10. Find all values of x that satisfy log(x – 6) + log(x + 3) = 1. -

Answers

Answer 1

To solve this equation, we can use the properties of logarithms to combine the two logarithmic terms into a single expression:

log[(x - 6)(x + 3)] = 1
Next, we can rewrite the equation using the definition of logarithms:
(x - 6)(x + 3) = 10
Expanding the left-hand side, we get:
x^2 - 3x - 18 = 10
Simplifying further, we get:
x^2 - 3x - 28 = 0

Now we can factor the quadratic equation to get:
(x - 7)(x + 4) = 0
Therefore, the solutions are:
x = 7 or x = -4
However, we need to check if these values satisfy the original equation.
, then log(7 - 6) + log(7 + 3) = log(1) + log(10) = 0 + 1 = 1, so 7 is a valid solution.
If x = -4, then log(-4 - 6) + log(-4 + 3) = log(-10) + log(-1) is undefined, since the logarithm of a negative number is not defined in the real number system. Therefore, -4 is not a valid solution.
In conclusion, the only value of x that satisfies the equation is x = 7.
To find all values of x that satisfy the equation log(x - 6) + log(x + 3) = 1, we will use the properties of logarithms to simplify and solve for x.

First, we'll use the property of logarithms that states log(a) + log(b) = log(ab):
log((x - 6)(x + 3)) = 1
Now we'll convert the equation from logarithmic form to exponential form:
10^1 = (x - 6)(x + 3)
10 = x^2 - 6x + 3x - 18
Now, we have a quadratic equation:
x^2 - 3x - 28 = 0
We'll solve this equation using factoring:
(x - 7)(x + 4) = 0
This gives us two possible values for x:
x = 7 or x = -4

However, we must check whether these values satisfy the original equation, as logarithms are undefined for negative or zero arguments. If we plug x = 7 into the original equation, we get:
log(1) + log(10) = 1
0 + 1 = 1, which is true.
If we plug x = -4 into the original equation, we get:
log(-10) + log(-1)
Both arguments are negative, so the logarithms are undefined.
Therefore, the only value of x that satisfies the given equation is x = 7.

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Related Questions

A parachutist's rate during a free fall reaches 180 kilometers per hour. What is this rate in meters per second? At this rate, how many meters will the parachutist fall during 5 seconds of free fall? Do not round your answers.

Answers

Answer:

550 meters are covered

Step-by-step explanation:

Answer:

3000 meters per second

Step-by-step explanation:

!80 kilometers is equal to 1000 meters, so multiply 180 by 1000 and get 180,000 meters. Divide 180,000 by 60, since there are 60 seconds in a single minute, and you get the answer 3000, with the units being meters/second

What is the formula for test statistic Z?

Answers

The formula for the test statistic Z depends on the specific hypothesis test being conducted. However, the test statistic Z can be computed as:

Z = (x - μ) / (σ / √n)

The formula for the test statistic Z is:

Z = (x - μ) / (σ / √n)

where:

x is the sample mean

μ is the population mean (under the null hypothesis)

σ is the population standard deviation (under the null hypothesis)

n is the sample size

This formula is used for a z-test, which is a statistical test that assumes that the population is normally distributed and uses the standard normal distribution to calculate the p-value.

In some cases, the population standard deviation is unknown, and so the sample standard deviation (s) is used as an estimate. In these cases, the formula for the test statistic Z is:

Z = (x - μ) / (s / √n)

where s is the sample standard deviation.

It's important to note that the formula for the test statistic Z can vary depending on the specific hypothesis test being conducted.

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Avery bought a washing machine originally priced at $864.72 but on sale for 30% off. After 4% sales tax, what was the total cost?

Answers

Answer: 629.51

Step-by-step explanation: 30% of 864.72 is 259.416

864.72 - 259.416 = 605.304 4% of 605.3 = 24.212 605.3 + 24.21 = 629.51

PLEASE HELP ASAP TIMED WILL GIVE BRAINLYEST

Answers

Answer:

D. Is your answer

Step-by-step explanation:

i think it would be c

suppose you are testing the hypotheses h_0: \mu=10h 0 :μ=10 and h_a: \mu \ne 10h a :μ =10, and the p-valuep−value is 0.06.

Answers

The p-value of 0.06 suggests weak evidence against the null hypothesis.

Does the p-value provide strong evidence against the null hypothesis?

The p-value is a measure of the strength of evidence against the null hypothesis in a hypothesis test.

In this case, with a p-value of 0.06, it is considered relatively high. Typically, a significance level of 0.05 is used as a threshold to determine statistical significance.

Since the p-value (0.06) exceeds this threshold, we fail to reject the null hypothesis. However, it is important to note that the p-value does not provide direct evidence for the null hypothesis.

It only indicates that the observed data is not sufficiently unlikely under the assumption of the null hypothesis.

Therefore, while we don't have strong evidence against the null hypothesis, we also can't confidently conclude that the null hypothesis is true.

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Please help me with this!!

Answers

Answer:

Step-by-step explanation:

these triangles are not similar, you can tell, b/c the one given angle and that they are both right triangles, so you also know that the other angle , that is not given is not the same, in the two. hence the sides are not the same lengths or ratios of each other. they are NA

Find the highest concentration after how many hours

Answers

Using the derivative of the function, we cannot approximate the time when the concentration is highest since it does not exist.

What is the time of highest concentration

To find the time when the concentration is highest, we need to find the maximum of the concentration function. We can do this by finding the derivative of the function and setting it to zero, and then solving for t.

First, let's find the derivative of c(t):

c'(t) = [d/dt](120t / (3t^2 + 90))

c'(t) = (120(3t^2 + 90) - 120t(6t)) / (3t^2 + 90)^2

c'(t) = (360t^2 + 10800 - 720t^2) / (3t^2 + 90)^2

c'(t) = 10800 / (3t^2 + 90)^2

Now, we set c'(t) to zero and solve for t:

10800 / (3t^2 + 90)^2 = 0

10800 = 0 (since the denominator cannot be zero)

There is no solution to this equation, which means that c'(t) never equals zero, and therefore there is no maximum or minimum value for the concentration.

However, we can use the second derivative test to confirm this result. Taking the derivative of c'(t), we get:

c''(t) = d/dt

c''(t) = [d/dt](10800 / (3t^2 + 90)^2)

c''(t) = (-2 * 10800 * 3 * 2t) / (3t^2 + 90)^3

c''(t) = -129600 / (3t^2 + 90)^3

At any value of t, the denominator is positive, so the sign of the second derivative is determined by the numerator. Since the numerator is negative for all values of t, the second derivative is negative and therefore the function is concave down for all values of t. This means that there is no maximum value for the concentration, only a minimum value of 0.

Therefore, we cannot approximate the time when the concentration is highest since it does not exist.

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Need help answering this white showing my work

Answers

First you would want to order the number from least to greatest.
Second subtract the greatest number to the least number.

54-36

you should get the answer 18!

Answer:

Median: 48

Range: 18

Step-by-step explanation:

The range: is calculated by subtracting the lowest value from the highest value

The median: Arrange the data points from smallest to largest. If the number of data points is odd, the median is the middle data point in the list. If the number of data points is even, the median is the average of the two middle data points in the list.

I’m trying to figure out this question but can’t need help asap

Answers

Answer:

bottom right rectangle: 5x − y

bottom circle: 6x

Step-by-step explanation:

First, solve for the bottom right rectangle by finding the difference between the top right rectangle and the middle right circle:

(9x + 4y) − (4x + 5y)

= (9x − 4x) + (4y − 5y)

= 5x − y

Next, to find the bottom circle, add the bottom left rectangle with the bottom right rectangle (the one we just solved for):

(x + y) + (5x − y)

= (x + 5x) + (y − y)

= 6x

Mae raised $80 by selling boxes of cookies. Let
b represent the number of boxes of cookies sold.
Each box cost $2.50. Which equation should be
used to determine how many boxes of cookies
Mae sold?
A. 2.50+ b = 80
C. b÷ 2.50 = 80
B. b-2.50 = 80
D. 2.50b = 80

Answers

The answer is D cuz if you multiply 2.50 by b it should equal 80

Answer: D

Step-by-step explanation: 2.50xb=80 b= 32 boxes

What is mean, median and mode?

4 6 7 7 9 11 13 14 15

A. Mean = 9.56 Median = 11 Mode = 7

B. Mean = 9 Median = 86 Mode = 7

C. Mean = 9.56 Median = 9 Mode = 7

D. Mean = 10.75 Median = 9 Mode = 7

Answers

Answer: A. Mean = 9.56, Median = 11, Mode = 7

Step-by-step explanation:

The mean, median and the mode for the given data is 9.56, 9, and 7 respectively.

How to find the mean, median, and mode of the data?

Given data below:

4, 6, 7, 7, 9, 11, 13, 14, 15.

In order to find the mean, it can be calculated by dividing a sum of all the data points with the number of data points in the data set.

The formula is:

$\bar{M}=\dfrac{\sum M}{N}$

$\bar{M}=\dfrac{4+6+7+7+9+11+13+14+15}{9}$

$\bar{M}=\dfrac{86}{9}$

$\bar{M}=9.56$

Next, we will find the median.

In order to find the median, we got to place the numbers in value order and find the middle.

So,

$\text{Median}=9$

Lastly, we will find the mode.

To find the mode, order the numbers lowest to highest and see which number appears the most often.

So,

$\text{Mode}=7$

Thus, the mean, median and the mode for the given data is 9.56, 9, and 7 respectively.

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4. Ayla purchased two pairs of jeans for $30.50 and a shirt for $20.75. She paid with a one hundred dollar bill
How much change will Ayla get back?
851.25
$48.75
$81.75
$18.25

Answers

She will receive $48.75 back.

Answer:

i believe its $48.75

Step-by-step explanation:

I didn't know if each pair of jean was 30.50 each. I just did 30.50 + 20.75 to get 51. 25. Then i subtracted that from 100, 100- 51.25, to get 48.75

A car travels 160 miles in 4 hours. How many miles per hour does the car
travel?

Answers

Answer:

40 mph

Step-by-step explanation:

160÷4 = 40 miles per hour

Answer:

40miles per hour

Step-by-step explanation:

distance traveled/time spent=speed(velocity)

160/4=speed (velocity)

40mph

I don’t under what it is trying to say

Answers

Answer:

-2

Step-by-step explanation:

It’s asking you to solve the expression with the values given. After doing that, it’s asking you to simplify the result.

Expression - Does not have an equal sign, only the operation (multiplication, division, addition, subtraction).

c. find the mean, median, and standard deviation of heating degree days (hdd), broken down by season, for the california (code 0499). (ignore the first and last rows for the given location, the ones that contain -9999, the code for missing values.) round your answers to two decimal places, if necessary.

Answers

mean =1.532

median = 6.98

standard deviation = 3.5

mean for heating degree days and broken down by season for the california

according to the given values we find the mean

mean =

-1.45+ -2.5+-4.5+1.056+3.67+6.98+3.78+2.67+4.87+3.45+2.97+-4.06/12

=1.532

median for heating degree days and broken down by season for the california

according to the given values now we find the median

median = 6.98

standard deviation for heating degree days and broken down by season for the california

according to the given values now we find the standard deviation

standard deviation = square root of ∑($x_{i}$- μ)^2/n

= 3.5

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Use complete sentences to state who is correct and why.

Answers

Answer:

I dont think you gave the entire question but
bridget is saying x > 3
dana is saying x < 3

How do you plan to use Math in the future?

No links
Need this ASAP

Answers

Answer:

it's a philosophy

Step-by-step explanation:

Mathematics can't make you become great in life

it's just a philosophy for you to understand

Why did the National Assembly break away from the Estates General?

Answers

After Louis XVI's failed attempts to sabotage the Assembly and to keep the three estates separate, the Estates-General ceased to exist, becoming the National Assembly. It renamed itself the National Constituent Assembly on July 9 and began to function as a governing body and constitution-drafter.

National assembly

The National Assembly was the first revolutionary government of the French Revolution and existed from June 14th to July 9th in 1789. The National Assembly was created amidst the turmoil of the Estates-General that Louis XVI called in 1789 to deal with the looming economic crisis in France.

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BRIDGE Arturo is designing a bridge for

science class using parallel supports for

the top and bottom beam. Find m_2if

m_1 = 60°

Answers

the measure of m_2 is 120°, making the two angles of the bridge Arturo 60° and 120° respectively.

Bridge Arturo is the name given to a bridge designed by Arturo for his science class. It consists of two parallel beams that are supported by two different angles, m_1 and m_2.

The bridge Arturo is designing requires two supports of different angles, m_1 and m_2. The measure of m_1 is given as 60°. To find the measure of m_2, we can use the fact that the sum of the angles of a triangle is 180°. Since m_1 is given as 60°, subtracting this from 180° gives us 120°. Therefore, the measure of m_2 is 120°.

