The expression is the result of applying the change of base formula to a logarithmic expression.

Which could be the original expression?

Answer:

[tex]A=9\pi\ square\ units[/tex]

Step-by-step explanation:

we know that

The base of the cylinder is a circle

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=6/2=3\ units[/tex] ----> the radius is half the diameter

substitute

[tex]A=\pi (3)^{2}[/tex]

[tex]A=9\pi\ units^{2}[/tex]

BBBBBBBBBBBBBBBBB

the answer is B

Answer:

  3 1/3 bags

Step-by-step explanation:

5 × 2/3 = (5×2)/3 = 10/3 = 3 1/3

The total quantity of leaves gathered is equivalent to 3 1/3 full bags.

Replace cos^2(θ) with 1-sin^2(θ), and cot(θ) with cos(θ)/sin(θ).

  cos^2(θ)cot^2(θ) = cot^2(θ) - cos^2(θ)

  (1 -sin^2(θ))cot^2(θ) =  . . . . . replace cos^2 with 1-sin^2

  cot^2(θ) -sin^2(θ)·cos^2(θ)/sin^2(θ) = . . . . . replace cot with cos/sin

  cot^2(θ) -cos^2(θ) = cot^2(θ) -cos^2(θ) . . . as desired

Your answer would be B) 3/11, hope this helps!

Remember there are 11 muffins in the bag

Answer:

The answer is B. 3/11

Answer:

Step-by-step explanation:

There are several different ways you can work problems like this. The method you may prefer may be different from the one I prefer. At least, they include ...

___

1. There are 12 inches in a foot.

  23 ft 7 in - (13 ft 11 in) = (23 -13) ft (7 -11) in = 10 ft (-4) in = 9 ft 8 in

__

2. There are 4 quarts in a gallon.

  18 gal 2 qt - (5 gal 3 qt) = (18 -5) gal (2 -3) qt = 13 gal (-1) qt = 12 gal 3 qt

__

3. There are 3 feet in a yard and 12 inches in a foot.

  21 yd 1 ft 7 in -(12 yd 2 ft 9 in) = (21 -12) yd (1 -2) ft (7 -9) in

  = 9 yd (-1) ft (-2 in)

  = 8 yd 2 ft (-2) in

  = 8 yd 1 ft 10 in

First we must find out the slope of the points

The equation for slope is

[tex]\frac{y_{2} - y_{1}}{x_{2}-x_{1}}[/tex]

Let's plug in our points

[tex]\frac{3 - 3 }{5 -1 }  = \frac{0}{4}[/tex]

Our slope is 0

When lines are parallel, that means we have they have the same slope

So a line that is parallel to r would have a slope of 0!

Answer:

Final answer is given by x=-4, y=3

Step-by-step explanation:

Question says to use the given graph to determine the number of solutions the system where given system is x = - 4,  y = - x - 1

Graph is missing but we can still find the solution.

plug first equation x=-4 into other equation y=-x-1

y=-x-1

y=-(-4)-1

y=4-1

y=3

Hence final answer is given by x=-4, y=3

or we can also write that as (-4,3)

I guess the function is

[tex]f(x)=\dfrac6{(1-x)^2}[/tex]

Rather than computing derivatives of [tex]f[/tex], recall that for [tex]|x|<1[/tex], we have

[tex]g(x)=\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n[/tex]

Notice that

[tex]g'(x)=\dfrac1{(1-x)^2}[/tex]

so that [tex]f(x)=6g'(x)[/tex]. Then

[tex]f(x)=6\displaystyle\sum_{n=0}^\infty nx^{n-1}=6\sum_{n=1}^\infty nx^{n-1}=6\sum_{n=0}^\infty(n+1)x^n[/tex]

also valid only for [tex]|x|<1[/tex], so that the radius of convergence is 1.

Answer:

(1) 40 is a common multiple of 6 and 10

False:

Multiples of 6: 6, 12, 18, 24, 30, 36, 42...

Multiples of 10: 10, 20, 30, 40...

(2) The fraction 5/6 is greater than 7/10

True:

Find common denominators. Note that what you multiply to the denominator, you multiply to the numerator.

(5/6) x (5/5) = 25/30

(7/10) x (3/3) = 21/30

25/30 > 21/30 ∴ 5/6 is greater than 7/10

(3) The fraction 42/60 is an equivalent form of 7/10

True:

Find a common denominator. Note that what you multiply to the denominator, you multiply to the numerator.

