What is the solution set to this equation?
log4 (x + 3) + log4x =1

A. x=0
B. x=1
C. x=1 and x= -4
D. x=-3 and x=0

What Is The Solution Set To This Equation?log4 (x + 3) + Log4x =1 A. X=0B. X=1C. X=1 And X= -4D. X=-3

Answers

Answer 1

Answer:

B

Step-by-step explanation:

Using the rules of logarithms

log x + log y = log (xy)

[tex]log_{b}[/tex] x = n , then x = [tex]b^{n}[/tex]

Given

[tex]log_{4}[/tex] (x + 3) + [tex]log_{4}[/tex] x = 1 , then

[tex]log_{4}[/tex] x(x + 3) = 1

x(x + 3) = [tex]4^{1}[/tex] = 4

x² + 3x = 4 ( subtract 4 from both sides )

x² + 3x - 4 = 0 ← in standard form

(x + 4)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x - 1 = 0 ⇒ x = 1

However, x > 0 , thus x = 1


Related Questions

Jon has to pay $7.00 admission for the skating rink in $1.50 per hour to rent rollerblades. How many hours can he skate for $19?

Answers

Answer: 8 hours

Step-by-step explanation:

Given information

Admission fee = $7.00

Hour rent fee = $1.50

Number of hours = h

Total fee = $19

Set equation according to the given information

Total fee = admission fee + (hours) × (hour rend fee)

Substitute values into the equation

19 = 7 + 1.5h

Subtract 7 on both sides

19 - 7 = 7 + 1.5h - 7

12 = 1.5h

Divide 1.5 on both sides

12 / 1.5 = 1.5h / 1.5

[tex]\boxed{h=8}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

In algebra - what can the letter "d" represent? For example, what does "d" stand for in this expression "2d + 3"? *

Answers

Answer:

A constant you need to find when given what the equation is equal to.

Answer:

Here, 'd' is the variable of 2.

Solve the compound inequality 8x > –32 or 6x ≤ –48.

Answers

Answer:

x>-4 x≤-8

Step-by-step explanation:

What is a dichotomous key?

a tool that allows scientists to measure how much glucose is produced by plants

a tool that allows for the identification of an organism based on a series of paired statements that are based on characteristics

a tool that is used to predict the types of offspring produced when two plants are crossed

a tool that is used to measure the height of a plant

Answers

the answer is: a tool that allows for the identification of an organism based on a a series of paired statements that are based on characteristics.

Refer to the figure at the right to answer each question. 5. Are points H, J, K, and L coplanar? 6. Name three lines that intersect at X. 7. What points do plane WXYZ and HW have in common? 8. Are points W, X, and Y collinear? 9. List the possibilities for naming a line contained in plane WXKH​

Answers

Problem 5

Answer: Yes the points are coplanar

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

Explanation:

Note how all four points are in the same plane, aka face, along the top of the 3D block. The term "coplanar" simply means "all in the same plane", so that's why the points are coplanar.

In contrast, the set of points {H,J,K,Z} are not all coplanar because H,J,K are in the top plane, while Z is not.

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

Problem 6

Answer: line segments WX, XY, and XK

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

Explanation:

All three lines mentioned above involve the letter X in some fashion. The order doesn't matter. Also, those lines intersect at the common point X.

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

Problem 7

Answer: point W

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

Explanation:

The plane WXYZ is the bottom face, in which we can think of as the floor of the building. The segment HW is from the floor and goes up vertically. We can consider this to be like a pole beam of the structure. The plane and segment both have point W in common. Note that the letter "W" is found in the sequences WXYZ and HW, and it's the only common letter.

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

Problem 8

Answer: The points are not collinear

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

Explanation:

To be collinear, the points must all be on the same straight line. We see that isn't the case with points W, X and Y.

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

Problem 9

I'm not entirely sure what your teacher is asking here, so I would ask for a second opinion.

what is 40% of 4x-10?

Answers

[tex] \frac{40}{100 } \times 4x - 10[/tex][tex] \frac{40 \times 4x + 10}{100} [/tex]

The algebraic expression for The quotient of 86 and x

Answers

Answer: 86 ÷ x or 86 / x

Step-by-step explanation:

A quotient is a number that results when one number is divided by another.

Therefore, in order to get the quotient, numbers or terms should process division which the final answer would be quotient.

In the process, [÷ ] or [/] the division signs shall be applied.

The quotient of 86 and x represents 86 divided by x, which the final result would be [tex]\boxed {86/x}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

I believe the answer you are looking for is simply just 86÷x or 86/x.

Solve for f.

