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: $x + y + z$
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!
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS
Answer:
(6, 5)
step-by-step explanation:
original coordinates of B: (-4, -5)if translated horizontally there will be change in x axis.
new coordinates: (-4+10, -5) → (6, -5)if reflected over x-axis, use the formula: (x, y) → (x, -y)
new coordinates: (6, 5)find the simple intrest on rs 1200 at 5%per annum for 2 years
Answer:
Rs.120
Step-by-step explanation:
given,
Principal (P) = Rs.1200
Time (T) = 2 yrs
Rate (R) = 5%
Simple interest = ?
solution,
simple interest = PTR/100
= Rs.1200*2*5/100
= Rs.12000/100
= Rs.120
Therefore,the simple interest is Rs.120.
someone help me with this !!
You invest $700 earning 6% interest each year.
Write an equation showing how much money is in your
account each year.
A)f(x) = 700 + 6x
B)f(x) = 700 -0.06%
C)f(x) = 700 - 1.06%
D)f(x) = 700 - 1.6%
Answer:
700+1.06
Step-by-step explanation:
Slope of x 15 17 19 21 y -10 2 14 26
Answer:
6
Step-by-step explanation:
the xs increase by 2 and the ys increase by 12 12/2 is 6
Summary What is an example of a sequence of transformations that, if performed in a different order-would result in a different image?
Answer:
an architect used the same floor plans in different locations and orientations to complete the layout of a housing complex.
Step-by-step explanation:
uwu
pls answer i will mark u brainlist
What is the value of m in the equation 5m − 7 = 6m 11? 18 1 −18 −1.
Answer:
-7 = m
Step-by-step explanation:
5m − 7 = 6m
Subtract 5m from each side
5m-5m − 7 = 6m-5m
-7 = m
1.2x + 4.8y = 18 where does the graph intersect the y and x axis
Answer:
X-intercept: 15,0
Y-intercept: 0,3.75
Step-by-step explanation:
In your own words, explain why when we multiply terms that have the same bases, we add the exponents.
When multiplying exponents, remember the first rule: when multiplying similar bases, add powers together. 52% + 56% =? The bases of the equation remain unchanged, while the exponents' values are added together. Adding the exponents is only a quick way to get at the answer. Simply add the exponents to multiply exponential expressions with the same base. Simplify. The product rule applies because the base of both exponents is a. With a common basis, add the exponents.
The area of the triangle below is 4.14 square inches. What is the length of the buse?
Answer:
3.6
Given:
are of triangle=4.14
height=2.3
Step-by-step explanation:
area of the triangle=1/2 × base × height
4.14 = 1/2 × base × 2.3
4.14 = 2.3/2 × base
by cross multiplying,
4.14 × 2 = 2.3 × base
8.28 = 2.3 × base
8.28/2.3 =base
To remove the decimal point, multiply with 100 in both numerator and denominator
8.28×100 / 2.3×100 = base
828/230 = base
base = 3.6
hope it helps you!
Answer:
3.6 inches.
Step-by-step explanation:
Area = 1/2 * base * height
4.14 = 1/2 * base * 2.3
1/2 * base = 4.14 / 2.3
base = 4.14 * 2 / 2.3
= 3.6.
Hi! Do any of you know how I can solve this exercise?? I know the final result is 2, but I'm not sure what I have to do to get to that answer
Answer:
Step-by-step explanation:
( 0.5 )³ × [tex]2^{4}[/tex] = ( 0.5 × 2 )³ × 2 = 1³ × 2 = 2
Can you find the PERIMETER of this shape pls
Answer:
25.7 m
Step-by-step explanation:
Hello!
We have two sides each measuring 5m, so the length of the straight edges is 2(5m) or 10m
We also have two identical semi-circle circumferences, so if we find the circumference of the whole circle, we can find the total length of the curved edges.
C = 2πrC = 2(3.14)(2.5)C = 5(3.14)C = 15.7Now, we can add up the two lengths:
Perimeter = straight sides + curved sidesPerimeter = 10m + 15.7mPerimeter = 25.7mall four sides of the baseball diamond are 90 ft long.
if you ran in a straight line from first base to third base, what would the distance be rounded to the nearest whole number?
a. 13 feet
b. 16,200 feet
c. 127 feet
d. 180 ft
Answer:
d. 180 ft
Step-by-step explanation:
Answer:
well that will be 180ft
Step-by-step explanation:
Can anyone solve this please? ASAP
Answer:
5a) 4
5b) 4
Step-by-step explanation:
You'll use Pythagorean theorem throughout this problem a lot. So, to find X, You have a right triangle with one leg of 6, and one leg of 2. 2 squared plus 6 squared equals c squared. 4 + 36 = c squared then you get 40 = c squared.
To get c by itself you'd square root both sides. So that leaves you with X = the square root of 40.
Now, to get Y, you have another triangle with a leg of 4, and another leg of the square root of 40. 4 squared = 16, and the square root of 40 squared is just 40. So, 16 + 40 = c squared. 56 = c squared, then again, to get the c value by itself you need to square root both sides, leaving you with Y = the square root of 56.
Hey I really need help with metric conversions test is tomorrow.
What are the coefficient(s) in the expression: 3x+2r-7
Answer:
3
Step-by-step explanation:
Hunter kicked a soccer ball. The ball went 332 yards in 38 second. At that rate, how far would the ball go in 1 second?
The distance that he would the ball go in 1 second will be 8.8 yards.
How to calculate the rate?From the information, Hunter kicked a soccer ball. The ball went 332 yards in 38 second.
Therefore, at that rate, the distance that he would the ball go in 1 second will be:
= Total distance / Time
= 332 / 38
= 8.8 yards.
Learn more about rate on:
brainly.com/question/25793394
#SPJ1
Write as many expressions as you can for
this picture:
How do u do this
Martin bikes at a constant speed to a finish line that is 15 mi away. After 20 mins, he is 10 mi from the finish line. After 30 mins, he is 7.5 mi from the finish line. If a graphics shows his distance y from the finish line, in miles, after x minutes, what is the slope of the graph, and what does it represent? A) 15; Martin’s initial distance from the finish line. B) 15; Martin’s final distance from the finish line. C) -0.25; the rate at which Martin’s distance from the finish line changes per minute. D) -0.25; the rate at which Martin’s distance from the start line changes per minute
Answer:
I believe the answer would be C
????? ????? ????? ????? ???? ??
Solution:
We know that:
The base angles are equivalent.This means that:
This triangle is an isosceles triangle.The legs of the triangle are equivalent.Let's use Pythagoras theorem to find z.
Finding z using Pythagoras theorem.
[tex](8\sqrt{x} )^{2} = z^{2} + z^{2}[/tex]⇒ [tex](8\sqrt{x} )( 8\sqrt{x} ) = 2z^{2}[/tex]⇒ [tex](8)(8)(2)= 2z^{2}[/tex]⇒ [tex](8)(8)= z^{2}[/tex]⇒ [tex]64= z^{2}[/tex]⇒ [tex]\sqrt{64} = \sqrt{z^{2}}[/tex]⇒ [tex]8 = z[/tex]Thus, the value of z is 8.
whoever can figure this our for my ill give u brainlist :)
Answer:
16 hours
Step-by-step explanation:
Given:
Time Mary spends on math homework per week: 2 2/3 hoursTime Mary spends on art homework per week: 3 1/3 hoursTherefore, time spent on both homeworks over 4 weeks:
= 4 × (math homework + art homework )
[tex]=4(2 \frac23+1\frac13)[/tex]
[tex]=4\left(\dfrac83+\dfrac43\right)[/tex]
[tex]=4\left(\dfrac{12}3\right)[/tex]
[tex]=4(4)[/tex]
[tex]=16 \textsf{ hours}[/tex]
PlS can anyone help me ASAP
Answer:
yo what is that
Step-by-step explanation:
Write an equation of a line that passes through the point (0,-2) and is perpendicular to the image shown.
options:
y= 3x −2
y= −1/3x − 2
y= 1/3x
y= 3x − 10
Answer:
Brainliest Answer would be appreciated. Option 1 is the best
Step-by-step explanation:
The slope of the line on the graph is -1/3. A perpendicular line's slope is always the negative reciprocal of it, so your slope of the perpendicular line would be 3.
