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3 years ago

Which relationships have the same constant of proportionality between y and x as in the equation y=1/2x Choose 3 answers:

Mathematics

2 answers:

Andrew [12]3 years ago

3 0

Answer:

A and B has the same constant of proportionality

Step-by-step explanation:

$y \propto x$

$y = kx ----1$

Where k is the constant of proportionality

We are supposed to find Which relationships have the same constant of proportionality between y and x as in the equation $y=\frac{1}{2}x$

On comparing with 1

$k = \frac{1}{2}$

A)6y = 3x

$y = \frac{3}{6}x\\y = \frac{1}{2}x$

So, this equation has the same constant of proportionality

B) $(x_1,y_1)=(2,1)\\(x_2,y_2)=(4,2)$

To find the equation :

Formula : $y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

So, $y - 1=\frac{2-1}{4-2}(x-2)\\y-1=\frac{1}{2}(x-2)\\y-1=\frac{1}{2}x-1\\y=\frac{1}{2}x$

So, this equation has the same constant of proportionality

$(x_1,y_1)=(1,2)\\(x_2,y_2)=(2,4)$

To find the equation :

Formula : $y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

So, $y - 2=\frac{4-2}{2-1}(x-1)\\y - 2=2(x-1)\\y - 2=2x-2\\y=2x$

So, this equation do not has the same constant of proportionality

$(x_1,y_1)=(2,1)\\(x_2,y_2)=(3,2.5)$

To find the equation :

Formula : $y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

So, $y - 1=\frac{2.5-1}{3-2}(x-2)$

$y-1=1.5(x-2)\\y-1=1.5x-3\\y=1.5x-2$

So, this equation do not has the same constant of proportionality

Hence A and B has the same constant of proportionality

denis-greek [22]3 years ago

3 0

Answer:

It is A,B,E

Step-by-step explanation:

sorry i didn't provide an explanation but I just took the assnigment and I got it right. Again sorry

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Step-by-step explanation:

Step 1: Given that the perimeter = 100 cm, let width be x cm and then length = 12 + x.

Perimeter of a rectangle = 2(length + width)

100 = 2(x + 12 + x)

100 = 4x + 24

4x = 100 - 24 = 76

∴ x = 76/4 = 19 cm

∴ Length = 19 + 12 = 31 cm

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3 years ago

A rectangle's length is three times its width. Let w denote the rectangle's width. What polynomial represents the rectangle's ar

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2 years ago

Drag each tile to the correct box. Vector t, with a magnitude of 4 meters/second and a direction angle of 60°, represents a swim

astraxan [27]

Answer:

From top to bottom, the boxes shown are number 3, 5, 6, 2, 4, 1 when put in ascending order.

Step-by-step explanation:

It is convenient to let a calculator or spreadsheet tell you the magnitude of the sum. For a problem such as this, it is even more convenient to let the calculator give you all the answers at once.

The TI-84 image shows the calculation for a list of vectors being added to 4∠60°. The magnitudes of the sums (rounded to 2 decimal places—enough accuracy to put them in order) are ...

... ║4∠60° + 3∠120°║≈6.08

... ║4∠60° + 4.5∠135°║≈6.75

... ║4∠60° + 4∠45°║≈7.93

... ║4∠60° + 6∠210°║≈3.23

... ║4∠60° + 5∠330°║≈6.40

... ║4∠60° + 7∠240°║≈ 3

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In the calculator working, the variable D has the value π/180. It converts degrees to radians so the calculation will work properly. The abs( ) function gives the magnitude of a complex number.

On this calculator, it is convenient to treat vectors as complex numbers. Other calculators can deal with vectors directly

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Doing it by hand

Perhaps the most straigtforward way to add vectors is to convert them to a representation in rectangular coordinates. For some magnitude M and angle A, the rectangular coordinates are (M·cos(A), M·sin(A)). For this problem, you would convert each of the vectors in the boxes to rectangular coordinates, and add the rectangular coordinates of vector t.

For example, the first vector would be ...

3∠120° ⇒(3·cos(120°), 3·sin(120°)) ≈ (-1.500, 2.598)

Adding this to 4∠60° ⇒ (4·cos(60°), 4°sin(60°)) ≈ (2.000, 3.464) gives

... 3∠120° + 4∠60° ≈ (0.5, 6.062)

The magnitude of this is given by the Pythagorean theorem:

... M = √(0.5² +6.062²) ≈ 6.08

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Using the law of cosines

The law of cosines can also be used to find the magnitude of the sum. When using this method, it is often helpful to draw a diagram to help you find the angle between the vectors.

When 3∠120° is added to the end of 4∠60°, the angle between them is 120°. Then the law of cosines tells you the magnitude of the sum is ...

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2 years ago

Which mathematical equation represents the solution for k in the equation h + 3 = jk + 6k ?

Tomtit [17]

Answer:

The answer is D. h+3/j+6.

Step-by-step explanation:

Given:

The equation h + 3 = jk + 6k.

Now, to get the mathematical expression.

$h + 3 = jk + 6k$

So, taking $k$ common on R.H.S we get:

$h + 3 = k(j + 6)$

Then, dividing both sides by $j+6$ we get:

$\frac{h+3}{j+6} =k$

Thus,

$k=\frac{h+3}{j+6}$

Therefore, the answer is D. h+3/j+6.

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3 years ago

A salesperson at a jewelry store earns 9% commission each week. Last week, sold$720 worth of jewelry. How much did make in co

EastWind [94]

Answer:

The total the salesperson makes is $64.80.

Explanation:

Since nine percent of $720 is $64.80, that is what the salesperson gets per week if they sell $720 worth of jewelry per week. The amount the store gets is $655.20. Thank you for reading, and please mark Brainliest if you got it right!

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3 years ago