Write each expression as a single logarithm.
log 5-k log 2

The factored form of the cubic equation x³ + 27 is equal to (x + 3) · (x - 3 / 2 - i 3√3 / 2) · (x - 3 / 2 + i 3√3 / 2). The roots of the cubic equation are - 3, 3 / 2 + i 3√3 / 2 and 3 / 2 - i 3√3 / 2.

In this problem we find a cubic equation of the form x³ + a³, whose factor form can be found by using algebra properties:

f(x) = x³ + 27

f(x) = (x + 3) · (x² - 3 · x + 9)

f(x) = (x + 3) · (x - 3 / 2 - i 3√3 / 2) · (x - 3 / 2 + i 3√3 / 2)

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Answer: do you have a pic??

Step-by-step explanation:

When zulaki recorded -3/10 degrees celcius as the starting temperature of a salt water solution and recorded 1/5 degrees as the. ending temperature, the change in temperature is 1/2 degree.

It should be noted that from the information, science class, zulaki recorded -3/10 degrees celcius as the starting temperature of a salt water solution and recorded 9/10 degrees as the. ending temperature.

Therefore,the change in temperature will be the subtraction of the temperature given. This will be illustrated as:

= 1/5 - (-3/10)

= 1/5 + 3/10

= 2/10 + 3/10

= 5/10

= 1/2

The change on temperature is 1/2 degree.

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In science class, zulaki recorded -3/10 degrees celcius as the starting temperature of a salt water solution and recorded 1/5 degrees as the. ending temperature. What was the change in temperature?

The range of the function f(x) = 2.250x is 22.5 <= f(x) <= 36

The range of a function is the set of output values of the graph.

This in other words mean the range of a function is the set of y values of the graph.

The function is given as

f(x) = 2.250x

Where there are at least 10 but no more than 16 players on the baseball team

This means that the domain of the function is

10 <= x <= 16

Substitute the domain values in the given function

So, we have

f(x) = 2.250x

f(10) = 2.250 * 10

Evaluate

f(10) = 22.5

f(x) = 2.250x

f(16) = 2.250 * 16

Evaluate

f(16) = 36

The range of the function is then represented as

f(10) <= f(x) <= f(16)

So, we have

22.5 <= f(x) <= 36

Hence, the range of the function f(x) = 2.250x is 22.5 <= f(x) <= 36

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Complete question

ou are in charge of ordering hats for a youth baseball team. Each hat costs $22.50. There are at least 10 but no more than 16 players on the baseball team. The total cost of ordering hats can be modeled by the function f(x)=22.50x, where x represents the number of hats ordered.

What is the range of the function?

Answer:

24 reminder 4

Step-by-step explanation:

Reminder is 4

316/13 = 24 R 4

Answer:

$142.60

Step-by-step explanation:

an increase of 15% on the original cost of 100% means

percentage increase = 100% + 15% = 115% , then

cost = 115% × $124 = [tex]\frac{115}{100}[/tex] × $124 = 1.15 × $124 = $142.60

Answer:

no

Step-by-step explanation

an example of vertical angles would be 6 and 8

pls give brainliest :)

Answer:

Step-by-step explanation: 2x5=10

:) have a good day

The average rate of change of the function between the points is -4/7

The constant average rates of change of a function is also regarded as the slope or the gradient of the function

Here, we have the points to be

(-3, 16) and (4, 12)

The average rates of change between these points is calculated as

Average rate of change = [f(b) - f(a)]/[b - a]

So, we have

Average rate of change = [12 - 16]/[4 + 3]

Evaluate the sum and the difference

So, we have

Average rate of change = -4/7

Hence, the average rate of change between the points is -4/7

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Answer: 74

Step-by-step explanation: calculator

The ratio that compares the championship won by Australia to the total number of championship is 6/41 which means that of the total 41 championship Australia has won 6 of the championship.

According to the question we have been given that,

 Total number of championship = 41

  Total number of championship won by Australia = 6

Thus we need to find the ratio that compares the championship won by Australia to the total number of championship.

For this the ratio will be :   [tex]\frac{number of championship won by Australia}{Total number of championship }[/tex]

                                       = 6/41

Hence the ratio that compares the championship won by Australia to the total number of championship is 6/41 which means that of the total 41 championship Australia has won 6 of the championship.

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Answer:

3 is the greatest common factor that can go into 9 and 48

The greatest common factor of 9 and 48 is 3.

The greatest common factor (GCF) is the largest positive integer that divides two or more numbers without leaving a remainder. In other words, it is the largest number that is a factor of both (or all) of the given numbers.

For example, the GCF of 12 and 18 is 6, beca

To find the greatest common factor (GCF) of 9 and 48, we need to determine the largest number that both 9 and 48 can be divided by evenly.

We can start by listing the factors of each number:

9: 1, 3, 9

48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Then we can look for the greatest factor that appears in both lists. In this case, the greatest common factor of 9 and 48 is 3, since it is the largest number that appears in both lists of factors.

Therefore, the GCF of 9 and 48 is 3.

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Answer: 6

Step-by-step explanation:

The solved logarithmic function is log (2x + y) = 4 log (2) and log (4x - y) = 0 for 2x + y = 2⁴ and 4x - y = 1 respectively.

What is a logarithmic and exponential function?

Logarithmic functions and exponential functions are inverses of each other. The logarithmic function is denoted by using the word log while exponential by using the alphabet,  e. For example log 10 = 1 and e^2.

Solving the given expressions: 2x + y = 16 and 4x - y = 1

Applying given properties of logarithmic and exponential function;

log a + log b = log (ab)

4 log x = log x⁴

e^(log x) = 1

e^(x + y) = (e^x) × (e^y)

Take the expression, 2x + y = 16

Applying log on both sides, we get,

log (2x + y) = log (16)

log (2x + y) = log (2⁴)

log (2x + y) = 4 log (2)

To Check Results,

Taking exponential on both sides,

e^[log (2x + y)] = e^(4 log 2)

2x + y = e^(log 2⁴)

2x + y = 2⁴

2x + y = 16

Thus, the answer is verified.

Take expression, 4x - y = 1

Applying log on both sides, we get,

log (4x - y) = log 1

log (4x - y) = 0

To Check Results,

Taking exponential on both sides,

e^[log (4x - y)] = e^0

4x - y = 1

Thus, the answer is verified.

Hence, the solved expression is log (2x + y) = 4 log (2) and log (4x - y) = 0 for 2x + y = 2⁴ and 4x - y = 1 respectively.

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Answer:

Step-by-step explanation:

63
because 9x7=63

and 7x9=63

Answer:

the point will not lie on any line. it will come in the first coordinate

Answer:

Shop C

Step-by-step explanation:

Without any calculations, you can eliminate stores B and D.

Shop A: $5.10/6 = $0.85/can

Shop C: $9.60/12 = $0.80/can

Answer:

It would be B

Step-by-step explanation:

Because A is 1.17 per can

B is 1.05 per can

D is 1.11 per can

and C is 1.25 per can

The graph of the inequality expression where the inequality expression is given as y ≤ 3/4x − 4 is (d)

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The inequality expression is given as

y ≤ 3/4x − 4

The inequality symbol in the above inequality expression is

≤

This implies that the inequality expression is a less than or equal to

When an inequality expression has a sign of equal to, then the line of the inequality graph will be a solid line

Also, the inequality symbol implies that the bottom part is shaded

Hence, the graph of the inequality expression where the inequality expression is given as y ≤ 3/4x − 4 is (d)

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Answer:

G = 6(2)^n

Step-by-step explanation:

a) At 1 month he will have 12 guppies, at 2 months he will have 24 guppies and at 3 months he will have 48 guppies.

b) G = 6(2)^n

This is following the exponential formula.

c) G = 6(2)^6.5 = 543 guppies

d) At this rate, there will be no room for the guppies to continue growing.

Answer:b

Step-by-step explanation:

b

The average rate of change of [tex]f[/tex] over an interval [tex][a,b][/tex] is the difference quotient

[tex]\dfrac{f(b) - f(a)}{b - a}[/tex]

Over the interval [tex]3\le x\le5[/tex], we have

[tex]\dfrac{f(5) - f(3)}{5 - 3} = \dfrac{27 - 3}{5 - 3} = \dfrac{24}2 = \boxed{12}[/tex]

Answer: The total would be 33.6 points.

