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3 years ago

Find the constant of variation k for the direct variation. 4x = -6(y)

Mathematics

1 answer:

shepuryov [24]3 years ago

3 0

Answer: $k=-\frac{2}{3}$

Step-by-step explanation:

By definition, a direct varition is expressed as following:

$y=kx$

Then, y is directly proportional to x and k is the constant of variation.

Therefore, given the direct variation:

$4x=-6y$

You must solve for the variable y as you can see below:

$4x=-6y\\\\y=-\frac{4}{6}x\\\\y=-\frac{2}{3}x$

Therefore, as you can see, the constant of variation is the following:

$k=-\frac{2}{3}$

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If an area of the rectangle below is 39 square feet, sides are x-2 and x+8 find the area of x

Anna71 [15]

Answer:

x = 5.

Step-by-step explanation:

The area of a rectangle can be determined by the following formula.

A = l ⋅ w

l stands for length or the longer side.

w stands for width or the shorter side.

Now, we can plug the values we are given into the equation.

A = ( x − 2 ) ⋅ ( x + 8 )

The easiest way to multiply is to follow the acronym FOIL , which stands for First Outside Inside Last, and dictates the order in which you multiply these terms.

A = x 2 + 8 x − 2 x −16 = x 2 + 6 x − 16

Now, we can plug in the given value for the area.

39 = x 2 + 6 x − 16

Next, we simplify by moving all terms to one side and factor the equation.

0 = x 2 + 6 x − 55

Finally, we factor the equation. This means we reverse-FOIL, trying to determine the two things that we multiplied together.

0= ( x − 5 ) ⋅ ( x + 11 )

If the equation ultimately equals zero, either ( x − 5 ) or ( x + 11 ) or both equal zero. Therefore, we set each equal to zero to find the value of

x .

x − 5 = 0 x = 5 x + 11 = 0

x = − 11

Since x is a length, we know it cannot be negative. Thus, we can conclude that it equals 5.

4 0

3 years ago

The circular rug has a diameter of 8.2 feet. Which measurement is closest to the circumference of the rug in feet?

Tanya [424]

Answer:

circumference of a circle = 25.748feet

Step-by-step explanation:

the circular rug diameter = 8.2feet

π = 3.14

recall that the formulae for finding the circumference of a circle = πd

circumference of a circle = πd

circumference of a circle = 3.14 × 8.2

circumference of a circle = 25.748feet

3 0

3 years ago

Helllllllpppp pllllllssssss

kolezko [41]

Answer:

60⁰ hope I'm right

Step-by-step explanation:

I think

6 0

3 years ago

3. A coin is tossed four times and the resulting sequence of heads and/or tails is recorded. Define the events A, B, and C as fo

frosja888 [35]

Answer:

a.B and C

b.B is a subset of A

Step-by-step explanation:

We are given that a coin is tossed four times

Sample space={HHHH,HTTT,HHTT,HTHT,THTH,TTTH,TTHH,HTTH,THHT,HHHT,THHH,TTTT,HHTH,TTHT,THTT,HTHH}

A:Exactly two heads appear

A:{HHTT,HTHT,THTH,TTHH,HTTH,THHT}

B:Heads and tails alternate

B={HTHT,THTH}

C:First two tosses are heads

C={HHTT,HHTH,HHHH,HHHT}

a.We have to find mutually exclusive events

Mutually exclusive events: It is that events in which intersection of events is empty.

Event B and C are disjoint because $A\cap B=\phi$

Hence, B and C are mutually exclusive.

b.We have to find that sets which are subset of other.

We can see that B is subset of A because all elements of B contain in set A.

Therefore , event B is a subset of event A.

7 0

3 years ago

The point (12, 5) is on the terminal side of angle 0

max2010maxim [7]

That angle is arctan (5/12) which is 22.62 degrees.

4 0

3 years ago