If at least one independent variable is between-groups and at least one is within-groups, the design is referred to as:

A variable is an object that you are trying to measure. It has two types; independent and dependent variable. An independent variable is a variable that is not affected by other variables. A dependent variable on the other hand is a variable that depends on the other variables. Suppose you want to know the quality of sleep of the students in their academic performance. The quality of sleep is the independent variable and the academic performance is the dependent variable. There are also controlled variables in an experiment. A controlled experiment is an experimental setup designed to test the hypotheses. It has one or more conditions (independent variables) and measures (dependent variables). It is necessary to change more than one variable, but all of the experimental conditions will be controlled so that only the variables being examined change and the amount or way of change is measured.

where is the figure

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