Ria solves the equation 5 + 3r = 4 + 4r and gets r = r. She concludes that the
1 answer:
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Answer:
a. True
b. False
c. True
Step-by-step explanation:
<em>a.</em>
12 ÷ is equal to
Personally, I hate fractions so I make these into decimals by dividing the numerator by the denominator, but I'll do both to show you.
Decimal:
In your calculator, type 12
Then the division sign.
Then make parenthesis
in the parenthesis you will have (36/7)
End parenthesis
Press the equal sign and you should get a grand total of 2.333 repeating
To see if its equal to , you put 7 divided by 3 in your calculator next
If you do, you should get 2.333 repeating.
This shows they are equal.
Fraction:
<em>Keep, switch, flip</em>
The first step will be to make your whole number into a fraction.
÷
The first thing we use is keep
The first number in this equation is that
We're going to leave it as it is.
Next we have to use switch. To do this we make the ÷ into a ×
So your problem should look as so:
Lastly, we have flip.
The last number in our equation is
We are going to use the reciprocal of it which would be
So your problem should now look like this:
At this point, we can now cross multiply
So from the numerator 12 to the denominator 36, if we divided 36 by 12 its 3.
But the denominator 1 and the numerator 7 are already divided as much as they can be.
So now your expression should be:
This is because of that cross multiplication we did.
12 goes into 36, 3 times so 3 would substitute 36 while 1 would substitute 12
So now its just basic multiplication
So we can conclude that does in fact equal
<em>b.</em>
Multiplying a number by is the same as dividing by 2
This is false
When you multiply by 2, you are doubling the original number
When you multiply by , you are cutting the number in half
Ex:
18 * 2 = 36
18 * = 9
If it was dividing instead of multiplying, this would be true but since halves the number whether you multiply or divide it would not be true.
<em>c.</em>
of a number is less than this number
Basically, what this is saying is if you divide by , would it give you less than the original number.
The answer would be true
It would be division first of all because your looking for <em>of</em> a number.
Secondly, if you divide by a fraction or decimal, the number tends to be smaller than the number you started with.
Ex:
6 ÷ = 4 or 6 ÷ 1.5 = 4
Ex2:
682 ÷ = 454.6 repeating or 682 ÷ 1.5 = 454.6 repeating
I hope this helps! Don't be afraid to reach out with any further questions!
Consider the picture.
Let MN be the midsegment of the trapezoid.
That is M is the midpoint of AD, N is the midpoint of BC.
Being the midsegment of the trapezoid, MN is parallel to the bases.
Let O and K be the intersections of the diagonals with the midsegment.
MN//AB, so MO//AB, and since M is the midpoint of DA, O must be the midpoint of DB,
Similarly we prove that K is the midpoint of CA.
Thus O is F and K is E.
O and K lie on the midsegment MN, so F and E lie on the midsegment.
MO is a midsegment of triangle ABD so |MO|=1/2 |AB|=1/2 * 10=5
MK is a midsegment of triangle ADC, so |MK|=1/2 * |DC|=1/2 * 22=11
|OK|=|MK|-|MO|=11-5=6 (units)
Let MN be the midsegment of the trapezoid.
That is M is the midpoint of AD, N is the midpoint of BC.
Being the midsegment of the trapezoid, MN is parallel to the bases.
Let O and K be the intersections of the diagonals with the midsegment.
MN//AB, so MO//AB, and since M is the midpoint of DA, O must be the midpoint of DB,
Similarly we prove that K is the midpoint of CA.
Thus O is F and K is E.
O and K lie on the midsegment MN, so F and E lie on the midsegment.
MO is a midsegment of triangle ABD so |MO|=1/2 |AB|=1/2 * 10=5
MK is a midsegment of triangle ADC, so |MK|=1/2 * |DC|=1/2 * 22=11
|OK|=|MK|-|MO|=11-5=6 (units)