A. Their signs are the same.
b. one is negative, the other is positive
Answer:
97 in each bag
Step-by-step explanation:
485÷5=97
97*5=485
What a delightful little problem ! (Partly because I could see
right away how to do it, and had the answer in a few minutes,
after a lot of impressive-looking algebra on my scratch-paper.)
Three consecutive integers are . . . x, x+1, and x+2
The smallest two are . . . x and x+1
Their product is . . . . . x(x+1)
5 times the largest one is . . . 5(x+2)
5 less than that is . . . . . . 5(x+2)-5
Now, the conditions of the problem say that <u>x (x + 1) = 5 (x+2) - 5</u>
THAT's the equation we have to solve, to find 'x' .
Eliminate parentheses: x² + x = 5x + 10 - 5
Combine like terms: x² + x = 5x + 5
Subtract 5x from each side: x² - 4x = 5
Subtract 5 from each side: <u>x² - 4x - 5 = 0</u>
You could solve that by factoring it, or use the quadratic equation.
Factored, it says that (x + 1) (x - 5) = 0
From which <em>x = -1</em>
and <em>x = +5</em>
We only want the positive results, so our three consecutive integers are
5, 6, and 7 .
To answer the question, the smallest one is <em><u>5 </u></em>.
<u>Check</u>:
5 x 6 ? = ? (7 x 5) - 5
30 ? = ? (35) - 5
30 = 30
yay !
-- The square of the shortest side . . . 16² = 256
-- The square of the medium side . . . 30² = 900
-- Their sum . . . (256 + 900) = <u>1,156</u>
-- The square of the longest side = 35² = <u>1,225</u>
1,156 and 1,225 are not equal, so these 3 numbers
<em>can</em> be the sides of a triangle, but it's not a right one.
The statement is <em>false</em>. (choice 'b')
Answer:
No, 8:2 = 4:1 which is less than 5:1
Step-by-step explanation:
