Answer:
slope =
and -
, perpendicular
Step-by-step explanation:
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
y =
x + 11 is in this form with m = 
Rearrange 7x + 3y = 13 into this form
subtract 7x from both sides
3y = - 7x + 13 ( divide all terms by 3 )
y = -
x +
← in slope- intercept form
with m = - 
• Parallel lines have equal slopes
• The product of perpendicular slopes = - 1
The lines are not parallel since slopes are not equal
× -
= - 1
Hence lines are perpendicular
Answer:
f(g(x)) = 4x² + 16x + 13
Step-by-step explanation:
Given the composition of functions f(g(x)), for which f(x) = 4x + 5, and g(x) = x² + 4x + 2.
<h3><u>Definitions:</u></h3>
- The <u>polynomial in standard form</u> has terms that are arranged by <em>descending</em> order of degree.
- In the <u>composition of function</u><em> f </em>with function <em>g</em><em>, </em>which is alternatively expressed as <em>f </em>° <em>g,</em> is defined as (<em>f </em> ° <em>g</em>)(x) = f(g(x)).
In evaluating composition of functions, the first step is to evaluate the inner function, g(x). Then, we must use the derived value from g(x) as an input into f(x).
<h3><u>Solution:</u></h3>
Since we are not provided with any input values to evaluate the given composition of functions, we can express the given functions as follows:
f(x) = 4x + 5
g(x) = x² + 4x + 2
f(g(x)) = 4(x² + 4x + 2) + 5
Next, distribute 4 into the parenthesis:
f(g(x)) = 4x² + 16x + 8 + 5
Combine constants:
f(g(x)) = 4x² + 16x + 13
Therefore, f(g(x)) as a polynomial in <em>x</em> that is written in standard form is: 4x² + 16x + 13.
This is the answer its easy just simplify the inequality
Given is a piecewise function which follows different expressions according the the value of input x.
Given 
It says to find f(-4) i.e. the value of function f(x) at x = -4.
At point x = -4, f(x) is x³, if -5 ≤ x ≤ 2.
So, f(-4) = (-4)³
f(-4) = -4 × -4 × -4
f(-4) = -64.
Hence, option A is correct i.e. -64.
$49.06 x 100 = 4906 cents
4906/200= 24.53 = approx. 25 cents