MATHEMATICS HIGH SCHOOL

Which relationships have the same constant of proportionality between yyy and xxx as the equation 3y=27x3y=27x3, y, equals, 27, x? Choose 3 answers: Choose 3 answers: (Choice A) A y=9xy=9xy, equals, 9, x (Choice B) B 2y=18x2y=18x2, y, equals, 18, x (Choice C) C (Choice D) D xxx yyy 333 \dfrac{1}{3} 3 1 start fraction, 1, divided by, 3, end fraction 666 \dfrac{2}{3} 3 2 start fraction, 2, divided by, 3, end fraction 999 111 (Choice E) E xxx yyy 222 181818 444 272727 666 363636

Answers

Answer 1

Answer:

Answer:

A, B and C

Step-by-step explanation:

In the equation: 3y=27x

Making y the subject of the equation, we have:

$y=(27)/(3)x\ny=9x$

The constant of proportionality between y and x is 9.

We want to determine which relationships have the same constant of proportionality 9.

Option A

y=9x

The constant of proportionality is 9.

Option B

2y=18x

Divide both sides by 2 to obtain: y=9x

The constant of proportionality is 9.

Option C

x=3, y=1/3

Substitution into y=kx gives:

1/3=3k

k=9

The constant of proportionality is 9.

Option D

x=6, y=2/3

Substitution into y=kx gives:

2/3=6k

k=2/3*6=4

The constant of proportionality is 4.

Option E

When x=2, y=18

Substitution into y=kx gives:

18=2k

k=9

However, when x=4, y=27

Substitution into y=kx gives:

27=4k

k=6.75

This is not a proportional relation since the constant of proportionality is not equal.

The correct options are A, B and C

Answer 2

Answer:

The Proportional relationships y = 9x, 2y = 18x, and y = (1/3)x have the same constant of proportionality as the equation 3y = 27x.

The equation 3y = 27x represents a proportional relationship between y and x with a constant of proportionality of 9. To determine which relationships have the same constant of proportionality, we can compare the ratios of y to x in the given options.

A) y = 9x: The ratio of y to x is 9, which is the same as the constant of proportionality in the original equation. So, this option has the same constant of proportionality.

B) 2y = 18x: Dividing both sides of the equation by 2, we get y = 9x, which has the same constant of proportionality. Therefore, this option also has the same constant of proportionality.

D) y = (1/3)x: The ratio of y to x is 1/3, which is different from the constant of proportionality in the original equation. Therefore, this option does not have the same constant of proportionality.

So, the correct answers are A) y = 9x, B) 2y = 18x, and D) y = (1/3)x.

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Figure ABCD is a rhombus with point A (3, −1). What rule would rotate the figure 270° counterclockwise?(x,y)→(−y,−x)
(x,y)→(−y,x)
(x,y)→(y,x)
(x,y)→(y,−x)

Answers

Answer:

The correct option is 4.

Step-by-step explanation:

Given information: ABCD is a rhombus with point A (3, −1).

If a figure rotated 90° counterclockwise, then

$(x,y)\rightarrow (-y,x)$

If a figure rotated 180° counterclockwise, then

$(x,y)\rightarrow (-x,-y)$

If a figure rotated 270° counterclockwise, then

$(x,y)\rightarrow (y,-x)$

Therefore the rule $(x,y)\rightarrow (y,-x)$ would rotate the figure 270° counterclockwise.

The correct option is 4.

(x,y)→(y,−x)
.......

What is the answer for (20,8),(9,16) ?

Answers

The slope is -4 and another point would be (19,12) and the equation for the line (in slope-intercept form) is y=-4x+88

Answer:

at twice the father's rate of speed. At this rate; how many miles would the bicycle rider travel in 9 hours?

Step-by-step explanation:

at twice the father's rate of speed. At this rate; how many miles would the bicycle rider travel in 9 hours?

