Express the given quantity as a single logarithm. (Enter your answer using function notation - use In(x) instead of In x.) In(a + b) + In(a - b) – 4 Inc Differentiate the function. (Enter your answer using function notation - use In(x) instead of In x.) f(x) = 5.2 In(4x) - 52 Differentiate the function. (Enter your answer using function notation - use In(x) f(t) = sin(3 In x) Differentiate the function. (Enter your answer using function notation - use In(x) f(x) = ln(4 sin’z)

Answer:

30cm^2

Step-by-step explanation:

area of large rectangle = length x width

= 5 X 9 = 45 cm^2

area of small rectangle = length x width

= 3 X 5 = 15 cm ^2

45 - 15 = 30cm^2

Answer:

There is a \(\frac{2}{21}\) chance of picking caramel-filled chocolate.

Step-by-step explanation:

To set this up, you need to make it a fraction. The denominator of the fraction is how many total chocolates you can pick from. You can figure this out by adding all of the chocolate choices together:

68 hazelnut + 8 caramel + 8 orange = 84 chocolates.

The numerator is defined by the number of caramel chocolates, in this case it is 8. That means the fraction will look like:

\(\frac{8}{84}\)

Now that can be simplified down. I divided the top and bottom both by 4 to get  \(\frac{2}{21}\) and that is as far down as it can go. Therefore that is the probability you will get a caramel-filled chocolate.

Answer:

about 10 my boy

Step-by-step explanation:

big big big

Answer:

\(D=\sqrt{145 }\\\)

Step-by-step explanation:

We are actually using Pythagorean theorem here but to be simple

we can use the equation:

D(distance)=\(\sqrt{(x_{1}- x_{2} )^{2} +( y_{1}-y_{2})^{2}}\)

=

\(D=\sqrt{(15-3)^{2}+(6-7)^{2} } =\\D=\sqrt{(12)^{2}+(-1)^{2} } =\\\\D=\sqrt{144+1 } =\\D=\sqrt{145 }\\\)

(If you meant 16 instead of 6 the answer would be 15)

Hope this helps!

Answer:

distance = Sqrt((x2-x1)^2 +(y2-y1)^2)

Step-by-step explanation:

The complete square form of - 3x² + 33 = 48x is [x + 8]² = 75

To do this, we add and subtract a constant term to the quadratic expression to make it a perfect square.

In this case, we use the formula x² + 2bx + b² = (x + b)² to rewrite the quadratic expression as a perfect square trinomial, and then we solved for the variable by isolating the squared term and taking the square root.

Here we have

- 3x² + 33 = 48x

Keep 'x' terms on one side and constant terms sides on another side

=> - 3x² - 48x = - 33

Divide by - 3 on both sides

=> -3(x² + 4x)/3 = - 33/3  

=> x² + 16x = 11      

Take half of the 'x' term and square it and add on both sides

=> x² + 2(8x) (x) + (8)² = 11 + (8)²  

Which is in the form of x² + 2bx + b² = (x + b)²

=> [x + 8]² = 75

Therefore,

The complete square form of - 3x² + 33 = 48x is [x + 8]² = 75

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Answer:

324

Step-by-step explanation:

To evaluate (a) f(f(2)), we first evaluate f(2) which is 52-4 = 6. Then, we evaluate f(6) which is 56-4 = 26. So, f(f(2)) = 26.

To evaluate (b) g(g(3)), we first evaluate g(3) which is 23^2 = 18. Then, we evaluate g(18) which is 218^2 = 324. So, g(g(3)) = 324

Using the Intersecting secants theorem, the length of JK in the given diagram is 17

From the question, we are to determine the length of JK in the given diagram.

The diagram shows a circle with intersecting secants.

From the Intersecting secants theorem which states that "if two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment".

Then,

We can write that

JK × KL = NM × ML

From the given diagram,

KL = 14

NM = 14

ML = 17

Substituting the values

JK × 14 = 14 × 17

JK = (14 × 17) / 14

JK = 17

Hence, the length of JK is 17

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Answer:

is 8

Step-by-step explanation:

Answer:

3

one

will represent

the student

The value of n that satisfies the given polynomial expression is 10

From the question, we are to determine determine the corresponding value of n in the simplified expression.

