Answer:
3. f(12) = -10; f(37) = -60
4. f(12) = -102; f(37) = -352
Step-by-step explanation:
3. Put the numbers in the formula and do the arithmetic:
f(12) = 12 -2(12-1) = 12 -22 = -10
f(37) = 12 -2(37-1) = 12 -72 = -60
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4. The explicit formula for an arithmetic sequence with first term a1 and common difference d is ...
an = a1 +d(n -1)
Your sequence has a first term a1=8 and a common difference d=-10.
As above, fill in the numbers and do the arithmetic.
f(12) = 8 -10(12 -1) = -102
f(37) = 8 -10(37-1) = -352
Answer:
(base × height) × 0.5
Step-by-step explanation:
Formula of the Area of a Triangle => (base × height) × 0.5
Y-(y value of P)=-1/m(X-(X value of P))
You did it right (almost, I got 21 instead of 19) but didn't finish. You need to show your discriminant is never negative.
x² + (p+1)x = 5-2p
x² + (p+1)x +(2p-5) =0
Real roots mean a positive (or at least non-negative) discriminant:
D = b² - 4ac = (p+1)² - 4(1)(2p - 5) = p² + 2p + 1 - 8p + 20
D = p² - 6p + 21
It's not totally obvious that D>0; we prove that by completing the square by noting
(p-3)² = p² - 6p + 9
so
p² - 6p = (p-3)² - 9.
D = p² - 6p + 21
D = (p-3)² - 9 + 21
D = (p-3)² + 12
Now we clearly see D>0 always because the squared term can't be negative, so D is always at least 12. We always get two distinct real roots.
<u>Explanation</u><u>:</u>
From the given figure ,
AB || CD
PQ is a transversal
Given angles are 50° and 130°
50° and x are linear pair
⇛ 50°+x = 180°
⇛ x = 180°-50°
⇛ x = 130°
Therefore, "x" = 130°
and
130° and y are vertically opposite angles which are equal.
⇛ "y" = 130°
Therefore, y = 130°
<u>Additional</u><u> </u><u>comment</u><u>:</u><u>-</u>
- If two parallel lines Intersected by a transversal then
- Corresponding angles are equal.
- Vertically Opposite angles are equal.
- The sum of two adjacent angles is equal to 180° then they are called Linear Pair.
