Answer:
q=35
Step-by-step explanation:
x2 - 12x + q = 0
Let the two roots be r and r+2.
Factor the quadratic expression:
(x - r)[x - (r + 2)] = 0
Expand, simplify, group like terms, and get
x2 - 2(r + 1)x + r(r + 2) = 0
Compare to
x2 - 12x + q = 0
and set equal the coefficients of like terms:
Coefficient of x:
-2(r + 1) = -12 ⇒ r + 1 = 6 ⇒ r = 5
(Then the other root is r + 2 = 5 + 2 = 7)
Constant term:
r(r + 2) = q ⇒ 5(5 + 2) = q
q = 35
Test the solution:
(x - 5)(x - 7) = x2 - 12x + 35
With two roots differing by 2, you get an equation of the form
x2 - 12x + q = 0
with q = 35.
Answer:
1. hexagon
2. 4
4. H
5. 6
6-8. count how many sides there are in the shape and multiply the given area to the number of sides you counted. for 6 it's a pentagon. 5 sides. Multiply 8.5 X 5. use calculator for the rest of that section if needed
9-11. they are equilateral triangles. Search up the formula and plug in and solve
Step-by-step explanation:
Answer:
60in : 11in
Step-by-step explanation:
12 inches in 1 foot.
12in. * 5ft.
1. True: the absolute value works exactly in this way: it turns negative numbers into their positive counterpart (e.g.: |-3|=3), and it does nothing on positive numbers (e.g.: |10|=10). So, the absolute value of a negative number will always be a positive number.
2. True (see above)
3. False: for example, you can pick -100 and 30. Their absolute value is 100 and 30, and 100>30. So, the absolute value of a negative number is greater the absolute value of a positive number.
