Define operation $\heartsuit$ so that \[ a \heartsuit b = \dfrac{a + b}{2}. \] Let $H$ be a function defined by \[H(x,y,z) = \left(x \heartsuit y\right) \heartsuit z - x \heartsuit \left(y \heartsuit z\right). \] Write an expression for a simplified version of this function: $H(x,y,z) = \boxed{\phantom{blaaaaaaaaaa^2_2}}$ Write an expression, not an equation. Sample answer: $x + y + z$
Answers
Answer:
(-x+z)/4
Step-by-step explanation:
Evaluate the $\heartsuit$ operation to simplify.
\begin{align*}
H(x,y,z) &= \left(x \heartsuit y\right) \heartsuit z - x \heartsuit \left(y \heartsuit z\right) \\
&= \left(\dfrac{x+y}{2}\right) \heartsuit z - x \heartsuit \left(\dfrac{y+z} 2\right) \\
&= \dfrac{\dfrac{x+y}{2} + z}{2} - \dfrac{x + \dfrac{y+z}{2}}{2}
\end{align*}This looks ugly, but it works out! Continue by multiplying each fraction's numerator and denominator by $2$, in order to eliminate the complex fractions.
\begin{align*}
H(x,y,z) &= \dfrac{\dfrac{x+y}{2} + z}{2} - \dfrac{x + \dfrac{y+z}{2}}{2} \\
&= \dfrac{x + y + 2z}{4} - \dfrac{2x + y + z}{4} \\
&= \dfrac{(x+y+2z) - (2x + y + z)}{4}
&= \dfrac{-x+z}{4}
\end{align*}Surprisingly it simplifies all the way down to $H(x,y,z) = \boxed{\dfrac{-x + z}{4}}$. The value of $y$ is not even used!
![Define Operation $\heartsuit$ So That \[ A \heartsuit B = \dfrac{a + B}{2}. \] Let $H$ Be A Function](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/ksmxHZhxiCsrgQWQvZCuYTfppGHM2ezW.png)
Related Questions
a game show has 70 categories. There are 30 points in each categories. how many points are there in total on the game show?
Answers
100 points!!!!! How many more brick houses did Company N build than Company M?
Answers
Answer:
company N built 10 more brick houses
Step-by-step explanation:
if company M builds 2x as many wooden houses as the do brick houses that would be 1/2 of 100 which is 50, and the ratio of wood houses to brick houses for company M is 5:3, 5x20=100 3x20=60. 60-50=10
Answer:
10 houses
Step-by-step explanation:
If Company M builds half as many brick houses as wood houses, then if this company builds 100 wood houses, it builds 50 brick houses.
For Company N, create a linear equation showing the relationship between wood houses (x) and brick houses (y). For every increase in x by 5, y increases by 3:
y = (3/5)x
Therefore, when x = 100: y = (3/5)(100) = 60
So Company N builds 60 brick houses when it builds 100 wood houses.
Company N - Company M = 60 - 50 = 10 houses
Therefore, Company N built 10 more brick houses than Company M.
Help me asp 25 points and will mark
Answers
For Tommy’s earnings, use slope formula, which is y=y2-y1/x2-x1, take two random points from the table, (4,32) and (5,40)
(4,32) is (x1,y1). (5,40) is (x2,y2)
40-32/5-4= 8/1
The answer is 8. y=8x
Miranda earns more money per hour than Tommy.
3 increased by the product of q and r
Answers
Answer:
3 + qr
Step-by-step explanation:
"increased by" means adding.
"product" indicates multiplication.
You can show that q and r are multiplied together in many ways:
qr
q(r)
(q)r
q×r
q•r
q*r
This is how you translate the phrase into an algebraic expression.
3 + qr
1+1 =? sos sos sos sos sos sos sos sos sos sos sos
Answers
Answer:
I think its 2 bro
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
LOL LOL LOL LOL
What's your highest tile in 2048?
I got 131072
Find the measure of angle x in the figure.
Note: Angles not drawn to scale.
Angle x measures=
Answers
Answer:
x = 125°
Step-by-step explanation:
There are 7 angles in this shape. The sum of the angles in a shape like this is calculated using a formula.
