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3 years ago

What is the domain of f(x)=-5x+4

Mathematics

1 answer:

ANTONII [103]3 years ago

4 0

Answer:

f(x) = -5x + 4

Domain refers to the values of x that would result to a defined value of y. Since the given f(x) is a linear function, then all the values of x would give a corresponding value of y. So, the domain of f(x)=-5x+4 are all real numbers.

Or, plot the given equation to check.

The graph of f(x)=-5x+4 is shown below.

Since the graph is a straight line and can be extended continuously on both ends, this indicates that every values of x, there is a corresponding value of y.

Hence, the domain of the given function are all real numbers.Step-by-step explanation:

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3 years ago

Find the slope of a line through (4, 5) and (4, -5). Determine if the line is vertical, horizontal, or neither.

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2 years ago

Two boats depart from a port located at (–8, 1) in a coordinate system measured in kilometers and travel in a positive x-directi

miss Akunina [59]

Answer:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

Step-by-step explanation:

1st boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=1\\ \\b=-2a$

Equation:

$y=ax^2 -2ax+c$

The y-coordinate of the vertex:

$y_v=a\cdot 1^2-2a\cdot 1+c\Rightarrow a-2a+c=10\\ \\c-a=10$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-2a\cdot (-8)+c\\ \\80a+c=1$

Solve:

$c=10+a\\ \\80a+10+a=1\\ \\81a=-9\\ \\a=-\dfrac{1}{9}\\ \\b=-2a=\dfrac{2}{9}\\ \\c=10-\dfrac{1}{9}=\dfrac{89}{9}$

Parabola equation:

$y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}$

2nd boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=0\\ \\b=0$

Equation:

$y=ax^2+c$

The y-coordinate of the vertex:

$y_v=a\cdot 0^2+c\Rightarrow c=-7$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-7\\ \\64a-7=1$

Solve:

$a=-\dfrac{1}{8}\\ \\b=0\\ \\c=-7$

Parabola equation:

$y=\dfrac{1}{8}x^2 -7$

System of two equations:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

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Answer:

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2 years ago

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12^13–12^12+12^11 is divisible by 7 and 19.

fiasKO [112]

Answer:

The statement is true

Step-by-step explanation:

The question is as following :

$12^{13}-12^{12}+12^{11}$ is divisible by 7 and 19, true or false?

The given expression is $12^{13}-12^{12}+12^{11}$

Take $12^{11}$ as a common

$12^{13}-12^{12}+12^{11} = 12^{11}*(12^2-12^1+12^0)\\= 12^{11} *(144-12+1)\\=12^{11} * 133\\= 12^{11} * 7 * 19$

So, $12^{11} * 7 * 19$ divided 7 = $12^{11} * 19$

And $12^{11} * 7 * 19$ divided 19 = $12^{11} * 7$

$12^{13}-12^{12}+12^{11}$ is divisible by 7 and 19 (True)

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2 years ago