What is the equation of the line that is perpendicular to a line with a slope of 2, and intersects that line at (4,2)? y=−2x+10 y=−1/2x+4 y=−1/2x−4 y=2x−6

The equation would be y = -1/2x + 4

Step-by-step explanation:

In order to find the equation of the line, we first need to look at the slope. Perpendicular lines have opposite and reciprocal slopes. Since the original slope was 2, we know the perpendicular slope would be -1/2. Now we can use this and a point in point-slope form to find the equation.

y - y1 = m(x - x1)

y - 2 = -1/2(x - 4)

y - 2 = -1/2x + 2

y = -1/2x + 4

t = 3

step-by-step explanation:

put t = 3 in this expression :

(3²-1)(3²-2)(3² - 3)(3² - 4) = 8×7×6×5 = 56×30 = 1680

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true