We know how much 16 keychains is, now we need to find how much one is.
19.68 / 16 = $1.23
$1.23 is the price of one keychain, now you can multiply that by 25 to see how much 25 keychains cost.
Answer:
m∠ABC = 60°
The distance from C to AB = 3 cm
The distance from l to AB = 1.5 cm
Step-by-step explanation:
The median of ΔABC = BM
The length of MC = 3 cm
Type of triangle given as ΔBMC = Equilateral triangle
Line MN is parallel to AB and passes through M intersecting CB at N
Given that BM is a median, we have;
MC = AM = 3 cm
BM = MC = CB = 3 cm, from ΔBMC = Equilateral triangle
CN = NB by midpoint theorem
∴ CB = CN + NB = 2·CN = 3 cm
The distance from C to AB = CB = 3 cm
The distance from C to AB = 3 cm
CN = 3/2 = 1.5
CN = NB = 1.5
The distance from l to AB = CN = 1.5 cm
The distance from l to AB = 1.5 cm
m∠ABC = m∠BMC = m∠MBC = 60° Interior angles of an equilateral triangle.
m∠ABC = 60°
Let <em>a</em> and <em>b</em> be the zeroes of <em>x</em>² + <em>kx</em> + 12 such that |<em>a</em> - <em>b</em>| = 1.
By the factor theorem, we can write the quadratic in terms of its zeroes as
<em>x</em>² + <em>kx</em> + 12 = (<em>x</em> - <em>a</em>) (<em>x</em> - <em>b</em>)
Expand the right side and equate the coefficients:
<em>x</em>² + <em>kx</em> + 12 = <em>x</em>² - (<em>a</em> + <em>b</em>) <em>x</em> + <em>ab</em>
Then
<em>a</em> + <em>b</em> = -<em>k</em>
<em>ab</em> = 12
The condition that |<em>a</em> - <em>b</em>| = 1 has two cases, so without loss of generality assume <em>a</em> > <em>b</em>, so that |<em>a</em> - <em>b</em>| = <em>a</em> - <em>b</em>.
Then if <em>a</em> - <em>b</em> = 1, we get <em>b</em> = <em>a</em> - 1. Substitute this into the equations above and solve for <em>k</em> :
<em>a</em> + (<em>a</em> - 1) = -<em>k</em> → 2<em>a</em> = 1 - <em>k</em> → <em>a</em> = (1 - <em>k</em>)/2
<em>a</em> (<em>a</em> - 1) = 12 → (1 - <em>k</em>)/2 • ((1 - <em>k</em>)/2 - 1) = 12
→ (1 - <em>k</em>)²/4 - (1 - <em>k</em>)/2 = 12
→ (1 - <em>k</em>)² - 2 (1 - <em>k</em>) = 48
→ (1 - 2<em>k</em> + <em>k</em>²) - 2 (1 - <em>k</em>) = 48
→ <em>k</em>² - 1 = 48
→ <em>k</em>² = 49
→ <em>k</em> = ± √(49) = ±7
Answer:
n>1
Step-by-step explanation:
