Given loga(m) = 10 and loga(n) = 20, find loga(mn2). (Enter an exact number.)

Based on the interval, the average rate of change of the function is 4.0

The graph that completes the question is added as an attachment

From the graph, we can see  that the equation of the graph is a quadratic equation

Also, from the question:

We have the interval to be:

The interval is given as

x = -4 to x = 2

This can be represented as

(a, b) = (-4, 2)

From the attached graph, we have

f(-4) = 22

f(2) = -2

The estimate of the average rate of change f is calculated as(to one decimal place)

Rate = [f(b) - f(a)]/[b - a]

Substitute the known values in the above equation

This gives

Rate = [f(2) - f(-4)]/[2 + 4]

Substitute the known values in the above equation

So, we have

Rate = [-2 - 22]/[2 + 4]

Evaluate

Rate = -4.0

Hence, the estimate (to one decimal place) of the average rate of change of the graph is 4.0

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Answer:

13

Step-by-step explanation:

The term is in an arithmetic progression.

That means there is 6 between each term and the next one.

Givens

a = -30

d = 6

last term an = 42

Formula

L = a + (n - 1)*d

Solution

42 = -30 + (n -1 )*6               Add 30 to both sides

42+30 = (n - 1) * 6                Combine the terms on the left.

72 = (n - 1)*6                        Divide both sides by 6

72/6 = n - 1

12     = n - 1                          Add 1 to both sides

12 + 1 = n

n = 13

Answer: I can not see the picture

Step-by-step explanation:

can you show it?

Answer:

55°

Step-by-step explanation:

The angle is part of a 90° angle, so you do 90°-35° to get 55°.

Give branliest please. :)

Answer:

90 degrees - 35 degrees = x degrees, this will give you 55 degrees

Answer:

x^2 + y^2 = 25

Step-by-step explanation:

x = 5 cos t

            cos t = x/5

y = 5 sin t

           sin t = y/5

cos^2 t + sin^2 t = 1

(x/5)^2 + (y/5)^2  = 1

x^2/25 + y^2/25 = 1

(x^2 + y^2)/25 =1

x^2 + y^2 = 25

Answer:

Step-by-step explanation:

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle. In this case, the diameter is given as 14 cm, so we can substitute that into the formula:

C = π(14 cm)

Multiplying, we get:

C = 14π cm

So the circumference of the circle is 14π cm. The units are centimeters, since circumference is a length measurement.

Answer:2  hope this helps it was right on my test

Step-by-step explanation: it was right on the test i took

Group B has lower range.

Group A shows variability.

Mean is the best to make concussion about age of Salsa students.

Upon visual examination, it appears that Group A is likely to have a lower average age of music students compared to Group B.

This inference is supported by the observation that the majority of data points in Group B are concentrated around younger ages.

In contrast, Group A exhibits a more dispersed distribution of data points across a wider range of ages, including higher.

So, Group B has lower range.

and, Group A shows variability.

Lastly, Mean is the best to make concussion about age of Salsa students.

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Answer:

Expressions A, C, D are equivalent

Step-by-step explanation:

Equivalent expressions:

Two expressions are equivalent if they give the same result. So

Option A:

3(2 + 4x)  =3*2 + 3*4x = 6 + 12x

So equivalent

Option B:

3(2 + 6x) + 2x = 3*2 + 3*6x + 2x = 6 + 18x + 2x = 6x + 20. So not equivalent

Option C:

5(1+2x) + 1 + 2x = 5*1 + 5*2x + 1 + 2x = 5 + 10x + 1 + 2x = 6 + 12x.

Equal, so equivalent

Option D:

7*(1+2x) - 2x - 1 = 7*1 + 7*2x - 2x - 1 = 7 + 14x - 2x - 1 = 6 + 12x

Equal, so equivalent.

Option E:

7*(1+2x) + 2x - 1 = 7*1 + 7*2x - 2x - 1 = 7 + 14x + 2x - 1 = 6 + 16x

Different, so not equivalent.

Since the score recorded at the end of the first round is 6, this score could represent the following: B. The difference between John's score and Kamira's score.

In Geometry and Mathematics, a number line refers to a type of graph that is usually composed of a graduated straight line, which typically comprises both negative and positive numerical values (numbers) that are located at equal intervals along its length.

Assuming the variable J represent John's score and the variable K represent Kamira's score on the number line. In this scenario and exercise, we would determine the solution for the given scenario by solving as follows;

J + K = 1 + 7 = 8

K - J = 7 - 1 = 6

|K - J| = |7 - 1| = |6| = -6

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer: a = b*r/n

Step-by-step explanation: Hope this helps :^)

Answer:

x = 3

Step-by-step explanation:

Let's solve your equation step-by-step.

