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3 years ago

How many solutions does this system of equations have?

Mathematics

2 answers:

Vsevolod [243]3 years ago

6 0

Answer:

B.) two

Step-by-step explanation:

These equations have two solutions, one for solving for each variable. There is a solution for solving for x, and one for y. For both of these equations,

x = 5 -4y and y = 5/4 - x/4

Rudiy273 years ago

3 0

Answer:

B. two

Step-by-step explanation:

3x = -12y + 15
x + 4y = 5

Use the elimination method to solve the system of equations. Move the terms like so. As you can see I kept the first equation the same but multiplied the second equation by -3.

3x = -12y + 15
-3x = -12y - 15

Now add. 3x and -3x cancel; so does 15 and -15.

0 = -24y

Divide by -24. 0 div'd by -24 is equal to 0.

y = 0

Substitute y into the second equation.

x + 4(0) = 5

x + 0 = 5

x = 5

You've got x = 5 and y = 0; these are two solutions to the system of equations.

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Find the Product of (s^2+5s)(s^3+4s^2).

nikklg [1K]

The result of the product $(s^2+5s)(s^3+4s^2)$ is $s^5+9s^4+20s^3$

The product is given as:

$(s^2+5s)(s^3+4s^2)$

Rewrite as:

$(s^2+5s)(s^3+4s^2) = (s^2+5s) \times (s^3+4s^2)$

Expand the expression on the right-hand side

$(s^2+5s)(s^3+4s^2) = s^2\times (s^3+4s^2)+5s \times (s^3+4s^2)$

Distribute the expressions

$(s^2+5s)(s^3+4s^2) = s^5+4s^4+5s^4+20s^3$

Evaluate like terms

$(s^2+5s)(s^3+4s^2) = s^5+9s^4+20s^3$

Hence, the result of the product $(s^2+5s)(s^3+4s^2)$ is $s^5+9s^4+20s^3$

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3 years ago

Write an equation for the translation of <img src="https://tex.z-dn.net/?f=y%5Cfrac%7B3%7D%7Bx%7D" id="TexFormula1" title="y\fra

lisov135 [29]

<h2><u>Answer:</u></h2><h2> $\boxed{\boxed{y=\frac{3}{x-6}-6}}$ </h2><h2 /><h2><u>Solution Steps:</u></h2>

______________________________

<h3>1.) Substitute x, y, and general form using the formulas:</h3>

Formula for x: $x=d=6$

Formula for y: $y=k=-6$

Formula for general form y: $y=\frac{a}{x-d}+k=y=\frac{3}{x-6}+(-6)$

Note:

<em> - When doing problems like this, it's best to list out each formula and do the drag down method, and replace methods rather than doing it the entire mathematical way, as doing it that way takes a long time and it's more confusing than it should be.</em>

<u>Equation at the end of Step 1:</u>

$y=\frac{3}{x-6}+(-6)$

<h3>2.) Simplify the d and k forms:</h3>

$y=\frac{3}{x-6}+(-6)=y=\frac{3}{x-6}-6$

<em> - The x(d) stays the same since the 6 was positive and we plugged it in making it negative, so it doesn't need to be changed. (Another way to know if you need to change it is if the original </em> $(d)$ <em> or </em> $(k)$ <em> when plugged in, you had to put them in parenthesis then most likely it needs to be changed. </em>

<em> - The y(k) changes from </em> $+(-6)$ <em> to </em> $-6$ <em> because when a </em> $(+)$ <em> and </em> $(-)$ <em> are next to each other, the rule is </em> $+$ <em>. The Minus always wins in this type of problem situation.</em>

So the answer is c, $\bold{y=\frac{3}{x-6}-6}$ .

______________________________

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