Step-by-step explanation:

Titans Score: 11.15

Running Back Score: 11.75

Wide Receiver: 1.05 less than Running Back (11.75 - 1.05), which would be 10.7 points.

11.15 + 11.75 + 10.7 = 33.6 total points

Answer: the problem was a little confusing but I'm assuming the answer is 10.7 making the final answer 32.97

Step-by-step explanation: if the titans scored (11.15) points and the running back scores (11.75) points and the wide receiver scores 1.05 points less then the running back it would be...

  11.75 (the running backs points)

- minus

  1.05

__________

=10.07(how many points the wide receiver had)

Then 10.07+ 11.15+ 11.75=32.97

Hope I got it right! <3

The minutes that have passed, m, when Tank A contains the following amounts of water will be:

151 liters = 3 minutes

191.5 liters = 7.5 minutes

270.25 liters = 16.25 minutes

p liters = (p-124) / 9 min

It should be noted that for 151 lit = (151 - 124)/9 = 3 min

Also, for 191.5 lit = (191.5-124) /9

= 67.5/9 = 7.5 min = 7 min 30 sec

It should be noted that for 270.25 lit = (270.25 - 124)/9 = 146.25/9 = 16.25 = 16 min 15 sec

For p lit = (p-124) / 9 min

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Tank A initially contained 124 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute.

How many minutes have passed, m, when Tank A contains the following amounts of water?

151 liters

191.5 liters

270.25 liters

p liters

Follow • 1

Answer:9.3

Step-by-step explanation:

Area= length times width

132.99= 14.3xw

Divide by 14.3

W= 9.3

The value of logarithmic expression (2logbx/3 + 3logby / 4) - 5logbz is logbx/3^2(by / 4)^3/logbz^5.

By considering the given logarithmic expression

(2logbx/3 + 3logby / 4) - 5logbz

logb(x/3)^2 +log(by / 4)^3-log(bz)^5

logb(x/3)^2(by / 4)^3-logbz^5

logbx/3^2(by / 4)^3/logbz^5

The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.

Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).

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it is 22 units <3 your welcome

The cost of one packet of biscuit is £1.60.

The total amount that Aisha paid for the items she purchased is a function of the total cost of bread rolls, ketchup and biscuits.

Total cost of the items purchased = total cost of bread rolls + total cost of biscuits + total cost of ketchup

Total cost of bread rolls = cost per packet x number of packets bought

2 x £1.20 = £2.40

Total cost of ketchup = cost of one bottle x number of bottles bought

1 x £2.10 = £2.10

Total cost of biscuits = cost of one packet  x number of packets bought

3 x b = 3b

Total cost = £2.40 + £2.10 + 3b = £4.50 + 3b

Total amount paid by Aisha = note given - change received

£10 - 70p

£10 - £0.70 = £9.30

Total amount paid by Aisha =  total cost

£9.30 = £4.50 + 3b

£9.30 - £4.50 = 3b

£4.80 = 3b

b = £4.80 / 3

b = £1.60

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After solving the equation, x = 2/5 is the value of x in [tex]3^{X+2} = 27^{2x}[/tex]

⇒ [tex]3^{X+2} = 27^{2x}[/tex]

⇒ [tex]3^{X+2} = ((3)^3)^{2x}[/tex]

⇒ [tex]3^{X+2} = (3)^{6x}[/tex]

⇒ [tex]3^{X+2} = (3)^{6x}[/tex]

⇒ x+2 = 6x

⇒ 2 = 6x - x

⇒ 2 = 5x

⇒ x = 2/5

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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The inequality comparing the elevations is -220 > -282  and -220 feet is closer to sea level.

The elevation of Bad Water Basin = -282 feet

The elevation of the Salt Creek = -220 feet

We are asked to compare the elevations and find which is greater than the other.

So we know that on a number line -220 is greater than -282.

This can be understood in the same sense that -1 > -2 on the number line.

So the inequality comparing the elevations is -220 > -282.

Now consider the sea level as 0 on the number line.

Then clearly -220 is closer to 0 on number line.

Hence the elevation closer to the sea level = -220 feet.

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Answer:

Step-by-step explanation:

A measure of central tendency is a summary statistic that represents the center point or typical value of a dataset. These measures indicate where most