Which of the following shows extraneous solutions to the logarithmic equation? (See picture)

Which Of The Following Shows Extraneous Solutions To The Logarithmic Equation? (See Picture)

Answers

Answer 1

Answer:

Option 3

Step-by-step explanation:

log4(x) + log4(x - 3) = log4(-7x + 21)

log4(x² - 3x) = log4(-7x + 21)

x² - 3x = -7x + 21

x² + 4x - 21 = 0

x² + 7x - 3x - 21 = 0

x(x + 7) - 3(x + 7) =0

(x + 7)(x - 3) = 0

x = -7, 3

-7 and 3, both are e extraneous solutions because logs of non-positive numbers don't exist

At x = 3,

-7x + 21 = 0


Related Questions

The width of a rectangle is 5 x minus 7.5 feet and the length is 7.5 x plus 8 feet. Find the perimeter of the rectangle. (help please :) )

Answers

Answer:

-2.5+(-2.5)+15.5+15.5=26

Step-by-step explanation:

26 i think

FIRST TO ANSWER (CORRECTLY) GETS BRAINLIEST
I NEED HELP ASAP WE DIDN'T LEARN THIS :/

Answers

Answer:

A. 20°

Step-by-step explanation:

ΔABC's full internal angle measurements = 180°

m∠CAB = 80°

m∠ACB = 50°

m∠DBA = 30°

m∠DBC = ?

Add the measurements of the angles together, and subtract from the total:

m∠DBC = 180 - (80 + 50 + 30)

m∠DBC = 180 - (160)

m∠DBC = 20°

A. 20° is your answer.

~

Answer:

∠DBC = 20°

Step-by-step explanation:

∠A + ∠C + ∠ABC = 180   { sum of all angles of triangle}

50 + 80 + ∠ABC = 180

130 +∠ABC = 180

∠ABC  = 180 - 130

∠ABC = 50°

∠ABD + ∠DBC = ∠ABC

30 + ∠DBC = 50

∠DBC = 50 - 30

∠DBC = 20°

What is 70% of 35?
А. 24.5
В. 35
C. 14
D. 28

Answers

Step-by-step explanation:

Step 1:  Find the answer

70% * 35

0.7 * 35 = x

24.5 = x

Answer: Option A, 24.5

The answer is A.

Just multiply 70% by 35

Which rule represents the table's values?
A)
y = 3x + 1
y = 2x + 11
y = 3x - 1
y = 4x - 15

Answers

Answer:

There is no table given to match the values

WILL GIVE 20 POINTS

write an equation parallel to the function y=-4x+1 and goes through the point (1,1)

Y=???

Answers

Answer:

-4x + 5

Step-by-step explanation:

to be parallel, you need the same slope,

so it has to be -4x

and to go through the point (1,1) the y intercept has to be 5

because if you are using that slope, going down four and over one starting at (0,5) will connect the line to (1,1)

If it helps to draw it out or somehow visually see it, that would be a great idea

but in sum, the only answer is  y = -4x + 5

(i didn't see someone had already answered)

(but the answer above uses the slope of 2x and I am unsure why because it says -4x on your question)

(so I guess you could just look at both and see what you need :))


A student is selected at random. What is the probability, as a decimal rounded to the nearest
thousandth, that the selected student is going on the field trip given that the student is an eleventh
grader?

Answers

Answer:

0.245

Step-by-step explanation:

Probability is the chance or likelihood that an event will occur.

Probability = Expected outcome of event/Total outcome of event

Since we are to find the probability that the selected student is going on the field trip given that the student is an eleventh

grader;

The expected outcome of event will be 13 as located on the table.

Total outcome of event will be the total number of students that went for the field trip.

