A test has twenty questions worth 100 points. The test consists of True False quedo points each and multiple choice questions worth 11 pointeach This system of equations
used to find how much of each question type he has
x 20
3. Ily=100
Where r represents the number of true false questions and y represents the multiple there
questions. The solution to the system is (15,5). What does this solution represent?

There are 5 multiple choice questions

Step-by-step explanation:

No of questions = 20

A test has 20 questions worth 100 points.

The test consists of True False question worth 3 points each and multiple choice questions worth 11 points each.

Let r represents the number of true false questions and y represents the multiple choice questions.

ATQ,

x+y = 20 (1)

3x+11y = 100 (2)

We need to find the number of questions of each type.

Multiply equation (1) by 3.

3x + 3y = 60 ...(3)

Subtract equation (2) from (3).

3x + 3y - (3x+11y) = 60-100

3x+3y-3x-11y = -40

-8y = -40

y = 5

Put the value of y in equation (1)

x+5=20

x = 15

The solution to the system is (15,5). Hence, there are 5 multiple choice questions and 15 true/false questions.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4