Answer:
The value of q and p is 4 and -24 respectively.
Step-by-step explanation:
Being 
, the line x=4 is a vertical asymptote to the graph of f(x). The line r is an asymptote of a function if the graph of the function is infinitely close to the line r. That is, an asymptote is a line to which a function approaches indefinitely, without ever touching it.
Being a rational function that which can be expressed as the quotient of two polynomials, a vertical asymptote occurs when the denominator is 0, that is, where the function is not defined. In this case:
x - q= 0
Solving:
x= q
Being the line x=4 the vertical asymptote, then
<u><em>4=q</em></u>
Then the function f (x) is:
The y intercept is (0,4). This is, x= 0 and y=4. Replacing:
Solving:
4*(-4)= p+8
-16= p+8
-16 - 8= p
<u><em>-24= p</em></u>
<u><em>The value of q and p is 4 and -24 respectively.</em></u>
Answer:
Rectangle D is reflected over the x-axis and then translated 8 units right will result in rectangle E
Step-by-step explanation:
The coordinates of rectangle D are:
(-1, 1)
(-1, 4)
(-3, 1) and
(-3, 4)
The rule of reflection across x-axis is given by:
Next, translate this 8 unit right which is given by:
⇒(7, -1) , (5, -1) , (5, -4) and (7, -4) represents the coordinate of rectangle E.
Therefore, Rectangle D if reflected over the x-axis and then translated 8 units right will result in rectangle E
Answer:
ΔGHI and ΔDEF are similar by SSS criteria
Step-by-step explanation:
Consider triangle GHI and triangle DEF
In ΔGHI, GH = 2, HI =4 and GI = 3.5
In ΔDEF , DE =4, EF = 6 and DF = 7
GH/DE = 2/4 =1/2
HI/EF = 3/6 = 1/2
GI/DF = 3.5/7 = 1/2
The corresponding sides are in same ratio by SSS criteria
ΔGHI and ΔDEF are similar
Answer:
84.5
Step-by-step explanation:
Use trig functions to find x. Trig functions are special relationships which exits between the sides of right triangles. Since you need to find x the hypotenuse and you have the adjacent side to 77 degree angle use cosine.
Cos 77 = 19/x
0.22495 = 19/x
19/0.22495 = x
84.5 = x
