 times larger than Tuvalu's GDP.
Step-by-step explanation:
Given: Gross Domestic Product (GDP) of France = $2.0 x [tex]10^{12}[/tex]
Gross Domestic Product (GDP) of Tuvalu = $4.0 x [tex]10^{7}[/tex]
To determine the number of times in which the GDP of France is greater than that of Tuvalu, divide the GDP of France by the GDP of Tuvalu.
[tex]\frac{2.0*10^{12} }{4.0*10^{7} }[/tex] = [tex]\frac{2000000000000}{40000000}[/tex]
= [tex]\frac{200000}{4}[/tex]
= 50000
Therefore, France's GDP is 50 000 times larger than Tuvalu's GDP.
Is X +3 a factor of 2X squared minus 2X -12
Answer: No, x+3 is not a factor of 2x^2-2x-12
========================================================
Explanation:
Let p(x) = 2x^2 - 2x - 12
If we divide p(x) over (x-k), then the remainder is p(k). I'm using the remainder theorem. A special case of the remainder theorem is that if p(k) = 0, then x-k is a factor of p(x).
Compare x+3 = x-(-3) to x-k to find that k = -3.
Plug x = -3 into the function
p(x) = 2x^2 - 2x - 12
p(-3) = 2(-3)^2 - 2(-3) - 12
p(-3) = 12
We don't get 0 as a result so x+3 is not a factor of p(x) = 2x^2 - 2x - 12
----------------------------------------
Let's see what happens when we factor p(x)
2x^2 - 2x - 12
2(x^2 - x - 6)
2(x - 3)(x + 2)
The factors here are 2, x-3 and x+2
The following graph represents the cost and revenue functions for custom-made computers. How many computers
have been sold at the break-even point?
a 12
b 9
C 5
d. 0
Answer:
A. 12
Step-by-step explanation:
PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELPPPPPP!!!!
Select the missing property.
(9+3)v
Commutative property of addition
Commutative property of multiplication
Associative property of addition
Associative property of multiplication
Distributive property
Answer:
Associative property of addition
Step-by-step explanation:
yes