Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation. (-4,6); y=1/4x-3 (write an equation for the perpendicular line in slope-intercept form.)

NOTE: Perpendicular line have opposite(negative) reciprocal slope

For the line y = 1/4x - 3 it has slope of 1/4

but the perpendicular line with point (-4,6) has slope of -4 (negative reciprocal)

(y - y1) = m (x - x1)

(y - 6 ) = -4 (x --4)

(y - 6) = -4 (x + 4)

y - 6 = -4x -16

y = -4x -16 + 6

y = -4x -10

none of the option is correct.

step-by-step explanation:

it says to find which expression equals 9^3 sqrt 10 = ?

9^3 sqrt 10 = 729 sqrt 10.

checking option a. 5 sqrt 10 + 4 sqrt 10

5 sqrt 10 + 4 sqrt 10

= 9 sqrt 10.

checking option b. 5^3 sqrt 10 + 4^3 sqrt 10

5^3 sqrt 10 + 4^3 sqrt 10

= 125 sqrt 10 + 64 sqrt 10

= 189 sqrt 10.

checking option c. 5 sqrt 10 + 4^3 sqrt 10

5 sqrt 10 + 4^3 sqrt 10

= 5 sqrt 10 + 64 sqrt 10

= 69 sqrt 10.

checking option d. 5^3 sqrt 10 + 4 sqrt 10

5^3 sqrt 10 + 4 sqrt 10

= 125 sqrt 10 + 4 sqrt 10

= 129 sqrt 10.

hence, none of the option is correct.

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

= 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls