The proof for the power property of logarithms appears in the table with an expression missing.
Step
Reason
log, M)
Given
log.((b"))
Substitution
Properties of exponents
Logarithm property log, (b) = 0
Substitution
Commutative property of multiplication
Flog, (M).
Frilog, (M)
Which expression is missing from the proof?
log, (6**)
log, (6*-))
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Answer:

Step-by-step explanation:

Answer:

$12 is owed

Step-by-step explanation:

5 + 5 + 8 = 18

18 - 6 = 12

Answer:

The future value of investment at 6 % compounded quarterly is                $ 4782.472  

Step-by-step explanation:

Given as :

The principal amount = $ 4000

The rate of interest compounded quarterly = 6 %

The time period = 3 years

Let The future amount = A

From Compounded method

Amount = Principal × [tex](1+\dfrac{\textrm rate}{4\times 100})^{4\times \textrm time}[/tex]

Or, Amount = 4000 × [tex](1+\dfrac{\textrm 6}{4\times 100})^{4\times \textrm 3}[/tex]

Or, Amount = 4000 × [tex](1.015)^{12}[/tex]

Or, Amount = 4000 × 1.195618

∴ Amount = $ 4782.472

Hence The future value of investment at 6 % compounded quarterly is  $ 4782.472  Answer

Answer:

9.5

Step-by-step explanation:

The cost of movie tickets is $9.50 per person.

Now, if the variable x represents the number of people and t represents a total cost in dollars, then we can write the equation that models the above situation as

t = 9.5x ......... (1)

From this above two-variable linear equation it is clear that the slope of the line is 9.5. And its unit is dollars per person. (Answer)

Answer:

0.5%

Step-by-step explanation:

8/1600=0.005=0.5%

Answer:

0.5%

explanation:

8/1600=0.005=0.5%

Answer:

minerals

Step-by-step explanation:

Rocks are either SEDIMENTARY , IGNEOUS, or METAMORPHIC. Almost all rocks made of minerals, but different rocks contain different mixtures of minerals.

hope this helps :)

Answer:

sand

Step-by-step explanation:

sand because sand is made of different substance and for a lon

g time it starts to sit and without water its hard for them to sit, and sand has more similar substance between some that was one living and mineral.

Answer:

(- 10, 5 )

Step-by-step explanation:

Given the 2 equations

5x + 12y - 10 = 0 ( add 10 to both sides )

5x + 12y = 10 → (1)

2x - 3y + 35 = 0 ( subtract 35 from both sides )

2x - 3y = - 35 → (2)

Multiplying (2) by 4 and adding to (1) will eliminate the y- term

8x - 12 y = - 140 (3)

Add (1) and (3) term by term

5x + 8x + 12y - 12y = 10 - 140, that is

13x = - 130 ( divide both sides by 13 )

x = - 10

Substitute x = - 10 into either (1) or (2) and solve for y

Substituting in (1)

5(- 10) + 12y = 10

- 50 + 12y = 10 ( add 50 to both sides )

12y = 60 ( divide both sides by 12 )

y = 5

Solution is (- 10, 5 )

Answer: 6 gallons

Step-by-step explanation:

1/3 = 2/6. 1/2 = 3/6

2/6 already + 3/6 = 5/6, it

To determine the total capacity of Goran's gas tank, we set up and solved an algebraic equation, finding that the total capacity of the tank is 18 gallons.

The student's question is about figuring out the total capacity of Goran's gas tank based on the information given. To solve this problem, we can set up a simple algebraic equation based on the proportions of the tank's capacity that are filled. Since filling the tank with 3 gallons of gas takes it from being 1/3 full to 1/2 full, we know that these 3 gallons represent the difference between 1/3 and 1/2 of the tank's total capacity.

Let's denote the total capacity of the tank as 'T' gallons. According to the question:

We can now set up the equation:

1/3 * T + 3 = 1/2 * T

To find 'T', we need to solve for T:

1/2 * T - 1/3 * T = 3

This simplifies to:
(3T - 2T) / 6 = 3
T/6 = 3

Now multiply both sides by 6 to solve for T:
T = 18

Therefore, the total capacity of Goran's gas tank is 18 gallons.

