Answer:
I think that it should be
[tex] {(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3} = 3(a - b)(b - c)(c - a)[/tex]
Step-by-step explanation:
Here,
we take , a - b = A,b-c = B , c - a= C
A+B+C = 0
we know that,
[tex] {a}^{3} + {b}^{3} + {c}^{3} - 3abc = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca)[/tex]
Here , A+B+C = 0
so,
A^3 +B^3 + C^3 = 3 ABC
now we put the values
[tex]{(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3} = 3(a - b)(b - c)(c - a)[/tex]
I am done .
I think that it should be
{(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3} = 3(a - b)(b - c)(c - a)
Step-by-step explanation:
Here,
we take , a - b = A,b-c = B , c - a= C
A+B+C = 0
we know that,
{a}^{3} + {b}^{3} + {c}^{3} - 3abc = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca)
Here , A+B+C = 0
so,
A^3 +B^3 + C^3 = 3 ABC
now we put the values
{(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3} = 3(a - b)(b - c)(c - a)
I am done .
Write two equivalent expressions using the commutative property that can be used to find the total number of points Dean Scored on his math test
Answer:
2
Step-by-step explanation:
Find the product.
(X+9) (5)
PLEASE HELP!!! ASAP!!!
Answer:
Your correct answer is = 5x + 45
Step-by-step explanation:
To find this, you will need to learn to multiply polynomials.
Jack challenged Jill to a race around a curve of a track. Jack took lane 8 with Jill at lane 1. If the radius of lane 1 is half of lane 8, what is the distance in metres Jack has to run if Jill ran a distance of 50m?
Answer:jac ganko
Step-by-step explanation:
Morgan had 11 inches of snow on her lawn. The temperature then increased and the snow began to melt at a constant rate of 1.5 inches per hour. Assuming no more snow was falling, how much snow would Morgan have on her lawn 2 hours after the snow began to melt? How much snow would Morgan have on her lawn after tt hours of snow melting?
Answer:
two hours after the snow started melting, the depth of the snow would be 8 inches.
Step-by-step explanation:
The melting can be represented by a linear function of the snow depth (D(t)) as a function of time (t). We consider that the initial value is: 11 inches deep at time = 0 (zero). and then decreasing at a rate of 1.5 inches per hour (that is a negative slope = -1.5).
[tex]D(t)=11-1.5\,t[/tex]
Therefore, 2 hours after the snow started melting, one would have:
[tex]D(2)=11-1.5\,(2)=11-3=8\,\,inches[/tex]
One afternoon Anne leave her house and walk 5 blocks north to the post office then she walk 2 blocks north to the bank finally she walk 3 blocks south to the coffee shop were is the coffee shop relative to her house
Answer:
B
Step-by-step explanation:
A tunnel must be made through a hill. As a result, a surveyor and an engineer create a sketch of the area. The sketch, displayed below, includes information they have either researched or measured. They need to build a tunnel from the point E to the point H on the sketch. Calculate the distance from E to H. When similar triangles are used, explain how you know they represent similar triangles before performing the calculation.
Answer:
498 m
Step-by-step explanation:
The AAA theorem states that triangles are similar if all three corresponding angles are equal.
1. Compare triangles FHS and ILS
(a) Reason for similarity
∠F = ∠I = 90°
∠S is common.
∴ ∠H = ∠L
(b) Calculate SL
[tex]\begin{array}{rcl}\dfrac{SF}{SH} & = & \dfrac{SI}{SL}\\\\\dfrac{225}{380} & = & \dfrac{225 + 475}{SL}\\\\225SL & = & 380 \times 700\\& = & 266000\\SL & = & \textbf{1182 m}\\\end{array}[/tex]
2. Compare triangles ILS and GLE
(a) Reason for similarity
∠I = ∠G = 90°
∠L is common.
∴ ∠S = ∠E
(b) Calculate LE
[tex]\begin{array}{rcl}\dfrac{IS}{GE} & = & \dfrac{LS}{LE}\\\\\dfrac{700}{180} & = & \dfrac{1182}{LE}\\\\700LE & = & 180 \times 1182\\& = & 212800\\LE & = & \textbf{304.0 m}\\\end{array}[/tex]
3. Calculate EH
LE + EH + HS = LS
304.0 m + EH + 380 m = 1182 m
EH + 684 m = 1182 m
EH = 498 m
The distance from E to H is 498 m.
sin theta=-1/2 then cos theta=
Answer:
cos 30°= 0.866Step-by-step explanation:
Step one:
Applying the SOH CAH TOA principle
assuming all dimensions are in cm
Step two:
Given data
opposite= 1 cm
hypotenuse= 2 cm
we can now solve for θSin(θ)= opp/hyp
Sin(θ)= 1/2
Sin(θ)= 0.5
θ= sin-1 0.5
θ= 30°
hence from tables cos 30°= 0.866
Write an expression for the volume and simplify your answer. 3x x+1 x+4
Answer:
volume=3x³+15x²+12x
Step-by-step explanation:
v= l*w*h =(3x )(x+1) (x+4)
v=3x(x²+5x+4)
volume=3x³+15x²+12x
Which way would you choose to solve 3/x=6/14 ?
Explain your reasoning.
Answer:
I'd cross multiply to solve this equation.
Step-by-step explanation:
Since we have a fraction where we're finding a ratio:
[tex]\frac{3}{x} = \frac{6}{14}[/tex],
I'd find it easiest to cross multiply. This is because we are finding an equivalent to a ratio, so cross multiplication works best here.
Let's solve it.
[tex]14\cdot 3 = 42\\42\div6=7[/tex]
x = 7
Hope this helped!
A steady stream of water flows into a partially-filled rectangular tank. After 6 minutes, there are 87 gallons of water in the tank. After 21 minutes, there are 222 gallons. Write an equation to represent the volume of water in the tank y after x minutes. How much water was in the tank to begin?
Answer: y=9x+33
33 gallons of water to begin with.
Step-by-step explanation:
So we essentially are given two coordinates: (6,87) and (21,222). To find an equation, we simply need to find the slope and y-intercept. We know it's a linear equation because it's a steady stream, meaning a constant slope.
The slope is:
So, the rate at which the stream flows is 9 gallons per minute.
Now, let's find the initial amount of water. To do this, we can use point-slope form. Pick either of the two points. I'm going to use (6,87).
So, there were 33 gallons of water in the tank to begin with.
Answer:
There were 33 gallons.
Step-by-step explanation:
Write the following as an inequality:
y is no greater than 4 but more than -2.
Answer:
4>Y>-2 :) ..............
Answer:
[tex]\boxed{-2 < y \leq 4}[/tex]
Step-by-step explanation:
For y is no greater than 4, it would be either less than or equal to 4. So, the inequality for it would be:
y ≤ 4
Now, the inequality for y more than -2:
-2 < y
Combining the inequality:
-2 < y ≤ 4
John and will also ran for Middle School council president. There are 90 students voting in middle school. If the ratio of Will's votes to John's votes are the same how many vo
Hi!
This problem is the fifth in a series of seven about ratios. At first glance the problem may look to be beyond 6.RP.1, which limits itself to “describe a ratio relationship between two quantities. However, even though there are three quantities (the number of each candidates' votes), they are only considered two at a time.
In the first problem students define the simple ratios that exist among the three candidates. It opens an opportunity to introduce unit rates.
The subsequent problems are more complex. In the second problem, students apply their understanding of ratios to combine two pools of voters to determine a new ratio. In the third problem, students apply a known ratio to a new, larger pool of voters to determine the number of votes that would be garnered.
Solutions
Solution: Question #1
a. John's votes to Will's, 16 to 8, or 2 to 1. Marie's votes to Will's, 12 to 8, 3 to 2, or 32 to 1, the unit ratio. Marie's votes to John's, 12 to 16, 3 to 4, or 34 to 1, the unit ratio.
Solution: Question #2
2. Will now has 8 + 12 = 20 votes to John's 16 votes, so the ratio of Will's votes to John's votes is 20 : 16, 5 : 4, or 54 : 1, the unit ratio.
Solution: Question #3 - Computing votes
There are different ways to approach this problem, but both begin with the fact that Will gets votes in a 5 to 4 ratio compared with John and require recognizing that a 5 to 4 ratio means a total of 9 equal parts. Then it is straightforward to compute:
59×90=50 votes for Will
49×90=40 for John
50−40=10 more votes for Will.
Solution: Question #3 - Applying fractions
One can solve the problem by working fractions by recognizing that Will getting votes in a 5 to 4 ratio means a total of 9 equal parts. It follows that Will gets 59 of the 90 votes and John gets 49 of the 90 votes:
59−49=19 of the voters
19×90=10 more votes for Will
Solution: Question #3 - Equivalent Ratios
An alternate very basic solution to Question 3 involves creating a series of equivalent ratios. This approach may be selected by students who are still developing an understanding of proportional situations. Students may begin with the ratio of 5 to 4 and proceed to find a ratio such that the sum of numerator and denominator is 90. This sequence may appear as follows:
5/4 = 10/8 = 15/12 = 20/16 = 25/20 = 30/24 = 35/28 = 40/32 = 45/36 =50/40
Then 50 - 40 = 10 more votes for Will
Overall answer
10 more votes for will
The nth term of a geometric sequence is a sub n =a sub 1 times r ^n-1 , where a sub 1 is the first term and r is the common ratio. Identify a sub 1 and r for each geometric sequence.
Answer/Step-by-step explanation:
Common ratio of a sequence can be gotten by dividing any of the consecutive term in a sequence, by the term before it.
