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4 years ago

How do I simplify this?

Mathematics

1 answer:

vladimir1956 [14]4 years ago

8 0

Answer:

Domain: all real numbers except 0 and -3

Vertical asymptotes: x = 0; x = -3

Step-by-step explanation:

The domain is the set of numbers that can be substituted for x.

The expression has x in the denominator. Since division by zero is undefined, x cannot have any value that would cause a zero in the denominator. To find which values of x cause a zero in the denominator, we set the denominator equal to zero and solve the equation for x.

2x^2 + 6x = 0

Factor 2x.

2x(x + 3) = 0

Divide both sides by 2.

x(x + 3) = 0

x = 0 or x + 3 = 0

x = 0 or x = -3

Since the values x = 0 and x = -3 cause the denominator to equal zero, these two values of x must be excluded from the domain.

Domain: all real numbers except 0 and -3

The vertical asymptotes happen at the x values excluded from the domain.

Vertical asymptotes: x = 0; x = -3

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67. The line contains the point (4,0) and is parallel<br> to the line defined by 3x = 2y.

olganol [36]

Answer:

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

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form:

$y=mx+b$ where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)

Parallel lines will always have the same slope but different y-intercepts.

<u>1) Determine the slope of the parallel line</u>

Organize 3x = 2y into slope-intercept form. Why? So we can easily identify the slope, m.

$3x = 2y$

Switch the sides

$2y=3x$

Divide both sides by 2 to isolate y

$\frac{2y}{2} = \frac{3}{2} x\\y=\frac{3}{2} x$

Now that this equation is in slope-intercept form, we can easily identify that $\frac{3}{2}$ is in the place of m. Therefore, because parallel lines have the same slope, the parallel line we're solving for now will also have the slope $\frac{3}{2}$ . Plug this into $y=mx+b$ :

$y=\frac{3}{2} x+b$

<u>2) Determine the y-intercept</u>

$y=\frac{3}{2} x+b$

Plug in the given point, (4,0)

$0=\frac{3}{2} (4)+b\\0=6+b$

Subtract both sides by 6

$0-6=6+b-6\\-6=b$

Therefore, -6 is the y-intercept of the line. Plug this into $y=\frac{3}{2} x+b$ as b:

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

I hope this helps!

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3 years ago

Express 0.24 as a percent

Hatshy [7]

Answer: 24%

Step-by-step explanation:

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3 years ago

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3 years ago

Through (2,2) parallel to y=x+4 <br>in slope intercept form.

Tema [17]

Answer:

y = x

Step-by-step explanation:

slope of y=x+4 is 1

parallel means same slope = 1

so y - 2 = 1*(x - 2)

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4 0

2 years ago

Please I need help!!

telo118 [61]

The regression equation which correctly models the data in this table is y = 1.49x - 107.5,

<h3>How to determine the regression equation?</h3>

From the table of data values, we have the following parameters:

∑x = 632

∑y = 404

∑x² = 80.142

∑xy = 51.448

Mathematically, the regression equation is represented by the following slope equation:

y = Bx + A

Next, we would determine A by using this expression:

A = (∑y·∑x² - ∑x·∑xy)/(n∑x² - (∑x)²)

A = (404×80,142 - 632×51,448)/(5×∑x² - (632)²)

A = (32,377,368 - 32,515136)/(5×80142 - 399,424)

A = -137,768/1286

A = 107.5

For B, we have:

B = (n∑xy· - ∑x·∑y)/(n∑x² - (∑x)²)

B = (5×51,448 - 632×404)/(5×∑x² - (632)²)

B = 1.49.

y = Bx + A

y = 1.49x - 107.5

Read more about regression equation here: brainly.com/question/28037520

#SPJ1

7 0

2 years ago

How do I simplify this?​

How do I simplify this?