Answer:
Proved
Step-by-step explanation:
Taking R.H.S
=> [tex](x+y+z)[x(x+w^2y+wz)+wy(x+w^2y+wz)+w^2z(x+w^2y+wz)][/tex]
=> [tex](x+y+z)(x^2+w^2xy+wxz+wxy+w^3y^2+w^2yz+w^2xz+w^4yz+w^3z^2)[/tex]
Remember ∴ ω³ = 1
So we'll replace all ω³'s with 1
=> [tex](x+y+z)(x^2+y^2+z^2+w^2xy+wxy+w^2yz+w^4yz+w^2xz+wxz)[/tex]
=> [tex](x+y+z)[x^2+y^2+z^2+xy(w^2+x)+w^2yz+w^3*wyz+xz(w^2+w)][/tex]
Remember ∴ ω²+ω = -1
=> [tex](x+y+z)[x^2+y^2+z^2+xy(-1)+yz(w^2+w)+xz(-1)][/tex]
=> [tex](x+y+z)(x^2+y^2+z^2-xy-yz-xz)[/tex]
According to formula:
x³+y³+z³-3xyz = [tex](x+y+z)(x^2+y^2+z^2-xy-yz-xz)[/tex]
So, it becomes
=> [tex]x^3+y^3+z^3-3xyz[/tex]
What is the slope of the line given by the equation y=-3X?
A. 1/3
B. -1/3
C. -3
D. 3
Answer:
[tex]\boxed{-3}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation is determined by the constant equation [tex]y=mx+b[/tex] where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept of the line.
Therefore, we can use the equation given and implement it to find your slope.
[tex]y=-3x[/tex]
Our equation does not have a y-intercept, [tex]b[/tex]. Therefore, it can just be inferred as [tex]+0[/tex].
Because we do have a [tex]m[/tex], we can then find out what our slope is: [tex]\boxed{-3}[/tex].
If T={x:X is an integer between 1 and 4} (A) List down the elements of set T in set notation. B write down the number of elements in set T . C list down all the subsets of set T.D separate the proper and improper subsets of T.
Answer:
The answer is given below
Step-by-step explanation:
A) Integers are whole numbers (without fraction) that are either positive or negative. If T={x:X is an integer between 1 and 4}, therefore the elements in set T = {2, 3}
B) Since the elements in set T = {2, 3}, then the number of elements in set T = 2
C) The subsets of set T are {}, {2}, {3} and {2,3}
D) Proper subset of set T are subsets of T that is not equal to T. The proper subsets of T are {2} and {3}
An improper subset of set T contains all the element of set T and a null element. The improper subset of set T are {2,3} and {}
help me asap please i dont understand
Answer:
We have 2 rational solutions
0 irrational solutions
0 complex solutions
Step-by-step explanation:
a^2 + 8a + 12 = 0
Using the discriminant
b^2 -4ac where ax^2 + bx+ c
so a =1 b = 8 and c = 12
8^2 -4(1)*12
64 - 48
16
Since the discriminant is greater than 0, we have 2 real solutions
since we can take the square root of 16, we have rational solutions
We have 2 rational solutions
Since this is a quadratic equations, there are only 2 solutions so there are
0 irrational solutions
0 complex solutions
Answer:
2 Rational Solutions
0 Irrational Solutions
0 Complex Solutions
Step-by-step explanation:
The discriminant of the quadratic formula is the name given to the portion underneath the radical (or the square root)"
[tex]x = \frac{1}{2} (-b\frac{ + }{ - } \sqrt{ {b}^{2} - 4ac })[/tex]
Discriminant = D = b²-4ac
If D is less than 0 you have two complex solutions.
If D is equal to 0 you'll have one real solution.
If D is bigger than 0 you'll get two real solutions.
So here we have:
a=1
b=8
c=12
Which means D=64-4(1)(12)=64-48=16>0
D is bigger than 0, so you'll have two real solutions. And since 16 is a perfect square, they'll both be rational numbers.
n a group of 60 students, 18 students take algebra I, 20 students take Algebra II, and 10 students take both subjects. How many students don’t take either of these subjects?
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820
Answer:
32 students take neither of the subjects
Step-by-step explanation:
If we add the 20+18 we get 38. But 10 of the students are counted twice. So subtract 10 from 38 to get 28. This way each of the students that take both subjects are only counted once. Then, we take the total number of students, 60 and subtract the 28 students taking algebra classes to get 32 students.
PLEASE HELP ASAP don’t have much time.