Thus,
For the sequence, [tex] 3, 9, 27. . . [/tex] : [tex] a_1 = 3 [/tex]
[tex] r = \frac{9}{3} = 3 [/tex]
For the sequence, [tex] 8, 4, 2, 1. . . [/tex] : [tex] a_1 = 8 [/tex]
[tex] r = \frac{4}{8} = \frac{1}{2} [/tex]
For the sequence, [tex] -16, 64, -256 . . [/tex] : [tex] a_1 = -16 [/tex]
[tex] r = \frac{64}{-16} = -4 [/tex]
Please help I really need to get it right
Answer:
Alternate interior angles.
17x + 6 = 18x - 1.
x = 7.
Step-by-step explanation:
According to the diagram below, the angles are alternate interior angles.
Since they are alternate interior angles, they are congruent. So, 17x + 6 = 18x - 1.
17x + 6 = 18x - 1
18x - 1 = 17x + 6
x = 7
Hope this helps!
Heather used a graphing utility to find the equation of the line of best fit in this scatter plot. VA PW1ALG131_Using Models from Data After reading equation of the line from the graphing utility, Heather wrote in her notebook that the line of best fit is represented by the equation y = 0.77x + 1.34. Heather likely an error when writing the equation of the line in her notebook because the slope and the y-intercept of the equation she recorded.
The answers are did not make, and both the slope and the y-intercept match if the line of the best fit is represented by the equation y = 0.77x + 1.34
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
We have a line of best fit:
y = 0.77x + 1.34
Here the slope of the line is 0.77 and y-intercept is 1.34
From the graph and line of best fit, we can say heather did not make an error when writing the equation of the line in her notebook because both the slope and the y-intercept match the slope and the y-intercept of the equation she recorded
Thus, the answers are did not make, and both the slope and the y-intercept match if the line of the best fit is represented by the equation y = 0.77x + 1.34
Learn more about the line of best fit here:
brainly.com/question/14279419
#SPJ2
Answer:
Heather likely did not make an error when writing the equation of the line in her notebook because both the slope and the y-intercept match the slope and the y-intercept of the equation she recorded.
1. In triangle ABC. A-54.2° B=71.5º, a=12 4cm. Find b
Answer:
13
Step-by-step explanation:
Convert 125 degrees into radians. (NEED ASAP)
Answer:
[tex]\boxed{\frac{25\pi }{36}}[/tex]
Step-by-step explanation:
Use the formula to convert from degrees to radians: [tex]x * \frac{\pi }{180}[/tex], where x is the value in degrees.
[tex]125 * \frac{\pi }{180}[/tex] = [tex]\frac{125\pi }{180}[/tex]
Then, simplify your fraction ⇒ [tex]\frac{125\pi }{180} = \boxed{\frac{25\pi}{36} }[/tex]
What is 1/9 of 63% of 6000?
Answer:
420
Step-by-step explanation:
To find 63% of 6000, we can do 0.63 * 6000 = 3780 because 63% = 0.63.
1/9th of that is 1/9 * 3780 = 420.
Answer:
420
Step-by-step explanation:
Let's first start by finding 63% of 6000 so we can later find 1/9 of that number.
We can set up a percentage proportion.
[tex]\frac{x}{6000} = \frac{63}{100}[/tex]
[tex]6000\cdot63=378000\\378000\div100 = 3780[/tex]
Now to find 1/9 of 3780.
[tex]\frac{1}{9} \cdot \frac{3780}{1}\\\\\frac{3780}{9} = 420[/tex]
So, the answer is 420.
Hope this helped!
A constant force of 85 N accelerates towards a 10 kg box from a speed of 3.0 m/s to a speed of 7.0 m/s as it goes 14 m along a horizontal floor. What is the coefficient of friction between the box and the floor?
Answer:
Step-by-step explanation:
Let us find the acceleration of box .
v² = u² + 2as
Putting the values
7² = 3² + 2 a x 14
a = 1.43 m /s²
If coefficient of friction be μ
force of friction = μ mg
= μ x 10 x 9.8
= 98μ
Net force pushing the box
= 85 - 98μ
Applying newton's second law
85 - 98μ = 10 x 1.43
98μ = 85 - 14.3
μ = .72
I NEED HELP PLZ Event A and event B are independent events. Given that P(B)=13 and P(A∩B)=16, what is P(A)?
Answer:
19
Step-by-step explanation:
Write 2(6² + 4²) as the sum of two perfect square.
Find the area of equilateral triangle with side a.
Answer:
[tex]\frac{\sqrt{3} }{4} a^2[/tex]
Step-by-step explanation:
To find the area of an equilateral triangle, we can apply a formula.
[tex]A=\frac{\sqrt{3} }{4} s^2[/tex]
[tex]A= area\\s=side \: length[/tex]
The side length is given a.
