Determining Points on a Line Given a Direct Variation
y
x
y
What other points are on the line of direct variation through
(5, 12)? Check all that apply.
(0,0)
(2.5, 6)
36
32
28
24
(3, 10)
(7.5, 18)
20
18
(12.5, 24)
12
00
(15, 36)
x
Draw
8
12
10
Click or tap the graph to plot a point.
Tone
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 .
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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
What is the constant rate of change between the values of x and y in the table?
The answer is -3/2. ( I used the formula y/x)
jasmine deals 2 cards. whats the probability of dealing 2 hearts in a row if she didn't replace the card after it was dealt?
WILL GIVE BRAINLIEST FOR CORRECT ANSWER
pOiNtS gIvE aWaY i DoNt HaVe MuCh BuT hErE yA gO
Answer:
Gracias generous mane •‿•
Step-by-step explanation:
Answer:yes
Step-by-step explanation:
Diagram shows the distance-time graph of teo cars. FGHI shows the journey of car J from town K to town L. MGN shows the journey of car P from town L to town K. When did the two cars meet?
Answer:
1100 is when the two cars met
Step-by-step explanation:
the two lines intercept at 1100, 60km
Which statement is true? CLEAR CHECK 0.25 = 14 because 25100 = 14 0.20 = 2010 because 0.20 means 20 tenths 0.23 > 12 because 0.23 = 23 0.4 = 14 because they are on the same place on a number lin
Answer:
because 25/100 = 1/4
0.20 = 20/100
Step-by-step explanation:
because 25/100 = 1/4
0.20 = 20/100
because 0.20 means 20 tenths 0.23 > 1/2
because 0.23 = 23
0.4 = 1/4
because they are on the same place on a number lin
Clare analyzes oil prices in her economics class. She finds that the mean oil price between 1988 and 2002 is $27 per barrel with a standard deviation of $5.50 per barrel. Select the z-score for a price of $35.25 per barrel. (Select one answer)
0.67
1.5
8.25
-8.25
Answer:
Option 2: 1.5 is the correct answer.
Step-by-step explanation:
Given information is:
Mean = μ = $27
SD = σ = $5.50
A z-score simply tells us how far a selected data value from the mean is.
Z-score is denoted by z and is given by the formula:
[tex]z = \frac{x-mean}{SD}[/tex]
Let x = $35.25
Putting the values of mean and SD we get,
[tex]z = \frac{35.25-27}{5.50}\\z = \frac{8.25}{5.50}\\z =1.5[/tex]
The value of z-score for a price of $35.25 per barrel is 1.5
Hence,
Option 2: 1.5 is the correct answer.
A rectangular pool has a sidewalk around it. The pool measures 6 feet by 10 feet and the total area of the pool and sidewalk is 96 square feet. What is the width of the sidewalk?
Answer:
width of the sidewalk = 1 feet
Step-by-step explanation:
Area of the pool = length × width
Length = 10 feet
Width = 6 feet
Area of the pool = length × width
= 10 feet × 6 feet
= 60 feet²
Area of the pool = 60 feet²
Total area = Area of the pool + Area of sidewalk
96 feet² = 60 feet ² + Area of sidewalk
Area of sidewalk = 96 feet² - 60 feet ²
Area of sidewalk = 36 feet²
Length of pool + sidewalk = 10 + 2x
width of pool + sidewalk = 6 + 2x
( 10 + 2 x ) ( 6 + 2 x ) -60 = 36
60 + 20x + 12x + 4x² - 60 = 36
4x² + 32x - 36 = 0
4x² + 36x - 4x - 36 = 0
4x (x + 9) -4(x + 9) = 0
(4x - 4) (x + 9) = 0
4(x - 1) (x + 9) = 0
(x - 1) = 0 (x + 9) = 0
x = 1 or x = -9
The width of the side walk can't be a negative value
Therefore, width of the sidewalk = 1 feet
A rectangular pool has a sidewalk around it. Width of the sidewalk is 1 feet.
Given
A rectangular pool has a sidewalk around it. The pool measures 6 feet by 10 feet and the total area of the pool and sidewalk is 96 square feet.
