c) 2-e-* y = 3 sin(6x) and find the rate of change at x = 2

Product Property of Roots The product property of roots states that the square root of the product of two numbers is equal to the product of their square roots. In other words, for any non-negative numbers a and b, the square root of the product of a and b equals the product of the square roots of a and b.

The equivalent expression to √(ab) using the product property of roots is √a * √b. The reason is that by definition of the product property of roots, the square root of the product of a and b is equal to the square root of a multiplied by the square root of b, that is, √(ab) = √a * √b. Therefore, the correct answer is option A, which is √(ab).

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Answer:

Yes

Step-by-step explanation:

You must use the quadratic formula

-b√b^2 -4ac/2a --> -8√-(-8)^2 -4(12)(1)/2(12)

8 +/- 4/24

(1/2, 1/6)

Yes, we can factor 12x²-8x+1=0 and the factors are x=1/6 and x= 1/2.

A factor in maths is one of two or more numbers that divides into a number without a remainder, making it a whole number.

In other words, a factor is a number that divides another number evenly.

   12x² -8x +1=0

⇒ 12x² -2x- 6x+1=0

⇒ 2x (6x-1) -1 (6x-1)=0

⇒ (2x-1) (6x-1)=0

⇒ 2x-1 = 0, 6x-1 = 0

⇒ x=1/2, x=1/6

Therefore, the factors of 12x²-8x+1=0 are 1/2, 1/6.

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Answer:

28

Step-by-step explanation:

2(7)(2) =28

The value of 2ab when a = 7 and b = 2 is 28.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

2ab

For a = 7 and b = 2.

= 2 x 7 x 2

= 14 x 2

= 28

Thus,

The value of 2ab is 28.

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The path c(t) = (4cos(2t), 4sin(2t)) traces out an ellipse in the plane.

To see this, we can observe the parametric equations. The x-coordinate of the curve is given by 4cos(2t), and the y-coordinate is given by 4sin(2t). These equations describe the motion of a point in the plane as the parameter t varies.

If we examine the equations, we can see that the x-coordinate varies between -4 and 4 as t ranges from 0 to π (or 0 to 2π if we want a full revolution). Similarly, the y-coordinate varies between -4 and 4 in the same interval.

This range of values indicates that the curve lies within a rectangular region with horizontal sides at y = -4 and y = 4, and vertical sides at x = -4 and x = 4.

Since the x and y coordinates are both multiples of 4 times the cosine and sine of 2t respectively, we have a scaling factor of 4. This scaling ensures that the curve is symmetric about the origin.

Combining these observations, we can conclude that the path c(t) traces out an ellipse centered at the origin, with a major axis of length 8 (from -4 to 4 along the x-axis) and a minor axis of length 8 (from -4 to 4 along the y-axis).

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Answer: x=32, y=45, z=45

Step-by-step explanation:

Now, x is cut in half on a flat plane which is a supplementary angle (2 angles that add up to 180 degrees) so just subtract 148 from 180 and you get 32.

Since a line cuts y and z equally in half and the line it is connected to is perpendicular (right angle), we can safely say both angles are equal to 45 degrees.

Answer:

you spell it bully

hope it helps you out :)

Answer: it’s spelled Bully

Step-by-step explanation: B-U-L-L-Y

Answer:

C. –x + 8y = 56

Step-by-step explanation:

Write in standard form.

x  −  8 y  =  − 56

This is a linear function in the slope - intercept form:

y = m x + b and we need a standard form:

a x + b y = c

y = 1/8 x + 7   / * 8 ( we will multiply both sides of equation by 8 )

8 y = x + 56

- x + 8 y = 56  / * ( - 1 )

x - 8 y = - 56

The equation is  y = 1/8x + 7

Standard form equation is Ax + By = C,  where A > = 0.

First eliminate the fractions by multiplying the equation by 8

8y = x + 56

Subtract x from each side

-x + 8y = 56

SInce x coeficient can't be negative multiply the equation by negative one.

x - 8y = -56

The probability of rolling a 7 with two dice is 1/6.

Probability is the measure of how likely something is to happen. It is expressed as a number between 0 and 1, where 0 indicates that something is impossible and 1 indicates that something is certain. Probability is used in a variety of ways, including to measure the chance of winning a game, the likelihood of an event occurring, or the probability of a certain outcome from a given set of data. Probability can also be used to make predictions about the future, as well as to analyze data and make decisions.

Therefore, the probability of Calamitous Clod rolling a 7 is also 1/6. This is because the probability of rolling a certain number on a die is the same regardless of the number of dice being used. Therefore, the probability of Calamitous Clod rolling a 7 is 1/6.

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The determinant of the matrix 3PQ is given as follows:

9630.

The matrix P for this problem is defined as follows:

P = [9 -3]

     [2 4]

The matrix Q for this problem is defined as follows:

Q = [3  -2]

      [4  6]

To multiply matrices, the rows of the first are multiplied by the columns of the second, hence:

Hence the matrix PQ is given as follows:

PQ = [15 -35]

        [22 20].