Answer:

20100 decimeters

Step-by-step explanation:

1 kilometer=10,000 decimeters

2 1/100=201/100

201/100*10,000=20100

Answer:

[tex]\large\boxed{2\dfrac{1}{100}\ kilometers=20100\ decimeters}[/tex]

Step-by-step explanation:

[tex]PREFIXES\\\\mega\ (M)=10^6\\\\kilo\ (k)=10^3\\\\hecto\ (h)=10^2\\\\deko\ (da)=10\\\\decy\ (d)=10^{-1}=0.01\\\\centi\ (c)=10^{-2}=0.01\\\\mili\ (m)=10^{-3}=0.001\\\\mikro\ (\mu)=10^{-6}=0.000001[/tex]

[tex]2\dfrac{1}{100}=2.01\\\\2\dfrac{1}{100}\ km=2.01\ km=2.01\cdot10000\ dm=20100\ dm\\\\1\ kilometers=10000\ decimeters[/tex]

Scott has ridden 12% of the course.

Step-by-step explanation:

Length of bike course = 50 miles

Distance covered = 6 miles

Distance covered in percentage = [tex]\frac{Distance\ covered}{length\ of\ bike\ course}*100[/tex]

Distance covered in percentage = [tex]\frac{6}{50}*100\\[/tex]

Distance covered in percentage = [tex]\frac{600}{50}[/tex]

Distance covered in percentage = 12%

Scott has ridden 12% of the course.

Keywords: percentage, distance

Learn more about percentages at:

#LearnwithBrainly

Answer:

B) 1/4c^4

Step-by-step explanation:

Because 3/12=1/4 and c^8/c^12=1/c^4.

Answer:C) 8; The elephants’ rate in miles per hour

Step-by-step explanation:

First write the question as an equation that can be solved to give you a numerical answer.

[f(4)=4(4)+8] / [g(4)=(4)-1]

Then solve the equation.

24/3=8

Finally use background information to give you the context.

Since the problem gives you the function for distance and the function for time then it can be concluded that the context will be the elephants’ rate in miles per hour

C is correct i got the answer right on my test :)

Answer:

Jewelry box:  1/6 yard

Step-by-step explanation:

4/5 (not 4\5) of her 5/6 yard goes into a dress:   (4/5)(5/6 yd) = 2/3 yard.

This is the same as 4/6 yard.  The amount of lace remaining, to be used on a jewelry box, is 5/6 - 4/6, or 1/6 yard.

Dawn used 1/6 yard of lace on the jewel box. This was calculated by subtracting the amount of lace used on the dress (2/3 yard) from the total lace available (5/6 yard).

The subject of your question pertains to Mathematics, specifically fractions and their applications. To find out how much lace Dawn used on the jewel box, we need to subtract the amount of lace used on the dress from the total amount of lace. Dawn has 5/6 yard of lace and she utilized 4/5 of it on the dress. To find out the part used on the dress in the same unit, multiply the total lace (which is 5/6) by the part used (which is 4/5), so (5/6)*(4/5) = 20/30 or 2/3 yard. To find out what part of the lace was used on the jewel box, subtract the dress lace from the total lace. So, 5/6 - 2/3 gives us 1/6 yard of lace that is used on the jewel box.

