Answer:
Step-by-step explanationAl final de esta lección, debes ser capaz de:
Reconocer una relación de variación directa
Encontrar la fórmula de una relación de variación directa
Resolver problemas verbales asociados con variaciones directas
Introducción
x = Horas Trabajadas 0 1 2 3 4
y = Dólares Ganados 0 3 6 9 12
La tabla anterior muestra la relación entre las horas trabajadas y el dinero en dólares, que obtuvo Juan trabajando a razón de $3.00 por hora. En esta tabla, podemos ver que el dinero ganado es igual al producto de las horas trabajadas por 3. Otra manera de decir eso es que la constante de variación o proporción es igual o 3. También se puede observar que cada vez que x aumenta en un 1, la variable y aumenta en 3. Otra manera de decir eso es que la razón de cambio es igual a 3.
En la aplicación de abajo, mueve el botón de la barra “constante de variación” a 3. Observa que los puntos de la gráfica coinciden con los valores en la tabla, y que con cada aumento de 1 en x, la variable y aumenta 3 y que la relación entre las variables es y = 3 × x .
Lo sentimos, pero la GeoGebra Applet no se pudo iniciar. Por favor, asegzrese de que Java 1.4.2 (o posterior) esta instalado y activo en su navegador ( Haga clic aqum para instalar Java ahora )
Cajas de Leche 0 1 2 3 4
Botellas de Leche 0 4 8 12 16
Si cada caja de leche contiene 4 botellas, la tabla anterior muestra la relación entre el número de cajas de leche y el número de botellas que contienen. En esta tabla, podemos ver que el número de botellas de leche se obtiene multiplicando el número de cajas de leche por 4.
En la aplicación de arriba, mueve el botón de la barra constante de variación a 4. Observa que los puntos de la gráfica coinciden con los valores en la tabla, y que con cada aumento de 1 en x, y aumenta 4 y que la relación entre las variables es y = 4 × x.
.
Cantidad de dólares 0 1 2 3 4
Cantidad de galletas que se puede comprar 0 2 4 6 8
Si una galleta cuesta 50 centavos, la tabla anterior muestra la relación entre la cantidad de dólares y la cantidad de galletas que se puede comprar. En esta tabla, podemos ver que la cantidad de galletas se obtiene multiplicando la cantidad de dólares por 2.
En la aplicación de arriba, mueve el botón de la barra constante de variación a 2. Observa que los puntos de la gráfica coinciden con los valores en la tabla, y que con cada aumento de 1 en x, la variable y aumenta en 2 y que la relación entre las variables es y = 2 × x
.
En todas estas relaciones de los ejemplos anteriores, una variable es igual a otra variable multiplicada por una constante distinta de cero. Estas relaciones se conocen como proporciones directas o variaciones directas.
Definición
Dadas dos variables x y y, los enunciados:
y varía directamente como x,
y es directamente proporcional a x y
y es proporcional a x
todos significan que y = kx, para algún número real fijo k.
Al número k se le llama la constante de variación o constante de proporcionalidad. El valor de k también representa la razón de cambio de la relación. Es decir, cada aumento de 1 en x va a corresponder a un aumento de k en y.
Pasos para hallar la Fórmula para Relaciones de Variación Directa
Las relaciones de variación directa tienen la forma y = kx donde x y y son variables y k es una constante distinta de cero. La fórmula para una relación de variación directa se puede hallar mediante los siguientes pasos:
Paso 1: Traducir el enunciado a una fórmula de variación directa.
y es directamente proporcional a x significa
y =k·x
Paso 2: Sustituir las variables conocidas para encontrar k.
Paso 3: Sustituir k y escribir la fórmula.
Ejemplos
Ejemplo 1
u es proporcional a v. Si u = 16 cuando v = 4, escribe la fórmula para la relación entre u y v.
Paso 1: Traducir el enunciado a una fórmula de variación directa.
u es proporcional a v significa
u =k·v
Paso 2: Sustituir valores conocidos para encontrar k.
