Practice
Example 1
Write each equation in exponential form.
1. log₁5 225 = 2
4. log3 243 = 5
10. ()³ = 343
Example 2
Write each equation in logarithmic form.
7. 27 = 128
Example 3
Evaluate each expression.
13. log2 64
16. log27 81
2. 1093 27 = -3
19. logg 512
5. log4 64 = 3
8. 3-4 = 1
11. 29 = 512
14. log100 100,000
17. 1094 32
20. log, 1
Practice
3. logs 25= -2
6. log432 = 5/2
9. 7-2 = 49
12. 643 = 16
15. log5 625
ace
18. log₁0 0.00001
21. logg 4

Answer: 13

Step-by-step explanation:

The slope of the line that passes through (5, 8) and (11, 5) in its simplest form is - 1/2

The slope of a line refers to the change in the dependent variable (y) as a result of a change in the independent variable (x).

The slope can be found by the formula:

= Change in y / Change in x

Given the points, (5, 8) and (11, 5):

Change in y = (5 - 8)

Change in x = (11 - 5)

The slope can therefore be found to be:
= (5 - 8 ) / (11 - 5)

= -3 / 6

= - 1/2 in simplest form

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The RTS of the isoquant is 1000K, indicating the rate at which labor can be substituted for capital while maintaining constant production. The labor to capital cost ratio is 0.5. To minimize the cost of producing q units per hour, the specific value of q is needed to find the optimal combination of K and L along the expansion path, represented by the cost function C(K, L) = 40K + 20L.

The RTS (Rate of Technical Substitution) measures the rate at which one input can be substituted for another while keeping the production level constant. To determine the RTS, we need to calculate the derivative of the production function with respect to L, holding q constant.

Given the production function q = 1000KL, we can differentiate it with respect to L:

d(q)/d(L) = 1000K

Therefore, the RTS of the isoquant for production level q is 1000K.

The ratio of labor to capital cost can be calculated by dividing the labor cost by the capital cost.

Labor cost = $20/hour

Capital cost = $40/machine/hour

Ratio of labor to capital cost = Labor cost / Capital cost

                              = $20/hour / $40/machine/hour

                              = 0.5

The ratio of labor to capital cost is 0.5.

To find the combination of K and L that minimizes the cost of producing q units per hour, we need to set up the cost function and take its derivative with respect to both K and L.

Let C(K, L) be the total cost function.

The cost of capital is $40 per machine per hour, and the cost of labor is $20 per hour. Therefore, the total cost function can be expressed as:

C(K, L) = 40K + 20L

To produce q units per hour at minimal cost, we need to find the values of K and L that minimize the total cost function while satisfying the production constraint q = 1000KL.

The expansion path of the firm represents the combinations of K and L that minimize the cost at different production levels q.

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Answer:

22

Step-by-step explanation:

30 - 12 :3 ×2

30 - 4 ×2

30 - 8

22

Answer:

22

Step-by-step explanation:

The order of operations states that 12÷3×2 (division and multiplication) is done first from left to right .

12÷3×2 = 4 × 2 = 8

Therefore , 30 - 12 ÷ 3 × 2 = 30 - 8 = 22.

So, the answer is 22. Hope this helps!

The cone have measures for the base, lateral, and surface areas as 77.6 mm², 330 mm², and 408.6 mm² respectively.

The formula for the surface area of a cone is:

A = πr² + πrs

Where: A = surface area r = radius of the base s = slant height of the cone

Base area = 22/7 × 5 mm × 5 mm

Base area = 78.6 mm²

Lateral area = 22/7 × 5 mm × 21 mm

Lateral area = 330 mm³

Surface area = 78.6 mm + 339 mm²

Surface area = 408.6 mm²

Therefore, the cone have measures for the base, lateral, and surface areas as 77.6 mm², 330 mm², and 408.6 mm² respectively.

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Answer:

Solution given:

we have

let angle be x

secx=1

1/cosx=1

1=Cosx

x=Cos-¹(1)

x=0°,360°

the exact value is 0° or 360°

The measure of side A'B' for the triangle A'B'C' is equal to 4 using a scale factor of 1/2 to dilate it.

Scale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.

The dilation if the triangle ABC implies it is bigger than the triangle A'B'C' with a scale factor 1/2 since AC = 10 and A'C' = 5

side A'B' = 8 × 1/2

side A'B' = 4

Therefore, the measure of side A'B' for the triangle A'B'C' is equal to 4 using a scale factor of 1/2 to dilate it.

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Answer:

the answer is B, 4. :)

Answer:

so what exactly is the question? it's not complete yet, I guess..what do you want me to find?

tan 145° is equal to csc 55°. Given that csc 55° is not provided in the options, none of the given options is correct. cotangent is the reciprocal of the sine function.