Total outcome = 12+9+13+19

Total outcome of event = 53

Probability = 13/53

Probability = 0.245(to nearest thousandth)

Find the distance between the points (10, 12) and (10, -8).
units

Answers

pt1= (10,12)

pt2= (10,-8)

_________________

distance = √ (x1 - x2)² + (y2 - y1)²

_________________

=√ (0)² + (-20)²

______

=√400

=20 units

Answer:

Step-by-step explanation:

5x + 8 = 2x + 14

Need a little bit of help would be thankful xxx

Answers

Answer: x = 2

Step-by-step explanation: 5x + 8 = 2x + 14

                                             5x + 8 - 2x = 2x + 14 - 2x

                                             3x + 8 - 8 = 14 - 8

                                             3x = 6

                                             3x/3 = 6/3

                                             x = 2

                                             

For this problem, x would equal 2.

x=2

-Dhruva;)

The volume of a cone is 48π cubic inches. The cone has a height of 36 inches. Mark is finding the radius of the cone. Complete his work. 1. Rewrite the formula including the area of the base: 2. Substitute the values into the formula: 3. Simplify the right side: 4. Divide 12π to both sides: Step 5 is to . The radius of the cone is . V = 1 3 πr²h 48π = 1 3 πr²(36) 48π = 12πr² 4 = r²

Answers

Answer:

C and A

Step-by-step explanation:

Step 5 is to ( C ) take the Square root of both sides

The radius of the cone is ( A ) 2 inches

The radius of the cone is 2 inches.

The volume of cone:

The volume of a cone is determined by the amount of space occupied by the cone. A three-dimensional figure having a single circular base is known as a cone. The base and the vertex are connected by a curved surface. A cone with a radius of r has a volume V that is one-third the area of the base B times the height h.

[tex]V=\frac{1}{3} \pi r^{2} h[/tex] or [tex]V=\frac{1}{3} Bh[/tex],

Since, [tex]B=\pi r^{2}[/tex]

How to determine the volume of cone?

Given that the volume of cone V is 48π cubic inches and Height of the cone h=36 inches.Volume of cone [tex]V=\frac{1}{3} \pi r^{2} h[/tex] -------1

Here, the base of the cone is circular in shape and the area of circle is [tex]\pi r^{2}[/tex]. Consider [tex]B=\pi r^{2}[/tex]

Substituting the area of base in the equation (1).

[tex]V=\frac{1}{3} \pi r^{2}[/tex]

    [tex]= \frac{1}{3} Bh[/tex]

Substitute the given values in the equation (1).

⇒ [tex]48\pi =\frac{1}{3} \pi r^{2} 36[/tex]

⇒ [tex]\frac{48\pi }{36\pi } =\frac{r^{2} }{3}[/tex]

⇒ [tex]\frac{12(3)}{9}=r^{2}[/tex]

⇒[tex]4=r^{2}[/tex]

⇒ [tex]r=2[/tex]

Thus, the radius of the cone is 2 inches.

Learn more about cone here- https://brainly.com/question/1315822 #SPJ2  

Find the value of x in the triangle shown below.
5.7
66

Answers

Answer:

x = 48°

Step-by-step explanation:

Since the triangle is an isosceles triangle, the two base angels will have the same measure.

So..

66 +66 = 132

And since all triangles have a sum of 180°, then..

180 - 132 = 48

The walls and ceiling of a hotel room are to be painted. The floor is a 14-foot square and the ceiling is 8 feet high. Ignoring any doors or windows, what is the surface area of the walls and the ceiling to be painted

Answers

Answer

112 square feet no

Explanation
I just multiplied I remember solving it that way when I was in middle school

The total surface area to be painted in the hotel room is 644 square feet.

To calculate the surface area of the walls and the ceiling to be painted in a room, we separate the two calculations since the walls and the ceiling have separate dimensions. The floor of the room is a 14-foot square, which means that each side of the wall is 14 feet long. The ceiling also has the same dimensions as the floor. The room has a height of 8 feet.

The area of the ceiling is equal to the area of the floor since they are both squares with the same side length, which is calculated as follows:

Area of ceiling = Side length × Side length

Area of ceiling = 14 feet × 14 feet = 196 square feet

Next, we calculate the surface area of the walls. There are four walls in the room, and each wall has the same height of 8 feet. The wall area is calculated as follows:

Area of one wall = Side length × Height

Area of one wall = 14 feet × 8 feet = 112 square feet

Since there are four walls, total wall area = 4 × 112 square feet = 448 square feet

Finally, we add the area of the ceiling to the total wall area to get the total surface area to be painted:

Total surface area = Ceiling area + Wall area

Total surface area = 196 square feet + 448 square feet = 644 square feet

Therefore, the total surface area of the walls and ceiling of the room that will be painted is 644 square feet, ignoring any doors or windows.

Both pyramids in the figure have the same base area as the prism. The ratio of the combined volume of the pyramids to the volume of the
prism expressed as a fraction in simplest form is.