–9(–2f − 8) = –6f

f =

Answers

Answer:

f = - 3

Step-by-step explanation:

Given

- 9(- 2f - 8) = - 6f ← distribute left side

18f + 72 = - 6f ( add 6f to both sides )

24f + 72 = 0 ( subtract 72 from both sides )

24f = - 72 ( divide both sides by 24 )

f = - 3

Please help me answer this

Answers

Answer:

[tex]D)\ 25\%[/tex]

Step-by-step explanation:

The following equation can be used to relate the speed time and distance of an object in motion,

[tex](Speed)*(Time)=(Distance)[/tex]

One can also rewrite this equation in terms of time:

[tex](Speed)=\frac{(Distance)}{(Time)}[/tex]

Let this equation represent the relation between Mr.Wang's initial speed and travel time. However, in this problem, Mr.Wang faced a decrease in his speed,  more specifically, a (20%) decrease. Subtract (0.2) from (1) to find Mr.Wang's speed in relation to his original speed. Let (x) represent the increase in time that Mr. Wang had to incur in order to reach his destination. Model this situation,

[tex](Speed)*(Time)=(Distance)[/tex]

[tex]0.8(Speed)*x(Time)=(Distance)[/tex]

Now use inverse operations to solve for the coefficient (x):

[tex]0.8(Speed)*x(Time)=(Distance)[/tex]

[tex]x(Time)=\frac{(Distance)}{0.8(Speed)}[/tex]

Using the relation state above: ([tex](Speed)=\frac{(Distance)}{(Time)}[/tex]) one can state the following:

[tex]x(Time)=\frac{(Distance)}{0.8(Speed)}[/tex]

[tex]x(Time)=\frac{1}{0.8}(Time)[/tex]

Thus, (Time) can be omitted from this equation, as it appear on both sides as a factor, hence one can then solve for (x):

[tex]x(Time)=\frac{1}{0.8}(Time)[/tex]

[tex]x=\frac{1}{0.8}[/tex]

Divide (1) by (0.8):

[tex]x=\frac{1}{0.8}\\x=0.25[/tex]

Multiply the decimal by (100) to put it into the percent form:

[tex]x=0.25\\x=25\%[/tex]

in thailand the population of town is 48700 men and 41600 women what percentage of the total percentage are men

Answers

Answer:

53.931339977852% (you can round)

Step-by-step explanation:

You add up 48,700 and 41,600 and you would get 90,300 as the overall population. Then you would put it in fraction form if you want to convert it into a percentage. The fraction form would be 48,700/90,300. You could simplify it to 487/903. Then you do  487            x      . You would cross multiply and get

                                              ___    =    ___

                                              903           100

903x = 48700. Then you would divide each side by 903 and get x = 53.931339977852% (you can round)

Answer:

Approximately 53.9%

To be exact, answer is 48700/903

Step-by-step explanation:

Percentage of men = Men ➗ Total population

48700 + 41600 = 90300

48700/90300 is approximately 0.539

0.539 * 100 = 53.9

3. Lucy is a curator at the local art museum. She earns an annual salary of 2 $53,160. Calculate the amount of her paycheck if she is paid monthly. semimonthly, biweekly, or weekly.​

Answers

Step-by-step explanation:

pleas check your answer in this photo please marks me as brainliests..please and follow me...

f(x) = -2x - 7 and g(x) = x+8/x find (g of f) (-7)

Answers

68/7

it the process

the total process is in above picture

f(x)=-x^2-4x-19

Find f(−9)

Answers

Answer:

-64.

Step-by-step explanation:

f(x)=-x^2-4x-19            Replacing x by -9:-

f(-9)= -(-9)^2-4(-9)-19

= -81 + 36 - 19

= 36 - 100

= -64.

Answer:

-64

Step-by-step explanation:

f(x)=-x^2-4x-19

Let x = -9

f(-9) = - (-9)^2 -4(-9) -19

     = -81 +36 -19

     =-64

(4-xy)(5x-3y)-(x+y)(x-3y)

Answers

Answer:

20x-12y-5x²y+3xy²-x²+2xy+3y²

Step-by-step explanation:

(4-xy)(5x-3y)-(x+y)(x-3y)

20x-12y-5x²y+3xy²-(x+y)(x-3y)

20x-12y-5x²y+3xy²-x²+2xy+3y²

Question 101 3.1 What is the constant difference between the consecutive terms? < 612,18.24 e 7.14.21.28​

Answers

Answer:

The constant between two consecutive terms is called the common difference. The common difference is the number added to any one term of an arithmetic sequence that generates the subsequent term.

What is the range of this equation? f(x) = x + 41 – 2

Answers

The range is the set of all valid
y
y
values. Use the graph to find the range.
Interval Notation:
(


,

)

a total of $10,000 is invested in two funds, Fund A and Fund B. Fund A pays 5% annual interest and Fund B pays 7% annual interest. The combined annual interest is $630. How much of the $10,000 is invested in Fund A?