The given expression is

(12x⁵ + 6x³ + x) - (x + 26)(2nx² + 1)

First, we will simplify this expression

(12x⁵ + 6x³ + x) - (x + 26)(2nx² + 1)

(12x⁵ + 6x³ + x) - (2nx³ + x + 52nx² + 26)

(12x⁵ + 6x³ + x - 2nx³ - x - 52nx² - 26)

Simplify further

(12x⁵ + 6x³ - 2nx³ - 52nx² - 26)

(12x⁵ + (6 - 2n)x³ - 52nx² - 26)

By comparison with (12x⁵ - 14x³ - 520x² - 26)

(6 - 2n)x³ = - 14x³

and

- 52nx² = - 520x²

Solve (6 - 2n)x³ = - 14x³ for n

(6 - 2n)x³ = - 14x³

6 - 2n = - 14

6 + 14 = 2n

20 = 2n

n = 20/2

n = 10

Similarly,

Solve - 52nx² = - 520x² for n

52n = 520

n = 520/52

n = 10

Hence, the value of n is 10

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Answer:

7/48

Step-by-step explanation:

First, you would find common denominator

1/12 + 1/16 = 1*4/12*4 + 1*3/16*3 = 4/48 + 3/48 = 7/48

or

Add 4/48 + 3/48 = 4+3/48= 7/48

We can express the number 98 in exponential form as 10 raised to the power of 2. This means that by multiplying the base, which is 10, by itself twice, we obtain the value of 98.

To express 98 in exponential form, we need to determine the base and exponent that can represent the number 98.

Exponential form represents a number as a base raised to an exponent. Let's find the base and exponent for 98:

We can express 98 as 10 raised to a certain power since the base 10 is commonly used in exponential notation.

To find the exponent, we need to determine how many times we can divide 98 by 10 until we reach 1. This will give us the power to which 10 needs to be raised.

98 ÷ 10 = 9.8

Since 9.8 is still greater than 1, we need to continue dividing by 10.

9.8 ÷ 10 = 0.98

Now, we have reached a value less than 1, so we stop dividing.

From these calculations, we can see that 98 can be expressed as 10 raised to the power of 1 plus the number of times we divided by 10:

98 =\(10^1\) + 2

Therefore, we can write 98 in exponential form as:

98 = \(10^3\)

In summary, 98 can be expressed in exponential form as 10^2. The base is 10, and the exponent is 2, indicating that we multiply 10 by itself two times to obtain 98.

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Answer:

x = 8

Step-by-step explanation:

Step 1: Write out the expression

x + 2x = 24

Step 2: Combine like terms

3x = 24

Step 3: Isolate x

x = 8

And we have our final answer!

Answer:

X=8

Step-by-step explanation:

Answer:

Slope=− 1.083/1.083 =−0.542

x−intercept= 144/13 =11.07692

y−intercept= 144/24 =6.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Intercepts of a Line

The x-intercept of a given line is the point where the line crosses the x-axis and the y-intercept of a given line is the point where the line crosses the y-axis.

We are given the following line:

-12x + 18y = 108

To find the x-intercept, we set y=0 and solve for x:

-12x + 18*0 = 108

-12x = 108

x = 108 / (-12) = -9

The x-intercept is the point (-9,0)

To find the y-intercept, we set x=0 and solve for y:

-12*0 + 18y = 108

18y = 108

y = 108 / 18 = 6

The y-intercept is the point (0,6)

Answer:

The simplified version of this equation is -3x - 12.

Step-by-step explanation:

To simplify this equation, distribute -3 to both x and 4.

-3(x+4) = -3x -12

Answer:

-3x-12 as an expression

Step-by-step explanation:

To solve this problem, we need to distribute!

Multiply -3 by both the x and the 4

When we do this, we get:

-3x and -12

Note: when you multiply a positive by a negative, you get a negative so it turns into a negative number

Note 2: When you see an x without a number in front of it, it becomes 1x. In this problem, that is why it is a -3x because -3 x 1 is -3

Hope this helps! :) Please award brainliest if possible!

Kiet will make his another observation at every multiples of 6 until it reaches at 60 which is at 2 : 00 pm.

Given that,

Kiet needs to observe a science experiment every 6 minutes for one hour.

He makes his first observation at 1:00 p.m.

Now he needs to make the observation every 6 minutes.

This means that his second observation will be at 1:06 pm.

Third observation will be at 1:12 pm.

Fourth will be at 1:18 pm.

It goes on like this for every multiples of 6.

His last observation will be at 2:00 pm which is at the 60th minute after 1.

Hence Kiet will make his observations at every multiples of 6 until it reaches 60.

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Answer:

The height of the triangle would be

5

√

15

c

m

or

19.36

c

m

Step-by-step explanation:

Answer: The exact answer is 3.61 weeks, so the "about" answer is 4 weeks.

Step-by-step explanation:

b = $85 + w (10+8)

b = 85 + w (18)

b = 85 + 18w

b is the total amount need in the bank account, so $150.

$150 = $85 + 18w

$150 - $85 = $85 - $85 + 18w

$65 = 18w

$65 / 18 = 18w / 18

3.611 weeks = w

So, it will take about 4 weeks to get $150 in his bank account.

Hope this helps!

Simplify the expression

Put b=150

Answer: 924 paths

Step-by-step explanation:

Since there is no shorter path, we know that the path must consist of 6 blocks to the north and 6 blocks to the east. Thus, the problem is equivalent to finding the number of ways to arrange 6 N's (for north) and 6 E's (for east) in a sequence such that no two N's are adjacent and no two E's are adjacent.

