What is the slope and the perpendicular slope on the points given?

The slopes are:

blue: 4/3 = 1⅓

green: -4/3 = -1⅓

I used rise over run to work these out

- and

Step-by-step explanation:

Calculate the slope m using the slope formula

m =

with (x₁, y₁ ) = (- 8, 8) and (x₂, y₂ ) = (4, - 8) ← 2 points on green line

m = = = -

Repeat with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (4, 2) ← 2 points on the blue line

m = =

Since the product of the slopes = - × = - 1

Then the lines are perpendicular

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

~

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.