(7/10) x (6/6) = 42/10

42/10 = 42/10 ∴ 7/10 = 42/10

(4) The only value that can be used as a common denominator is 60.

False:

While 60 is a plausible denominator, there are other denominators that can be used. Remember that what you do to the denominator, you do to the numerator.

(5) Ten is a multiple of 6.

False:

Multiples of 6: 6, 12, 18, 24, 30...

~

The validity of the true or false statements about the fractions 5/6 and 7/10 cannot be determined without the specific statements. In mathematics, comparing fractions requires finding a common denominator or converting them to decimals.

The question pertaining to whether the following statements about the fractions 5/6 and 7/10 are true involves understanding these numerical values and their relationships.

Please note that information from different sections that seem to provide contradictory answers cannot be used verbatim to answer your question directly, as the true or false nature of statements about these fractions was not specified in the excerpts provided. In mathematics, it is crucial to consider each expression individually and to apply mathematical principles to determine the validity of each statement.

Given that the statements to be verified are not presented, as a tutor on the Brainly platform, it is important to guide you on how to assess the veracity of statements about these fractions or any other numerical expressions. For instance, you would have to compare the two fractions by finding a common denominator or by converting both of them to decimal forms, to determine which one is greater, if that was part of the statements.

Answer:

  d)  9 inches

Step-by-step explanation:

By the Pythagorean theorem:

  WZ² = 15² -12.5² = 68.75

  WX² = 13² -12.5² = 12.75

Then the length of XZ can be found from ...

  XZ = √(WZ² +WX²) = √81.5 ≈ 9.028 . . . . closest to 9 inches (choice D)

Answer:

  42 square units

Step-by-step explanation:

The area of the rectangle is the product of its length and width:

  area = 6(x -8)

The area of the triangle is half the product of its base and height:

  area = (1/2)(x-3)·7

These two areas are equal, so we have ...

  6(x -8) = (1/2)(x -3)(7)

  6x -48 = 3.5x -10.5 . . . . eliminate parentheses

  2.5x = 37.5 . . . . . . . . . . . add 48 -3.5x

  x = 15 . . . . . . . . . . . . . . . divide by 2.5

The area of the rectangle is ...

  area = 6(15 -8) = 42 . . . . square units.

Answer:

1

Step-by-step explanation:

Factor and cancel common factors from numerator and denominator.

[tex]\displaystyle\frac{2y^3-y^2+2y-1}{y^3-y^2+y-1}\times\frac{2y^2-3y+1}{4y^2-4y+1}\\\\=\frac{(y^2+1)(2y-1)\times (2y-1)(y-1))}{(y^2+1)(y-1)\times (2y-1)^2}=\frac{(y^2+1)(2y-1)^2(y-1)}{(y^2+1)(2y-1)^2(y-1)}\\\\=1[/tex]

Answer:

D. 6.6 hours

Step-by-step explanation:

100/60= 1.66

Multiply 1.66 times 36 and get 6.6 hours

 Hope this helps!

The hour equivalent in decimal to 6 hours 36 minutes is,

D) 6.6 hours

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

A clock can be thought of as a circle having 12 steps and we know that circle is 360°,

So, the measure of each integer step of a clock is 30°.

We know, One hour is equivalent to 60 minutes.

Given, We have 6 hours and 36 minutes.

Therefore, The hour equivalent to 36 minutes is,

= 36/60.

= 3/5.

= 0.6 hours.

Therefore, 6 hours and 36 minutes is equal to 6.6 hours.

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Answer:

b= -1

Step-by-step explanation:

y=3x+b

8= 3(3)+b

b= -1

The value of b in the equation y = 3x + b that passes through (3, 8) is -1

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

The equation of the graph

Where, we have

y = 3x + b

Also, we have the point

(3, 8)

This means that

x = 3 and y = 8

When these values are substituted into the equation, we have

8 = 3 * 3 + b

This gives

8 = 9 + b

Evaluate the like terms

b = -1

Hence, the value of b is -1

[tex]3\tan3\theta-1=0[/tex]

[tex]3\tan3\theta=1[/tex]

[tex]\tan3\theta=\dfrac13[/tex]