Answers

The amount of the 10000  invested in each Fund A is $5,300

First step is to calculate the amount invested in Fund  B

Let x represent the amount invested at 7%

.07x+.05(10000-x)=630

Open the bracket

.07x+500-.05x=630

Collect like terms

.02x=630-500

.02x=130

x=130/.02

x=$6,500

Second step

Now let calculate  How much of the $10,000 is invested in Fund  A

Fund A amount invested=10000-6500

Fund A amount invested=$3500

Inconclusion The amount o of the 10000  invested in each  Fund A is $5,300

Learn more here:

https://brainly.com/question/11360350

According to the diagram above how long is the unknown piece

Answers

Answer:

17 mm

Step-by-step explanation:

11+? = 28

is the same as

28-?=11

The answer is 17mm.

Please mark me as brainliest if that helped. Thank you! ;)

2. Write an algebraic expression that models the cost of a telephone call is 35 cents plus 65 cents times the number of minutes. (use m for number of minutes)

Answers

Answer:

35 + 65 × m

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Please no links because they dont work :).

Answers

Answer:

C

Step-by-step explanation:

10y-3(y+5)

=10y-3y-15

=7y-15

I think the answer is C.

Step-by-step explanation:

hope it will help you

ive never liked algebra

Answers

Who does like honestly who ever made it needs to stop being alive

Answer:

y+11

Step-by-step explanation:

y-3/3+12

=y-1+12

=y+11

What is the sum of 15 and the square root of 144?

Answers

Answer:

27 pls mark me branilest

Answer:

27

Step-by-step explanation:

Hi there!

[tex]15+\sqrt{144}[/tex]

The square root of 144 is 12:

[tex]= 15+12[/tex]

[tex]= 27[/tex]

I hope this helps!

help
hvcjhjcfhjhgvhkgbnvg

Answers

Answer:

f(1)=1+2=3, as 1 is odd

f(2)=2*2=4

f(3)=3+2=5

f(4)=2*4=8

f(11)=11+2=13

a Find the Q2 and Q; of the following data. 5500, 6800, 4200, 3900, 7800, 6150, 4400, 7500 5 and 12 + 1 are in​

Answers

Step-by-step explanation:

Quartile Formula:

Formula for Lower quartile (Q1) = N + 1 multiplied by (1) divided by (4)

Formula for Middle quartile (Q2) = N + 1 multiplied by (2) divided by (4)

Formula for Upper quartile (Q3) = N + 1 multiplied by (3) divided by (4)

Formula for Interquartile range = Q3 (upper quartile) – Q1 (lower quartile)

i don't know how to work it out but i gave you some information.

Select the correct answer
What are the zeros of the graphed function?

Answers

Answer:

C. [tex]\displaystyle 0, 2, and\:4[/tex]

Step-by-step explanation:

Wherever the graph intersects the x-axis is considered your zero [x-intercept], therefore you have your answer:

[tex]\displaystyle [0, 0], [2, 0], and\: [4, 0][/tex]

I am joyous to assist you at any time.

How do you write 1.2247 as a percentage?

Answers

1.2247 as a percentage = 122.47%

I need help on my math packet!! Also I think I have an answer but I don’t know if it’s correct!
(+6) + (-9) =
Tysm if u helped!!

Answers

6 + (-9)
= 6 - 9
= -2

Hope it helps! If it is, Brainliest please!

Answer:

-3

Step-by-step explanation:

Adding a negative number is like subtracting. Subtracting more than the original positive number gets you in to the negative numbers.

Emma found a counter example to a given conditional. What are the truth values of the hypothesis and the conclusion? Explain.

Answers

The hypothesis value is used to verify or refute a claim.

The truth value of the hypothesis countered by Emma is trueThe conclusion is false

Note that:

If a conclusion is false, then there can be a counter to refute the conclusion; The hypothesis of this conclusion is trueHowever, if a conclusion is true, then there can't be any counter.

Because Emma found a counter, this means that the conclusion is false (as stated in 1, above)

Hence, the truth value of the hypothesis is true and the conclusion is false

Read more about hypothesis and conclusions at:

https://brainly.com/question/5497883

Helllllpppppppp!!!!!

Answers

Answer: The correct answer is C

Step-by-step explanation:The graph is horizontally stretched by a factor of 1/5 because you are literally multiplying x by 1/5. So, your answer is C. Hope it makes sense. mark me brainlest

What's the area of a room that 18ft by 10ft

Answers

It would be 108 square meters.

Answer:

180  square feet

Step-by-step explanation:

Square footage is calculated by multiplying width by length. So if a room is 18 foot wide by 10 foot long, 18 x 10 = 180 square feet.

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