Answers

Answer:

Is there a Picture or something to see

Step-by-step explanation:

Add. 6 1/3 + 4 ¾ + 3 7/12 =

13 11/12
14 2/3
13 2/3
14 7/8

Answers

Answer:

14 2/3

Step-by-step explanation:

On a coordinate plane, a line goes through (0, 4) and (2, 0). The first equation from the previous system of equations is graphed. Graph the second equation to find the solution of the system of equations. y = −2x + 4, y = − 1 3 x − 1 What is the solution to the system?

Answers

Answer:

{3,-2}

Step-by-step explanation:

ITS CORRECT

Answer: third option

Step-by-step explanation:

pls help! will give brainlist!

find each angle measure in the regular polygon

a. 144°
b. 135°
c. 180°
d. 140°

Answers

The answer is: A

A decagon is a 10-sided polygon, with 10 interior angles, and 10 vertices which is where the sides meet. A regular decagon has 10 equal-length sides and equal-measure interior angles. Each angle measures 144°
Answer: a. 144 degrees

=====================================================

Work Shown:

E = exterior angle

n = number of sides

For any regular polygon, E = 360/n.

In this case, n = 10 as there are 10 sides, so E = 360/n = 360/10 = 36 degrees is the measure of each exterior angle.

Each interior angle is 180-E = 180-36 = 144 degrees

--------------

An alternative is to plug n = 10 into the formula below to get the measure of each interior angle i

i = 180(n-2)/n

i = 180(10-2)/10

i = 180(8)/10

i = 1440/10

i = 144

note: S = 180(n-2) is the sum of all the interior angles of any convex polygon. Dividing this sum over n will evenly divide the angle total to each interior angle.

Define parallel lines.
Lines in the same plane that intersect.
Lines in the same plane that never intersect.
Lines in the same plane that intersect to form a 90° angle,
Einest the same plane that Ateneet teena
g
le

Answers

Answer:

Lines in the same plane that intersect to form a 90 degree angle

Step-by-step explanation:

Final answer:

Parallel lines in Euclidean geometry are lines in the same plane that never intersect, maintaining a consistent distance from each other. The parallel postulate ensures the uniqueness of parallel lines through a given point relative to a line.

Explanation:

Parallel lines are defined as lines in the same plane that never intersect no matter how far they are extended in either direction. This concept is a fundamental part of Euclidean geometry, and it is also important in understanding the basis of linear perspective, where parallel lines appear to converge as they recede into the distance.

Moreover, while discussing the relationship between planes and lines, if three nonparallel planes are considered, they typically intersect in a single unique point or along a single line, depending on their orientation and equations. In contrast, parallel lines would not provide such a point or line of intersection since they never meet.

100 nautical miles equals about 185 km to the nearest kilometer how far in kilometers is 140 nautical miles.

Answers

Answer:

100 nmiles = 185 km

1 km = 100 n miles / 185

0.541 n miles / 1 km

140 n miles / 0.541 n mile / km = 259 km

Answer is 259 km

Step-by-step explanation:

Find the area of the shaded figure in the diagram below. Use 3.14 for π and round your answer to the nearest tenth.
Hurry Please! I need this ASAP

Answers

Answer: 38.5

Step by Step:  

First you need to find the radius of the smaller circle. 2

Add 2 to 1 and 1 half which gives you 3.5

Next multiply 3.5 by 3.5 that equals 12.25

Lastly times 12.25 by 3.14 and you get 38.5

Answer:

yes that the right answer

A cathedral has a large, circular stained-glass window. A visitor measures the window and calculates that it has an area of 50.24 square feet. What is the window's circumference?

Use 3.14 for ​.

