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11111nata11111 [884]

2 years ago

12

If f(x) = x2 - 1, and g(x) = x + 2, then f(g(x)) = [? ]x2+[?]x+[?]

1 answer:

klio [65]2 years ago

4 0

Step-by-step explanation:

f.g(x) = f(x+2)

=(x+2)2 -1

=(x2+2*x*2+4)-1

=x2+4x+4-1

=x2+4x+3

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Two perpendicular lines intersect at the origin. If the slope of the first line is -1/2, what is the equation of the second line

Dovator [93]

bearing in mind that perpendicular lines have <u>negative reciprocal</u> slopes.

now, they both intersect at 0,0, namely they both pass through it, we know the slope of the first one, so

$\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{1}{2}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{2}{1}}\qquad \stackrel{negative~reciprocal}{+\cfrac{2}{1}\implies 2}}$

so, we're really looking for the equation of a line whose slope is 2, and runs through (0,0).

$\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})~\hspace{10em} slope = m\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=2(x-0)\implies y=2x$

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2 years ago

Factor equation<br> x2 – 5x – 6

Bingel [31]

Answer:

(x+1) (x−6)

Step-by-step explanation:

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2 years ago

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A cell phone provider charges $30 each month to have a cell on their plan, but their talk and text are not free. It costs $0.05

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The answer is 10x +0.05x +30=y

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The sum of 2112 + 2212 + 2312 when divided by 4, leaves no remainder. What will be the remainder when the sum of 2113 + 2213 + 2

trasher [3.6K]

Step-by-step explanation:

2112 + 2212 + 2312 / 4 leaves no remainder, as already the individual numbers could be divided by 4 without remainder.

2113 = 2112 + 1

2213 = 2212 + 1

so, we get a remainder of +1 and +1 for these 2 numbers, so we get in total a remainder of +2.

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2 years ago

15. Construct the slope-intercept form equation of the line passing through (-5,23) and (10,-5).

Radda [10]

Answer:

15<em>y</em> = -28 <em>x</em> + 205.

Step-by-step explanation:

Slope intercept form of equation is <em>y = mx + c</em> where m is slope and c is the y intercept.

Now slope of line passing through points (-5, 23) and (10, -5):

$m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} } = \frac{-5 -23}{10 + 5} = \frac{-28}{15}$

Now equation of line:

<em> y = mx + c</em>

substituting the value of m in above expression,

$y = -\frac{28}{15} x + c$

Now, since the line is passing through the point (-5, 23) therefore, x = -5 and y = 23. By substituting these values in above equation,

$23 = -\frac{28}{15} \times (-5) + c$

$23 = \frac{28}{3} + c$

$c = 23 - \frac{28}{3} = \frac{69 - 28}{3} = \frac{41}{3}$

So equation of line in slope intercept form:

$y = -\frac{28}{15} x + \frac{41}{3}$

Further solving,

15<em>y</em> = -28 <em>x</em> + 205.

3 0

2 years ago