16 = k· 4
k=164=4
Paso 3: Sustituir k y escribir la fórmula.
u =4v
Conclusión: la fórmula para expresar la relación entre u y v es u =4v
Ejemplo 2
p varía directamente como z. Si p = 210 cuando z = 200, escribe la fórmula para expresar la relación entre p y z .
Paso 1: Traducir el enunciado a una fórmula de variación directa.
p varía directamente como z significa
p = k·z
Paso 2: Sustituir valores conocidos para encontrar k.
210 = k· 200
k=210200=1.05
Paso 3: Sustituir k y escribir la fórmula.
p =1.05z:
Answer:
A, B, D, F On edge!
Step-by-step explanation:
Have a good day! :3
The graph of the line y = 5x + 7 would cross what number on
the y-axis? How do you know?
Answer: 7
Step-by-step explanation: 7 is the y intercept in the slope intercept form. y=slopex+y-intercept
The graph shows a system of equations:
Draw a line labeled y equals x plus 4 by joining the ordered pairs negative 4, 0 and 1, 5. Draw a line labeled 3 times y equals minus 2 x plus 2 by joining the ordered pairs negative 2, 2 and 4, negative 2.
What is the solution to the system of equations?
(−2, 2)
(2, 2)
(2, −2)
(−2, −2)
Answer:
I'm putting C but I'm not sure ill let you know if its right after the test
Step-by-step explanation:
Answer:
Its A- (-2,2)
Because the solution is where the two lines collide and meet. :)
A proportional relationship is linear.
True or False
Answer:
True
Step-by-step explanation:
Yes, A proportional relationship is linear.
Please help I need help please
Step-by-step explanation:
There are 84% out of 225. First find 10%. To do that divide the number by 10, so 225 ÷ 10 = 22.5 Next, do 22.5 x 8. Then you have 80%. Now, all that is need ed is the 4%. To get that, divide 225 by 100. Multiply the answer by 4 to get the 4%. Add the 80% and the 4% to get your answer. I really hope this helps. answers
Also, since I am just helping, I am un able to give you straight answers. I hope this also helps with work in the future.
Shela has $89 in her bank account. If she uses 30% of her money how mutch was the bill
Step-by-step explanation:
Sheila has $89 in her bank account original orihinally We want to determine the amount of money which she used to pay percentage a bill. This amount is expressed in terms of percentage of the original amount which she had in her bank.
She uses 30% of her money to pay a bill. Therefore, the amount she used to pay the bill =
30/100 89 = 0.3 ×89
= 26.70.
So Are Answer is 26.70
Two men are decorating a room. One has painted 20 m² and the
other only 6 m². They continue painting and manage to paint
another x m'each. If the first man has painted exactly three times
the area painted by the second man, find the value of x.
Answer:
1 m²Step-by-step explanation:
The first man painted:
x + 20The second man painted:
x + 6If the first man painted 3 times more, then:
x + 20 = 3(x + 6)x + 20 = 3x + 183x - x = 20 - 182x = 2x = 1A local appliance store advertised a “10% off sale” on ovens. Mrs. Jones found an oven she liked that cost $560 before the sale. What is the sale price of the oven?
a
$56.00
b
$504.00
c
$500.00
d
$616.00
#2 AND #4 PLEASE HELP!!
Answer and Step-by-step explanation:
For question number 2.
First, draw a triangle. Now label each angle with the letter N, O, and M.
M
/\
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/____________________________\
N O
Now, we see line NO. The angles that include line NO would be angle MNO and angle MON.
For question number 4:
We can see that there is a tick mark on side AC and side DF, meaning those two sides are congruent.
We then see that angle A is congruent to angle D, since there is that little curve mark, showing they are congruent.
Last, we see that they both triangles have 90 degree angles, shown with the square on the corner of the triangle..
Using the AAS Postulate (Angle Angle Side), we can say that triangle ABC is congruent to triangle DEF.
