1,000,000,000 standard form
one billion word form
<u>Step-by-step explanation:</u>
transform the parent graph of f(x) = ln x into f(x) = - ln (x - 4) by shifting the parent graph 4 units to the right and reflecting over the x-axis
(???, 0): 0 = - ln (x - 4)

0 = ln (x - 4)

1 = x - 4
<u> +4 </u> <u> +4 </u>
5 = x
(5, 0)
(???, 1): 1 = - ln (x - 4)

1 = ln (x - 4)

e = x - 4
<u> +4 </u> <u> +4 </u>
e + 4 = x
6.72 = x
(6.72, 1)
Domain: x - 4 > 0
<u> +4 </u> <u>+4 </u>
x > 4
(4, ∞)
Vertical asymptotes: there are no vertical asymptotes for the parent function and the transformation did not alter that
No vertical asymptotes
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transform the parent graph of f(x) = 3ˣ into f(x) = - 3ˣ⁺⁵ by shifting the parent graph 5 units to the left and reflecting over the x-axis
Domain: there is no restriction on x so domain is all real number
(-∞, ∞)
Range: there is a horizontal asymptote for the parent graph of y = 0 with range of y > 0. the transformation is a reflection over the x-axis so the horizontal asymptote is the same (y = 0) but the range changed to y < 0.
(-∞, 0)
Y-intercept is when x = 0:
f(x) = - 3ˣ⁺⁵
= - 3⁰⁺⁵
= - 3⁵
= -243
Horizontal Asymptote: y = 0 <em>(explanation above)</em>
The next number in this pattern should be A)28
Answer:
4/5:2/5 = ratio of degrees to time
2/5*2.5 = 1 min
4/5*2.5 = 10/5 = 2
2 degrees every min
Step-by-step explanation:
Keiko has a total of $5200
x is the amount of money in larger account
y is the amount of money in smaller account
x - y = $900
and x + y = $5200
<u>This creates two simultaneous equations:</u>
x - y = $900 ... (i)
x + y = $5200 ... (ii)
Adding (i) and (ii) :
2x = $6100 , x = $3050
y = x - $900 = $3050 - $900 = $2150
The amount of money in larger account (x) = $3050
The amount of money in smaller account (y) = $2150