Answer:
(x,y) -> (x, -y)
Step-by-step explanation:
This is a reflection about the x-axis.
Algebraically, it can be represented by:
(x,y) -> (x, -y)
since the position along the x-axis does not change, and the y-coordinates are flipped about the x-axis, therefore flipped in sign.
Answer: (A) vertical asymptote: x = 2, horizontal asymptote: y = 1
<u>Step-by-step explanation:</u>
<u>Vertical Asymptote</u> is the restriction on the x-value. The denominator cannot be zero, so x - 2 ≠ 0 ⇒ x ≠ 2
The restricted value on x is when x = 2 <em>which is the vertical asymptote</em>
<u>Horizontal Asymptote</u> (H.A.) is the restriction on the y-value. This is a comparison of the numerator (n) and denominator (m). There are 3 rules that will help you:
- n > m No H.A. (use long division to find slant asymptote)
- n = m H.A. is the coefficient of n divided by coefficient of m
- n < m H.A. is 0
In the given problem, n < m so y = 0, however there is also a vertical shift of up 1 so the H.A. also shifts up. This results in H.A. of y = 1
<span>2y = 4x + 8 ------> y = 2x + 4
4y = 4x + 20 ------> y = x+5
2x+4 =x+5
x = 1
y=x+5=1+5=6
Check:
</span>2*6 = 4*1 + 8 , 12 =12
4*6 = 4*1 + 20, 24 =24<span>
x=1,y=6
(1,6)
</span>
Answer:
Quotient: x+7
Remainder: -2
Step-by-step explanation:
Divide the terms (x² ÷ x =x)↓
(x² + 11x + 26) ÷ (x + 4) =x
Subtract x² + 4x (You have to the sign if each term)
(x² + 11x + 26) ÷ (x + 4) =x
-x² - 4x
-------------------
7x + 26
Divide the terms (7x ÷ x = 7)
x² + 11x + 26) ÷ (x + 4) =x + 7
Multiply the quotient by the dividend (x + 4) × 7 = 7x+28
(x² + 11x + 26) ÷ (x + 4) =x
-x² - 4x
-------------------
7x + 26
7x + 28
------------------
= -2 Remainder
Answer: $4840
Step-by-step explanation:
A = p(1+r/n)^nt
A = 2800(1+0.043)^13
A = 4840
