1. there are 4 candidates for a literature scholarship, 6 for political science, and 5 for economics. in how many ways can these scholarships be awarded? a. 120 b. 95 c. 115 d. 110 e. 100 2. if a fair coin is flipped 5 times, calculate the number of different outcomes in which the last coin flip is heads. a. 12 b. 10 c. 14 d. 8 e. 16 3. a class has 25 boys and 18 girls. the teacher wants to select 1 boy and 1 girl to represent the class in a function. how many ways can the teacher make the decision? a. 380 b. 450 c. 400 d. 430 e. 410 a restaurant has 240 options on the menu for pizza. each option contains exactly one type of vegetable, one type of meat, and one type of cheese. if there are 5 bread types and 8 cheeses available, how many meat options are there? 4. a. 4 b. 7 d. 8 e. 6

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

answer: the resulting cross section is a rectangle. solution: a plane parallel to the base of a triangular prism will intersect a cross section that is the same shape as its bases. so the cross section is a triangle.

step-by-step explanation: