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Agata [3.3K]
3 years ago
12

The equation of line CD is y = −2x − 2. What is the equation of a line parallel to line CD in slope-intercept form that contains

point (4, 5)
Mathematics
1 answer:
aniked [119]3 years ago
6 0

Answer:

\[y=-2x+13\]

Step-by-step explanation:

Equation of the line CD is given as \[y=-2x-2\]

Slope of the line CD = -2

Slope of the line parallel to CD = -2

Equation of the line parallel to CD is given by \[y=mx+c\]

\[y=-2x+c\]

But this line passes through (4,5)

Substituting the values in the equation:

\[5=-2*(4)+c\]

=> \[c=5+8=13\]

So the overall equation of the parallel line is given by \[y=-2x+13\]

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Consider the following series. 1 4 + 1 8 + 1 12 + 1 16 + 1 20 Determine whether the series is convergent or divergent. Justify y
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The series diverges

Step-by-step explanation:

First, let's find the sequence:

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4,8,12,16,20,...,=4n\hspace{8};\hspace{3}n\in Z

Hence, we can represent the series as:

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$$\Sigma a_n$$\\Diverges\hspace{3}if\\\\ \lim_{n \to \infty} a_n \neq 0

So:

\lim_{n \to \infty} 4n= 4 \lim_{n \to \infty} n\\ \\ \lim_{n \to \infty} n=\infty\\ \\4\infty= \infty\\\\Hence\\\\ \lim_{n \to \infty} 4n=\infty

Therefore, by the zero test, the series diverges

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Given the function f ( x ) = 4 x 2 − 5 x + 7 f ( x ) = 4 x 2 - 5 x + 7 . Calculate the following values: f ( − 2 ) = f ( - 2 ) =
qaws [65]

Given the function f(x) = 4x² - 5x + 7, the output values of f(-2), f(-1), f(0), f(1) and f(2) are 33, 16, 7, 6 and 13 respectively.

<h3>What are the output values of the given numbers in the function?</h3>

Given the function is the question;

  • f(x) = 4x² - 5x + 7
  • f(-2) = ?
  • f(-1) = ?
  • f(0) = ?
  • f(1) = ?
  • f(2) = ?

To determine the output value of f(-2), replace all occurrence of x with -2 in the function and simplify.

f(x) = 4x² - 5 x + 7

f(-2) = 4(-2)² - 5(-2) + 7

f(-2) = 4×4 + 10 + 7

f(-2) = 16 + 10 + 7

f(-2) = 33

To determine the output value of f(-1), replace all occurrence of x with -1 in the function and simplify.

f(x) = 4x² - 5 x + 7

f(-1) = 4(-1)² - 5(-1) + 7

f(-1) = 4×1 + 5 + 7

f(-1) = 4 + 5 + 7

f(-1) = 16  

To determine the output value of f(0), replace all occurrence of x with 0 in the function and simplify.

f(x) = 4x² - 5 x + 7

f(0) = 4(0)² - 5(0) + 7

f(0) = 0 + 0 + 7

f(0) = 7  

To determine the output value of f(1), replace all occurrence of x with 1 in the function and simplify.

f(x) = 4x² - 5 x + 7

f(1) = 4(1)² - 5(1) + 7

f(1) = 4×1 - 5 + 7

f(1) = 4 - 5 + 7

f(1) = 6  

To determine the output value of f(2), replace all occurrence of x with 2 in the function and simplify.

f(x) = 4x² - 5 x + 7

f(2) = 4(2)² - 5(2) + 7

f(2) = 4×4 - 10 + 7

f(2) = 16 - 10 + 7

f(2) = 13

Given the function f(x) = 4x² - 5x + 7, the output values of f(-2), f(-1), f(0), f(1) and f(2) are 33, 16, 7, 6 and 13 respectively.

Learn more about composite function here: brainly.com/question/20379727

#SPJ1

3 0
2 years ago
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