Find measure of angle M

The expression log₃(x²∛y²) using the laws of logarithms is 2log₃(x) + 2/3log₃(y)

From the question, we have the following parameters that can be used in our computation:

log₃(x²∛y²)

The product law of logarithms states that

log(ab) = log(a) + log(b)

Using the above as a guide, we have the following:

log₃(x²∛y²) =  log₃(x²) + log₃(∛y²)

The power law of logarithms states that

log(aᵇ) =  blog(a)

Using the above as a guide, we have the following:

log₃(x²∛y²) =  2log₃(x) + 2/3log₃(y)

This means that the values of A and B are A = 2 and B = 2/3

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Answer:

A. \(60 ft^3\)

Step-by-step explanation:

So to find the volume of a single box, we can determine that by multiplying the width by the height by the length. So:

2.5 × 2.4 × 2 = 12

Now because we have 5 of these boxes, and we know each box has a volume of 12, all we have to is multiply 12 by 5 to get 60.

Answer:

60 cubic feet

Step-by-step explanation:

Total volume of boxes = Number of boxes × Volume of I box

                                      = 5 × (Length × Width × Height)

                                     = 5 × (2 feet × 2.5 feet × 2.4 feet)

                                     = 60 cubic feet

∴Option A

Answer:

61%

Step-by-step explanation:

We can see that out of all the people that were surveyed, 54% were 10th graders. Since 33% out of all the ones surveyed were 10th graders that chose robotics, the fraction would be 33/54 which is 0.611.

This is 61% approx.

Answer:

61%

Step-by-step explanation:

A P E X

Answer:

  -1

Step-by-step explanation:

The average rate of change is the ratio of the difference in y-values to the difference in x-values of corresponding points.

At x=-1, f(x) = (-1)^2 -(-1) -1 = 1

At x=1, f(x) = (1)^2 -(1) -1 = -1

So, points on the graph are (-1, 1) and (1, -1).

Then the change in y over that interval is -1 -1 = -2.

The change in x over that interval is 1 -(-1) = 2.

The average rate of change is ...

  ∆y/∆x = -2/2 = -1 . . . . average rate of change on (-1, 1)

Answer:

141

Step-by-step explanation:

First, we choose two variables to represent the two unknown numbers, the number of hamburgers and the number of cheeseburgers.

Let x = number of hamburgers.

Let y = number of cheeseburgers.

Now we use the given information to write two equations using the variables we defined above.

"If a hamburger shop sold a combined total of 423 hamburgers and cheeseburgers"

x + y = 423

"the number of cheeseburgers sold was two

times the number of hamburgers sold"

y = 2x

We have a system of two equations.

x + y = 423

y = 2x

Since the second equation is already solved for y, we can easily use the substitution method. We substitute what y equals to (2x) for y in the first equation.

x + y = 423

x + 2x = 423

3x = 423

x = 141

Since we let x = number of hamburgers, we have the answer.

Answer: 141

Answer:

d 90

Step-by-step explanation:

hope this helped you

Answer:

B. 200 acres

Step-by-step explanation:

Create an estimate by rounding the size of each of their farms to the nearest hundred.

Kim's farm is approximately 1,300 acres, since 292 is closest to 300.

Jack's farm is approximately 1,100 acres, since 104 is closest to 100.

Using these estimates, find the difference between them:

1,300 - 1,100

= 200

So, the best estimate of the size difference is B. 200 acres

Standard Deviation for given set of data is 0.25634797778466.

What is standard deviation?

Given that,

Sample size :12.3,11.9,12.5,12.1,12.6,11.9,12.2,12.1

Count, N: 8

Sum, submission x: 97.6

Mean, x: 12.2

Variance, s2:  0.065714285714286

s^2 = Σ(xi - x)^2/N - 1

= (12.3 - 12.2)2 + ... + (12.1 - 12.2)^2/8 - 1

= 0.46/7

=  0.065714285714286

s =  √0.065714285714286

=  0.25634797778466

Standard Deviation for given set of data is 0.25634797778466.

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Step-by-step explanation:

Since force doesn't depend on mass and varies directly, you can set up a proportion. group the F's together and the acceleration together, as so

\( \frac{20}{16} = \frac{5}{x} \)

Next, cross m multiply

\(20x = (16)(5)\)

\(20x = 80\)

Lastly, divide by 20

\(x = 4m {s}^{2} \)

The acceleration of the object when force is 16N is 4m/s².

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, The force acting on the object varies directly with the object's acceleration.

Therefore, F ∝ a.

F = ka.

20 = 5k.

k = 4.

Now,

16 = 4a.

a = 4.

So, The acceleration is 4m/s²

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Answer:

5.60

Step-by-step explanation:

Answer: $5.60

Step-by-step explanation:

Given:

We must find:

Let t = total cost.

We will multiply 0.35 by 16 to get the answer.