Let 'w' be the width of sidewalk
The pool measures 6 feet by 10 feet . The width of the rectangular pool with side walk is 6+x+x=6+2x
The length of the rectangular pool with side walk is 10+2x
The total area of the pool and side walk is length times width
Total area= [tex](6+2x)(10+2x)\\[/tex]
[tex]96=(6+2x)(10+2x)\\96=60+32x+4x^2\\60+32x+4x^2-96=96-96\\4x^2+32x-36=0[/tex]
apply quadratic formula to solve for x
[tex]x=\frac{-32\pm \sqrt{32^2-4\cdot \:4\left(-36\right)}}{2\cdot \:4}\\x=\frac{-32\pm \:40}{2\cdot \:4}\\x= \frac{-32+40}{2\cdot \:4}=1\\x=\frac{-32-40}{2\cdot \:4}=-9[/tex]
Width of the sidewalk cannot be negative
so the width of the sidewalk is 1 feet
Learn more : brainly.com/question/21860114
Given an inequality, what strategies can we use to determine where the boundary line is? Explain your strategies in detail.
4x+3y≥12
Answer:
Step-by-step explanation:
The strategy to determine the boundary line is that we need to remove the inequality sign and replace it with and equal to sign and then sketch the equation of the function which is
[tex]4x+3y=12[/tex]
to sketch the function we need the function's x-intercept which means the graphs crosses the x-axis at that specific point (x , 0) and y-intercept which means the graph crosses the y-axis at that specific point (0 , y).
Since both these points lie on line we can substitute it into the equation to find the x-y intercepts and hence sketch the line so here goes.
For x-intercept:
[tex]4x+3y=12\\4(x)+3(0)=12\\4x=12\\x=12/4\\x=3[/tex]
so the x-intercept is (3 , 0)
For y-intercept:
[tex]4x+3y=12\\4(0)+3(y)=12\\3y=12\\y=12/3\\y=4[/tex]
so the y-intercept is (0 , 4)
now we sketch these 2 points and draw a straight line joining both the points as shown in the image below.
What does 7/2h(-15h + 1 1/2) equal to? x doesn’t equal anything.
Answer: -7 (30h - 11) / 4h
Step-by-step explanation:
Answer:
Step-by-step explanation:
All you can do is remove the brackets.
7/2 h * -15h = -52.5 h^2
7/2 h * 1 1/2= 7/2h * 3/2 = 21/4 h =5.25 h
7/2h(-15h + 21/4) = - 52.5 h^2 + 5.25 h = -52 1/2 h^2 + 5 1/4 h
4. Find x. Please help and explain.
Answer:
x is in top of 5.9
Step-by-step explanation:
hope it helps u find x and if you still cant find it try some glasses
Answer:
11.8
Step-by-step explanation:
because those two 5.9 if you look those two segments put together make a line that is the same length as x so if you add them up it's 11.8
It takes 12 hours to fill a pool with two pipes, where the water in one pipe flows three times as fast as the other pipe. How long will it take the slower pipe to fill the pool by itself
what ordered pair is a solution to the equation y= -2/3x + 9?
(-3/2, 10), (0, 10), (-1, 10 2/3), (2/3, 10)
Answer:
(-3/2, 10)
Step-by-step explanation:
(x, y)
Set y = 10
10 = -2/3(x) + 9
x = -3/2
(-3/2, 10)
Set y = 10 2/3
10 2/3 = -2/3(x) + 9
x = -5/2
(-5/2, 10 2/3)
You can also plot the line and see which point is on the line which would be (-3/2, 10).
The ordered pair that represents the solution to y= -2/3x + 9 is: A. (-3/2, 10)
Recall:
An ordered pair, (x, y) is a solution to a given equation if we plug the x and y values of the ordered pair and the equation remains TRUE.Thus, plug in the ordered pair, (-3/2, 10) into y= -2/3x + 9:
10 = -2/3(-3/2) + 9
Simplify10 = 1 + 9
10 = 10 (TRUE)
Therefore, the ordered pair that represents the solution to y= -2/3x + 9 is: A. (-3/2, 10)
Learn more about solution to an equation on:
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1.2(4x – 1) = 8x – 2
2(4x – 1) = –8x – 2
whats the solution :one , infently, or no solutions
6x
Step-by-step explanation:
1.2(4x-1)=8x-2=6x
Pls help me ill give brainliest.
Pls do all 3 to get brainliest
Answer:
5. 8(a-5)= -40
8a-40= -40
8a= -40+40
8a=0
a=0/8
a=0
option c is correct.