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35

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Answer:

8,10 and 12

Step-by-step explanation:

The numbers are

(x-2)* (x-4)  = x^ -64

Diistributive

x^-4x-2x+8 = x^-64

Subtract x^ on both sides (It will be cancelled)

-6x+8 = -64

Subtract 8 on both sides

-6x=-72

Divide both sides by -6

x=12

12-2=10

12-4=8

 8*10=80                     12*12=144            144-80=64

80+64=144

Answer:

5 because 250 ÷50 equals 5

Step-by-step explanation:

Because its says she took out 50 each week and you divide by 250 by 50 and 50 represents out of her savings account and which equals 5 because the number of weeks and and she had 250 in there 5 weeks ago and she took 50 out each week so its 5 weeks

Answer:

(B) The inequality that represents this relationship is [tex]3x  < x^2 +15[/tex]

Step-by-step explanation:

Let us assume the given number = x

⇒ 3 times the given number = 3 (x)  = 3x

Square of the given number = [tex](x)^2  = x^2[/tex]

Now, According to the question:

The difference of (3 x) and 15 is no less than [tex] x^2[/tex]

⇒ [tex]3x - 15 < x^2\\ \implies 3x  < x^2 +15[/tex]

or, [tex]3x  < x^2 +15[/tex]

Hence, the given inequality is represented as [tex]3x  < x^2 +15[/tex]

Answer:

3x - 15 > [tex]x^{2}[/tex]

Step-by-step explanation:

Let the number be x

⇒3 times the number is 3x and square of the number is [tex]x^{2}[/tex]

Difference of 3 times a number and 15 is 3x -15

⇒This difference is no less than the square of the number

⇒The difference is greater than or equal to square of the number

⇒ 3x - 15 ≥ [tex]x^{2}[/tex]

Answer:

ln|sec θ + tan θ| + C

Step-by-step explanation:

The integrals of basic trig functions are:

∫ sin θ dθ = -cos θ + C

∫ cos θ dθ = sin θ + C

∫ csc θ dθ = -ln|csc θ + cot θ| + C

∫ sec θ dθ = ln|sec θ + tan θ| + C

∫ tan θ dθ = -ln|cos θ| + C

∫ cot θ dθ = ln|sin θ| + C

The integral of sec θ can be proven by multiplying and dividing by sec θ + tan θ, then using ∫ du/u = ln|u| + C.

∫ sec θ dθ

∫ sec θ (sec θ + tan θ) / (sec θ + tan θ) dθ

∫ (sec² θ + sec θ tan θ) / (sec θ + tan θ) dθ

ln|sec θ + tan θ| + C

Answer: that is an improper fraction but mixed it’s 1 5/6

Answer:

11/6 as an improper fraction is 1 5/6

Step-by-step explanation:

Answer:

f(n + 1) = –0.5f(n)

Step-by-step explanation:

The terms 9.6, –4.8, 2.4, –1.2, 0.6 alternate negative and positive. This means they must have a negative rate of change (because multiplying with negatives give both positive and negative numbers).

This narrows it down to:

f(n + 1) = –0.5f(n)

f(n + 1) = f(–0.5n)

Substitute f(n) for f(1)=9.6.

f(n + 1) = –0.5(n)

f(1 + 1) = –0.5(1)

f(2) = –0.5(9.6)

f(2) = -4.8

Since the second term is -4.8, f(n + 1) = –0.5f(n) is the recursive formula.

Answer:

it is f(n + 1) = –0.5f(n)

Step-by-step explanation:

I just took it on edge 2020

Answer:

Length n = 5 cm

Step-by-step explanation:

Given:

Each angle measure is of 60° for the triangle given in the figure.

Equilateral Triangle:

If all the angles measure of the triangle is 60° then the triangle is said to be an Equilateral Triangle.

Therefore, the triangle given in the figure is an Equilateral Triangle.

Another property of an Equilateral Triangle is

All the Three sides of an equilateral triangles are equal.

