Identify each of the following variables as continuous or discrete.
a. the weight of a dog
b. the result of a roll of dice
c. the weight of a bunch of bananas
d. the number of people in line at a box office to purchase theater tickets

a) a continuous variable

b) a discrete variable

c) a continuous variable

d) a discrete variable

Step-by-step explanation:

Well first we need to define what are the continuous and discrete variables. Discrete variables are those whose values are obtained by counting, but continuous variables those whose values are obtained by measurement.

a) The weight of a dog can be measured. Therefore, it is a continuous variable.

b) The result of a roll of dice can be counted. Therefore, it is a discrete variable.

c) The weight of a bunch of bananas can be measured. Therefore, it is a continuous variable.

d) The number of people in line at a box office to purchase theater tickets can be counted. Therefore, it is a discrete variable.

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form