The amendments that lowered the voting age to eighteen and gave women the right to vote were the thirteenth amendment and the fifteenth amendment. the twenty-fourth amendment and the twenty-fifth amendment. the eighteenth amendment and the twenty-first amendment. the nineteenth amendment and the twenty-sixth amendment.

Correct

Context/details:

19th Amendment

The 19th Amendment to the Constitution reads as follows:

The proposal to add such an amendment was first introduced in Congress in 1878, but Congress did not pass the amendment till 1919 -- after the experience of women taking on greater roles in the country during the First World War.  The amendment achieved ratification by a sufficient number of states and was added to the Constitution by August, 1920.

26th Amendment

During the 1960s in America, protests against the Vietnam War were active on college campuses across the country.  Part of those protests were the demands of young people chanting, "Old enough to fight, old enough to vote."  Since 18 was old enough to be drafted to fight in the war, young people argued for their right to vote as full citizens.

The 26th Amendment was passed by Congress on March 23, 1971.  It was ratified by the states faster than any other amendment, achieving ratification by July 1, 1971.

The 26th Amendment is worded as follows:  

the Nineteenth Amendment and the Twenty-sixth Amendment.

Explanation:

c, they united with once

offline recommendation systems option b

because recommendation systems produce a list of two ways

1. through collaborative filtering

or

2. through content-based filtering