Total of angles
= (n - 2)•180°
Put in 7, because there are 7 angles.
= (7 - 2)•180°
= 5•180°
= 900°
So the total of the angles should be 900°. We know all of the angles except one.
900° = 123°+129°+128°+128°+132°+135°+ x
900° = 775° + x
Subtract 775.
125° = x
The missing angle is 125°.
Find the coordinates of the midpoint of
segment XY for X(-2, 3) and Y(-8, -9).
Answers
Answer:
use formula
(x,y) =[ (x1+x2)/2 ,(y1+y2/2)]
=[(-2-8)/2, (3-9)/2]
=(-10/2 ,-6/2)
=(-5,-3)
This year, 17,884 people attended a basketball team’s first game, and 17,150 people attended their second game. What is the percent decrease from the first game to the second game in the number of people who attended? Round to the nearest tenth of a percent.
Answers
Rounded: 4.1
Answer:
4.1
Step-by-step explanation:
Help ASAP im in 6th so this could be easy for sum of you to answer! okay so click on this question to see the rest please help me! Billy's soccer team won 17 out of the 20 games played. Sam's soccer team lost 3 games of their 12-game season. Which statment is NOT true about the wins and losses for both Billy's and Sam's soccer teams?
Group of answer choices: A, Billy's soccer team won 17 games which represents 85% of their games.
B, Sam's soccer team won 9 games which represents 3/4 pf their games.
C, Both of their teams lost 3 games, so their losing percentage would be the same.
D,Sam's soccer team lost 3 games which represents 25% of their games.
Answers
Answer:
C
Step-by-step explanation:
I believe it is C because since they each have a different amount of games even though they both lost three, the percentage will be different. Just like if you missed 2 questions on a 4 question test you would fail, but if you missed two questions on a 20 question test you would get a good score.
Answer
C
Step-by-step explanation:
This figure represents a portable ramp that is being recovered on all sides.
How much material is needed to recover the ramp?
1288 m²
1416 m²
1443 m²
1680 m²
Right triangular prism. Each base is a right triangle such that the sides forming the right angle are labeled 7 m and 24 m, and the remaining side is labeled 25 m. The distance between the bases is 20 m.
Answers
The surface area of the right triangular prism shown is 1288 m²
What is an area?
Area is the amount of space occupied by a two dimensional shape or object.
The prism has a triangular base with 24 m and height of 7m..
The surface area of the prism = 2(0.5 * 24 * 7) + (25 * 20) + (20 * 7) + (24 * 20) = 1288 m²
The surface area of the right triangular prism shown is 1288 m²
Find out more on area at: https://brainly.com/question/25292087
8 x 8 x 8 x 8 using an exponent
Answers
Since 8 is multiplied 4 times
Hey there!
We have
8×8×8×8
Let's write it using an exponent.
8=8¹
8×8=8²
8×8×8=8³
8×8×8×8=8⁴
So we multiplied 8 times itself 4 times (that's why the exponent is 4)
Hope everything is clear.
Let me know if you have any questions!
#ILoveLearning
:-)
(First to answer CORRECTLY gets brainliest!)The Mayflower Compact could best be described as a/an...
a
basic agreement requiring colonists to obey Virginia law.
b
early attempt at self-government in the English colonies.
c
detailed list of reasons why the Pilgrims left England for the United States.
d
trade contract between Great Britain and merchants in the Virginia colony.
Answers
Answer:
b, early attempt at self-government in the English colonies.
The volume of this triangular prism is 32 cubic inches. What is the value of d?
Answers
Answer:
Divide the volume by the length of the prism to get the area of the face:
468/13 = 36 square yards.
The area of the face ( triangle) is 1/2 x base x height
Replace with what you have:
36 = 1/2 x 9 x g
Multiply both sides by 2 to remove the 1/2:
72 = 9 x g
Divide both sides by 9 to find g:
g = 72 /9
g = 8 yards.
please help me!! Look at the picture! Please!!!!
Answers
Answer:
First let's find how much money the 4% is.
4/100 x 180 = $7.20
Now we add that sales tax to the cost of the telescope;
180 + 7.20 = $187.20, is what she'll pay in total.
Can anyone please help me!! D: :D
Answers
Answer:
4
Step-by-step explanation:
18/6=3
24/6=4
42/6=7 ...
