1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
yarga [219]
2 years ago
10

Which of the following shows the extraneous solution to the logarithmic equation below???

Mathematics
2 answers:
avanturin [10]2 years ago
7 0
Short Answer x = - 6
Remark
You gave the second best answer. 

The trick here is not to divide both sides by 2. Solve the problem this way.

log_5(x + 1)^2 = 2 Take the antilog of both sides
(x + 1)^2 = 5^2       Expand the equation
x^2 + 2x + 1 = 25   Subtract 25 from both sides.
x^2 + 2x - 24 = 0    Factor
(x + 6)(x - 4) = 0     Find the zeros.

x + 6 = 0
x = - 6  <<<<<<<< Answer. This is the extraneous root.
The reason this is an extraneous root is that x<=0 do not have a logarithem

x - 4 = 0
x = 4    This is a legitimate result to the original equation.
Romashka-Z-Leto [24]2 years ago
5 0

Answer:

B

Step-by-step explanation:

You might be interested in
PLS HELP ILL MARK BRAINLIEST PLS HURRY IM GETTING TIMED!!!!!!!!!
Dennis_Churaev [7]

Answer:

100

Step-by-step explanation:

1.50*100

6 0
3 years ago
8x + 34. What does X equal
rosijanka [135]

Answer: x=-4.25

Step-by-step explanation:

First you put it in to y= mx+b form.

0=8x+34

Then you subtract 34 from both sides

-34=8x

Then you divide 8 from both sides

Leaving you with

x=-4.25

4 0
2 years ago
6. RVHS sold 143 Adult and Student tickets to the
slava [35]

Answer:

57 adult tickets, 86 student tickets

7 0
2 years ago
Lamaj is rides his bike over a piece of gum and continues riding his bike at a constant rate time = 1.25 seconds the game is at
Hitman42 [59]

Lamaj rides his bike over a piece of gum and continues riding his bike at a constant rate. At time = 1.25 seconds, the gum is at a maximum height above the ground and 1 second later the gum is on the ground again.

a. If the diameter of the wheel is 68 cm, write an equation that models the height of the gum in centimeters above the ground at any time, t, in seconds.

b. What is the height of the gum when Lamaj gets to the end of the block at t = 15.6 seconds?

c. When are the first and second times the gum reaches a height of 12 cm?

Answer:

Step-by-step explanation:

a)

We are being told that:

Lamaj rides his bike over a piece of gum and continues riding his bike at a constant rate. This keeps the wheel of his bike in Simple Harmonic Motion and the Trigonometric equation  that models the height of the gum in centimeters above the ground at any time, t, in seconds.  can be written as:

\mathbf {y = 34cos (\pi (t-1.25))+34}

where;

y =  is the height of the gum at a given time (t) seconds

34 = amplitude of the motion

the amplitude of the motion was obtained by finding the middle between the highest and lowest point on the cosine graph.

\mathbf{ \pi} = the period of the graph

1.25 = maximum vertical height stretched by 1.25 m  to the horizontal

b) From the equation derived above;

if we replace t with 1.56 seconds ; we can determine the height of the gum when Lamaj gets to the end of the block .

So;

\mathbf {y = 34cos (\pi (15.6-1.25))+34}

\mathbf {y = 34cos (\pi (14.35))+34}

\mathbf {y = 34cos (45.08)+34}

\mathbf{y = 58.01}

Thus, the  gum is at 58.01 cm from the ground at  t = 15.6 seconds.

c)

When are the first and second times the gum reaches a height of 12 cm

This indicates the position of y; so y = 12 cm

From the same equation from (a); we have :

\mathbf {y = 34 cos(\pi (t-1.25))+34}

\mathbf{12 = 34 cos ( \pi(t-1.25))+34}

\dfrac {12-34}{34} = cos (\pi(t-1.25))

\dfrac {-22}{34} = cos(\pi(t-1.25))

2.27 = (\pi (t-1.25)

t = 2.72 seconds

Similarly, replacing cosine in the above equation with sine; we have:

\mathbf {y = 34 sin (\pi (t-1.25))+34}

\mathbf{12 = 34 sin ( \pi(t-1.25))+34}

\dfrac {12-34}{34} = sin (\pi(t-1.25))

\dfrac {-22}{34} = sin (\pi(t-1.25))

-0.703 = (\pi(t-1.25))

t = 2.527 seconds

Hence, the gum will reach 12 cm first at 2.527 sec and second time at 2.72 sec.

7 0
3 years ago
The equation below shows the total volume (V), in cubic units, of 9 identical boxes with each side equal to s units:
timurjin [86]

36.864 cubic units is what the answer is

3 0
3 years ago
Other questions:
  • I'm trying to find the standard form for 8.97x10 to rh negative 1. Can you helpe?
    7·1 answer
  • In a list of numbers, the pattern increases by 0.001 as you move to the right. If the third number in the list is 0.046, what is
    6·1 answer
  • Which statements are true?
    6·1 answer
  • Somebody help its due​
    12·1 answer
  • Circle D is shown. Line segment F E goes through point D. Line segment C D is shown. Line segment G H goes from one side of the
    9·2 answers
  • Ratios for 42 and 54
    13·2 answers
  • In OE, m overline HQ =48,HI=JK , and JR = 7.5 . Find each measure. 1. m overline HI 2. m overline QI E AK 3. m overline JK 4. HI
    6·1 answer
  • Please help me Please​
    8·1 answer
  • The following structure is composed of three right rectangular prisms: two that each measure 12 inches by 10 inches by 5 inches
    11·1 answer
  • Ebony uses unit cubes to build the rectangular prism below.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!