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3 years ago

Which of these true conditional statements has a false converse ?

Mathematics

2 answers:

Harlamova29_29 [7]3 years ago

7 0

Answer:

Option B has a false converse.

Step-by-step explanation:

When we switch the hypothesis and conclusion of a conditional statement, then it is called the converse of that statement.

Here options A and C have a true converse.

If n is even then it is divisible by 2.

If 2x=4, then x=2.

But if x>10, then x>5 does not have a true converse.

We can write the converse as : if x>5 , then x>10 . This cannot be necessarily true as you can have x=6 which is not >10.

Therefore, option B has a false converse.

Digiron [165]3 years ago

3 0

B has a false converse.
let's make it into converse.
if x>5, then x>10.
this doesn't make sense because x could be 6 and 6 is smaller than 10

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Answer:

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Step-by-step explanation:

Let x be the number of tons of high grade steel and y be the number of tons ow low grade steel needed.

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NASA orders 500 tons of steel, so

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and specifies that it must be in the proportion 80% iron and 20% magnese, so

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From the first equation,

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Substitute it into the second equation:

$0.85(500-y)+0.67y=400\\ \\425-0.85y+0.67y=400\\ \\-0.18y=-25\\ \\y=\dfrac{2,500}{18}=138\dfrac{8}{9}\ tons\\ \\x=361\dfrac{1}{9}\ tons$

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