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1 year ago

Solve the system by graphing. Y = -X-4 4x-y=-1

Mathematics

1 answer:

max2010maxim [7]1 year ago

4 0

x = -1 and y = -3

Here, we want to solve the system of equations by graphing

A plot of both lines are required on same axes

The point at which they meet is the solution to the system

Kindly find attached a plot of the equations on same axes below;

As can be seen from the plot, the value of x is -1 while the value of y is -3

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15.8333333333

Step-by-step explanation:

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3 years ago

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3 years ago

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2 years ago

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

Determine whether each sequence is geometric? 1) 60,48,36,24,12,… 2) 3,6,12,24,48,…

balandron [24]

Answers:

Not geometric
Geometric

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Explanation for problem 1

Divide each term over its previous term.

term2/term1 = 48/60 = 0.8
term3/term2 = 36/48 = 0.75

We can stop here. The two results 0.8 and 0.75 do not match up, so we don't have a common ratio. Therefore, this sequence is not geometric. A geometric sequence must have each ratio of adjacent terms to be the same value throughout the list of numbers.

Side note: This sequence is arithmetic because we are subtracting the same amount each time (12) to generate each new term.

--------------------------------------

Explanation for problem 2

Like before, we'll divide each term by its previous term.

term2/term1 = 6/3 = 2
term3/term2 = 12/6 = 2
term4/term3 = 24/12 = 2
term5/term4 = 48/24 = 2

Each ratio found was 2. This is the common ratio and it shows we have a geometric sequence. It indicates that each term is twice that of its previous term. Eg: the jump from 12 to 24 is "times 2".

5 0

3 years ago