7x−3=18

Step 1: Add 3 to both sides.

7x−3+3=18+3

7x=21

Step 2: Divide both sides by 7.

7x/7 = 21/7

x=3

9514 1404 393

Answer:

  (x, y, z) = (-3, -1, 3)

Step-by-step explanation:

Many graphing calculators can solve matrix equations handily. Here, we use a combination of methods.

Use the last equation to write an expression for z.

  z = 4 -x +4y

Substitute this into the second equation:

  y -4(4 -x +4y) = -13

  y -16 +4x -16y = -13

  4x -15y -3 = 0

In genera form, the first equation can be written as ...

  3x +y +10 = 0

Now, the solution to these two equations can be found to be ...

  x = (-15(10) -1(-3))/(4(1) -3(-15)) = (-150 +3)/(4+45) = -3 . . . using "Cramer's rule"

  y = -(10 +3x) = -(10 -9) = -1 . . . . from the first equation

  z = 4 -(-3) +4(-1) = 3 . . . . . . . . from our equation for z

The solution to the system is (x, y, z) = (-3, -1, 3).

_____

Additional comment

Written as an augmented matrix, the system of equations is ...

  \(\left[\begin{array}{ccc|c}-3&-1&0&10\\0&1&-4&-13\\1&-4&1&4\end{array}\right]\)

Answer:

PEMDAS

Step-by-step explanation:

Parentheses, Exponents, Division and Multiplication, Addition and Subtraction. When I put an and I mean do them in order of left to right.

Answer:

PENDMAS

Step-by-step explanation:

Parenthesis, Exponent, Multiplication, Addition, Subtraction.

Answer:

Question 5 : 10% decay

Question 6 : Amar is right

Step-by-step explanation:

Answer:

The answer is -3/4.

Answer: -3/4

Step-by-step explanation:

The line is pointing downwards, making it negative and having a negative slope. The line goes down 3, over 4, so its slope is -3/4.

Answer:

product of 10 and 8

Step-by-step explanation:

8 is the quotient of 80 and 10 (80/10=8)

Answer:

i think C

Step-by-step explanation:

Answer:

Hi! The answer to your question is -14.2b+3.36d-216.05

Step-by-step explanation:

Simplify the Expression.

Answer:

B) 6

Step-by-step explanation:

Let the number be x

Product of 6 and square of number plue 15 : (6x²) + 15

Coefficient of x² = 6

The equation expressing the total cost in terms of the number of hours required to accomplish the task is C = 32h + 31.50

Let C be the entire cost of the job, and h represent the number of hours needed to accomplish the job.

The hourly charge for services is K32, hence the total cost for services is 32h.

There is a one-time fee of K31.50, making the total cost:

C = 32h + 31.50

Hence, the equation expressing the total cost in terms of the number of hours required to accomplish the task is C = 32h + 31.50

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The length of AC is 12.5 and the length of AD is 3.

A triangle is a three-sided polygon because it has three edges and three vertices. The most important attribute of a triangle is the sum of its internal angles to 180 degrees

Given triangle ABC,

and D is a point on AB and E is a point on AC,

and forms a triangle ADE,

and  DE is parallel to AC,

taking ΔABC and ΔBDE

∠B = ∠B  (common angle)

because DE is parallel to AC, so corresponding angles are equal,

so ∠A = ∠D

and ∠C = ∠E

ΔABC ≈ ΔBDE (triangles are similar)

since both triangles are similar the ratio of their corresponding sides is equal,

AB/BD = AC/DE = BC/BE

given BD = 2, BE = 4, DE = 5 and EC = 6

BC = EC + BE = 4 + 6

BC = 10

AC/DE = BC/BE

AC = 5(10/4)

AC = 12.5

and AB/BD = BC/BE

AB = 2(10/4)

AB = 5

AD = AB - BD

AD = 5 - 2

AD = 3

Hence AC = 12.5 and AD = 3.

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The figure is in image.

The value of y is 18

Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.

Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.

Therefore;

14/21 = 12/y

14y = 21 × 12

14y = 252

divide both sides by 14

y = 252/14

y = 18

Therefore the value of y is 18.

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Answer:

  (-20x -25)/(x^2-x-30)

Step-by-step explanation:

You want to simplify the rational expression (3x²)/(x²-x-30) -(3x+5)/(x-6).

