Answer:
[tex]\alpha^3-\beta^3 = \frac{28}{3}\sqrt{\frac{5}{3}}[/tex]
Step-by-step explanation:
Given quadratic equation is: [tex]3x^2 +6x-2=0[/tex]Comparing it with [tex]ax^2+bx+c=0[/tex], we find:[tex]a = 3,\: b= 6,\: c = -2[/tex]It is given that: [tex] \alpha\: and \: \beta[/tex] are roots of the given quadratic equation. So, we find the sum and the products of the roots.[tex] \implies \alpha + \beta =-\frac{b}{a}=-\frac{6}{3}=-2[/tex][tex] \& \:\alpha.\beta =\frac{c}{a}=-\frac{2}{3}[/tex]Since, one of the factors of [tex] \alpha^3-\beta^3[/tex] is [tex](\alpha - \beta)[/tex] . Therefore, now we will find the value of [tex](\alpha - \beta),[/tex] which can be obtained by the following formula.[tex]\alpha-\beta=\sqrt{(\alpha+\beta)^2-4\alpha\beta}[/tex][tex]\implies \alpha-\beta=\sqrt{(-2)^2-4\bigg(-\frac{2}{3}\bigg)}[/tex][tex]\implies \alpha-\beta=\sqrt{4+\frac{8}{3}}[/tex][tex]\implies \alpha-\beta=\sqrt{\frac{12+8}{3}}[/tex][tex]\implies \alpha-\beta=\sqrt{\frac{20}{3}}[/tex][tex]\implies \alpha-\beta=2\sqrt{\frac{5}{3}}[/tex][tex]\alpha^3-\beta^3 =(\alpha-\beta)^3+3\alpha\beta(\alpha-\beta)[/tex][tex] \implies \alpha^3-\beta^3 =\bigg(2\sqrt{\frac{5}{3}}\bigg)^3+3\bigg(-\frac{2}{3}\bigg)\bigg(2\sqrt{\frac{5}{3}}\bigg)[/tex][tex] \implies \alpha^3-\beta^3 =8\bigg(\sqrt{\frac{5}{3}}\bigg)^3-\bigg(\frac{6}{3}\bigg)\bigg(2\sqrt{\frac{5}{3}}\bigg)[/tex][tex] \implies \alpha^3-\beta^3 =8\times \frac{5}{3}\bigg(\sqrt{\frac{5}{3}}\bigg)-4\bigg(\sqrt{\frac{5}{3}}\bigg)[/tex][tex] \implies \alpha^3-\beta^3 = \frac{40}{3}\bigg(\sqrt{\frac{5}{3}}\bigg)-4\bigg(\sqrt{\frac{5}{3}}\bigg)[/tex][tex] \implies \alpha^3-\beta^3 = \bigg(\frac{40}{3}-4\bigg)\bigg(\sqrt{\frac{5}{3}}\bigg)[/tex][tex] \implies \alpha^3-\beta^3 = \bigg(\frac{40-12}{3}\bigg)\bigg(\sqrt{\frac{5}{3}}\bigg)[/tex][tex] \implies \alpha^3-\beta^3 = \frac{28}{3}\sqrt{\frac{5}{3}}[/tex]The value of a³-B³ from the given quadratic equation is 12.05.
What are roots of a quadratic equation?The roots to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
Given that, a and B are the roots of the equation 3x²+6x-2=0
By comparing 3x²+6x-2=0 with ax²+bx+c=0, we get a=3, b=6 and c=-2
The roots of a quadratic equation ax² + bx + c = 0 are given by x = [-b ± √(b² - 4ac)]/2a.
Now, substitute a=3, b=6 and c=-2 in quadratic formula
That is, x = [-6 ±√(6² - 4×3×(-2))]/2×3
= [-6 ±√60]/6
= (-6±2√15)/6
= (-3±√15)/3
So, a=(-3+√15)/3 and B=(-3-√15)/3
Now, a³-B³ = [(-3+√15)/3]³- [(-3-√15)/3]³
= 12.05
Therefore, the value of a³-B³ from the given quadratic equation is 12.05.
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Which graph represents the solution set of the inequality -14 5 < x?
Answer:
First graphStep-by-step explanation:
-14.5 < x ⇒ x > -14.5
A polygon has one less side than a quadrilateral. What is the polygon?
A certain circuit is properly fused for a 5-horsepower motor. If the motor is to be replaced by several 5/8 horsepower motors, how many motors will the fuses be able to carry?
