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3 years ago

Which function represents a reflection of f(x) = (2)x over the x-axis?

Mathematics

1 answer:

Xelga [282]3 years ago

7 0

To reflect across the x axis y=-f(x) the y coordinate's sign is changed and the x coordinates stay the same.

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Select the pair of equations whose graphs are perpendicular.

viktelen [127]

$k:\ y=m_1x+b_1\ \ \ \ and\ \ \ \ l:\ y=m_2x+b_2\\ \\the\ line\k\ is\ perpendicular\ to\ the\ line\ l\ \ \ \Leftrightarrow\ \ \ m_1\cdot m_2=-1\\----------------------------\\\\A.\\2y=-3x+5\ \ \Rightarrow\ \ \ y=- \frac{3}{2} x+2.5\ \ \Rightarrow\ \ m_1=- \frac{3}{2} \\\\2x+3y=4\ \ \Rightarrow\ \ 3y=-2x+4\ \ \Rightarrow\ \ y=- \frac{2}{3}x+1 \frac{1}{3} \ \ \Rightarrow\ \ m_2=- \frac{2}{3} \\\\m_1\cdot m_2=- \frac{3}{2} \cdot (- \frac{2}{3})=1 \neq -1$

$B.\\5x-8y=9\ \ \Rightarrow\ \ -8y=-5x+9\ \ \Rightarrow\ \ \ y= \frac{5}{8} x-1 \frac{1}{8} \ \Rightarrow\ \ m_1= \frac{5}{8} \\\\12x-5y=7\ \Rightarrow\ \ -5y=-12x+7\ \ \Rightarrow\ \ y= \frac{12}{5}x-1 \frac{2}{5} \ \ \Rightarrow\ \ m_2= \frac{12}{5} \\\\m_1\cdot m_2= \frac{5}{8} \cdot \frac{12}{5}= \frac{3}{2} \neq -1$

$C.\\y=2x-7\ \ \Rightarrow\ \ m_1=2 \\\\x+2y=3\ \Rightarrow\ \ 2y=-x+3\ \ \Rightarrow\ \ y= -\frac{1}{2}x+1 \frac{1}{2}\ \ \Rightarrow\ \ m_2=- \frac{1}{2} \\\\m_1\cdot m_2= 2 \cdot (- \frac{1}{2})= -1\ \ \Rightarrow\ \ y=2x-7\ \ \ \ \perp\ \ \ \ x+2y=3$

$
D.\\x+6y=8\ \ \Rightarrow\ \ 6y=-x+8\ \ \Rightarrow\ \ \ y=- \frac{1}{6} x+1 \frac{1}{3}\ \ \Rightarrow\ \ m_1= -\frac{1}{6} \\\\y=2x-8\ \Rightarrow\ \ m_2= 2 \\\\m_1\cdot m_2= -\frac{1}{6} \cdot2=- \frac{1}{3} \neq -1$

7 0

3 years ago

Find a4 for the arithmetic series with S4=-36 and a1=9

erastova [34]

ANSWER

The 4th term is -27

EXPLANATION

The sum of the first n-terms of an arithmetic sequence is

$S_n= \frac{n}{2} (2a_1+d(n-1))$

It was given that,

$S_4 = - 36$

$a_1 = 9$

$- 36= \frac{ 4}{2} (2 \times 9+d(4-1))$

$-36=2(18+3d)$

$-18=18+3d$

$-18 - 18 = 3d$

$3d = - 36$

$d = - 12$

The n-term is given by:

$a_n=a_1+ (n-1)d$

We substitute n=4 to get,

$a_4=9+ (4-1) \times -12$

$a_4=9+ 3\times -12$

$a_4=9 - 36$

$a_4= - 27$

5 0

3 years ago

What is the slope of a line perpendicular to the line whose equation is 9x-6y=36

VladimirAG [237]

Answer: -2/3

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Solve using the substitution method<br> 4x-2y=8 <br> y=1/2x +2

bekas [8.4K]

Hello there! the answer would be x = 3/4.

You are given the two equations: 4x - 2y = 8 and y = 1/2x + 2. You are asked to solve via substitution. To do this, substitute the value of y in the second given equation into the first given equation, and solve using PEMDAS.

4x - 2(1/2x + 2) = 8 - Start by distributing 2 into (1/2x + 2).

4x - 1x + 4 = 8 - Combine like terms.

3x + 4 = 8 - Subtract 4 from both sides.

3x = 4 - divide both sides by 3.

x = 3/4. This is your final answer.

I hope this was helpful, have a great day! :)

7 0

3 years ago

what is the quotient of 0.457 and 0.12? round to the hundredths place show your work Will.mark brainiest

ExtremeBDS [4]

I stopped the division process once I got to the thousandths place. 0.457 ÷ 0.12 ≈ 3.808. Rounded to the hundredths place, the answer is 3.81.

3 0

4 years ago