Answers

Answer:

25.133

Step-by-step explanation:

area is pi*r^2. divide area by 3.14 and then sqrt to find radius. 6.28*radius= circumference, so 6.28*4=25.133

Answer:

25.12

Step-by-step explanation:

1. Use the formula for the area of a circle to find the radius

[tex]A=\pi r^2[/tex]

[tex]50.24=\pi r^2[/tex]

[tex]16=r^2[/tex]

[tex]\sqrt{16} =r[/tex]

[tex]4=r[/tex]

2. Use this value to find the circumference

[tex]C=2\pi r[/tex]

[tex]C=2\pi 4[/tex]

[tex]C=2(12.56)[/tex]

[tex]C=25.12[/tex]


A dot plot titled Age of Eagles going from 7 to 12. 7 has 1 dot, 8 has 2 dots, 9 has 4 dots, 10 has 2 dots, 11 has 3 dots, 12 has 2 dots. A dot plot titled Age of Lions going from 7 to 12. 7 has 0 dots, 8 has 0 dots, 9 has 2 dots, 10 has 2 dots, 11 has 5 dots, 12 has 4 dots.
The dot plots show the ages of players on two soccer teams. Which statements are true? Check all that apply.
The Lions have more variability in the ages of their players.
The Eagles have more variability in the ages of their players.
The Lions have more players.
The Eagles have more players.
The mean of the ages of Lions is less than the mean of the ages of Eagles.

Answers

Answer:

2 and 4

Step-by-step explanation:

nice try though

The true statements about the dot plots are:

B. Eagles have more variability (5)

D. The Eagles have more players (14)

What is the Variability of a Data?

Variability is a measure of the degree to which the data values vary from the average value. In a dot plot, the range (max value - min value) is a measure of variability. The larger the range, the more the variability.

Range for age of the 14 players of eagles = 12 - 7 = 5

Range for age of the 13 players of lions = 12 - 9 = 3

The true statement are:

B. Eagles have more variability (5)

D. The Eagles have more players (14)

Learn more about variability of data on:

https://brainly.com/question/23481121

#SPJ2

PLEASE HELP FAST
What is the total surface area of the square pyramid below?
A. 100 cm2
B. 200 cm2
C. 280 cm2
D. 380 cm2

Answers

Answer:

10(10) + 4(1/2)(10)(14) = 100 + 280 = 380 cm²

The correct answer is D.

Use the ratios above to make a conclusion about the angles measures of triangle ABC and triangle JKL

Answers

Answer:

One is bigget

Step-by-step explanation:

Find the probability of this event. Enter the answer as a fraction in simplest form, as a decimal, and as a percent.

You choose a marble at random from a bag containing 12 red, 4 blue, 5 green, 7 yellow, and 32 black marbles.

The marble is red.

The probability expressed as a fraction is:___
The probability expressed as a decimal is:___
The probability expressed as a percent is:___

Answers

Answer:

12/60, 0.2, 20%

hope i was helpful :)

will give the brainliest!!!!!

Answers

The answer is 40
Just multiply the 8 and the 5
Answer : 40


The area of a a rectangle is base x height. The base is 5 and the height is 8 , you multiply the two and you get 40!

hope this helps and have an awesome day !

evaluate the expression for p=2
81-p

Answers

p=2 so 81-p is equal to 81-2 which equals 79

Answer:

79

Step-by-step explanation:

substitute 2 in for p in the equation 81-2

solve. 81-2=79

Which table represents a function? sorry the image is sideways.​

Answers

It is the table in the orange box

Answer:

The one with the orange background represents function.

Step-by-step explanation:

x-coordinates:-2, -1, 0, 1, 2

y-coordinates: -1,-1,0,1,2

Find sin(a) in the triangle?
A.)12/35
B.)12/37
C.)35/12
D.)35/37

Answers

Answer:

12/37

Step-by-step explanation:

sin alpha = opposite side/ hypotenuse

sin alpha = 12/37

Which is a factor of x2 - 9x + 14?
X-9
x-2
x + 5
X +7


ANSWER
x-2
b

Answers

Answer:

(x - 2)

Step-by-step explanation:

Given

x² - 9x + 14

Consider the factors of the constant term (+ 14) which sum to give the coefficient of the x- term (- 9)

The factors are - 2 and - 7, since

- 2 × - 7 = + 14 and - 2 - 7 = - 9, thus

x² - 9x + 14 = (x - 2)(x - 7) ← in factored form

Thus (x - 2) is a factor of the expression

Sean says that to add a number to –100 and still have –100 is to add zero. Candice says that she can add two numbers to –100 and still have –100. Who is correct and why?

Answers

Answer:

Step-by-step explanation:

Candice is correct because you can add 1 to -100 and get -99

then add -1 to -99 and you would get -100

Answer:

They are both correct

Step-by-step explanation:

hope this helps

1 x (-4) - 8 x 9/-3

Answers

Answer: I'm sure it's 20

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