Using logarithmic laws: log(a) + log(b) = log(ab)
log₄ (x + 9) + log₄ (x + 21) = log₄ [(x + 9)(x + 21)] = 3
Since we want the equation in terms of x, the next intuitive step is take 4 to the power of both sides, because the left hand side will simplify easily.
Solving the quadratic we get:
BUT, for the logarithmic equation to be defined, x > -9, so x≠ -25
Thus, the only solution is x = -5.
Answer:
yup!
Step-by-step explanation:
we have
we know that
The absolute value has two solutions
Subtract both sides
Step 1
Find the first solution (Case positive)
Subtract both sides
Multiply by both sides
Step 2
Find the second solution (Case negative)
Adds both sides
<u>Statements</u>
<u>case A)</u> The equation will have no solutions
The statement is False
Because the equation has two solutions------> See the procedure
<u>case B)</u> A good first step for solving the equation is to subtract 0.5 from both sides of the equation
The statement is True -----> See the procedure
<u>case C)</u> A good first step for solving the equation is to split it into a positive case and a negative case
The statement is False -----> See the procedure
case D) The positive case of this equation is 0.5 – |x – 12| = 0.25
The statement is False
Because the positive case is -----> see the procedure
case E) The negative case of this equation is x – 12 = –0.75
The statement is True -----> see the procedure
<u>case F)</u> The equation will have only 1 solution
The statement is False
Because The equation has two solutions------> See the procedure
Answer:
You would need 9/4 or 2 1/4 gallons of paint
Step-by-step explanation:
You would need 2 1/4 gallon of paint because if 1/3 of the room takes 1/4 paint, then 3/4 would finish a room, multiply the three by three for three rooms and there you have 9/4 or 2 1/4 gallons
<span>Part a) the max of g(t) occurs when t=0.6 seconds, for f(t) since the parabola is concave down due to the negative sign then we know that there is a max on the parabola, the max for f(t) occurs at (13/16,169/16) 169/6=10.5625inches at time 0.8125seconds
Part b) f(t) has greater x intercepts, meaning that when the labrador will land later than the fox when it jumps over the hurdle</span>