Find the center, vertices, and foci of the ellipse with equation x squared divided by one hundred plus y squared divided by sixty four = 1.

Step-by-step explanation:

The general equation of an ellipse is:

(x − h)²/a² + (y − k)²/b² = 1

where (h, k) is the center.

If a > b, the ellipse is horizontal, so the vertices are at (h ± a, k), and the foci are at (h ± c, k), where c² = a² − b².

If b > a, the ellipse is vertical, so the vertices are at (h, k ± b), and the foci are at (h, k ± c), where c² = b² − a².

x²/100 + y²/64 = 1

The center is (0, 0).

This is a horizontal ellipse, so the vertices are at (-10, 0) and (10, 0).

The distance between the foci and the center is c = √(100 − 64) = 6, so the foci are at (-6, 0) and (6, 0).

Graph: desmos.com/calculator/kd6z9qvhi0

figure c

step-by-step explanation:

hope this .

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752