To find the value of tan 145°, we can use the relationship between tangent and cotangent:

tan x = 1 / cot x

Since cotangent is the reciprocal of the sine function, we can rewrite the given equation as:

csc 55° = 1 / sin 55°

To find the value of sin 55°, we can use the fact that sin x = cos (90° - x):

sin 55° = cos (90° - 55°)

       = cos 35°

Now, we need to find the value of cos 35°. We can use a trigonometric identity:

cos (90° - θ) = sin θ

cos 35° = sin (90° - 35°)

       = sin 55°

Substituting this value back into the equation, we have:

csc 55° = 1 / sin 55°

       = 1 / cos 35°

Now, let's find the value of tan 145° using the relationship between tangent and cotangent:

tan 145° = 1 / cot 145°

Since cotangent is the reciprocal of the sine function, we can rewrite the equation as:

tan 145° = 1 / sin 145°

To find the value of sin 145°, we can use the fact that sin x = sin (180° - x):

sin 145° = sin (180° - 145°)

        = sin 35°

Now, we have:

tan 145° = 1 / sin 145°

        = 1 / sin 35°

Since we previously found that csc 55° = 1 / cos 35°, we can substitute this value into the equation:

tan 145° = 1 / sin 35°

        = csc 55°

Therefore, tan 145° is equal to csc 55°. Given that csc 55° is not provided in the options, none of the given options is correct.

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Answer:

11

Step-by-step explanation:

m - 8 (less than or equal to) 2

= m(less than or equal to) 10

So anything before 10 not after

Answer:

It is E. past me

Step-by-step explanation:

m-8+8=2+8

m≤ 10

So m has to be 10 or smaller so 11 is not a solution

Given a rectangle with the length of x+2 and width of 3x - 1. The area of a rectangle is given by the product of the length and width.

Thus, the area of this rectangle can be found as follows:Area = (x+2)(3x-1

Area = 3x^2 - x + 6x - 2

Area = 3x^2 + 5x - 2

Hence, we can express the area of the given rectangle in terms of the variable x as 3x^2 + 5x - 2. Therefore, the correct option is none of the provided options.

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Answer:

23

Step-by-step explanation:

The number of points that she would need to score in her 12th game in order to decrease the interquartile range by 1 point is; 23

An interquartile range is one of the measure of variability that measures the spread of middle 50% of the data.

The formula to calculate interquartile range is:

IQR = Q₃ - Q₁

where;

Q₃ is third quartile

Q₁ is first quartile

The given points when arranged in increasing order gives us:

13, 15, 17, 18, 20, 20, 21, 22, 24, 25,27

Q₁ is the (n + 1)/4 terms = 3rd term.

Thus; Q₁ = 17

Q₃ is 3(n + 1)/4 term = 9th term.

Thus; Q₃ = 24

Then; IQR = 24 - 17

IQR = 7

The desired interquartile range should decrease by 1 point. Thus;

Desired IQR = 7 - 1 = 6.

To find the score of the 12th game, let us try  23 points as the score of the 12th game:

Thus;

Q₁ = 17.5

Q₃ = 23.5

IQR = 23.5 - 17.5

IQR = 6

Thus, required number of points is 23.

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Answer:

3

Step-by-step explanation:

-5 = 3x - 14    Add 14 to both sides

+14        +14

     9 = 3x

Divide both sides by 3

9/3 = 3    3x/3 = x

         3 = x

Answer:

x = 3

Step-by-step explanation:

Solution:

-5 = 3x - 14

Pass the -5 to the right side and change its sign.

0 = 3x - 14 + 5

Then we do the same with the 3x

-3x = -14 + 5

Substrate 5 by 14 and leave the negative sign

-3x = -9

Divide -3 by -9. ( We are dividing two negative numbers, so the answer has to be positive )

x = 3

Answer:

A. It is the graph of y = x translated 7 units up.

Step-by-step explanation:

Imagine you have a friend named Y who always copies what you do. If you walk forward, Y walks forward. If you jump, Y jumps. If you eat a sandwich, Y eats a sandwich. You and Y are like twins, except Y is always one step behind you. Now imagine you have another friend named X who likes to give you money. Every time you see X, he gives you a dollar. You're happy, but Y is jealous. He wants money too. So he makes a deal with X: every time X gives you a dollar, he also gives Y a dollar plus seven more. That way, Y gets more money than you. How do you feel about that? Not so happy, right? Well, that's what happens when you add 7 to y = x. You're still doing the same thing as before, but Y is getting more than you by 7 units. He's moving up on the money scale, while you stay the same. The graph of y = x + 7 shows this relationship: Y is always above you by 7 units, no matter what X does. The other options don't make sense because they change how Y copies you or how X gives you money. Option B means that Y copies you but with a delay of 7 units. Option C means that Y copies you but exaggerates everything by 7 times. Option D means that Y copies you but gets less money than you by 7 units.