Here,

measure of each angle is 60° ...... { Given}

length of one side = 5 cm       ........{Given}

∴  Length n = 5 cm

Answer:

i. ) The fraction[tex]\frac{1.7}{1.3}[/tex] as a number with one decimal place is 1.3.    

ii. ) The height of the tree is 37.9 m

Step-by-step explanation:

One decimal Place:

Some examples,

4.23     ————————- 4.2

97.456    ———————- 97.5

7324.89456   ————— 7324.9

0.95      ————————- 1.0

76      —————————- 76.0

Therefore,  the fraction[tex]\frac{1.7}{1.3}[/tex] as a number with one decimal place is 1.3.  

ii. )

Given

[tex]\frac{x}{29} =\frac{1.7}{1.3} \\x= 29\times \frac{1.7}{1.3}\\x =\frac{49.3}{1.3}\\x = 37.923....\\x=37.9\ m\ \textrm{rounded to one decimal place}[/tex]

Therefore, the height of the tree is 37.9 m

Answer:

125tiles

Step-by-step explanation:

800*10=8000

8000/64=125

Option C. (A’UB') is the correct answer

Step-by-step explanation:

If A and B are two sets

Then

We can say the the elements that are not in set a can only be obtained by finding its complement

So,

all of the elements which are not in set  A = A'

Similarly

those elements not in set B = B'

Combining these means that elements of both sets will be : A'UB'

Hence,

Option C. (A’UB') is the correct answer

Keywords: Sets, complements

Learn more about sets at:

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Answer:

-1.6

Step-by-step explanation:

Simple division but with a negative number. Positive ÷ Negative = Negative and vice versa

Answer:

-1.6

Step-by-step explanation:

edge-

There are 2088 TVs in his whole hotel.

Step-by-step explanation:

No. of floors = 58

No. of rooms = 18 per floor

Total rooms = No. of floors * No. of rooms per floor

[tex]Total\ rooms = 58*18\\Total\ rooms=1044[/tex]

As every room has two TVs, therefore,

Total TVs = Total rooms * 2

[tex]Total\ TVs=1044*2\\Total\ TVs=2088[/tex]

There are 2088 TVs in his whole hotel.

Keywords: multiplication

Learn more about multiplication at:

#LearnwithBrainly

Answer:

[tex]x\leq -27[/tex]

Step-by-step explanation:

Given:

[tex]\frac{x}{-9}\geq 3[/tex]

Multiplying both sides by -9, we get

[tex]-9\times \frac{x}{-9}\leq -9\times 3\\x\leq -27[/tex]

On multiplying both sides of an inequality by a negative number, the sign of the inequality changes as evident in the above equation.

So, the value of [tex]x[/tex] varies as:

[tex]x\leq -27[/tex]

Answer:

option A (-1, 2.5) is correct

Step-by-step explanation:

Given

Let A(1, 1)

Let B(1, 4)

Let C(-3, 4)

Let coordinates of the circumcenter is (x, y)

Using distance formula

[tex]OA = OB[/tex]

[tex]OA^{2}=OB^{2}[/tex]

[tex](x-1)^{2}+(y-1)^{2} =(x-1)^{2}+(y-1)^{4}[/tex]

[tex]x^{2} +1-2x+y^{2} +1-2y=x^{2} +1-2x+y^{2} +16-8y[/tex]

[tex]8y-2y=16-1[/tex]

[tex]y=\frac{15}{6}[/tex]

[tex]y=2.5[/tex]

[tex]OA = OC[/tex]

[tex]OA^{2}=OC^{2}[/tex]

[tex](x-1)^{2}+(y-1)^{2} =(x-(-3))^{2}+(y-4)^{4}[/tex]

[tex](x-1)^{2}+(y-1)^{2} =(x+3)^{2}+(y-4)^{4}[/tex]

[tex]x^{2} +1-2x+y^{2} +1-2y=x^{2} +9+6x+y^{2} +16-8y[/tex]

[tex]-6x-2y-2x+8y=25-2[/tex]

put the y value in this equation

[tex]-8x+6\times\frac{15}{6} = 23[/tex]

[tex]-8x=23-15\\-8x=8\\x=-1[/tex]

So the coordinates of the circumcenter is (1, 2.5)

Midpoints: AB (1, 2.5), BC (-1, 4). Perpendicular bisectors: AB (y = 2.5), BC (x = -1). Intersection at (-1, 2.5), hence circumcenter is (-1, 2.5).

So, the correct answer is A. (-1, 2.5).