Recall that the tangent function has a period of [tex]\pi[/tex] so that

[tex]3\theta=\tan^{-1}\dfrac13+k\pi[/tex]

for any integer [tex]k[/tex]. Then

[tex]\theta=\dfrac13\tan^{-1}\dfrac13+\dfrac{k\pi}3[/tex]

We get 6 solutions in the interval [0, 2π) for [tex]0\le k\le5[/tex],

[tex]\theta\approx0.107[/tex]

[tex]\theta\approx1.154[/tex]

[tex]\theta\approx2.202[/tex]

[tex]\theta\approx3.249[/tex]

[tex]\theta\approx4.296[/tex]

[tex]\theta\approx5.343[/tex]

1. -x-5y=21

-5y=x+21

y= -1/5x-21/5

2.-2x-5y=25

-5y=2x+25

y= -2/5x-5

Answer:80

Step-by-step explanation:

Let's pretend we start a stopwatch when the birth and death light flash together.  The birth light will flash at 10 seconds, 20 seconds, 30 seconds, etc.  The death light will flash at 16 seconds, 32 seconds, 48 seconds, etc.

So the trick here is to find the least common multiple (LCM) of 10 and 16.  To do that, we write the prime factorization of each:

10 = 2×5

16 = 2⁴

The LCM must include all these prime factors without any duplicates.  So the LCM = 2⁴×5 = 80.  We can check our answer by dividing:

80 / 10 = 8

80 / 16 = 5

So 80 is indeed a multiple of both 10 and 16.

By using the concept of HCF and LCM, the result obtained is

The birth and death light will flash again after 80 seconds.

What is HCF and LCM of two numbers?

HCF means Highest Common Factors. HCF of two numbers a and b is the highest number which divides both a and b

LCM means Lowest Common multiple. LCM of two numbers a and b is the lowest numbers which is divisible by both a and b

HCF and LCM can be calculated by division method and prime factorization method.

Also there is an important formula relating HCF and LCM

HCF [tex]\times[/tex] LCM = Product of two numbers

Here,

The birth light would flash every 10 seconds,

The death light every 16 seconds,

The immigration light every 81 seconds,

The emigration light every 900 seconds,

They will flash again after LCM (10, 16)

Now,

10 = [tex]2 \times 5[/tex]

16 = [tex]2 \times 2 \times 2 \times 2[/tex]

LCM of 10 and 16 = [tex]2 \times 2 \times 2 \times 2 \times 5[/tex] = 80

The birth and death light will flash again after 80 seconds.

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B can be right but if he dont do the exercises it is wrong

so it is C because d=day so it is 15 day and the results of the function is calories he used to do the exercises so the answer is C

Answer:

  C is the correct answer

Step-by-step explanation:

There is no "work." The question is a reading comprehension question, so the work goes on in your brain, where the words are interpreted. The problem statement tells you ...

  "... the amount of calories he has used, f(d), is a function of the number of days, d, he has exercised with the new routine."

You are comparing this wording to the answer choice wording. The best match is to C (as you know), which says ...

  "f(15) = 5250 means after 15 days of exercising with his new routine, Vincent has used 5250 calories."

Answer:

55.53 feet.

Step-by-step explanation:

We have been given that a flagpole stands in the middle of a flat, level field. 50 feet away from its base, a surveyor measures the angle to the top of the flagpole as 48 degrees.

We can see from attached photo that flagpole, the surveyor forms a right triangle with respect to ground.    

[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]

[tex]\text{tan}(48^{\circ})=\frac{h}{50}[/tex]

[tex]\text{tan}(48^{\circ})*50=\frac{h}{50}*50[/tex]

[tex]1.110612514829*50=h[/tex]

[tex]h=1.110612514829*50[/tex]

[tex]h=55.53062574[/tex]

[tex]h\approx 55.53[/tex]

Therefore, the height of the flagpole is approximately 55.53 feet.

Answer:

  If no one came to the dinner, the charity would still raise about $1250

Step-by-step explanation:

The variable x represents the number of people who attend the charity dinner. When x=0, no people came to the dinner.

The variable y represents the amount of money raised (in dollars). When x=0, the value of y is about 1250. That is, the charity raises about $1250 when no people came to the dinner.

Answer:

D.  If no one came to the dinner, the charity would still raise about $1250

Step-by-step explanation:

I just took the test, and I got 100%!!!

