Answer:
sec²(x) - sec(x) + tan²(x) = (sec(x) - 1)(2sec(x) + 1)
Step-by-step explanation:
sec²(x) - sec(x) + tan²(x) =
= sec²(x) - sec(x) + [sec²(x) - 1]
= sec²(x) - sec(x) + [(sec(x) + 1)(sec(x) - 1)]
= sec(x)[sec(x) - 1] + [(sec(x) + 1)(sec(x) - 1)]
= (sec(x) - 1)(sec(x) + sec(x) + 1)
= (sec(x) - 1)(2sec(x) + 1)
Answer:
10 terms
Step-by-step explanation:
equate the sum formula to 55 and solve for n
n(n + 1) = 55 ( multiply both sides by 2 to clear the fraction )
n(n + 1) = 110 ← distribute parenthesis on left side
n² + n = 110 ( subtract 110 from both sides )
n² + n - 110 = 0 ← in standard form
Consider the factors of the constant term (- 110) which sum to give the coefficient of the n- term (+ 1)
the factors are + 11 and - 10 , since
11 × - 10 = - 110 and 11 - 10 = + 1 , then
(n + 11)(n - 10) = 0 ← in factored form
equate each factor to zero and solve for n
n + 11 = 0 ⇒ n = - 11
n - 10 = 0 ⇒ n = 10
However, n > 0 , then n = 10
number of terms which sum to 55 is 10
Answer:
m < 5
Step-by-step explanation:
10m-5 < 45
Add 5 to both sides
10m - 5 + 5 < 45 + 5
Simplify
10m < 50
Divide both sides by 2
10m/10 < 50/10
Simplify
m < 5
<u><em>Kavinsky</em></u>
Answer:
4x2−12x+9=0
Step-by-step explanation:
The equation, 2x2+x+3=0, does not have a solution
The equation, x2+5x−3=0, equals -5/2+1/2√37 and -5/2+-1/2√37
The equation, x2−5x+4=0, equal 1 and 4
The equation, 4x2−12x+9=0, equals only 3/2
Hope this Helps
Answer:
Each shirt cost $<u>7</u> and each pair of shorts cost $<u>17</u> .
Step-by-step explanation:
let shirts be represented as x
let shorts be represented as y
Younger brother spent $79 on 4 new shirts and 3 pairs of shorts.
4 x + 3 y = $79 .......equation 1
Older brother purchased 7 new shirts and 8 pairs of shorts and paid a total of $185.
7 x + 8 y = $185 .......equation 2
multiply equation 1 by 7 and equation 2 by -4 and add both equations to get the value of y.
7 × (4 x + 3 y = $79) ⇒ +28 x + 21 y = $553
-4 × (7 x + 8 y = $185) ⇒ <u> -28 x - 32 y = - $740</u>
0 - 11 y = - $187 ⇒ -11 y = - $187
y =
⇒ y = $17
shorts = y = $17
put value of y in equation 1
4 x + 3 ( $17 ) = $79 ⇒ 4x + $51 = $79 ⇒ 4x = $79 - $51
4x = $28 ⇒ x =
⇒ x = $7
Shirts = x = $7