What is the area of this parallelogram?
Please help :)
Answers
Answer:
D
Step-by-step explanation:
Remark
We will change the dimensions to decimals
h = 3 7/8 = 3.875
b = 6 1/2 = 6.5
Formula
Area = h * b
Solution
Area = 3.875 * 6.5
Area = 25.1875
0.1875 = 3/16
Answer: Area = 25 3/16
Answer: D
How is y = x + 4.5 related to y = x ?
Answers
Answer: the graphs of the two lines are ||.
Step-by-step explanation: Notice that in this problem, we have
the parent graph y = x and the equation y = x + 4.5.
Notice that both of these equations have the same slope.
When two equations have the same slope and
have different y-intercepts, the lines are ||.
Answer :it related because it is a slope form.
Step-by-step explanation:
good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.
Answers
Answer:
2x² - 12 + 8x
Setting up the equation:
Let that [SOMETHING] be L
⇒ 3x² + 8x - 16 - (L) = x² - 4To avoid confusion, let's use parenthesis:
⇒ (3x² + 8x - 16) - (L) = (x² - 4)Simplifying the equation:
Subtract "(3x² + 8x - 16)" both sides to isolate "(L)":
⇒ (3x² + 8x - 16) - (3x² + 8x - 16) - (L) = (x² - 4) - (3x² + 8x - 16)⇒ -(L) = (x² - 4) - (3x² + 8x - 16)Take the "-" in the parenthesis:
⇒ -(L) = (x² - 4) + (-3x² - 8x + 16)Open the parenthesis:
⇒ -L = x² - 4 - 3x² - 8x + 16Combine like terms and simplify:
⇒ -L = x²(1 - 3) + (-4 + 16) - 8x⇒ -L = x²(-2) + (12) - 8x⇒ -L = -2x² + 12 - 8xPut both terms in parenthesis:
⇒ -(L) = (-2x² + 12 - 8x)Multiply both sides by -1:
⇒ (L) = -(-2x² + 12 - 8x)⇒ L = 2x² - 12 + 8xThus, the [SOMETHING] is 2x² - 12 + 8x.
Answer:
[tex]2x^2+8x-12[/tex]
Step-by-step explanation:
[tex]P=3x^2+8x-16[/tex]
[tex]= x^2-4[/tex]
The Quantity Subtracted
Let the Quantity be called "y"
[tex]P=y\\3x^2+8x-16-y=x^2-4[/tex]
Bring together like terms
[tex]y= 3x^2-x^2+8x-16+4\\y= 2x^2 + 8x-12[/tex]
is this relation A function? (a lot of points i’ll give)
Answers
Ecologists measure the body length and wingspan of 127 butterfly specimens caught in a single field.
Answers
The wingspan of 127 butterfly specimens is an illustration of the line of best fit
The equation of the line of best fit is y = 3xThe slope means that as the wingspans increase and lengths of these butterflies increaseHow to determine the equation of the line?From the line of best fit of the graph (see attachment), we have the following points
(x,y) = (0,0) and (20,60)
Since the line passes through the origin, the equation of the line would be:
[tex]y = \frac{y_1}{x_1} * x[/tex]
So, we have:
[tex]y = \frac{60}{20} * x[/tex]
[tex]y = 3x[/tex]
Hence, the equation of the line of best fit is y = 3x
Interpret the slopeIn (a), we have the slope to be:
Slope = 3
The slope (3) is greater than 0.
This means that as the wingspans increase and lengths of these butterflies increase
Read more about line of best fit at:
https://brainly.com/question/17261411
39.4 is what percent of 64 round to the nearest 100
Answers
Answer:61.7
Step-by-step explanation:
maths
Answer:
61.56%
Step-by-step explanation:
Find 39.4 out of 64 as a decimal:
Convert decimal to percent:
0.615625 × 100 = 61.5625% (Move decimal 2 places to the right)
61.56% (Round to the nearest hundredth)
The price of a gallon of gasoline dropped by $0.08 on Wednesday and by 0.25 of that amount on Thursday. Which best represents how the price of a gallon of gasoline changed on Thursday? –0.32 –0.02 0.02 0.32
Answers
Answer:
- 0.32
Step-by-step explanation:
because if you add 0.08 and 0.25 you get 0.32 but then you are subtracting that from the original price so I think it would be - 0.32
Answer:
-0.32
Step-by-step explanation:
I just answered that question
What is an equation of the line that passes through the points (5, -3) and
(-3, -3)?