Answer:

-4y - 7x^3 + 2

Step-by-step explanation:

So first lets combine the y terms together, doing this we  get:

-4y + 1 - x^3 - 3x^3 + 1 - 3x^3

Now lets combine the terms with x^3 together

-4y + 1 - 7x^3 + 1

Lastly, lets add the constants

-4y - 7x^3 + 2

To find the absolute maximum and minimum values of the function f(x) = x^5 - x^3 + 6, we can use both a graphical approach and a calculus approach. The graphical approach involves plotting the function and identifying the highest and lowest points on the graph. The calculus approach involves taking the derivative of the function, finding critical points, and evaluating the second derivative to determine whether the critical points are maximum or minimum values.

To find the absolute maximum and minimum values of the function, we need to graph it within the given interval and identify the highest and lowest points. By plotting the function and examining the graph, we can see that the absolute maximum value is approximately 6.66 at x ≈ 1, and the absolute minimum value is approximately 5.33 at x ≈ -1.

To find the exact maximum and minimum values, we need to use calculus. We take the derivative of the function f(x) = x^5 - x^3 + 6, which is f'(x) = 5x^4 - 3x^2. Setting f'(x) = 0 and solving for x, we find that x = 0 is a critical point. To determine whether it is a maximum or minimum, we take the second derivative f''(x) = 20x^3 - 6x and evaluate it at x = 0. Since f''(0) > 0, x = 0 is a relative minimum. Plugging x values outside the given interval into the function, we find that f(-1) ≈ 5.33 is the exact minimum value, and f(1) ≈ 6.66 is the exact maximum value.

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Answer:

  (4x -5)(16x^2 +20x +25)

Step-by-step explanation:

The factoring of the difference of cubes is something you might want to memorize, or keep handy:

  (a³ -b³) = (a -b)(a² +ab +b²)

Here, the minus sign in the middle tells you this is a difference. The power of x is a clue that this might be the difference of cubes. Your knowledge of cubes of small integers tells you ...

so you can recognize this as ...

  (4x)³ - 5³ . . . . . the difference of cubes.

___

Since you are familiar with the factorization above, you can easily write down the factoring of this expression using a=4x, b=5.

  (4x -5)(16x² +20x +25)

_____

For "completeness", here is the factorization of the sum of cubes:

  a³ +b³ = (a +b)(a² -ab +b²)

Note the linear factor (a +b) has the same sign as the sign between the cubes. The sign of the middle 2nd-degree term (ab) is opposite that.

Answer:

[tex]\boxed{\text{4995 pages}}[/tex]

Step-by-step explanation:

The question is asking you to find the equation of a straight line that passes through two points

Let x = the number of pages

and y = the cost

Then the coordinates of the two points are (1543, 77.40) and (7361, 368.30).

(a) Calculate the slope of the line

[tex]\begin{array}{rcl}m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\ & = & \dfrac{368.30 - 77.40}{7361 - 1543}\\\\& = & \dfrac{290.90}{58.18}\\\\ & = & 0.05000\\\end{array}[/tex]

In other words, the cost is 5¢ per page.

(b) Calculate the y-intercept

[tex]\begin{array}{rcl}y & = & mx + b\\368.30 & = & 0.05 \times 7361 + b\\368.30 & = & 368.05 + b\\b & = & 0.25\\\end{array}[/tex]

(c) Write the equation for the line

y = 0.05x + 0.25

That is, the cost is 25¢ plus 5¢ per page

(d) Calculate the pages you can print for $250

[tex]\begin{array}{rcl}y & = & 0.05x + 0.25\\250 & = & 0.05x + 0.25\\249.75 & = & 0.05x\\x & = & 4995\\\end{array}\\\text{ You can print }\boxed{\textbf{4995 pages}}[/tex]

The figure below shows the graph of your equation, with slope 0.05 and y-intercept at (0,0.25).

It looks as if you could print 5000 pages, but you must pay that 25¢ (5 pages worth) up-front, so you can print only 4995.

Answer:

4995 pages

Step-by-step explanation:

The question is asking you to find the equation of a straight line that passes through two points

Let x = the number of pages

and y = the cost

Then the coordinates of the two points are (1543, 77.40) and (7361, 368.30).

(a) Calculate the slope of the line

In other words, the cost is 5¢ per page.

