Which is the equation in slope-intercept form for the line that passes through (-2, 15) and is perpendicular to 2x + 3y = 4?

a. y = 2/3x + 18
b. y = 3/2x + 18
c. y = 3/2x - 12
d. y = -3/2x + 18

B

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 2x + 3y = 4 into this form

Subtract 2x from both sides

3y = - 2x + 4 ( divide all terms by 3 )

y = - x + ← in slope- intercept form

with slope m = -

Given a line with slope m then the slope of a line perpendicular to it is

= - = - = , hence

y = x + c ← is the partial equation of the perpendicular line

To find c substitute (- 2, 15) into the partial equation

15 = - 3 + c ⇒ c = 15 + 3 = 18

y = x + 18 → B

12.5 feet

step-by-step explanation:

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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