Answer: 4
Step-by-step explanation:
numerator - denominator
Numerator: w¹³ Denominator: w⁸ · w¹
13 - (8 + 1)
13 - 9 = 4
Raymond works for an architecture firm. His company has a contract to design a building on a rectangular plot of land that has an area of 421,808 square meters. The plot of land is 328 meters wide. What is the length of the plot?
Answer:
1286 meters long
Step-by-step explanation:
421,808 divided by the width of the plot gives you 1,286 meters for the width.
Can somebody please help me!!
Step-by-step explanation:
Simply you replace X and Y by their values
Given: x=-1 y=-4
10 - (-X)^3 + y^2
=10 + X^3 + Y^2
Now replace X and Y
=10 + (-1)^3 + (-4)^2
=10 - 1 + 16
= 25
Given: Q = 7m + 3n, R = 11 - 2m, S = n + 5, and T = -m - 3n + 8.
Simplify [Q - R] + [S - T].
10m - 7n - 14
10m + 5n - 24
10m - 5n + 24
10m + 7n - 14
Answer:
The answer is 10m + 7n - 14
Step-by-step explanation:
Q = 7m + 3n
R = 11 - 2m
S = n + 5
T = -m - 3n + 8
[Q - R] + [S - T] is
[ 7m + 3n - (11 - 2m) ] + [ n + 5 - ( - m - 3n+8)]
Solve the terms in the bracket first
That's
( 7m + 3n - 11 + 2m ) + ( n + 5 + m + 3n - 8)
( 9m + 3n - 11 ) + ( m + 4n - 3)
Remove the brackets
That's
9m + 3n - 11 + m + 4n - 3
Group like terms
9m + m + 3n + 4n - 11 - 3
The final answer is
10m + 7n - 14Hope this helps you
Find the measure of the remote exterior angle. m∠x=(4n−18)°m∠y=(n+8)°m∠z=(133−6n)° m ∠ x = ( 4 n − 18 ) ° m ∠ y = ( n + 8 ) ° m ∠ z = ( 133 − 6 n ) °
Answer:
67°
Step-by-step explanation:
The question is incomplete. Here is the complete question.
Find the measure of the remote exterior angle. m∠x=(4n−18)°, m∠y=(n+8)°, m∠z=(133−6n)° angle Z being the exterior angle.
Before we can get the exterior angle Z, we need to first calculate the value of n.
In geometry, the sum of interior angles is equal to the remote exterior angle.
m∠z = m∠x + m∠y
(133-6n)° = (4n-18)°+(n+8)°
133-6n = 4n-18+n+8
-6n-4n-n = -18-133+8
-11n = -143
n = 143/11
n = 13°
Since the exterior angle m∠z =(133-6n)°
Substituting n = 11 into the equation will give:
m∠z = 133-6(11)
m∠z = 133-66
m∠z = 67°
The remote exterior angle is 67°
Answer: 55
Step-by-step explanation:
Complete the equation: x2 + 10x + ___ = 2
Solve for x. 9^x = sqrt 729 A.)1/4 B.)1/3 C.)3/4 D.)3/2 please help this is urgent!!!
Answer:
D
Step-by-step explanation:
Using the law of radicals/ exponents
[tex]\sqrt{a^{3} }[/tex] ⇔ [tex]a^{\frac{3}{2} }[/tex]
Consider the right side
[tex]\sqrt{729}[/tex] = [tex]\sqrt{9^{3} }[/tex] = [tex]9^{\frac{3}{2} }[/tex]
Thus
[tex]9^{x}[/tex] = [tex]9^{\frac{3}{2} }[/tex]
Since the bases on both sides are equal, equate the exponents, so
x = [tex]\frac{3}{2}[/tex] → D
look at the image and answer it
Answer:
The circumference of circle is 14π cm.
Step-by-step explanation:
Given that the formula of circumference is C = 2×π×r where r represents radius of circle. In this case, diameter of circle is 14cm so the radius will be 7cm. Then, you have to substitute the value into the formula :
[tex]c = 2 \times \pi \times r[/tex]
[tex]let \: r = 7[/tex]
[tex]c = 2 \times \pi \times 7[/tex]
[tex]c = 14\pi \: \: cm[/tex]
Answer:
14[tex]\pi[/tex]
units = cm
Step-by-step explanation:
circumference = 2 x [tex]\pi[/tex] x r
c = 2 x [tex]\pi[/tex] x 7 - it's 7 because the diameter is 14 and radius is half the diameter
c = 14 x [tex]\pi[/tex]
c = 43.98229715
in terms of pi c = 14 [tex]\pi[/tex]
units = cm
Which ordered pair is a solution if the equation? 2x + 3y = 10
Answer:
See below.
Step-by-step explanation:
Try each ordered pair in the equation. Each ordered pair is of the form (x, y). Replace x and y in the equation by values of x and y, respectively, in each ordered pair. Whichever ordered pair makes the equation a true statement is the answer.
For example:
Try (2, 3):
2x + 3y = 10
2(2) + 3(3) = 10
4 + 9 = 10
13 = 10
Since 13 = 10 is a false statement, (2, 3) is not a solution.
Try (2, 2):
2x + 3y = 10
2(2) + 3(2) = 10
4 + 6 = 10
10 = 10
Since 10 = 10 is a true statement, (2, 2) is a solution.
A ball, thrown vertically upwards, from the ground, has its height h (in meters) expressed as a function of time t (in seconds), elapsed after the launch, by the law h(t) = 20t - 5t2. According to this information, determine the height at which the ball is 3 seconds after the throw and the maximum height reached by the ball.
Answer:
a. 15 meters.
b. 20 meters.
Step-by-step explanation:
a. The height of the ball at 3 seconds. 20 * 3 - 5 * (3)^2 = 60 - 5 * 9 = 60 - 45 = 15.
The ball will be 15 meters high.
b. The maximum height reached by the ball.
To get that, we need to find the vertex of the parabola. We do so by doing -b/2a to find the x-coordinate of the vertex.
In this case, a = -5 and b = 20.
-20 / 2(-5) = -20 / -10 = 20 / 10 = 2.
Then, we find the y-coordinate by putting 2 where it says "t".
h(2) = 20(2) - 5(2)^2 = (40) - 5(4) = 40 - 20 = 20 meters.
Hope this helps!
Answer:
pen
Step-by-step explanation:
Jesse takes two data points from the weight and feed cost data set to calculate a slope, or average rate of change. A rat weighs 3.5 pounds and costs $4.50 per week to feed, while a Beagle weighs 30 pounds and costs $9.20 per week to feed.
Answer:
The slope is [tex]s =[/tex] $0.1774 / pounds
Step-by-step explanation:
From the question we are told that
The weight of the rat is [tex]w_1 = 3.5 \ pound[/tex]
The cost of feeding the rat per week is [tex]c_1 =[/tex]$4.50
The weight of a Beagle is [tex]w_2 = 30 \ pound[/tex]
The cost of feed a Beagle per week is [tex]c_2 =[/tex]$9.20
Now the slope can be evaluated mathematically as
[tex]s = \frac{c_2 -c_1 }{w_2 -w_1 }[/tex]
substituting values
[tex]s = \frac{9.20 -4.50 }{30 -3.5 }[/tex]
[tex]s =[/tex] $0.1774 / pounds
Can someone please help me I need help please help me please help
Answer: just graph these two equations
option a: y = 5x + 10
option b: y = 7.5x
and then tell at what number of event would having a card and not having a card is cheaper.
Step-by-step explanation:
the initial cost, $10, is your b value for the equation y = mx + b so yo would start here on the y axis. but for the second option you start at zero since you don't have a b value
Answer:
use this hope help you
option a: y = 5x + 10
option b: y = 7.5x
and then tell at what number of event would having a card and not having a card is cheaper.
Step-by-step explanation:
Find the equation of the line passing through the point (–1, –2) and perpendicular to the line y = –1∕2x + 5. Choices are in the attachment...
Find the coefficient of fourth term of (-x -3)^5
Answer:
-270
Step-by-step explanation:
Here, we want to know the coefficient of the fourth term.
The coefficients according to pascal triangle for the expansion is 1 5 10 10 5 1
So the expansion looks as follows;
1[(-x)^5(-3)^0] + 5[(-x)^4(-3)^1)] + 10[(-x)^3(-3)^2) + 10[(-x)^2(-3)^3] + ...........
So the fourth term we are dealing with is
10[(-x)^2(-3)^3)]
So the value here is
10 * x^2 * -27
= -270 x^2
So the coefficient is -270
Help is appreciated. Easy I just am always confused
Answer:
BA=BC
Step-by-step explanation:
Which equation represents a circle with a center at (2,-3) and a radius of 11
Answer:
x^2-4x+y^2+6y-108=0
Step-by-step explanation:
[tex]The- equation- of- circle- with -center- at- (h,k) -and -a -radius- of- r -is: \\(x-h)^2 +(y-k)^2 = r^2\\h = 2 , \\ k = -3\\r = 11\\(x-2)^2+(y-(-3))^2 = 11^2\\(x-2)^2+(y+3)^2 = 121\\x^2-4x+4 +y^2+6y+9 = 121\\x^2 -4x+y^2+6y+4+9=121\\x^2 -4x+y^2+6y+13=121\\x^2 -4x+y^2+6y=121-13\\x^2 -4x+y^2+6y= 108\\x^2 -4x+y^2+6y-108 = 0[/tex]
A freight train averages 20 miles per hour traveling to its destination with full cars and 30 miles per hour on the return trip with empty cars. What is the train's average speed for the entire trip
Answer:
24mph
Step-by-step explanation:
Let's say the distance between the destination is 10 miles. The train will reach the destination in 30 min for the first round and 20 min the second. Now, we can say, the train took 50 min to go 20 miles. Which is also 24mph. (5min=2miles)
The train's average speed for the entire trip is equal to 25 mph.
