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2 years ago

Find the equation of the line through (10, 4) that is parallel to the line with the equation

Mathematics

1 answer:

lyudmila [28]2 years ago

6 0

Answer:

x + y = 14

Step-by-step explanation:

Parallel lines have the same slope, so the line's slope will be -1.

Plug this slope and the given point into y = mx + b to find b:

y = mx + b

4 = -1(10) + b

4 = -10 + b

14 = b

Then, plug this and the slope into y = mx + b

y = -x + 14

Then, put this into standard form by moving the x to the other side:

x + y = 14 is the equation in standard form

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How does the graph of f(x)=3lx+2l+4 relate to its parent function?

Sergeeva-Olga [200]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\

\begin{array}{rllll} 
% left side templates
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}$

$\bf \begin{array}{llll}
% right side info
\bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}
\\\\
\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\end{array}$

$\bf \begin{array}{llll}


\bullet \textit{ vertical shift by }{{ D}}\\
\qquad if\ {{ D}}\textit{ is negative, downwards}\\\\
\qquad if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}
\end{array}$

now, with that template above in mind, let's see this one

$\bf parent\implies f(x)=|x|
\\\\\\
\begin{array}{lllcclll}
f(x)=&3|&1x&+2|&+4\\
&\uparrow &\uparrow &\uparrow &\uparrow \\
&A&B&C&D
\end{array}$

A=3, B=1, shrunk by AB or 3 units, about 1/3
C=2, horizontal shift by C/B or 2/1 or just 2, to the left
D=4, vertical shift upwards of 4 units

check the picture below

7 0

2 years ago

Pls help with sum geometry

kaheart [24]

YES! quite easily.

I hope you can see the two pairs of corresponding angles between the parallel lines. they'll be equal

and then there's a pair of vertically opposite angle at centre.

that means all pairs of corresponding angles are equal, thus, triangles are similar by AAA

4 0

3 years ago

Read 2 more answers

What is the final step in solving the inequality - 2(5 - 4x)< 6x - 4?

mezya [45]

Answer: X < 3

Step-by-step explanation:

-6 < -2x -- Divide by -2

3 > x --- The sign flips when dividing in negative numbers.

Since three is greater than x

X is less than 3

meaning

X < 3

3 0

3 years ago

The amount of attendance at a dinner must go from being 57 people to 65 people. What is the percent of change

cestrela7 [59]

Answer:

Step-by-step explanation:

5 0

2 years ago

Need a quick answer please

Lesechka [4]

Answer:

AC = 38

Step-by-step explanation:

AB = BC

4 - 5x = 2x + 25

-7x = 21

x = -3

AC = 2(BC) = 2(2x + 25) = 4x + 50 = 4(-3) + 50 = -12 + 50 = 38

AC = 38

4 0

3 years ago