Multiplying by the constant, the matrix 3PQ is given as follows:

3PQ = [45  -105]

          [66     60]

Hence the determinant is given as follows:

45 x 60 - (-105) x 66 = 9630.

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Step-by-step explanation:

4.since two sides are congruent and two angles are equal so they are similar and we can say:

\( \frac{14}{42} = \frac{7}{x} \\ x = 21\)

DF is 21

5.since two sides are congruent and two angles are equal so they are similar and we can say:

\( \frac{6}{9} = \frac{10}{x} \\ x = 15\)

EF is 15

6.

\(since \: \: \frac{4}{20} = \frac{6}{30} \: \: so \: we \: can \: say \: they \: are \: similar \: so \: we \: have \\ \\ \frac{4}{20} = \frac{5}{x} \\ \\ x = 25\)

DF is 25

Recalll that the general equation fo the line is of the form y=mx+b where m is the slope and b is the y intercept. Also, remember that if we have two lines y=m1x+b1 and y=m2x+b2, they are perpendicular if and only if m1*m2=-1.

Let's construct the equation of the line we want. Say y=mx+b. So we must find the value of m and b. We are given the line y=5x-4. The slope of this line is 5. Since we want them to be perpendicular, it must happen that

if we divide by 5 on both sides, we get

this means that the equation we want, so far, is

Now, since this line passes through the point (3,8) it must happen that whenever we replace x by 3, y should be replaced by 8. Then we have the equation

Then, if we add 3/5 on both sides, we get

So, the equation of our perpendicular line is

If we have n identical books and k distinct shelves, with at most one book on each shelf, we can think of this as placing n balls into k distinct bins. Each ball (book) can only go into one bin (shelf). This is a classic combinatorial problem known as the "stars and bars" problem.

The solution can be expressed as (n + k - 1) choose (k - 1), or C(n+k-1,k-1), which is the number of ways to choose k-1 "dividers" to separate n "stars" (books) into k bins (shelves).

Intuitively, we can see that we need to place k-1 dividers among n stars, which is equivalent to choosing k-1 positions out of n+k-1 total positions to place the dividers. The remaining spaces will each contain one book, and we can do this in C(n+k-1,k-1) ways.

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Answer: Approximately 390,244 people per square mile

Work Shown:

Density = population/area

Density = (8 million people)/(20.5 square miles)

Density = 390,243.9024 approximately

This rounds to 390,244 since we're talking about the number of people.

To solve this problem we ned to isolate the "w" variable on the left side of the equation, as shown below:

The correct answer is the second option.

The perimeter of a triangle whose one side is 29 inches, another side is 1/35 of the perimeter and the third side is 1/7 of  the perimeter is 6.733 inches (approx).

In the question, we are given:

Side 1 = 29 inches,

Side 2 = 1/35 of perimeter,

Side 3 = 1/7 of perimeter

We are to find the perimeter of the triangle.

We know that in a triangle the sum of all sides is equal to the perimeter of the triangle.

We can represent it as:

Perimeter = Side 1 + Side 2 + Side 3

Let's use this formula to find the perimeter of the triangle.

On substituting the values of the sides given:

Perimeter= 29 + 1/35 (Perimeter) + 1/7 (Perimeter)

Simplifying the above equation:

Let's first bring the variables (perimeter) on one side of the equation by subtracting 1/35 (Perimeter) and 1/7 (Perimeter) from both sides of the equation.

Perimeter - 1/35 (Perimeter) - 1/7 (Perimeter) = 29

Now,

LCM of 35 and 7 is 35, Therefore, we can write

1/35 as 1/5 × 1/7 and

1/7 as 1/7 × 1/1Perimeter - (1/5 × Perimeter) - (1/7 × Perimeter) = 29

Multiply both sides by 35 (LCM of 5 and 7)3

5 Perimeter - 7 Perimeter - 5 Perimeter = 29 × 353 Perimeter - 12 Perimeter

= 1015 Perimeter = 101Perimeter = 101/15

Hence, the perimeter of the triangle is 6.733 inches (approx).

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Answer: I think the answer is 4.

Step-by-step explanation:

I am not sure because i am just in 5th grade (10) so might be wrong and i am so sorry if its wrong.

Answer:

15

Step-by-step explanation:

This is a ratio problem. First step is the figure out what changed from 2 to 6. 2*3 = 6, so by a factor of 3.

In order to have them be equal fractions, you must do the same to the bottom. 5* 3= 15. There you have it :)

Using the concept of asymptote of the function it can be concluded that the number of boxes of cereals sold is 0 after 0 weeks, it will keep falling after reaching the maximum sales and cereals sold is always positive as the cereals introduced so the correct option are A, C and E.

A line that a curve approaches but never touches is an asymptote. The graph of a function converges to a line known as an asymptote, in other words. When graphing functions, asymptotes are usually not necessary to be drawn. The curve must not contact the asymptote when we graph them using dotted lines (imaginary lines). As a result, the asymptotes are merely made-up lines. When either the value of x or y tends to or -, the distance between the asymptote of a function, y = f(x), and its graph is close to zero.