Bridge Arturo is a bridge designed by Arturo for his science class. It consists of two parallel beams which are supported at two different angles, m_1 and m_2. The measure of m_1 is given as 60°, which means that m_2 must be 120°, as the sum of the angles of a triangle is 180°. Hence, the measure of m_2 is 120°, making the two angles of the bridge Arturo 60° and 120° respectively.

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Write the equation of the line that passes through the points (1,4) and (-7,1). Put
your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.

Answers

There are two possible answers

y - 4 = (3/8)(x - 1)y - 1 = (3/8)(x + 7)

There are two answers because there are 2 points given. Both equations convert to the slope intercept form equation y = (3/8)x + 29/8

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

Work Shown:

First we need the slope

m = (y2 - y1)/(x2 - x1)

m = (1-4)/(-7-1)

m = -3/(-8)

m = 3/8

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

Using this slope along with the point (x1,y1) = (1,4) gets us the following equation

y - y1 = m(x - x1)

y - 4 = (3/8)(x - 1)

which is one way to express the equation in point-slope form

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

Or we could easily use the other point as (x1,y1). The order of the points does not matter.

y - y1 = m(x - x1)

y - 1 = (3/8)(x - (-7))

y - 1 = (3/8)(x + 7)

is another valid answer.

Please help me I need to finish this :)

Answers

The correct answer for the problem above is A.

Help please, I'm desperate!

Answers

B. 2.8
Because, 4-1.2=2.8

Answer:

Step-by-step explanation:

For bubble answers:

1. A

2. B

3. B

4. C

5. A

6. B

7. C

8. B

9. B

One or two may be wrong sorry

The point S(0,–2) is translated 4 units left. What are the coordinates of the resulting point, S'?

Answers

S(0,-2)

Translated 4 units left means y coordinate is kept constant.x coordinate is decreased by 4

i.e

$\\ \sf{:}\Rrightarrow 0-4=-4$

New co-ordinates are

(-4,-2)

Jose makes $34 in 2 hours. How much does he make in 40 hours?

Answers

Answer:

680

Step-by-step explanation:

Jose's income in 2hours = $34

in 1 hour = 34 divide by 2 = 17

income made in 40 hours = 17 multiplied by 40 = $680

jose makes 680$ in 40 hours

What is the domain of the function shown on the graph?

Answers

Answer: Choice D $-\infty < x < \infty$

This is another way of saying "the set of all real numbers". This is because there are no restrictions we must place on x. The graph extends infinitely in both left and right directions as the arrows indicate. Any x value can be plugged in to get some y output.

In interval notation, the domain would be written as $(-\infty, \infty)$

Peter gets paid $20 just for accepting a yard job. He then earns $3 for every hour spent on gardening. He wants to buy a mountain bike which costs $800. How many hours does he need to work on gardening to earn enough money

Answers

Answer:

260 hours

Step-by-step explanation:

first take out the 20 fixed cost that doesn't change no matter how long he gardens from 800

divide the remainder which is 780 by 3 which is the amount he gets paid for every hour he gardens. He would have to work 260 hours for the bike if he only takes one yard job

Clare is paid 90$ for 5 hours of work. At this rate, how many seconds dose it take for her to earn 25 cents?

Answers

Answer:

84 seconds

Step-by-step explanation:

Because if you divide all of that you would get that answer

Simplify 8(y - 4) * please

Answers

the answer should be 8y - 32

Answer:

Step-by-step explanation:

8y-32 which could also mean that y = 4 by dividing

Given the function f(x), what is the transformation f(x-r), is a real number and r>0?
A the graph shifts r units down
B the graph shifts r units up
C the graph shifts r units right
D the graph shifts r units left

Answers

Answer:

0 - r = the graph shifts r units left

Step-by-step explanation:

When you have 2 x intercepts of 0, -r then you shift left to negative

Hey guys!
Help me ....
Question is in the attachment....
Don't copy and don't spam
Don't answer if you don't know...
I need to understand it... please explain me
Thank You!

Answers

The slope of line r is -1/2

The equation of line q is given as

$-2x + y =1$

Make y the subject

$y =1 + 2x$

Rewrite the equation, as follows:

$y =2x + 1$

The slope of the above equation is:

$m = 2$

Line r is perpendicular to line q.

So, the slope (m2) of line r is calculated as:

$m_2 = -\frac 1m$

This gives

$m_2 = -\frac 12$

Hence, the slope of line r is -1/2