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3 years ago

How would you solve this by elimination?

Mathematics

1 answer:

jekas [21]3 years ago

5 0

To solve this equation by elimination, what you would do is multiply one of the equations by -1, or distribute -1 to each term in the equation, any of the 2 equations. Then align the equations and add them together.

-(X + 3y = 3)
-X - 3y = -3

-X - 3y = -3
X + 6y = 3
__________
3y = 0
y = 0/3 = 0.

Now we can solve for x, by simply plugging the value of y into any of the 2 equations.

X + 6y = 3
X + 6(0) = 3
X + 0 = 3
X = 3.

The solution to your system of equations would be (3,0).

Check this by plugging in the point to the other equation and see if it is true.

X + 3y = 3
(3) + 3(0) = 3
3 + 0 = 3
3 = 3.

Thus it is the solution.

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Evaluate the indicated limit algebraically. Change the form of the function where necessary. Please write clearly with descripti

alukav5142 [94]

Answer:

$\displaystyle \lim_{x\to \infty}\frac{3x^2+4.5}{x^2-1.5}=3$

Step-by-step explanation:

We want to evaluate the limit:

$\displaystyle \lim_{x\to \infty}\frac{3x^2+4.5}{x^2-1.5}$

To do so, we can divide everything by x². So:

$=\displaystyle \lim_{x\to \infty}\frac{3+4.5/x^2}{1-1.5/x^2}$

Now, we can apply direct substitution:

$\Rightarrow \displaystyle \frac{3+4.5/(\infty)^2}{1-1.5/(\infty)^2}$

Any constant value over infinity tends towards 0. Therefore:

$\displaystyle =\frac{3+0}{1+0}=\frac{3}{1}=3$

Hence:

$\displaystyle \lim_{x\to \infty}\frac{3x^2+4.5}{x^2-1.5}=3$

Alternatively, we can simply consider the biggest term of the numerator and the denominator. The term with the strongest influence in the numerator is 3x², and in the denominator it is x². So:

$\displaystyle \Rightarrow \lim_{x\to\infty}\frac{3x^2}{x^2}$

Simplify:

$\displaystyle =\lim_{x\to\infty}3=3$

The limit of a constant is simply the constant.

We acquire the same answer.

6 0

3 years ago

Students surveyed boys and girls separately to determine whether they wanted outdoor

vazorg [7]

Answer:

111 girls

Step-by-step explanation:

Given

Boys: Every 17 outdoor ≈ 20 indoor

Girls: 3:2 outdoor to indoor

First, we'll determine the ratio of outdoor to indoor for boys;

Recall that;

17 choose indoor while 20 choose outdoor;

The ratio of outdoor to indoor is;

20 : 17

Convert to fraction:

$\frac{20}{17}$

Let x represent number of boys that choose indoor when 85 boys chose outdoor;

The ratio of outdoor to indoor is;

x : 85

Convert to fraction

$\frac{x}{85}$

Equate both fractions

$\frac{20}{17} = \frac{x}{85}$

Multiply both sides by 85

$85 * \frac{20}{17} = \frac{x}{85} * 85$

$85 * \frac{20}{17} = x$

$\frac{1700}{17} = x$

$100 = x$

$x = 100$

This implies that when 85 chose outdoor, 100 chose indoor for boys;

Total = 100 + 85

Total = 185 boys surveyed

Recall that the question says the same number of boys and girls were surveyed

This implies that

Total Girls Surveyed = 185

For the girl ratio;

Outdoor to Indoor= 3:2

Number of girls that chose outdoor is as follows;

$Outdoor = \frac{3}{3 + 2} * Total$

$Outdoor = \frac{3}{3 + 2} * 185$

$Outdoor = \frac{3}{5} * 185$

$Outdoor = \frac{555}{5}$

$Outdoor = 111$

Hence, the number of girls that chose outdoor is 111

4 0

3 years ago

The primary purpose of the passage is to

astra-53 [7]

The primary purpose of the passage is to: indicate a specific ability that is useful in a negotiation (Option B).

<h3>What is a comprehension passage?</h3>

In a comprehension passage, some questions are given that follow the passage. The questions are to be answered by using the data given in the passage, even if it differs from real-life facts.

Now,

The focus of the passage is on how an essential talent for negotiators to have is the capacity to perceive things from our opponent's perspective.
We can infer from this setting that the main objective of the passage is B, i.e., to indicate a specific ability that is useful in a negotiation.

To learn more about comprehension passages, refer to the link:

brainly.com/question/24716030

#SPJ4

8 0

2 years ago

Y = 3/2x + 3 What is the slope?

ElenaW [278]

Answer:

Step-by-step explanation:

the slope would be 1.5 or 3/2 because that is how much X is being multiplicated by.

3 0

3 years ago