Option A is correct as according to the option A: - B(w)= \(\frac{120w}{150+w^{2} }\), w=0.

On putting the value of w=0 in above function implies B(w)=0.

Hence, number of boxes of cereals sold is 0 after 0 weeks.

Option C is correct as function B(w) is decreasing function after reaching its maxima according to graph.

Option E is correct as B(w)= \(\frac{120w}{150+w^{2} }\), if w>0

implies that B(w)>0 as numerator>0 and denominator>0.

Based on the asymptote of function the number of boxes of cereals never reach 0 after cereals introduced in the store.

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The dimensions of the rectangular pen to minimize the amount of material needed is 4L which gives 160ft.

The minimum length or breadth of the open space type, as measured along the longest two (2) straight lines meeting at a right angle to define the lot's maximum length and width.

With regard to the above problem,

let us say L is the lenght of the rectangle and W is the width

Based on the formula for the area of a rectangle,

L x W  = 1600ft

To minimize the perimeter, of the rectangle, we must assume that:

L = W

that is L² = 1600

If we applied square root to both sides of the equation, we'd have


L = 40

Thus the minimum perimeter is given as: 4L = 4 x 40 = 160ft.

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Answer:

1/70 of pound

Step-by-step explanation:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

Applying the fractions formula for division,

Answer:

substitution property of equality

Step-by-step explanation:

im assuming this means that you substitute x's value of 2 into the equation y=3x2-11. i'm guessing that it's meant to be 3x2, instead of 3.2. i hope this makes sense, and i hope i answered it as you needed!

Answer:

substitution property of equality

Step-by-step explanation:

if

  x = 2

  y = 3x - 11

then

  y = 3 x 2 - 11

2 was substituted for x

Answer:

"A) 12n + 14m + 4" would be the standard form.

Step-by-step explanation:

the expression written correctly in standard form would be "A) 12n + 14m + 4"

10m + 3(n + 8) + 4(m - 5) + 9n you need to first clear the parenthesis by applying distributive property:

10m + 3(n + 8) + 4(m - 5) + 9n = 10m + 3n + 24 + 4m - 20 + 9n

After that you combine like terms

= 10m + 4m + 3n + 9n + 24 - 20 = 14m + 12n + 4

"A) 12n + 14m + 4" would be the standard form.

The second part of step 1 in the ideas process, after the problem has been identified, is to research and gather information.

This involves gathering data and information related to the problem, analyzing it, and understanding its implications. It is important to have a clear understanding of the problem and the factors that contribute to it before moving forward with generating ideas. This research can include a variety of methods such as surveys, focus groups, interviews, and market analysis.

The information gathered can help to identify potential solutions and ensure that the ideas generated are relevant and effective. Once the research and analysis are complete, it is time to move on to step 2, which is generating ideas.

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Answer:

A. 40º

B. 90º

C. 53.5º

D. 34º

E. 90º

F. 52.9º

G. 90º

H. 59.6º

I. 119.1º

J. 30.4º

K. 90º

L. 72º

M. 107.3º

N. 47.7º

O. 36º

P. 90º

3^2 + (8 - 2) x 4 - 6/3

=9 + 24 - 2

=33 - 2

=31

Answer:  31

("x" = * right? not x)

Step-by-step explanation:

\(3^{2}\)+(8-2) * 4 - \(\frac{6}{3}\)

= 9+6 * 4 - 6/3

= 9+24 - 6/3

= 9+24-2

= 31

Answer:

D

Step-by-step explanation:

Because you have to multipy 6 · 3 when you divide  you subract the exponents. therefore it will be m.

The rectangular prism having a length of 1 feet, width of 2 feet and that

is 1 feet deep, gives the area Mila stained as 8 square feet.

The given dimensions of the rectangular prism bin are;

Length of the bin = 2 foot

Width of the bin = 1 feet

Depth of the bin = 2 feet

Required:

The surface area of the rectangular prism bin.

Solution:

The surface area, S. A., of the rectangular prism bin is given as follows;

S. A. = Length × Width + Depth × Width + Length × Depth

Which gives;

S. A. = 2 × 1 + 2 × 1 + 2 × 2 = 8

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the number of people who do not watch any of the channels was 80 people.

Given the sets A = {c, a, r, e, t} and B = {a, e, i, o, u}, represent the union set (A U B). To find the union set, just join the elements of the two given sets. We have to be careful to include elements that are repeated in both sets only once.

Knowing that:

To calculate the total number of people who watch at least one of the channels:

\(Total = G + R - (G R)\\Total = 300 + 270 - 150\\Total = 420\)

The total number of people is 500, so:

\(Number of people who do not watch any channel = 500 - 420\\Number of people who do not watch any channel = 80\)

Therefore, there are 80 people who do not watch any of the channels.

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