#teamtrees #WAP (Water And Plant) #ELM (Every Life Matters)
write and solve this equation: Samantha is one year less than twice her brother Jack’s age. If the sum of their ages is 41, how old is Samantha?
Answer:
Samantha's age = 27 years
Step-by-step explanation:
Let Jack's age be = xAs Samantha is one year less than twice her brother Jack’s age.
So Samantha's age = 2x-1As the sum of their ages is 41.
Thus, the equation become
x+2x-1 = 41
3x-1 = 41
3x = 42
Dividing both sides by 3
x = 14
It indicates that Jack's age = 14 years
Therefore,
Samantha's age = 2x-1 = 2(14)-1 = 27 years
the quotient of y and 221 is equal to 21
Answer: the answer is 10.54 I think
Step-by-step explanation:
In a unit circle, ø = 270º. Identify the terminal point and sin ø.
A. Terminal point (0,-1); sin Ø=-1
B. Terminal point (0,-1); sin ø= 0
C. Terminal point (-1,0); sin Ø=-1
D. Terminal point (-1,0); sin Ø=ø
Using the trigonometric circle, it is found that the correct option regarding the terminal point and sin ø is given by:
A. Terminal point (0,-1); sin Ø=-1
What is the trigonometric circle?It is a circle of radius 1 that contains the following set of points:
[tex](x,y) = (\cos{(\phi)}, \sin{(\phi)})[/tex]
The sine of 270º is of -1, hence the cosine is 0, which means that the correct option is:
A. Terminal point (0,-1); sin Ø=-1
More can be learned about the trigonometric circle at https://brainly.com/question/24349828
The terminal point and sin ø are (0,-1) and sin Ø=-1.
What is the trigonometric circle?It is a circle of radius 1 unit.
The sine of 270º is of -1, hence the cosine is 0, which means that
Terminal point (0,-1); sin Ø=-1
Thus, the correct option is A.
Learn more about the trigonometric circle
https://brainly.com/question/24349828
#SPJ5
Your bill at a restaurant is $36.00. How much tip should you leave if the average amount for a tip
is 15%?
Pls help meh
Answer:
I'de say about 5.40$ would be a good 15% tip
Step-by-step explanation:
Answer:
5.40
Step-by-step explanation
HELP! i need this done in 20 min
Answer:
No because when you divide a whole number by a fraction you always get a quotient that is smaller than the whole number.
Step-by-step explanation:
Answer:
Idk They are right
Step-by-step explanation:
Look a person on top and Give them them Big B
40 POINTS THERE IS MORE THAN 1 ANSWER BRAINLIEST IF CORRECT
Which of the following statements are true regarding the direction of a number? Select all that apply.
A.It is the absolute value of the number.
B.A negative direction is to the left of zero on a horizontal number line.
C.Numbers have no direction.
D.A positive direction is to the right of zero on a horizontal number line.
Answer:
Whole numbers are also integers. There are other integers which are the opposites of the whole numbers (−1, −2, −3, ...). These negative numbers lie to the left of 0 on the number line. Integers are the whole numbers and their opposites.
Find the values of w, x and y.
Answer:
w= 27.47 degree
x=9.99 cm
y=12.02 cm
Step-by-step explanation:
The value of w:
In a right-angled triangle [tex]\tan \theta = \frac {\text{Perpendicular}}{\text{Base}}[/tex]
[tex]\tan w = \frac {\text{Perpendicular}}{25+9}\;and \; \tan 63 = \frac {\text{Perpendicular}}{9}[/tex]
So, [tex]34 \tan w = 9\tan (63)[/tex]
[tex]\tan w = (9/34)\tan(63)=0.52 \\\\w=\tan^{-1}(0.52) \\\\[/tex]
w= 27.47 degree
The value of x:
In a right-angled triangle [tex]\sin \theta = \frac {\text{Perpendicular}}{\text{Hypotaneous}}[/tex]
sin (27) =x/22
x= 22sin(27)
x=9.99 cm
The value of y:
By using Pythagoras theorem,
[tex]y^2+y^2=17^2 \\\\2y^2 = 289 \\\\y^2 =289/2= 144.5 \\\\y=\sqrt {144.5} \\\\[/tex]
y=12.02 cm
GUYS URGENT PLS HELP
V= πr^2h = cylinder volume equation
V=4 /3 πr^3 = volume of the shpere
use the equation and add them up
PLEASE HELP!!! ILL GIVE BRAINLIEST!