Answers
Answer:
y= - 3
Step-by-step explanation:
note that the y- coordinates of both points are - 3
This indicates the line passing through them is a horizontal line, parallel to the x- axis with equation
y = c ( c is the value of the y- coordinates the line passes through ), that is
y = - 3
Cameron wants to buy a new bike that costs $112. He is saving $8 per week. How many weeks will it be until Cameron has all the money he needs to buy the
bike
Answers
the answer is 14
Step-by-step explanation:
Sebastian goes out to lunch. The bill, before tax and tip, was $8.75. A sales tax of 5% was added on. Sebastian tipped 17% on the amount after the sales tax was added. How much tip did he leave? Round to the nearest cent.
Answers
Answer:
1.56
Step-by-step explanation:
just do 8.75x1.05, then multiply that number by .17.
please mark as brainlest.
1) Explain what opposite reciprocals means. Then explain how it is important/relevant in geometry.
Answers
Answer:
Step-by-step explanation:
a
Opposite means add a negative sign in front of it.
The opposite of 6 is -6,
7 --> -7,
-10 --> 10.
Reciprocal means flip it.
Reciprocal of 6 is 1/6
of 7 is 1/7
of -10 is -1/10
Opposite reciprocal means add a negative sign AND flip it.
6 --> -1/6
7 ---> -1/7
-10 --> 1/10
In geometry, perpendicular lines on a graph have opposite reciprocal slopes.
4x + 6+ 3= 17
Show answer
Answers
Answer:
x= 2
Step-by-step explanation:
4x+6+3=17
4x+9=17
-9 -9
4x= 8
4x/4 = 8/4
x= 2
Hope this helps!
6. Solve the equation x2 = 80.
Answers
Answer:
x=4√5
Step-by-step explanation:
An equation is formed of two equal expressions. The value of x in the given equation is ±4√5.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given equation can be solved for x as shown below,
x² = 80
x² = 2×2×2×2×5
x = √(2×2×2×2×5)
x = ± 4√5
Hence, the value of x in the given equation is ±4√5.
Learn more about Equation here:
https://brainly.com/question/14686792
#SPJ2
Another model rocket is accelerating at a rate of 3m/s squared with aforce of 1N. What is the mass of the rocket? plssssss hurry!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! like right now plss
ty
Answers
Answer:
0.33333333333e3
Step-by-step explanation:
e = infinity
Bianca took out a $2,600 unsubsidized stafford loan. she will be attending school for four years, and she wishes to have the loan paid off five years before its normal ten-year duration is finished. the loan has an interest rate of 6.2%, compounded monthly. how much will she have to pay monthly to avoid interest capitalization? a. $12.40 b. $19.29 c. $13.43 d. $17.36
Answers
The total amount Bianca has to pay monthly to avoid interest capitalization is $13.43.
What is compound interest?Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.
The formula for the final amount of annual payment is given as,
[tex]A_p=P\times\left(\dfrac{r}{1-1+r}\right)^t\\[/tex]
Here, P is principal amount, the rate is r and time period is t.
Bianca took out a $2,600 unsubsidized stafford loan. She will be attending school for four years, and she wishes to have the loan paid off five years before its normal ten-year duration is finished.
Total months in ten years,
[tex]t=10\times12\\t=120[/tex]
The loan has an interest rate of 6.2%, compounded monthly. The interest rate is,
[tex]r=0.062[/tex]
Put the values in the above formula as,
[tex]A_p=(2600)\times\left(\dfrac{0.062}{1-1+0.062}\right)^{120}\\A_p=161.32[/tex]
Total payment paid by her in 1 year of time is,
[tex]M_p=\dfrac{161.32}{12}\\M_p=13.43[/tex]
Thus, the total amount Bianca has to pay monthly to avoid interest capitalization is $13.43.
Learn more about the compound interest here;
https://brainly.com/question/24274034