Answer:
Step-by-step explanation:
Equation
2(x + 4) = x - 1
Solution
2x + 8 = x - 1 Subtract x from both sides
2x-x + 8 = - 1 Combine the left
x + 8 = - 1 Subtract 8 from both sides
x + 8-8 = - 1-8
x = - 9
Check
<em>LHS</em>
2(-9 + 4)
2(- 5)
-10
<em>RHS</em>
-9 - 1
- 10
Answer:
C. 11 log x
Step-by-step explanation:
= 5 log (10) x + 3 log (10) x^2
= log(10) x^5 + log(10) (x^2)^3
= log(10) x^5 + log(10) x^6
= log (10) x^11
=11 log (10) x
or
= 11 log x
Answer is C.
Answer:
28.9°
Step-by-step explanation:
This is a Trigonometry question
From the above, question,
The horizontal distance = Adjacent = 29 feet
The distance of the kite from the ground = Opposite= 14 feet
We solve using the Trigonometric function of Sine
sin θ = Opposite/Adjacent
sin θ = 14/29
θ = arc sin (14/29)
θ = 28.865727415°
Approximately = 28.9°
Therefore, the angle measure of x = 28.9°
Answer:
(1, 5 ) and (3, - 1 )
Step-by-step explanation:
Given the 2 equations
3x + y = 8 → (1)
x² + xy = 6 → (2)
Rearrange (1) expressing y in terms of x by subtracting 3x from both sides
y = 8 - 3x → (3)
Substitute y = 8 - 3x into (2)
x² + x(8 - 3x) = 6 ← distribute and simplify left side
x² + 8x - 3x² = 6
- 2x² + 8x = 6 ( subtract 6 from both sides )
- 2x² + 8x - 6 = 0 ← divide both sides by - 2
x² - 4x + 3 = 0 ← in standard form
(x - 1)(x - 3) ← in factored form
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 3 = 0 ⇒ x = 3
Substitute these values into (3) for corresponding values of y
x = 1 : y = 8 - 3 = 5 ⇒ (1, 5)
x = 3 : y = 8 - 9 = - 1 ⇒ (3, - 1)
Solutions are (1, 5 ) and (3, - 1 )