Also, since you are passing through the point (0, -2), -2 would be your y-intercept, making your equation for the perpendicular line y = 3x - 2.
Which of the following is the measure of the largest angle in the triangle shown?
19x + 7x + 10x = 180°
36x = 180
x = 5°
largest angle = 19 * 5 = 95°
Answer:
C. 95°
Step-by-step explanation:
19x+ 7x +10x = 180 (sum of the interior angles of a triangle is 180)
36x = 180
x= 180÷36
x= 5
Magnitude of the largest angle
= 19× x
= 19× 5
= 95
14x + 28y + 21 what is this factored?
Answer:
7(2x + 4y + 3)
Step-by-step explanation:
Find a common factor between all of the terms. In this case, it is 7, so divide all three numbers by 7. Put the 7 on the outside of the parentheses and put the divided numbers, with the correct signs and variables, inside the parentheses.
What is the length of bd
Answer:
B
Step-by-step explanation:
I would use the Pythagorean theorem to solve distances between 2 points, and this case is no exception.
We need to find the positive difference in their x coordinates and y coordinates.
The difference in x coordinates: 7
The difference in y coordinates: 8
Now we can use the Pythagorean theorem:
7^2+8^2 = x^2
49+64 = x^2
113 = x^2
x = sqrt(113)
Therefore, the answer is B.
Cesar y Ana reciben uuna cuerda de igual longitud.Cesar corta 40/100 de su cuerda para jalar un paquete mientras que Ana corta 9/25 para amarrar dos maletas¿quien usa mayor longitud de cuerda?,justifica
César ha cortado el segmento de cuerda de mayor longitud para amarrar una maleta.
Cómo determinar el segmento más largo utilizado de cuerdas
Una fracción es un número real formado por dos números enteros, un numerador y un denominador, respectivamente.
En esta pregunta debemos determinar quien tiene la mayor longitud de cuerda y para ello debemos aplicar propiedades tal que ambas fracciones tengan el mismo denominador. En consecuencia, la persona que tendría la mayor fracción tendría además el mayor numerador. A continuación, procedemos a realizar las siguientes operaciones:
40/100, 9/25
Al dividir cada término de la primera fracción por 4, tenemos lo siguiente:
10/25, 9/25
Por tanto, César ha cortado el segmento de cuerda de mayor longitud para amarrar una maleta. [tex]\blacksquare[/tex]
Para aprender más sobre fracciones, invitamos cordialmente a ver esta pregunta verificada: https://brainly.com/question/24570029
hi i will give a lot of points please help tho
Answer:
the answer is x=7
Step-by-step explanation:
trust me or you will go bald
3(q - 7) = 27
Solve for q
Answer:
3(q-7)=27
3q-21=27
3q=48
q=16
Step-by-step explanation:
please pass this on... ( #helpsavelives )
Who ever is reading this:
I love u.
U matter.
The world needs u
hang in there ik it may be bad but u deserve the world <3
ur beautiful no matter ur shape, size, color, gender.. anything
don't give up i need u to live.
i wish i could take everyones problems so yall wouldn't have to have em but i cant so just know ily and if anyone needs to talk u can talk to me
Pls pass this on. Everyone deserves to know this. ♥️♥️
just copy and paste its not hard pls this could save someones life
Answer:
q = 16
Step-by-step explanation:
3(q - 7) = 27
3q - 21 = 27 | +21
3q = 48 | :3
q = 16