6. for d,
-1<d<1
I think the answer is option d , which is missing in the attachment.
the 4 question is missing.
so I am not able to answer that
Find the x value of the system of equations. Use the technique of ELIMINATION to solve this problem. Proper work must be shown on your work submission. 3x-2y=4 5x+y=11 the answer choices are 2 , -1 , 1 , -2
Answer:
2
Step-by-step explanation:
Given the equation :
3x - 2y = 4 - - - (1)
5x + y = 11 - - - (2)
Multiply (1) by 1 and (2) by 2
3x - 2y = 4 - - - - - (3)
10x + 2y = 22 - - (4)
Add (3) and (4)
13x = 26
x = 26/13
x = 2
how many of the equations listed below represent the line passing through the points (2,3) and (4,-7)
Answer: 3 equations
Step-by-step explanation:
The 4th one doesn’t work for both pairs.
1st : 3 - 7 = -4 | 5 x 2 = 10 5 x 4 = 20
10 - 20 = -10.
-4 does not equal -10
2nd equation : -7 - 7 = -14
5 x 4 = 20| 5 x 4 = 20 20 - 20 = 0
-14 does not equal 0
The only one equation that represents the line passing through both points is y = -x + 5. which is the correct answer that would be an option (D).
What is an equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
To determine the number of the given equations representing the line passing through the points (2,3) and (4,-7), you can substitute the coordinates of these points into the equations and see if they are satisfied.
If an equation is satisfied by both points, then the line described by that equation passes through both points.
Here are the given equations:
A. y = 3x + 5
B. y = -7x + 1
C. y = x + 1
D. y = -x + 5
E. y = -1/3x + 1
Substituting the coordinates of the point (2,3) into each of these equations, we find that equations A, C, and D are satisfied by this point.
Substituting the coordinates of the point (4,-7) into each of these equations, we find that equations B and D are satisfied by this point.
Therefore, the only one equation that represents the line passing through both points is D. Thus, the answer is 1.
Learn more about the equation here:
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#SPJ2
The question seems to be incomplete the correct question would be
how many of the equations listed below represent the line passing through both points (2,3) and (4,-7).
A. y = 3x + 5
B. y = -7x + 1
C. y = x + 1
D. y = -x + 5
E. y = -1/3x + 1
can someone help with this equation?
Answer:
OK what is equation ??????
Who's ur favorite song artist?
A subtract 3g^2 + 5g + 2g - 2 from 6g^2 + 6 - 4g + 2g^2
1. Collect like terms.
(6g^2+2g^2-3g^2)+(6-2)+(-4g+5g+2g)
2. Simplify
5g^2+4+3g
Sorry i'm hoping that helps, i'm on a school computer i cant see the picture you attached but i did 6g^2 + 6 - 4g + 2g^2 - 3g^2 + 5g + 2g - 2 because that's what it seemed you were asking.
Brian is baking apple pies to donate to a local retirement home. Apples are selling for $2.90 a pound. How much will it cost Brian to buy 3.8 pounds of apples
Step-by-step explanation:
Brian would need $2.90 * 3.8 = $11.02 to buy the 3.8 pounds of apples.
Answer:$11.02
Brian would need ($2.90 * 3.8 = $11.02)to buy all the 3.8 pounds of apples.
HELP PLZ! SERIOUS ANSWERS ONLY THO!
You are going to design an advertisement for a new polynomial identity that you are going to invent. Your goal for this activity is to demonstrate the proof of your polynomial identity through an algebraic proof and a numerical proof in an engaging way! Make it so the whole world wants to purchase your polynomial identity and can't imagine living without it!
You may do this by making a flier, a newspaper or magazine advertisement, making an infomercial video or audio recording, or designing a visual presentation for investors through a flowchart or PowerPoint.
You must:
Label and display your new polynomial identity
Prove that it is true through an algebraic proof, identifying each step
Demonstrate that your polynomial identity works on numerical relationships
Warning! No identities used in the lesson may be submitted. Create your own using the columns below. See what happens when different binomials or trinomials are combined. Square one factor from column A and add it to one factor from column B to develop your own identity.
Column A Column B
(x − y) (x2 + 2xy + y2)
(x + y) (x2 − 2xy + y2)
(y + x) (ax + b)
(y − x) (cy + d)
Which of the following is a monomial?
A.−5x
B.5x+1
C.x2+x
D.x+5+x−7
Answer:
A.
Step-by-step explanation:
A monomial is an expression in algebra that contains one term, like 3xy. Monomials include: numbers, whole numbers and variables that are multiplied together, and variables that are multiplied together. A polynomial is a sum of monomials where each monomial is called a term.
