Write the sum of the three angles and set this sum equal to 180. Use (degree measure) to denote the third, unknown, angle:
4x - 7 + 6x-4 + (degree measure) = 180
Now subtract 4x - 7 + 6x-4 from both sides. We get:
(degree measure) = 180 - (4x - 7 + 6x-4). Simplify this:
= 180 + 7 - 4x - 6x + 4, or
= 180 + 11 - 10x, or
(degree measure) = 191 - 10x (answer)
This represents the degree measure of the third angle in the triangle.
Machiavelli promoted the idea that a ruler should be gentle most of the time, but when necessary the ruler must make use of any form of manipulation, deceit, and even murder to achieve his ends.
Answer:
1, 4 or 7
Step-by-step explanation:
The divisibility rule/shortcut for 3 is that the sum of its digits is divisible by 3. So, you currently have 29 (7+1+7+6+2+6+0), and you have to make that number divisible by 3.
adding 1 gets you 30, which we know is divisible by 3.
then, instead of trying every digit, we can note that
30 , 33 , 36 , 39 ....
are divisible by 3.
But the most we can add to the sum of 29 is 9 (because that is the highest digit possible)--so numbers above 38 are irrelevant
so, we want to find out if we can make 29 into 30, 33, or 36
adding 1 to 29 = 30
adding 4 to 29 = 33
adding 7 to 29 = 36
So, by making the first digit 1 , 4 , or 7, you make the number divisible by 3 (making the sentence true)
-- A rectangle has 4 sides.
-- Each side has the same length as the side directly across from it.
-- So there are two sides that are both the width of the rectangle,
and another two sides that are both the length of the rectangle.
-- In this particular rectangle, when you add up all four sides,
the sum is 32 feet.
-- The width of the rectangle is 9 feet. So there are two sides that are
both 9 feet. When you add those up, you have 18 feet.
-- The REST of the 32 feet belongs to the other two sides.
That much is (32 - 18) = 14 feet. That's what the other two
sides add up to when you add them.
-- The other two sides are equal. So each of them is half of 14 = 7 feet .
This rectangle, or the description of it, is slightly weird.
The length of the rectangle is shorter than the width.
But that's OK. Two sides are 9 feet, and two sides are 7 feet, and
when you add them all up, you get 32 feet, so our solution is correct.
Let them call the sides anything they want to.
No because distributive property only for multiplication
