Determine the domain and range. Please help!!

Mathematics

1 answer:

kipiarov [429]2 years ago

8 0

The domain is the set of all numbers. The range is also the set of all real numbers.

Why is this the case? Because the line extends forever in both directions along the x and y axis. We can plug in any x value and solve for y, or vice versa, and we don't have any restrictions for the input or output.

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To write "the set of all real numbers" in interval notation, you would write $(-\infty, \infty)$

This is the interval from negative infinity to positive infinity, spanning the entire real number line.

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Line CD passes through points C(3, –5) and D(6, 0). What is the equation of line CD in standard form? 5x + 3y = 18 5x – 3y = 30

ddd [48]

$\bf C(\stackrel{x_1}{3}~,~\stackrel{y_1}{-5})\qquad 
D(\stackrel{x_2}{6}~,~\stackrel{y_2}{0})
\\\\\\
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{0-(-5)}{6-3}\implies \cfrac{0+5}{6-3}\implies \cfrac{5}{3}
\\\\\\
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-5)=\cfrac{5}{3}(x-3)\implies y+5=\cfrac{5}{3}(x-3)$

$\bf \stackrel{\textit{multiplying both sides by LCD of 3}}{3(y+5)=3\left[ \cfrac{5}{3}(x-3) \right]}\implies 3y+15=5(x-3)
\\\\\\
3y+15=5x-15\implies -5x+3y=-30\implies \stackrel{\textit{multiplying by -1}}{5x-3y=30}$

bearing in mind the standard form uses all integers, and the x-variable cannot have a negative coefficient.

6 0

2 years ago

Read 2 more answers

Multiply.<br> (d+7)(d-7)<br> Simplify your answer.

romanna [79]

Answer:

$\huge\boxed{(d+7)(d-7)=d^2-49}$

Step-by-step explanation:

$\bold{METHOD\ 1:}\\\\(d+7)(d-7)\qquad|\text{use}\ (a+b)(a-b)=a^2-b^2\\\\=d^2-7^2=d^2-49\\\\\bold{METHOD\ 2:}\\\\(d+7)(d-7)\qquad|\text{use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(d)(d)+(d)(-7)+(7)(d)+(7)(-7)\\\\=d^2-7d+7d-49\qquad|\text{combine like terms}\\\\=d^2+(-7d+7d)-49\\\\=d^2-49$