(Y-2,2x+1)=(x-1,y+2)
Answer:
x=2 and y=3
Step-by-step explanation:
y-2=x-1
or,x-y=-1.......(1)
again,
2x+1=y+2
or,2x-y=1.......(2)
now,
solving equations (1)&(2),we get,
x=2 and y=3
If a $1000 computer is marked off 35%, what is the sale price?
A) $300
B) $350
C) $650
D) $1350
What I did was I took the $1000 and subtracted the percent off (35% equals 350)
[tex]1000 - 350 = 650[/tex]
The total cost of the sale price is $650 (C)
Thank you! btw can i please get brainly :3
Answer:
650
Step-by-step explanation:
1000-350=650
A persons blood type is denoted with A, B, and O, and the symbols + and — The blood type A+ is read as A positive the blood type be is tested B negative use the data to write in this ratio in 3 different ways
Answer:
6. O+ to A+ donors = 90 to 45; 90 : 45 and 90/45
7. AB- donors to AB+ donors = 4 to 6; 4 : 6 and 4/6
8. B+ to total donors = 20 to 195; 20 : 195 and 20/195
9. O- donors to A- donors = 9 to 21; 9 : 21 and 9/21
10. B- donors to B+ donor = 0 to 20; 0 : 20 and 0/20
11. O- donors to total donors = 9 to 195; 9 : 195 and 9/195
12. A+ donors and B+ donors to AB+ donors = 65 to 6; 65 : 6 and 65/6
13. A- donors and B- donors to AB- donors = 21 to 4; 21 : 4 and 21/4
14. the ratio 90/9 is a comparison of O+ donors to O- donors
Step-by-step explanation:
A ratio is a relationship where for every x unit of one quantity there are y units of another quantity. A ratio can be written in three ways:
x to y
x:y, or
x/y
For the given questions;
6. O+ to A+ donors = 90 to 45; 90 : 45 and 90/45
7. AB- donors to AB+ donors = 4 to 6; 4 : 6 and 4/6
8. B+ to total donors = 20 to 195; 20 : 195 and 20/195
9. O- donors to A- donors = 9 to 21; 9 : 21 and 9/21
10. B- donors to B+ donor = 0 to 20; 0 : 20 and 0/20
11. O- donors to total donors = 9 to 195; 9 : 195 and 9/195
12. A+ donors and B+ donors to AB+ donors
A+ donors and B+ donors to = 45 + 20 = 65
therefore, A+ donors and B+ donors to AB+ donors = 65 to 6; 65 : 6 and 65/6
13. A- donors and B- donors to AB- donors
A- donors and B- donors = 21 + 0= 21
therefore, A- donors and B- donors to AB- donors = 21 to 4; 21 : 4 and 21/4
14. O+ donors = 90; O- donors = 9
therefore, the ratio 90/9 is a comparison of O+ donors to O- donors
You bought a soda for $0.50, then sold it for $1.00. What was the percent
change?
Answer:
50
Step-by-step explanation:
Answer:
I think the answer is 50%
Step-by-step explanation:
$1.00-$0.50=$0.5
0.5 as a percentage is 50%
4.
What is the slope of the line with the equation y = 4x + 12
a) 4
b) 1/4
C) -4
d) -1/4
A bag has 5 yellow marbles, 3 red marbles, and 2 blue marbles. Quinn randomly picks a marble from the bag and returns it before another is picked. How many times would Quinn expect to a blue marble if he picks a marble 200 times
Answer:
He would expect to see the blue marble 40 times. Hope this helps!
Step-by-step explanation:
Answer:
40 blue marbles
Step-by-step explanation:
You would find the probability of a blue marble
2 blue/ ( 5+3+2) total
2 divided by 10 is 1/5
Then, you multiply 200 and 1/5 together, which would equal 40.
Quinn should expect to pick 40 blue marbles.
Mr. Clemens painted his barn for 3 and 4/5 hours in the morning. He painted the barn for 5 and 3/4 hours in the afternoon. How many more hours did Mr. Clemens paint the barn in the afternoon than in the morning?
Answer:
1 19/20 hours
Step-by-step explanation:
We solve the above question using Subtraction operation
Hence:
The number rod hours Mr. Clemens painted the barn in the afternoon than in the morning is calculated as:
5 3/4 hours - 3 4/5 hours
5- 3 +( 3/4 - 4/5)
Lowest Common Denominator = 20
2 + (15 - 16/20)
2 + -1/20 hours
= 1 19/20 hours