(b) Calculate the y-intercept

(c) Write the equation for the line

y = 0.05x + 0.25

That is, the cost is 25¢ plus 5¢ per page

(d) Calculate the pages you can print for $250

The figure below shows the graph of your equation, with slope 0.05 and y-intercept at (0,0.25).

It looks as if you could print 5000 pages, but you must pay that 25¢ (5 pages worth) up-front, so you can print only 4995.

Answer:

f(x) = 3 if x ≤ -2

     =  1 if x > -2 ⇒ attached figure

Step-by-step explanation:

* Lets explain how to answer the question

- For the part of the graph on the left side (2nd quadrant)

- There is a horizontal line start from x = -∞ and stop at x = -2

- The end of the line is black dot means x = -2 belongs to the function

- The horizontal line drawn at y = 3

∴ The equation of the horizontal line is y = 3

∴ The function represents this part of graph is y = 3 if x ≤ -2

- The other part of the graph is also horizontal line start from

  x = -2 to x = ∞

- The end of the line is white dot means x = -2 does not belong

 to the function

- The horizontal line drawn at y = 1

∴ The equation of the horizontal line is y = 1

∴ The function represents this part of graph is y = 1 if x > -2

* f(x) = 3 if x ≤ -2

       =  1 if x > -2

- The answer is attached

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Answer:

  No.

Step-by-step explanation:

50/50 solder is shown to melt at 214 °C. If the soldering iron only heats to 204 °C, it cannot melt the solder. The solder will only be melted if it is heated to a temperature at or higher than its melting point.

Changing the function f(x)=2sin(x/2)-1 to the function g(x)=2sin(x)-5 shifts the graph of f(x) downward by 4 units and changes the period from 4π to 2π.

Changing the function f(x)=2sin(x/2)-1 to the function g(x)=2sin(x)-5 has the effect of shifting the graph of f(x) downward by 4 units and changing the period of the graph from 4π to 2π.

By comparing the two functions, we can see that the constant -1 in f(x) has changed to -5 in g(x), resulting in a downward shift of 4 units. The factor of 1/2 in the argument of the sine function in f(x) has been removed in g(x), which changes the period from 4π to 2π.

Overall, the graph of f(x) has been shifted downward and compressed horizontally to form the graph of g(x).

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Answer: 827 pounds.

Step-by-step explanation:

The formula for calculate density is:

[tex]d=\frac{m}{V}[/tex]

Where "m" is the mass and "V" is the volume.

The formula for calculate the volume of a cylinder is:

[tex]V=\pi r^2h[/tex]

Where "r" is the radius and "h" is the height.

Calculate the volume of the cylindrical maple tree stump, which is 3 feet high and has a radius of 1.5 feet:

[tex]V=(3.14)(1.5ft)^2(3ft)=21.195ft^3[/tex]

Substitute the volume into and the density 39 pounds per cubic foot, into the formula [tex]d=\frac{m}{V}[/tex] and solve for "m". Then, the weight of the stump to the nearest pound is:

[tex]39\frac{lb}{ft^3}=\frac{m}{21.195ft^3}\\\\m=(39\frac{lb}{ft^3})(21.195ft^3)\\\\m=827lb[/tex]

Answer:

To find the median, set the numbers in order and the median is the number in the middle. If there was an even number of number then you would the two middle numbers and average it.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

So the median in this case would be 5

Answer: 6

Step-by-step explanation:

Median means the middle. You cross out a number from each side until you get one number and it’s 6. If there was uneven amount of numbers, and you were left with two numbers you add them and divide of how many numbers there are

Answer:

Step-by-step explanation:

4. The graph is showing you x < -7 ∪ 5 < x. The difference between the end points is 12, suggesting that the inequality will be of the form | f(x) | > 6. We want the expression for f(x) to be zero at the midpoint of the excluded interval, which is (-7+5)/2 = -1. The inequality that matches this requirement is ...

  | x+1 | > 6 . . . . . . . matches choice A

__

7. The graph shows a domain of x-values less than 3, so the domain in interval notation is (-∞, 3).

The graph shows the range of y-values from -∞ to -1, including -1. In interval notation, the range is (-∞, -1].

None of the answer choices match ...

  Domain (-∞, 3), range (-∞, -1].

(Your computer might say C is correct, but it is not. Talk to your teacher about this question.)