Answer: Last Option (Red In Colour)
Reason: Since Point Slope Form is y -y1 = m(x-x1), We just plug in the numbers. Four will go into the x1 spot, and Zero will go into the y1 spot, and 1/2 in the m spot since it's the slope. So, after plugging everything in, the equation is y - 0 = 1/2 ( x- 4)
I hope this helps, and Happy Holidays! :)
Help!!!! This is for math
За + 16 = 5а
PLEASE HELP
Answer:
8 = a or a = 8
Step-by-step explanation:
3a+16=5a
-3a -3a
16= 2a
/2 /2
8=a
Answer:
a = 8
Step-by-step explanation:
In kite ABCD, mZBAE = 28º and mZBCE = 58°. Find mZABE.
B
E
А
С
D
mLABE =
Answer:
m∠ABE = 62°
Step-by-step explanation:
Since, the given quadrilateral is a kite, diagonals will intersect at 90°.
Therefore, m∠AEB = m∠CEB = 90°
m∠BAE = 28° [Given]
m∠BCE = 58° [Given]
From ΔABE,
m∠BAE + m∠BEA + m∠ABE = 180°
28° + 90° + m∠ABE = 180°
m∠ABE = 180° - 118°
= 62°
Therefore, measure of angle ABE = 62°.
Help!!
Find the solution of this system of equations
x- 10y = -59
-4x + 10y = 86
Answer:
x - 10y = -59
(+)-4x + 10y = 86
-3x = 27
x = -9
substitute x into x - 10y = -59
-9 -10y = -59
-10y = -50
y = 5
pls help !!!!!! i need the answer for this pleasee <33
Answer:
slope- intercept form is
y=mx+b
m= slope
b= y-int
looking at the chart we can see that the graph goes up 11 and right 6
so we now have
y= 11/6x+b
we could also do
m=(y2-y1)/(x2-x1) using our points
m=(21-10)/(-3-(-9)
m=11/6
then we can use an x value and its corresponding y value from the equation to find b
I will use the points -9,10
10= 11/6(-9)+b
10=-16.5+b
+16.5 +16.5
26.5=b
so your full equation is:
y=11/6x + 26.5
Step-by-step explanation:
complete the table i’ll give brainliest
Answer:
1. 4
2. 11
3. 18
4. 25
Step-by-step explanation:
9[15-(3+4)] I don’t know how to do this problem and Photomath can’t solve it either
Answer:
72
Step-by-step explanation:
9[15-(3+4)]
9[15-7]
9[8]
72
10m^5n^4/15m^2? Can someone help me
Answer:
2m^7n^4/3
Step-by-step explanation:
Assume y varies directly with x. If y = 80
when x = 8, find x when y = 40.
Answer:
4
Step-by-step explanation:
I JUST NEED HELP PLZZ
AND THANK YOU
Answer:
43
Step-by-step explanation:
Based on the pattern of the scatter plot, 43 seems to be the better option.
helpppp ahhhhhhh plz
Answer:
It's Parallel
Step-by-step explanation:
Perpendicular have to intersect
Can someone pretty pls help
Answer:
3÷4 = 0.75
Step-by-step explanation:
We are to find:
3÷ 4
3÷4 =
= 3 ÷ 4
= 3 × 1/4
= 3 × 0.25
= 0.75
How many solutions does the system of equations below have?
5
5
у
3
3
3
y = x
3
no solution
one solution
infinitely many solutions