Answer:

2. The more hours spent doing homework the better the test scores.

3. Just draw a line that runs through (1,50) (2,55) (3,60) (4,65)

4. Dunno

Step-by-step explanation:

Answer:

Number 4 would be 45%

Step-by-step explanation:

Answer:

No Solution

Step-by-step explanation:

26 + y = 8

-26

y = -18

proof 26 + (-18) = 8

83 - y = 2

+83

-y = 85

*-1

y = -85

-18 does not = -85 and I don't see an X in your system of equations

\({{ \Large{ \blue{ \rm{{⇛}}}}}} \rm \Large \: \: (2x + 9) \: (3x - 5)\)

\({{ \Large{ \blue{ \rm{{⇛}}}}}} \rm \Large \: \:2x \: (3x - 5) \: + \: 9 \: (3x - 5)\)

\({{ \Large{ \blue{ \rm{{⇛}}}}}} \rm \Large \: \: {6x}^{2} \: - \: {10x} \: + \: 27x \: - \: 35\)

\({{ \Large{ \blue{ \rm{{⇛}}}}}} \rm \Large \: \: {6x}^{2} \: + \: 17x \: - \:35\)

Answer:

222 diameter or d=222

Step-by-step explanation:

d=2r=2·111=222

Pls, choose me as brainliest!

Answer:

Hey! so the answer is X=7 and Y=6

Step-by-step explanation:

if you look at the pattern you'll see it adds up to 7 and 6 everytime so those are the answers.

Hoped this helped Im Eve btw. Hope you have a great day and consider marking this brainliest Thank you so much if you do! ✨

Answer:

\(\approx 2\ miles\)

Step-by-step explanation:

Difference of 10 seconds between the lightning flash and its thunder clap.

Given that the speed of light is infinite.

So, lightning will be seen at the same time it happens.

10 seconds is the time taken by the sound to reach to the person.

Time taken = 10 seconds

Speed of sound = 1080 ft/sec

To find:

Distance from lightning flash in miles.

Solution:

First of all, let us a have a look at the formula:

\(Distance = Speed \times Time\)

Putting the given values:

Distance = \(1080\times 10 = 108000\ feet\)

5280 feet = 1 mile

1 feet = \(\frac{1}{5280}\) miles

10800 feet = \(\frac{1}{5280}\times 10800 \approx 2\ miles\)

Answer:

47.5

Step-by-step explanation:

Covariance and correlation are two statistical measures used to explain the relationship between two random variables. Both covariance and correlation measure how two random variables are related.

Covariance is a statistical measure used to describe the strength and direction of the linear relationship between two random variables. Covariance can be used to define the direction of the relationship between the two variables, whether positive or negative.

Correlation, on the other hand, is a statistical measure used to determine the strength and direction of the linear relationship between two variables.

Hence, it is true that "they both measure how two random variables are related." The correct option is 1.

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The function f(x) is f(x) = (1/12) x⁴ - 2x² - 29.0278x + 126.1112

f(x) given that f'''(x) = 2x and satisfying the given conditions, we need to integrate the equation f'''(x) = 2x three times to find f(x).

Integration of f'''(x) = 2x gives: f''(x) = x² + C₁

Integration of f''(x) = x² + C₁ gives: f'(x) = (1/3) x³ + C₁x + C₂

Integration of f'(x) = (1/3) x³ + C₁x + C₂ gives: f(x) = (1/12) x⁴ + (1/2) C₁x² + C₂x + C₃

Now, we can use the given conditions to determine the values of the constants C₁, C₂, and C₃.

Using f(4) = 10:

(1/12)(4)⁴ + (1/2) C₁(4)² + C₂(4) + C₃ = 10

(1/12)(256) + (1/2) C₁(16) + 4C₂ + C₃ = 10

(64/12) + (8/2) C₁ + 4C₂ + C₃ = 10

(16/3) + 4C₁ + 4C₂ + C₃ = 10

4C₁ + 4C₂ + C₃ = 10 - (16/3)

4C₁ + 4C₂ + C₃ = 30/3 - 16/3

4C₁ + 4C₂ + C₃ = 14/3

Using f(7) = 25:

