Which pair of ratios forms a proportion?

Which strategie would eliminate a variable in the system of equations? −x+6y=8 7x−y=−2

NeX [460]

Answer:

substitution (or addition)

Step-by-step explanation:

A simple strategy for this system is to use substitution. The first equation is easily solved for x, so you could substitute that into the second equation:

x = 6y -8

7(6y -8) -y = -2 . . . . . x variable eliminated

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The second equation is easily solved for y, so you could substitute that into the first equation.

y = 7x +2

-x +6(7x +2) = 8 . . . . . y-variable eliminated

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The "addition" method is always a good way to eliminate a variable.

When the coefficient of a variable in one equation is a divisor of the coefficient of that variable in the other equation, a simple multiplication and addition will do.

To make the coefficient of x in the first equation the opposite of the coefficient of x in the second, multiply the first equation by 7. Adding that result to the second equation will eliminate x:

7(-x +6y) +(7x -y) = 7(8) +(-2)

42y -y = 56 -2 . . . . . . x-variable eliminated

Likewise, the second equation can be multiplied by 6 and added to the first to eliminate the y-variable:

(-x +6y) +6(7x -y) = (8) +6(-2)

-x +42x = -4 . . . . . . . . y-variable eliminated

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It is often the case that using either substitution or "addition" requires about the same amount of work.

Here, the solutions are (x, y) = (-4/41, 54/41).

3 0

3 years ago

A spinner of a board game can land on any one of three regionslabeled: A, B, and C. If the probability the spinner lands on B

Veseljchak [2.6K]

Answer:

The probability of the spinner landing on A is 0.1111.

Step-by-step explanation:

The possible outcomes of a board game is that it can lead on any three of the regions, A, B and C.

The probability of all the outcomes of an event sums up to be 1.

$P(E) = P(E_{1})+P(E_{2})+...+P(E_{n})=1$

According to the provided information:

P (B) = 3 P (A)

P (C) = 5 P (A)

Compute the probability of the spinner landing on A as follows:

$P(A)+P(B)+P(C)=1\\P(A)+3P(A)+5P(A)=1\\9P(A)=1\\P(A)=\frac{1}{9}\\=0.111111\\\approx0.1111$

Thus, the probability of the spinner landing on A is 0.1111.

3 0

3 years ago

The distance an airplane travels depends on how much time it spends flying. Which expression represents the distance the airplan

kogti [31]

Answer: B. $\text{Distance(20)}$

Step-by-step explanation:

The notation to express a dependent variable is given by :-

$Y(x)$ , where Y is depending variable which is dependent upon x ( independent variable).

The given statement : The distance an airplane travels depends on how much time it spends flying.

Here , Independent variable : Time

Dependent variable : Distance

Then , the notation to express distance (dependent variable) the airplane flies in 20 minutes is given by :-

$\text{Distance(20)}$

6 0

3 years ago

For the given function, x can have what value?

Lyrx [107]

Answer:

x cannot be -4,-3, or 13

x can be anything else

Step-by-step explanation:

There are infinitely many values x can take where the relation above will be a function.

For it to be a function, you just need to make sure each x is only assigned one y value.

So x couldn't be -4 because it would by assigned to y=2 and y=0.

x couldn't be -3 because it would be assigned to y=1 and y=0.

x couldn't be 13 because it would be assigned to y=5 and y=0.

So as long as x is not chosen to be -4,-3, or 13 your relation here is a function.

5 0

3 years ago

A right triangle has an area of 38 square units

oksian1 [2.3K]

Answer:

1 | 38

2 | 76

3 | 114

5 | 190

1/2 | 19

2/3 | 25.33

Step-by-step explanation:

I am assuming that you need to multiply the area by the scale factors

6 0

2 years ago