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3 years ago

11

Determine whether y varies directly with x. If so, find the constant of variation k and write the equation

2 answers:

nydimaria [60]3 years ago

8 0

y/x = k

6.4/4 = 1.6

11.2 / 7 =1.6

16/10 = 1.6

20.8 /13 =1.6

This is a direct variation and the constant is 1.6

y=1.6x

Svetlanka [38]3 years ago

3 0

Answer:

$y=1.6x$

Step-by-step explanation:

If y varies directly proportional with x, then equation is y=kx

where k is the constant of proportionality

$k=\frac{y}{x}$

LEts find out k

we use the table to find the value of k, divide y value by x value

$\frac{6.4}{4}=1.6$

$\frac{11.2}{7}=1.6$

$\frac{16}{10}=1.6$

$\frac{20.8}{13}=1.6$

1.6 is a constant . so k=1.6

y=kx

Replace the value of k, the equation becomes

$y=1.6 x$

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Write an inequality to show the remaining distance, d, in feet must she climb to reach the peak.

spayn [35]

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3 years ago

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Point A is located at (-5, 2) on a coordinate grid. Point A is translated 8 units to the right and 3 units up to create point A.

Molodets [167]

The closest distance between point A and point A' is 8.5 ⇒ B

Step-by-step explanation:

Let us revise the translation of a point

If the point (x , y) translated horizontally to the right by h units then its image is (x + h , y)
If the point (x , y) translated horizontally to the left by h units then its image is (x - h , y)
If the point (x , y) translated vertically up by k units then its image is (x , y + k)
If the point (x , y) translated vertically down by k units then its image is (x , y - k)

∵ Point A is located at (-5 , 2)

∵ Point A is translated 8 units to the right and 3 units up

- That means add x-coordinate by 8 and add y-coordinate by 3

∴ Point A' located at (-5 + 8 , 2 + 3)

∴ Point A' located at (3 , 5)

The distance between two points $(x_{1},y_{1})$ and $(x_{2},y_{2})$

is $d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

∵ Point a = (-5 , 2) and point A' = (3 , 5)

∴ $x_{1}$ = -5 and $x_{2}$ = 3

∴ $y_{1}$ = 2 and $y_{2}$ = 5

- Substitute these values in the rule of the distance

∵ $d=\sqrt{(3--5)^{2}+(5-2)^{2}}$

∴ $d=\sqrt{(3+5)^{2}+(3)^{2}}$

∴ $d=\sqrt{(8)^{2}+(3)^{2}}$

∴ $d=\sqrt{64+9}=73$

∴ d = 8.544 ≅ 8.5

The closest distance between point A and point A' is 8.5

Learn more:

You can learn more about the distance between two points in brainly.com/question/6564657

#LearnwithBrainly

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Solve for x in the equation x² + 14x + 17 = - 96

gavmur [86]

Answer:

Solutions of x are;

x = -7 + 8i and x = -7 -8i

Step-by-step explanation:

Given the equation: $x^2+14x+17 = -96$

Add 96 both sides we get;

$x^2+14x+17+96 = 0$

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Using quadratic formula $ax^2+bx+c = 0$ then the solution is given by:

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

On comparing we have;

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or

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Simplify:

$x = \frac{-14\pm 16i}{2}$ ; where i is the imaginary, $i^2= -1$

or

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Is there any information you forgot to give? Double check yourself.

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