The fuse with a rating of 5 horsepower would be able to carry 8 number of 5/8 horsepower motors.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A certain circuit is properly fused for a 5-horsepower motor. The number of motor, if several 5/8 horsepower motors is used is given by:
Number of motors = 5 hp ÷ (5/8 hp) = 8 motors
The fuse with a rating of 5 horsepower would be able to carry 8 number of 5/8 horsepower motors.
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The graphs below have the same shape. The equation of the red graph is
F(x) = x. What is the equation of the blue graph?
G(X) = ?
F(X) =
6
5
O A. G(x) = (x-5)
O B. G(X) = (x+5)
O C. G(x) = x° +5
O D. G(x) = x°-5
Answer: The graphs below have the same shape. The equation of the blue graph is f(x)=x^2. Which of these is the equation of the red graph, g(x)
Step-by-step explanation:
The equation of the blue graph is,
⇒ G (x) = (x + 5)³
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
We have to given that;
The equation of the red graph is
⇒ F(x) = x³
Now, The graph of blue line is 5 units left to the graph of red graph.
Hence, The equation of the blue graph is,
⇒ G (x) = (x + 5)³
Thus, The equation of the blue graph is,
⇒ G (x) = (x + 5)³
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4. Molly spent 1/3 of her summer vacation visiting her grandparents. If she was with them for 19 days, how
long was Molly's summer vacation?
The angles in a quadrilateral are 4y - 10°, y + 40°, 3y + 20° and 2y + 10° in order as you go around the quadrilateral.
a) Set up and solve an equation, to find the value of y.
b) Hence work out the value of each angle.
c) What type of quadrilateral is this?
Answer:
see explanation
Step-by-step explanation:
the sum of the interior angles of a quadrilateral = 360°
sum the 4 angles and equate to 360
4y - 10 + y + 40 + 3y + 20 + 2y + 10 = 360 , that is
10y + 60 = 360 ( subtract 60 from both sides )
10y = 300 ( divide both sides by 10 )
y = 30
then 4 angles are
4y - 10 = 4(30) - 10 = 120 - 10 = 110°
y + 40 = 30 + 40 = 70°
3y + 20 = 3(30) + 20 = 90 + 20 = 110°
2y + 10 = 2(30) + 10 = 60 + 10 = 70°
Since the angles measures are in order around the quadrilateral, then
the opposite angles are congruent, thus quadrilateral is a parallelogram
Help!!
f (x) =-3x+25; Find f(x)=52
Simplifying
-3x + 25 = 52
Reorder the terms:
25 + -3x = 52
Solving
25 + -3x = 52
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-25' to each side of the equation.
25 + -25 + -3x = 52 + -25
Combine like terms: 25 + -25 = 0
0 + -3x = 52 + -25
-3x = 52 + -25
Combine like terms: 52 + -25 = 27
-3x = 27
Divide each side by '-3'.
x = -9
Simplifying
x = -9
javier bought x pounds of olives for $4 per pound and y pounds feta cheese at $2 per pound. write an algebraic expression for the cost of javier’s purchase
Answer:
4x+2y
Step-by-step explanation:
x=pounds of olives
y= pounds of feta cheese
5. Brandon and Chloe ride their bikes for 4 hours along a flat, straight road. Brandon’s velocity, in miles per
hour, at time t hours is given by a differentiable function B for 0 st 54. Values of B(t) for selected times t
are given in the table above. Chloe's velocity, in miles per hour, at time t hours is given by the piecewise
function C defined by
C(t)
tep
for 0
12 – 3t – 12 for 2 <154.
(a) How many miles did Chloe travel from time t = 0 to time t = 2 ?
Do not write beyond this border.
Do not write beyond this border.
Answer:
Step-by-step explanation:
a) ∫from 0 to 2 of te^(4-t^2) dt. Let u = 4-t^2. du= -2dt. And, tdt= -dy/2.
If x=0, u= 4 and if x=2, u=0.
Therefore our new integral will be, -(1/2) ∫ from 0 to 4 of e^u du.
= -(1/2)(e^u) | 0 to 4
= -(1/2)(e^0 - e^4)
= -(1/2) + (1/2)e^4
= (1/2)(e^4 -1) miles
Therefore, from t=0 to t=2, Chloe has travelled a distance of (1/2)(e^4-1) miles.
b) At t=3, C(t)=12-3t-t^2
C(t) is already a function of velocity so simply plug in C(3), which is -6 miles/hour.
We also need to know acceleration.
C'(t)= -3 - 2t
C(3)= - 9 miles/hour squared.