Usually these problems are constructed so that the higher-degree polynomial denominator has the lower degree denominator as a factor. That is the case here.

  \(\dfrac{3x^2}{x^2-x-30}-\dfrac{3x+5}{x-6}=\dfrac{3x^2}{(x+5)(x-6)}-\dfrac{(x+5)(3x+5)}{(x+5)(x-6)}\\\\=\dfrac{3x^2-(3x^2+20x+25)}{x^2-x-30}\)

  \(=\boxed{\dfrac{-20x-25}{x^2-x-30}}\)

a) To find the average life of the ten batteries, we need to calculate the mean, which is the sum of all the values divided by the number of values.Sum of all values = 10.8 + 10.6 + 11.4 + 8.9 + 10.1 + 10.6 + 9.9 + 12.6 + 10.5 + 11.9 = 106.2

Number of values = 10

Average life = Sum of all values / Number of values = 106.3 / 10 ≈ 10.63

Therefore, the average life of the ten batteries, rounded to the nearest tenth of an hour, is approximately 10.6 hours.

b) Comparing the two advertisements:

i) The first advertisement claims that Atlas batteries are guaranteed to last 10 hours. This means that all Atlas batteries are expected to last at least 10 hours. However, based on the data provided, we can see that the average life of the batteries is approximately 10.6 hours, which is higher than the guaranteed 10-hour minimum

ii) The second advertisement claims that Atlas batteries have an average life of over 10 hours. This statement aligns with the data we have, as the average life of the batteries is indeed over 10 hours.

Based on the information provided, the second advertisement claiming that Atlas batteries have an average life of over 10 hours is more accurate, as the average life calculated from the given data is 10.6 hours.

In summary, the average life of the ten batteries is approximately 10.6 hours, and the second advertisement stating an average life of over 10 hours is more accurate based on the data provided.

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Answer:

156 seats were sold at the store and 244 at the gallery

Step-by-step explanation:

Let the amount of stalls be x

Let the price per ticket for gallery be y

If 400 seats were sold in total, then;

x+y = 400 ... 1

If concert tickets are sold for $ 8 for the stalls and $ 6 for the gallery with a total of $2888, then;

8x + 6y = 2888 ....2

Solve both equation simultaneously

x+y = 400 ... 1 * 8

8x + 6y = 2888 ....2 .*1

__________

8x+8y = 3200 .

8x + 6y = 2888

Subtract

__________

8y - 6y = 3200 - 2888

2y = 312

y = 312/2

y = 156

Since x = 400 - x

y = 400 - 156

y = 244

hence 156 seats were sold at the store and 244 at the gallery

The transformation in this problem is a translation combined with a reflection, hence yes, it is a rigid motion, as the side lengths of the transformed figure are equal to the side lengths of the original figure.

Examples of transformations are given as follows:

The dilation is the only transformation that is not a rigid motion, as it changes the side lengths of the figure.

The transformation for this problem has the rule defined as follows:

(x,y) -> (x + 2, -y).

The transformations are defined as follows:

Neither transformation is a dilation, hence it is a rigid motion.

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Using the same-side interior angles theorem,

\(8x+30+6x+24=180 \\ \\ 14x+54=180 \\ \\ 14x=126 \\ \\ \boxed{x=9}\)

Using vertical angles,

\(6(9)+24=10y+2 \\ \\ 78=10y+2 \\ \\ 10y=76 \\ \\ \boxed{y=7.6}\)

the work done by the force F on a particle moving counterclockwise around the closed path C is 9π by integral.

Green's Theorem states that:

∮C F · dr = ∫∫D (∂Q/∂x - ∂P/∂y) dA

Where C is the boundary of the region D, P and Q are the components of the vector field F, and dr is the vector differential along the boundary C.

In this case, the region D is a circle with radius 2, so we can express the boundary C as r = 2 cos θ. We also need to calculate the components of the vector field F. These are P = e^x - 3y and Q = e^y + 6x.

Plugging these values into Green's Theorem, we get integral:

∮C F · dr = ∫∫D (∂Q/∂x - ∂P/∂y) dA

= ∫∫D (e^y + 6 - (-3)) dA

= ∫∫D (e^y + 9) dA

= ∫ 0 2π ∫ 0 2 (e^2 cosθ

+ 9) (2 dθ)

= 4π ∫ 0 2 (e^2 cosθ + 9) dθ

= 9π

Therefore, the work done by the force F on a particle moving counterclockwise around the closed path C is 9π.

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