Plug a in the formula as the side length.
[tex]A=\frac{\sqrt{3} }{4} a^2[/tex]
Answer:
3 square root over 4 a square
Step-by-step explanation:
Kite A B C D is shown. Lines are drawn from point A to point C and from point B to point D and intersect. In the kite, AC = 10 and BD = 6. What is the area of kite ABCD? 15 square units 30 square units 45 square units 60 square units
Answer:
[tex]30 u^{2}[/tex]
Step-by-step explanation:
The computation of the area of kite ABCD is shown below:
Given data
AC = 10 ;
BD = 6
As we can see from the attached figure that the Kite is a quadrilateral as it involves two adjacent sides i.e to be equal
Now the area of quadrilateral when the diagonals are given
So, it is
[tex]\text { area of kite }=\frac{1}{2} \times d_{1} d_{2}[/tex]
where,
[tex]d_{1}=10\ and\ d_{2}=6[/tex]
So, the area of the quadrilateral is
[tex]=\frac{1}{2}(10)(6)\\\\=30 u^{2}[/tex]
Answer:
C
Step-by-step explanation:
I just took the test
If the surface area of a can is 1406.72 cm2, and the radius is 8 cm, the height
Answer:
20
Step-by-step explanation:
i got it right on a quiz
Height of a can is equal to [tex]\boldsymbol{6.99\,cm}[/tex].
Surface area of a cylinderSurface area of a cylinder [tex]=\pi r^2h[/tex] where [tex]r,h[/tex] denote radius, height of a cylinder respectively.
Surface area of a can [tex]=1406.72 \,cm^2[/tex]
Radius of a can [tex]=8 \,cm[/tex]
[tex]1406.72=\frac{22}{7}(8)^2h[/tex]
[tex]h=6.99\,cm[/tex]
Therefore, height of a can is equal to [tex]\boldsymbol{6.99\,cm}[/tex]
Find out more information about cylinder here:
https://brainly.com/question/3216899?referrer=searchResults
if p(x) = x+ 7/ x-1 and q (x) = x^2 + x - 2, what is the product of p(3) and q(2)? a. 50 b. 45 c. 40 d. 20 e. 6
Answer:
d. 20
Step-by-step explanation:
To answer the question given, we will follow the steps below:
we need to first find p(3)
p(x) = x+ 7/ x-1
we will replace all x by 3 in the equation above
p(3) = 3+7 / 3-1
p(3) = 10/2
p(3) = 5
Similarly to find q(2)
q (x) = x^2 + x - 2,
we will replace x by 2 in the equation above
q (2) = 2^2 + 2 - 2
q (2) = 4 + 0
q (2) = 4
The product of p(3) and q(2) = 5 × 4 = 20
PLEASE HELP: Which is a compound event?
Answer:
The correct option is;
Heads lands 3 times and tales lands 5 times in 8 coin flips
Step-by-step explanation:
A compound event is one in which the probability of more than one outcome or event to have occurred at the same time is sought. The probability of a compound event is the sum of the probabilities of the individual events less the probabilities already captured in both event probabilities
Answering compound event questions can be done by the use of a tabular or diagram format.
Therefore, the compound event in the list is heads lands 3 times and tales lands 5 times in 8 coin flips.
Please help me!!!! I really need help!!
Answer:
A. 25°
Hope it helped
Callie has a new kitten. The kitten weighs 3 pounds less than half the weight of Callie’s cat. Together, the cat and the kitten weigh 18 pounds. Which system of equations could be used to find the weight of each animal?
Answer:
y = [tex]\frac{1}{2} x - 3[/tex]
x + y = 18
Step-by-step explanation:
Let the kitten's weight be y and the cat's weight be x
Condition # 1:
y = [tex]\frac{1}{2} x - 3[/tex]
Condition # 2:
x + y = 18
Simplify :
a–(b–c)+(m+n)
x+a + (m – 2)
m + (a–k–b)
x + (a–b) – (c–d)
Answer:
The simplified expressions are
1) a - b + c + m + n
2) x + a + m - 2
3) m + a - k - b
4) x + a - b - c + d
Step-by-step explanation:
1) a - (b - c) + (m + n)
To simplify the above expression, we have;
a - (b - c) + (m + n) = a - b - (-c) + m + n = a - b + c + m + n
2) x + a + (m - 2)
To simplify the above expression, we have;
x + a + (m - 2) = x + a + m - 2
3) m + (a - k - b)
To simplify the above expression, we have;
m + (a - k - b) = m + a - k - b
4) x + (a - b) - (c - d) = x + a - b - c -(- d)) = x + a - b - c + d
How many solutions does this system have? 6 x + 3 y = negative 12. y = negative 2 x + 4. one two an infinite number no solution
Answer:
work is shown and pictured