Therefore, since velocity and acceleration are both negative, Chloes speed is increasing at t =3 hours.
in the diagram, AE is tangent to the circle at point a and secant DE intersects the circle at point C and D. the iines intersect outside of the circle at point E
10(1-7k) + 8( k+9)
Explain please
Step-by-step explanation:
[tex] = 10(1 - 7k) + 8(k + 9)[/tex]
Sort the expression in descending order....
[tex] = 10( - 7k + 1) + 8( k + 9)[/tex]
Now multiply....
[tex] = - 70k + 10 + 8k + 72[/tex]
Organize the similar terms...
[tex] = - 70k + 8k + 10 + 72[/tex]
[tex] = - 62k + 82[/tex]
hope it helped !!!
Calculate the Area: 6ft 3ft 8ft
I need this asap
Answer:
Answer is 72
Step-by-step explanation:
6 times 8 is 48. 3 needs to be divided by 2 to made into 1.5. Then multiply 48 and 1.5 to make 72ft your answer
Answer:
A= 12ft
Step-by-step explanation:
What is the mode? -5 0 -9 0 0 -9
The mode for this question is 0
ModeIn a set of numbers, the mode is the number that occurs most often. In other words, it measures how frequently a particular number occurs within a set of numbers. It is a type of average, like its counterparts, the median and mean.
To find the mode of a set of numbers,
List the set of numbers in ascending or descending order, including any duplicatesCount the number of times each number in the set of numbers occurs. The number that occurs the highest number of times is the mode of the set of dataWhat are the coordinates of the point on the directed line segment from (-6, 9)(−6,9) to (4, -1)(4,−1) that partitions the segment into a ratio of 1 to 4?
ALL IT SAYS IS SLOVE I REALLY NEED HELP PLEASEEE!!! THANK YOUUU
A. 2 1/16
B. 11/12
C. -11/12
D. -2 1/16
Answer:
The answer for your question is C
ixl 7th grade math determine the themes................................................................
Answer:
user could u make the second image attachment more clear cause that thing is blocking the themes
A sphere has a radius of 7/2 feet. What is the volume of the sphere in cubic feet in terms of pi?
Answer:
57.15π ft³
Step-by-step explanation:
Volume of a Sphere
4/3πr³Here, radius (r) = 7/2 ft.
Solving
V = 4/3 x π x 7/2 x 7/2 x 7/2V = 4/3 x 343/8 x πV = 343/6 x πV = 57.15π ft³A robot’s height is 1 meter 20 centimeters. How tall is the robot in millimeters?
A. 1,200 millimeters
B. 1020 millimeters
C. 120 millimeters
D. Not here
Answer:
A
Step-by-step explanation:
There are 1000 mm in one meter
and there are 10 mm in one cm
so
1000 + 20(10) = 1200mm
Therefore the answer is 1200mm
What is the value of k?
k =
A point located at (-5, -6) is reflected over the x-axis
(-5,6)
Step-by-step explanation:When a point is reflection a new, prime point (x') is created.
Formula
Whenever a point is reflected over the x-axis it follows a specific rule. The point goes from (x,y) to (x,-y). So, since the point is (-5, -6) we need to switch the sign of the y-value. This creates the new point (-5, 6).
Why?
Another way to remember this formula is to understand where it comes from. When reflecting over the y-axis, a point goes from the top 2 quadrants to the bottom 2 or vice versa. This means that the value is moving vertically. During vertical shifts, there is a change in the y-value. Additionally, because the x-axis is the seperation between negative and positive y-values, the y-value changes signs.
Grace and her friends are playing a game that uses two dice. Each die is a tetrahedron - a four‐sided shape with each side an equilateral triangle. Each side of the die contains one of the digits 1, 2, 3, or 4.
a. Create the sample space of all possible outcomes if you were to roll the two dice
simultaneously. List the digit on the first die first and the digit on the second die
second (i.e. 1,1; 1,2; and so on.)
b. What is the theoretical probability that the sum of the two numbers on a roll will
be five?
c. If Grace and her friends were to roll the two dice 100 times, how many of the
100 times could they expect to roll the same number on each die? (In other
words, the outcome would be 1,1 or 2,2 or 3,3 or 4,4.)
WILL GIVE BRAINLIEST! Please no jokes or links :)
Answer:
Step-by-step explanation:Very interesting problem. Be thankful it is not a six sided dice.Part A1 11 21 31 42 12 22 32 43 13 23 33 44 14 24 34 4Part BThere are 16 possible out comes1 44 12 33 24 out of the 16 outcomes are possibleP(5) = 4/16 = 0.25Part C The theoretical out come would be 4 times4/16 = 0.25On a hundred rolls, you would expect to get 25 sets of doubles.Step-by-step explanation:
In a triangle ABC, A=53 Degrees and C= 44Degrees thhen the value of B is:
The angle of elevation to a nearby tree from a point on the ground is measured to be 49
∘
∘
. How tall is the tree if the point on the ground is 53 feet from the tree? Round your answer to the nearest hundredth of a foot if necessary.