(1/12)(7)⁴ + (1/2) C₁(7)² + C₂(7) + C₃ = 25

(1/12)(2401) + (1/2) C₁(49) + 7C₂ + C₃ = 25

(200.0833) + (24.5) C₁ + 7C₂ + C₃ = 25

24.5C₁ + 7C₂ + C₃ = 25 - 200.0833

24.5C₁ + 7C₂ + C₃ = -175.0833

Using y'' = 0 at x = 2:

f''(2) = 2² + C₁ = 0

4 + C₁ = 0

C₁ = -4

Substituting C₁ = -4 in the previous equations

4(-4) + 4C₂ + C₃ = 14/3

-16 + 4C₂ + C₃ = 14/3

4C₂ + C₃ = 14/3 + 16/3

4C₂ + C₃ = 30/3

4C₂ + C₃ = 10

24.5C₁ + 7C₂ + C₃ = -175.0833

24.5(-4) + 7C₂ + C₃ = -175.0833

-98 + 7C₂ + C₃ = -175.0833

7C₂ + C₃ = -175.0833 + 98

7C₂ + C₃ = -77.0833

Solving the system of equations

4C₂ + C₃ = 10

7C₂ + C₃ = -77.0833

Subtracting the first equation from the second equation

(7C₂ + C₃) - (4C₂ + C₃) = -77.0833 - 10

3C₂ = -87.0833

C₂ = -87.0833/3

C₂ ≈ -29.0278

Substituting C₂ = -29.0278 in the first equation:

4C₂ + C₃ = 10 4(-29.0278) + C₃ = 10

-116.1112 + C₃ = 10

C₃ = 10 + 116.1112

C₃ ≈ 126.1112

Finally, we have the values of C₁, C₂, and C₃:

C₁ = -4

C₂ ≈ -29.0278

C₃ ≈ 126.1112

Therefore, the function f(x) is given by:

f(x) = (1/12) x⁴ - 2x² - 29.0278x + 126.1112

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Answer:

1.45

2. 135

Explanation:

1.  With a triangle all angles have to add up to 180, so what you would do is add up both angles we already know (43+92=135), then we subtract the sum from 180, (180-135=45) now you know the third angle.

2.  Just like a triangle, when finding angles on a line, it has to add up to 180. We already know that point M has an angle of 45 from the last problem, so all we have to do is subtract 45 from 180 (180-45=135). THats the measurement on TMS

Answer:

x = 73

Step-by-step explanation:

The sum of both angles is 158

85+x = 158

Subtract 85 from each side

85+x-85 = 158-85

x = 73

Answer:

65

Step-by-step explanation:

150 - 85=65

Answer:

Hello! :) I hope I’m correct!!

Step-by-step explanation:

I think (C) 30 is not a perfect square.

(A) 1 = perfect square

(B) 25 = perfect square

(C) 30 = NOT a perfect square

(D) 36= perfect square

{Note: The square root of 30 is not an integer, so therefore 30 is not a square number}

Since the question is asking to find a number that is NOT a perfect square...

The answer would be (C) 30

Hope this helps! If you have any questions about this, feel free to ask! Have a wonderful day! ^-^

~By, BrainlyAnime~ <3

Answer:

705.479 ounces

Step-by-step explanation:

Abcdefghijmnñopqrs

Answer: its A. 704 ounces

Step-by-step explanation:

20 kilograms transfers to 44 pounds that is in total 704 ounces.

\(sec(\theta) = \frac{1}{ \cos(\theta) } \\ \cos(\theta) = \frac{adj}{hyp}, \: \: \sec(\theta) = \frac{hyp}{adj} \)

Using the Pythagoras theorem,

\( {hyp}^{2} = {opp}^{2} + {adj}^{2} \\ {hyp}^{2} = {7}^{2} + {24}^{2} \\ {hyp}^{2} = 49 + 576 \\ {hyp}^{2} = 625 \\ hyp = \sqrt{625} \\ hyp = 25\)

Plugging in our values,

\( \sec(\theta) = \frac{hyp}{adj} \\ \sec(\theta) = \frac{25}{7} \)

So the last option is the correct one.

Answer:

\( \displaystyle \sec( \theta) = \frac{25}{7} \)

Step-by-step explanation:

remember that,

\( \displaystyle \sec( \theta) = \frac{hypo}{adj} \)

since we aren't given hypo we can consider Pythagoras theorem given by

\( \displaystyle {a}^{2} + {b}^{2} = {c}^{2} \)

\( \displaystyle \implies c = \sqrt{ {a}^{2} + {b}^{2} }\)

substitute the value of a and b:

\( \displaystyle c = \sqrt{ {7}^{2} + {24}^{2} }\)

simplify squares:

\( \displaystyle c = \sqrt{49 + 576}\)

simplify addition:

\( \displaystyle c = \sqrt{625}\)

simplify square root:

\( \displaystyle c = 25\)

with respect to \(\theta\) adj is 7 and hypo is 25 thus

substitute:

\( \displaystyle \sec( \theta) = \frac{25}{7} \)

and we are done!

According to the image, the table shows a relationship that is not proportional. First of all, you cannot multiply a number by 0 and get something other than 0. Anything multiplied by 0 is always 0.

Second, the rule is different for each row.

2x5=10

4x4=16

6x3.6=22

A proportional relationship must increase by the same amount, and this does not, which means it is not proportional.

Find common ratio

Yes they are proportional