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3 years ago

Variable y varies directly with variable x, and y = 16 when x = 12. Enter the constant of variation in lowest terms. y = x

1 answer:

5 0

k = 1.33 or 1 1/3

Formula of Direct variation. Where y is equal to the product of the constant of variation times x.

y = kx
16 = k * 12
k = 16/12
k = 1 4/12 = 1 1/3

Constant of variation is 1 1/3 or 1.33.

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Expand the polynomial and simplify: (4xy− 1 8 y^2)^2

Vinvika [58]

Answer: $4y^{2}(2x-9y)^{2}$

Step-by-step explanation:

We have the following polynomial:

$(4xy-18y^{2})^{2}$

This is a polynomial of the form $(a-b)^{2}=a^{2}-2ab+b^{2}$ . Following this rule to expand it, we have:

$(4xy)^{2}-2(4xy)(18y^{2})+(18y^{2})^{2}$

$16x^{2}y^{2}-144xy^{3}+324y^{4}$

Applying common factor $4y^{2}$ :

$4y^{2}(4x^{2}-36xy+81y^{2})$

Note the polynomial inside the parenthesis is a perfect square trinomial, which can be factored to $(2x-9y)^{2}$ . Hence, the final simplification is:

$4y^{2}(2x-9y)^{2}$

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3 years ago

A bag contains 15 marbles. The probability of randomly selecting a green marble is 1/5. The probability of randomly selecting a

slava [35]

Answer:

6 blue marbles

Step-by-step explanation:

Given;

Total number of marbles N = 15

probability of randomly selecting a green marble

P(G) = 1/5

The probability of randomly selecting a green marble, replacing it, and then randomly selecting a blue marble P(G∩B) = 2/25

P(G∩B) = P(G) × P(B)

P(B) = P(G∩B) ÷ P(G)

The probability of selecting a blue marble

P(B) = 2/25 ÷ 1/5 = 2/5

The number of blue marbles N(B) = P(B) × N

N(B) = 2/5 × 15 = 6

There are 6 blue marbles

7 0

3 years ago

Express this amount in dozens. (Use decimal form.) 7.5 cupcakes<br> ...?

kompoz [17]

0.625 dozen

1/12 x 7.5
= 0.625

4 0

3 years ago

"Given m = -2/5 and b = -7, write the equation of the line containing these points"

KatRina [158]

Answer: y = (-2/5)x - 7

This is the same as writing $y = -\frac{2}{5}x-7$

======================================================

Explanation:

Any linear equation is of the form y = mx+b, known as slope-intercept form

m = slope

b = y intercept

We'll replace m with -2/5 and replace b with -7 to get y = (-2/5)x + (-7) which simplifies to y = (-2/5)x - 7

4 0

2 years ago

Find the value of 6^-3

lana66690 [7]

Answer:

$\frac{1}{216}$

Step-by-step explanation:

→ First calculate 6⁻³

216

→ Remember that negative indices results in the reciprocal

$\frac{1}{216}$

3 0

3 years ago

Read 2 more answers