Let's denote N by 1 and E by 0. Then the problem is equivalent to finding the number of 12-digit binary sequences (i.e., sequences consisting of 0's and 1's) such that there are no consecutive 1's or consecutive 0's.

We can solve this problem using dynamic programming. Let F(n,0) be the number of n-digit binary sequences that end in 0 and have no consecutive 0's, and let F(n,1) be the number of n-digit binary sequences that end in 1 and have no consecutive 1's. Then we have the following recurrence relations:

F(n,0) = F(n-1,0) + F(n-1,1)

F(n,1) = F(n-1,0)

with initial values F(1,0) = 1 and F(1,1) = 1.

Using these recurrence relations, we can compute F(6,0) and F(6,1), and the total number of valid sequences is F(6,0) + F(6,1) = 132. Therefore, there are 132 different paths of length 12 blocks from your apartment to the math class.

Answer:

First one

Step-by-step explanation:

Answer: 3 tons

Step-by-step explanation: first I figured out how much 2 tons was which is 4000 pounds and then I divided 4000 by 8 which told me that each foot can hold 500 pounds So then I just did 500×10 which is 5000 pounds which is 3 tons

If an 8-foot column can hold 2 tons, then a 10-foot column can hold 1.28 tons.

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 maximum weight that a circular column can hold is inversely proportional to the square of its height.

∴ w ∝ 1/h² or w = k(1/h²).

An 8-foot column can hold 2 tons which is,

2 = k(1/8²).

2 = k(1/64).

k = 128.

Now, 10 feet column can hold,

w = 128(1/10²).

w = 128/100.

w = 1.28 tons.

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Vertically opposite angles are equal.

So,

(11y - 36)° = 63°

=> 11y - 36 = 63

Answer:

11y-36=63

Step-by-step explanation:

use the concept of vertically opposite angle

a) He needs 500 g of sugar to make apple crumble for 16 people.

b) She needs 45 g of flour to make apple crumble for 2 people.

c) 500g of apples is enough to make apple crumble for 6 people.

The amounts for this problem are obtained according to the proportions given in the problem.

For 8 people, the amount of sugar needed is of 250 g. For 16 people, the  number of people doubles, hence the amount of sugar needed will also double, as follows:

2 x 250 = 500 g.

For 2 people, the amount of each item is divided by 4, hence the amount of flour needed is given as follows:

180/4 = 45 g.

The amount of apple needed per people is of:

700/8 = 87.5 grams.

For 6 people, the amount is given as follows:

6 x 87.5 = 525 grams.

Hence 500g of apples is enough to make apple crumble for 6 people.

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Answer:

steps below

Step-by-step explanation:

15 tan³x=5tanx     .... (0,2π)

5tanx(3tan²x - 1) = 0

tanx = 0            x = π  (0° is excluded)

or 3tan²x - 1 = 0

(√3 tanx + 1) (√3 tanx - 1) = 0

tanx = 1 /√3      x = π/6 (30°)    or    x = 5π/6  (150°)

tanx = - 1 /√3      x = 7π/6 (210°)    or    x = 11π/6  (330°)

Answer:

I think B by I'm not sure

Step-by-step explanation:

I'm not good with this subject

The coordinates of vertices U(1 , -3) , V(4 , -3) , T(1 , -4) , W(4 , -4) becomes

U' (1, 3) , V'(4 , 3) , T'(1 , 4) , W'(5 , 4) after the reflection across x-axis occurs.

In the question given 4 coordinates,

U(1 , -3)

V(4 , -3)

T(1 , -4)

W(5 , -4)

the reflection across x-axis

U(1 , -3) →U' (1, 3)

V(4 , -3) → V'(4 , 3)

T(1 , -4) → T'(1 , 4)

W(5 , -4) → W'(5 , 4)

so  after the reflection across the x axis the coordinates of the vertices becomes ,

U' (1, 3) , V'(4 , 3) , T'(1 , 4) , W'(5 , 4)

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There is only 1 possible 11-card hand that can be formed from a 20-card deck.

To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.

The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.

The formula for combinations is:

nCk = n! / (k!(n-k)!)

Where "!" denotes the factorial of a number.

Substituting the values into the formula:

20C11 = 20! / (11!(20-11)!)

Simplifying further:

20C11 = 20! / (11! * 9!)

Now, let's calculate the factorial values:

20! = 20 * 19 * 18 * ... * 2 * 1

11! = 11 * 10 * 9 * ... * 2 * 1

9! = 9 * 8 * 7 * ... * 2 * 1

By canceling out common terms in the numerator and denominator, we get:

20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)

Performing the multiplication:

20C11 = 39,916,800 / 39,916,800

Finally, the result simplifies to:

20C11 = 1

Consequently, with a 20-card deck, there is only one potential 11-card hand.

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Answer:

123

Hope this helped!