To find the circumcenter of a triangle, we can use the following steps:

1. Find the midpoints of two sides of the triangle.

2. Calculate the slopes of the perpendicular bisectors of those sides.

3. Use the midpoints and slopes to find the equations of the perpendicular bisectors.

4. Find the point of intersection of the perpendicular bisectors, which is the circumcenter.

Let's begin:

Given vertices of the triangle:

A (1, 1)

B (1, 4)

C (-3, 4)

1. Finding the midpoints of sides AB and BC:

Midpoint of AB = ((x1 + x2) / 2, (y1 + y2) / 2)

Midpoint of BC = ((x2 + x3) / 2, (y2 + y3) / 2)

Midpoint of AB = ((1 + 1) / 2, (1 + 4) / 2) = (1, 2.5)

Midpoint of BC = ((1 + (-3)) / 2, (4 + 4) / 2) = (-1, 4)

2. Calculate the slopes of the sides AB and BC:

Slope of AB = (y2 - y1) / (x2 - x1)

Slope of BC = (y3 - y2) / (x3 - x2)

Slope of AB = (4 - 1) / (1 - 1) = 3 / 0 (undefined slope)

Slope of BC = (4 - 4) / (-3 - 1) = 0 / -4 = 0

The slope of AB is undefined because the difference in x-coordinates is zero, meaning it's a vertical line. For a perpendicular bisector, we need to take the negative reciprocal of this slope.

3. Calculate the negative reciprocals of the slopes of AB and BC:

Negative reciprocal of undefined slope = 0

Negative reciprocal of zero slope = undefined

4. Equations of the perpendicular bisectors:

For AB: The perpendicular bisector passes through the midpoint (1, 2.5) and has a slope of 0.

Using the point-slope form of a line equation: y - y1 = m(x - x1)

y - 2.5 = 0(x - 1)

y = 2.5

For BC: The perpendicular bisector passes through the midpoint (-1, 4) and has an undefined slope (vertical line).

So, the equation is x = -1.

Now, we find the point of intersection of the perpendicular bisectors.

The point of intersection is the circumcenter.

Since the perpendicular bisectors intersect at (-1, 2.5), which is the midpoint of AB, the circumcenter is at (-1, 2.5).

So, the correct answer is A. (-1, 2.5).

can be simplified to

[tex]-\frac{3p^8}{4q^3}[/tex]

Hopes this helps

if not then I'm sorrr

The quotient in simplified form for \(\frac{15p^{-4}q^{-6}}{-20p^{-12}q^{-3}}\) is \(-\frac{3p^8}{4q^3}\). This is found by dividing the numerical coefficients and subtracting the exponents for variables of the same base (negative exponents indicate reciprocals).

To find the quotient in simplified form for \(\frac{15p^{-4}q^{-6}}{-20p^{-12}q^{-3}}\), we perform division of the coefficients (15 divided by -20) and subtraction of the exponents for variables with the same base (p's and q's exponents) according to the rules of exponents. First, simplify the numerical coefficients:

\(\frac{15}{-20} = -\frac{3}{4}\)

Now, subtract the exponents for p (applying the formula x^p \cdot x^q = x^{(p+q)}):

\(p^{-4} - p^{-12} = p^{-4 + 12} = p^8\)

Next, apply the same process to the exponents of q:

\(q^{-6} - q^{-3} = q^{-6 + 3} = q^{-3}\)

Combine the results to get the simplified quotient:

\(-\frac{3}{4} × p^8 × q^{-3}\)

Remember that a negative exponent indicates a reciprocal, so we can write \(q^{-3}\) as \(\frac{1}{q^3}\). Therefore, the final answer is:

\(-\frac{3p^8}{4q^3}\)

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Answer:

1. A is d=1.75

Step-by-step explanation:

Answer:

1a) 10.50=6d

1b) d= 1.75

2a) w is less than or equal to 35

2b) It would not make sense to have a bag that weighed zero or below.

3a) The tree grows 15 ft for every since it was planted.

3b) h(t)=70+15x