Step-by-step explanation:

16 - 10 × 1/5 + 13

16 - 5 + 13

11 + 13

24

Step-by-step explanation:

10/5=2

16-2+13=27.

d. 27

According to Polynomial System, the correct answer is that the roots of f(x) are (x+1).

A polynomial system (sometimes just a polynomial system) is a set of simultaneous equations f₁ = 0,..., fₙ = 0. where fi is a polynomial in multiple variables such as x₁,..., xₙ over the fields. k.

This is due to the zero product property that when two binomials are multiplied by 0, one of their factors must be 0.

A simple example of a system of polynomial equations is

x²+y²- 5 = 0

      xy-2 = 0.

Its solutions are the four pairs (x, y) = (1, 2), (2, 1), (-1, -2), (-2, -1). These solutions are easily verified by substitution, but proving that there are no other solutions requires more work.

Based on above description, we can say that:

(x+1) must be 0.

(x+1)=0

x=-1

Thus, If (x-1)=0 then x is 1 instead of -1 in question.

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A. The following are sets A and B:

A = {2, 3, 5, 7, 11}

B = {1, 2, 3, 4, 6, 12}

C. Elements not in A or A' = ∅

B. The Venn diagram is attached

A universal set is a set which consists of all elements related to the given sets. It is denoted by U.

A. Set A:

A = {2, 3, 5, 7, 11}

Set B:

B = {1, 2, 3, 4, 6, 12}

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

A' = {1, 4, 6, 8, 9, 10, 12}

C. Elements not in A or A' = ∅

Complement of set A is refers to a set that contains the elements present in the universal set but not in set A.

Hence, the Venn diagram of sets A, B and U has been attached.

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Answer:

x = 11/10

Step-by-step explanation:

5(2x - 1) = 6

Distribute

10x -5 = 6

Add 5 to each side

10x-5+5 = 6+5

10x = 11

Divide each side by 10

10x/10 = 11/10

x = 11/10

Answer:

Liquidity management refers to a set of processes, strategies, and supporting mechanisms/tools that ensure a business or bank is able to access cash when and where it is needed. This cash could be used to pay for goods and services, payroll, debt repayment, or new investment opportunities

Step-by-step explanation:

Answer:

You should use Brainly so that we can help.

Step-by-step explanation:

Answer:

Do it.

Step-by-step explanation:

The solution of the compound inequality is x < 3/4 or x >2.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

A compound inequality:

4x - 5 < -2 or x + 1 > 3.

Solving inequality,

4x < -2 + 5 or x > 2

4x < 3 or x > 2.

x < 3/4 or x >2.

Therefore, the solution is x < 3/4 or x >2.

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Answer:

3 and 1/2 units

Answer:

3 and 1/2 units

Step-by-step explanation:

hope this helps you lol

E

Answer: 20%

Step-by-step explanation: Annual depreciation = $2,600 * 12 = $31,200

Annual depreciation rate = Annual depreciation /Depreciable costs

= $31,200 / ($188,000 - $32,000)

= 20%

Answer: B. 2(x - 3)(x - 4)

Step-by-step explanation:

Answer:

No Factors

Step-by-step explanation:

\(x^3-12x^2-19x+20 = 0\\Let \ p(x) = x^3-12x^2-19x+20\)

Factors of 20 = ±1, ±2 , ±4 , ±5 , ±10 and ±20

±1, ±2 and ±3 are not the factors of given polynomial.

Putting x = 4 in the given polynomial

\(p(4) = (4)^3+12(4)^2-19(4)+20\\p(4) = 64+192-76+20\\p(4) = 200\)

So, x = 4 is not a factor of p(x)

Putting x = -4 in the given equation

\(p(-4) = (-4)^3+12(-4)^2-19(4)+20\\p(-4) = -64+192-76+20\\p(-4) = 73\)

So, x = -4 in the given equation

Putting x = 5 in the given equation

\(p(5) = (5)^3+12(5)^2-19(5)+20\\p(5) = 125+300-95+20\\p(5) = 350\)

So, x = 5 is not a factor of p(x)

Putting x = -5 in the given equation

\(p(-5) = (-5)^3+12(-5)^2-19(-5)+20\\p(-5) = -125+300+95+20\\p(-5) = 290\)

So, x = -5 is not a factor of p(x)

Putting x = 10 in the given equation

\(p(10) = (10)^3+12(10)^2-19(10)+20\\p(10) = 1000+1200-190+20\\p(10) = 2030\)

So, x = 10 is not a factor of p(x)

Putting x = -10 in the given equation

\(p(-10) = (-10)^3+12(-10)^2-19(-10)+20\\p(-10) = -1000+1200+190+20\\p(-10) = 410\)

So, x = -10 is not a factor of p(x)

Putting x = 20 in the given equation

\(p(20) = (20)^3+12(20)^2-19(20)+20\\p(20) = 8000+4800-380+20\\p(20) = 12440\)

So, x = 20 is not a factor of p(x)

Putting x = -20 in the given equation

\(p(-20) = (-20)^3+12(-20)^2-19(-20)+20\\p(-20) = -8000+4800+380+20\\p(-20) = -2800\)

So, x = -20 is not a factor of p(x)

From the above solution, we conclude that the given equation can not be factorized and thus, has no factors.