Given the following data:
Distance A = 20 milesTime A = 1 hourDistance B = 30 milesTime B = 1 hourTo determine the train's average speed for the entire trip:
First of all, we would find the total distance and total time for the trip respectively.
For total distance:
[tex]Total\;distance = Distance\;A + Distance\;B\\\\Total\;distance = 20+30[/tex]
Total distance = 50 miles
For total time:
[tex]Total\;distance = Time\;A + Time\;B\\\\Total\;distance = 1+1[/tex]
Total time = 1 hour
Mathematically, average speed is given by the formula:
[tex]Average\;speed = \frac{Total\;distance}{Total\;time} \\\\Average\;speed = \frac{50}{2}[/tex]
Average speed = 25 mph.
Read more: https://brainly.com/question/17742679
A soda factory has a special manufacturing line to fill large bottles with 2 liters of their beverage. Every process is computerized. However, it doesn't always fill exactly 2 liters. It follows a normal distribution, with a mean of 1.98 liters and a variance of 0.0064 liters. If the amount of soda in a bottle is more than 1.5 standard deviations away from the mean, then it will be rejected.
Find the probability that a randomly selected bottle is rejected.
a. 0
b. 0.07
c. 0.04
d. 0.13
e. 0.19
Irum is sitting on the beach, watching the tide go in and out. Irum's distance from the shoreline (in meters) as a function of time (in hours) is graphed. What is the approximate average rate at which Irum's distance from the shoreline increases, between the 9th and the 13th hour marks?
Answer:
Hi, the Answer is 0.75.
Step-by-step explanation:
it is 0.75 because if you look on the graph, and you calculate the 3/4 slope between the two, 3/4= 0.75
Answer:
A) 0.75 meters per hour
Step-by-step explanation:
Can someone help me with this question please.
Answer:
98
Step-by-step explanation:
3 bed house= 33 rooms
4 bed house 40 rooms
4 bed house 25 rooms
each house is worth 2 houses. so u double everything
hope I got it right
Find the center and radius of the circle x2 + y2 –6y – 16 = 0
Answer:
centre=(0,3) radius =5
Step-by-step explanation:
– StartFraction 5 Over 3 EndFraction v plus 4 equals 8 minus StartFraction 1 Over 3 EndFraction v.(6x – 3) = –
Answer:
v=11/5 or v=2.2
Step-by-step explanation:
The wording of this question is a little confusing but if it says what I think it does (5/3v+4=8-1/3) then this is the answer.
The sum of three numbers is 84 The second number is 2 times the first. The third number is 16 less than the second. What is the second number?
Answer:
40
Step-by-step explanation:
First let x represent the first number.
Let 2x represent the second number.
Let 2x-16 represent the third number.
x + 2x + 2x-16 = 84
5x -16 = 84
5x = 84 + 16
5x = 100
Divide both sides of the equation by 5 so that x can stand alone.
[tex]\frac{5x}{5} = \frac{100}{5}[/tex]
x = 20
∴ First number = x = 20
Second number = 2x = 40
Third number = 2x - 16 = 24
For A (1, -1), B(-1,3), and C(4, -1), find a possible location of a fourth point, D, so that a
parallelogram is formed using A, B, C, D in any order as vertices.
Answer: c, b, a, d
Step-by-step explanation: that is correct
What else would need to be congruent to show that ABC was DEF by ASA
Answer:
ABC≅DEF ASA POSTULATE
There must be two angles and one side of ABC congruent to DEF
Step-by-step explanation:
Answer:
BC=EF
Step-by-step explanation:
Process of elimination and I just took the test so trust me.
What are the solutions to the system of equations graphed below?
Answer:
B) (2,0) and (0,-4)
Step-by-step explanation:
The answer to the system of equations is where the two intersect on the graph, in this case on the points (2,0) and (0,-4)