A yoga studio sells monthly memberships. the function f(x) = −x2 50x − 264 models the profit in dollars, where x is the number of memberships sold. determine the zeros, and explain what these values mean in the context of the problem.

Answers

The zeros represent the number of monthly memberships where no profit is made; x = 6, x = 44.

To determine the zeroes, calculate:

The function we have is: $f(x) = -x^(2) +50x-264$

That models the profit in dollars, where $x$ is the number of memberships sold.

In order to get the zeros we'll use the quadratic formula:

$x_(1,2) =(-b+-(b^(2)-4ac) )/(2a) \n$

For,

$a=-1,b=50,c=-264: x^(1,2) =\frac{-50+-\sqrt[]{50^(2) -4(-1)(-264)} }{2(-1)} \nx_(1) =\frac{-50+\sqrt[]{50^(2) -4(-1)(-264)} }{2(-1)} =\frac{-50+\sqrt[]{50^(2) -4*1*264} }{2(-1)}=\frac{-50+\sqrt[]{1444} }{-2} =6\nx_(2) =\frac{-50+\sqrt[]{50^(2) -4(-1)(-264)} }{2(-1)} =\frac{-50-\sqrt[]{50^(2) -4*1*264} }{2(-1)}=\frac{-50-\sqrt[]{1444} }{-2} =44\n$

So, the zeroes are $x=6, x=44$ .

Therefore, the zeros represent the number of monthly memberships where no profit is made; x = 6, x = 44.

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The complete question is given below:

A yoga studio sells monthly memberships. The function f(x) = −x2 + 50x − 264 models the profit in dollars, where x is the number of memberships sold.

Determine the zeros, and explain what these values mean in the context of the problem.

x = 6, x = 44; The zeros represent the number of monthly memberships that produce a maximum profit.

x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made.

x = 25, x = 361; The zeros represent the number of monthly memberships where no profit is made.

x = 25, x = 361; The zeros represent the number of monthly memberships that produce a maximum profit.

Answer:

The answer is: x = 6, x = 44; The zeros represent the number of monthly memberships when no profit is made.

If the triangle on the grid below is translated by using the rule (x, y) right-arrow (x + 5, y minus 2), what will be the coordinates of B prime? On a coordinate plane, triangle A B C has points (negative 1, 0), (negative 5, 0), (negative 1, 2). (–2, 0) (0, –2) (5, –7) (5, –2)

Answers

Answer:

(0, –2)

Step-by-step explanation:

I am assuming that point 'B' is (-5 , 0).

The translation rule is: $(x,y)\rightarrow(x+5,y-2)$ .

Apply the rule to point 'B':

$((-5,0)\rightarrow(-5+5,0-2))/((x,y)\rightarrow(x+5,y-2))\rightarrow\boxed{(0,-2)}$

B' should be (0, -2).

Answer:

Guy above me might be right but Im not sure. Im on the cumulative exam on edge.

Step-by-step explanation:

(05.02 LC)Solve the following system:

y = x + 3
2x + y = 9

(2, 5)
(5, 2)
(−2, 5)
(2, −5)

Answers

Your Answer: A.) (2 , 5) I also provided the steps.

Hope this helps y'all :)

Morgan is walking her dog on an 8-meter-long leash. She is currently 500 meters from her house, so the maximum and minimum distances that the dog may be from the house can be found using the equation |x – 500| = 8. What are the minimum and maximum distances that Morgan’s dog may be from the house?

Answers

The minimum distance is 492 meters from the house (500 - 8 = 492), and the maximum distance is 508 meters from the house (500 + 8 = 508). The dog may be slightly closer to the house, depending on how long the dog is, or if Morgan is using a leash extender.

The minimum and maximum distances that Morgan’s dog may be from the house are 492 and 508 meters.

How to calculate the distance?

From the information given, Morgan is currently 500 meters from her house.

The minimum distance will be:

= 500 - 8 = 492

The maximum distance will be:

= 500 + 8

= 508

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