Answer:

\(\boxed{\mathrm{No \: factors}}\)

Step-by-step explanation:

\(x^3 +12x^2 -19x= -20\)

Add 20 on both sides.

\(x^3 +12x^2 -19x+20= 0\)

Add 67x and 44 on both sides.

\(x^3 +12x^2 +48x+64= 67x + 44\)

Factor left side of the equation.

\((x+4)(x+4)(x+4)= 67x + 44\)

\((x+4)^3=67x+44\)

Subtract 67x and 44 on both sides.

\((x+4)^3-67x-44=0\)

Cannot be factored further.

This is a prime expression. A prime expression cannot be factored.

We cannot factor out x from the expression, there are no factors.

Answer:

a

Step-by-step explanation:

Answer: D

Step-by-step explanation: x is a variable, and so is the number of tractors he sells. he is going to get paid $1000 for sure each month.

So 150x(the number of tractors) + 1000(his pay each month)

The notion of finiteness refers to the idea that something has a definite limit or is not infinite. It is a concept that has been applied in various fields of study, such as mathematics, computer science, and philosophy.

In mathematics, finiteness is a fundamental concept used to define various mathematical objects and structures, such as sets, numbers, and sequences. It is also used to define the properties of functions and to study the properties of mathematical systems.

In computer science, the notion of finiteness is crucial for the design and analysis of algorithms and computer programs. Computer scientists use finite state machines, which are mathematical models that describe the behavior of a system that can be in one of a finite number of states.

This concept is essential to the development of computer programs that are efficient, reliable, and secure.

In philosophy, finiteness is a concept that is often used to reflect on the nature of human existence and the limits of human knowledge. It is also used to examine the concept of time and the nature of reality.

In general, the notion of finiteness is a fundamental concept that has many applications in various fields of study.

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The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Answer: 882.96

Step-by-step explanation:

The product of -16.98 and 5.2 is -88.296.

The given expression is -16.98 multiplied by 5.2. To find the product, multiply the two numbers:

-16.98 * 5.2 = -88.296.

Therefore, the product of -16.98 and 5.2 is -88.296. The correct answer is -88.296, which matches the second option. When multiplying a negative number by a positive number, the result is negative. The calculation involves multiplying the absolute values (16.98 and 5.2) and then assigning the negative sign to the product. In this case, the product is -88.296, as it accurately represents the multiplication of -16.98 and 5.2.

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Answer:

x = 41

Step-by-step explanation:

Thus, we can find x by setting (x + 22)°, (2x - 6)°, and x° equal to 180:

(x + 22) + (2x - 6) + x = 180

(x + 2x + x) + (22 - 6) = 180

4x + 16 = 180

4x = 164

x = 41

Thus, x = 41

Check the validity of the answer:

We can check that x = 41 is the correct answer by pluggin in 41 for x in (x + 22)°, (2x - 6)° and x° and seeing whether the sum is 180:

(41 + 22) + (2(41) - 6) + 41 = 180

63 + (82 - 6) + 41 = 180

63 + 76 + 41 = 180

139 + 41 = 180

180 = 180

Thus, our answer is correct.

Answer:

C = 14 pi inches

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

49 pi  = pi r^2

Divide each side by pi

49 pi/pi = pi /pi r^2

49 = r^2

Take the square root of each side

7 = r

The circumference is given by

C = 2 * pi *r

C = 2 * pi *7

C = 14 pi inches

Answer:

37,260

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

At  B   (  40 mins)  and  D (30 mins)   he is not moving....visiting .

The width of A is the time it took to get to first house = 20 mins

The width of C is t the time to get to second house = 60 to 70 = 10 mins

Riding toward home at C and E  ( the distance...the y-value....is getting less)

He is fastest where the line has greatest slope...where it is steepest =  C

He was away from home the width of the graph = 115 mins

Answer:

Step-by-step explanation:

According to the question we are given with a right traingle Where base is 35 and the perpendicular is 12.

We need to find the unknown side that is the longest side (Hypotenuse) .

By using pythagoras theorem :

\(\longrightarrow \rm \: \: (H)^2 = (B)^2 + (P)^2 \\ \)

here,

Putting the required values in the Pythagoras theorem we will get,,

\(\longrightarrow \rm \: \: (H)^2 = (35)^2 + (12)^2 \\ \\ \longrightarrow \rm \: \:(H)^2 =1225 + 144 \\ \\ \longrightarrow \rm \: \:(H)^2 = 1369 \\ \\ \longrightarrow \rm \: \:H = \sqrt{1369} \\ \\ \longrightarrow \rm \: \:H = 37 \\ \)

Therefore, Unknown side of the right triangle i.e hypotenuse is 37 .