Answer:60.97
Step-by-step explanation: tan 49 = opposite/adjacent = x/53
tan 49 = x/53
tan 49/1 = x/53
53 tan 49 = x
x = 60.969
x = 60.97
The height of tree is 60.97 feet tall on the ground is 53 feet from the tree.
What is a trigonometric function?Trigonometry uses the first six fundamental trigonometric functions. Trigonometric proportions are these functions. The six fundamental trigonometric functions are the sin function, cosine function, secant function, and so on.
As per the data given in the question,
tan 49° = opposite/adjacent
tan 49° = x/53
tan 49/1 = x/53
x = 53 tan 49°
x = 60.969 or,
x = 60.97 feet. (rounding off value)
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will mark brainlist if you answer:)))
Answer:
Option 3
Step-by-step explanation:
The interquartile range is the same in both with a value of 12. The median and the third quartile are clearly different with the middle bit of the box and the right bit of the box being in different places and the range is quite different with one being 32 and the other one being 24.
Suppose that the world price of baseball caps is €2 and there are no import restrictions on this product. Assume that Spanish
consumers are indifferent between domestic and imported baseball caps.
Instructions: Enter your answers as whole numbers.
a. What quantity of baseball caps will domestic suppliers supply to domestic consumers?
thousand
b. What quantity of baseball caps will be imported?
thousand
Now suppose a tariff of C1 is levied against each imported baseball cap.
C. After the tariff is implemented, what quantity of baseball caps will domestic suppliers supply to domestic consumers?
thousand
d. After the tariff is implemented, what quantity of baseball caps will be imported?
thousand
No
Drov
Based on the supply and demand of the baseball caps, the relevant supply quantities are:
a. 20,000 baseball caps. b. 60,000 baseball caps.c. 30,000 baseball caps. d. 40,000 baseball caps. What quantity of baseball caps will be supplied domestically?At the price of €2, the supply according to the graph is:
= 20,000 baseball caps.
What quantity will be imported?The quantity imported is shown as:
= Demand at €2 - Domestic supply at €2
= 80 - 20
= 60,000 baseball caps
What quantity will be supplied domestically with the tariff?A tariff of €1 would increase the price to €3.
At this price, the supply would be:
= 30,000 baseball caps.
At the new price, the quantity imported is:
= Demand at €3 - Domestic supply at €3
= 70,000 - 30,000
= 40,000 baseball caps.
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a 4 storey building is 29 feet tall between which two whole numbers does the height of each storey lie?
Answer:
7 and 8
Step-by-step explanation:
29÷4=7.25 and that is between 7 and 8
Choose SSS, SAS, or neither to compare
these two triangles are congruent
ASA
SSS
SAS
neither
A two-sided test of H0: μ=0, α=0.05 (two sided), yields a p-value of 0.19. Will the 95% confidence interval for μ include 0?
Group of answer choices
No
Unknown
Yes
Explanation
Rule: if the p-value is smaller than alpha, then we reject the null.
We're given a p-value of 0.19 and alpha = 0.05
Based on that rule, it means we fail to reject the null (i.e. "accept" the null), since the p-value is not smaller than alpha.
Therefore, we conclude that mu = 0 must be the case, which means this value is in the confidence interval.
If mu = 0 was outside the confidence interval, then we would reject the null.
HELP, I NEED THIS MY LIFE DEPENDS ON IT.
Answer:
it’s D
Step-by-step explanation:
it’s not anything else
ur wlcm :)
hope i helped
brainliest?
Answer:
Congruent (A), Parallel (B), and Discs (D).
Step-by-step explanation:
The bases of a cylinder must be two discs which are congruent and parallel to each other.
A clock shows a time of 6 o'clock. What is the measure
of the angle between the hands of the clock?
How many twelfths are there in 3?
How many degrees are there in of a full turn?
Help please
Question 1
Answer: 180 degreesReason: The minute and hour hand form a straight line, or straight angle, which is always 180 degrees in measure.
============================================================
Question 2
Answer: 36Reason: Split a pizza into 12 equal slices. Imagine having 3 such pizzas to get 3*12 = 36 slices in total. This leads to the idea that 36*(1/12) = 3.
============================================================
Question 3
Answer: 360 degreesReason: This is by definition of what it means to do a full rotation.
