What is the area of the sector having a radius of 8 and a central angle of 5π3
radians?
A. 320π/3 units²
B. 50π units²
C. 160π/3 units²
D. 140π/3units²

Answer:

5

Step-by-step explanation:

The matrix is in the form

a  b

c   d

The determinant is

ad -bc

2 *4 - 1 *3

8 - 3

5

Answer:

30

Step-by-step explanation:

Problem = 3x + 21 for x=3

3(3) +21 --- subsitute the three for the x

9 + 21 ---- multiply the 3s together

30 ----- add

Answer:

The answer is 282

because 94 in 4 mins so you need to use multiple 94 x 3 the answer is 282.

Answer:

The correct option is C.

Step-by-step explanation:

Given information: BCDE is a rectangular casing, DE = 3 cm and BE = 3 cm.

We need to find the smallest diameter of pipe that will fit the fiber optic line. It means we have to find the measure of DB.

The measure of all interior angles of a rectangle or square is 90°.

[tex]\angle DEB=90^{\circ}[/tex]

It means the DEB is right angled triangle.

According to the Pythagoras theorem:

[tex]hypotenuse^2=leg_1^2+leg_2^2[/tex]

In triangle DEB,

[tex](DB)^2=(DE)^2+(BE)^2[/tex]

[tex](DB)^2=(3)^2+(3)^2[/tex]

[tex](DB)^2=9+9[/tex]

[tex](DB)^2=18[/tex]

Taking square root both sides.

[tex]DB=\sqrt{18}[/tex]

[tex]DB=4.24264068712[/tex]

[tex]DB\approx 4.24[/tex]

Therefore the correct option is C.

Based on the information given, the smallest diameter will be C. 4.24 cm.

DB² = 3² + 3²

DB² = 9 + 9

DB² = 18

DB = ✓18

DB = 4.24

Therefore, the correct option is 4.24.

Learn more about diameter on:

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Answer:

X =3 and x =6

Step-by-step explanation:

Just look at the line where they cross another line,

Answer:

B x=3 and x=6

Step-by-step explanation:

The zeros of the function are where the function crosses the x axis

Looking at the graph

This function crosses at x=3 and x = 6

Answer:

4) (1,-1)

Step-by-step explanation:

Let the points be

[tex](x_1,y_1) = K(-5,-4)\\(x_2,y_2) = L(5,1)\\[/tex]

The formula for finding the coordinates of point that divides the line in a:b is:

[tex]x = \frac{bx_1+ax_2}{a+b} \\y = \frac{by_1+ay_2}{a+b}[/tex]

Here x and y are the coordinates of the point that will partition the line into given ratios

Our ratio is 3 to 2,

So,

a=3

b=2

Putting the values in the formula

[tex]x = \frac{(2)(-5)+(3)(5)}{3+2}\\x = \frac{-10+15}{5}\\x =\frac{5}{5}\\ x =1\\y = \frac{(2)(-4)+(3)(1)}{3+2}\\y = \frac{-8+3}{5}\\y = \frac{-5}{5}\\ y = -1[/tex]

Hence, the correct answer is:

4) (1,-1) ..

The coordinate of the point on the directed line segment is (1, -1). Then the correct option is D.

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of line, etc.

The coordinates of the point on the directed line segment from K (-5,-4) to L (5,1) portions the segment into a ratio of 3: 2.

Let the coordinate of the point be (x,y).

We know that the section formula

[tex]\rm (x,y) = (\dfrac{m_1x_2+m_2x_1}{m_1+m_2} ,\dfrac{m_1y_2+m_2y_1}{m_1+m_2})[/tex]

We have

m₁: m₂ = 3: 2

(x₁, y₁) = (-5, -4)

(x₂, y₂) = (5, 1)

Then we have

[tex]\rm (x, y) = (\dfrac{3*5 + 2*(-5)}{3+2} , \dfrac{3*1 + 2*(-4)}{3+2})\\\\\\(x, y) = (\dfrac{5}{5}, \dfrac{-5}{5})\\\\\\(x, y) = (1,-1)[/tex]

More about the coordinate geometry link is given below.

https://brainly.com/question/1601567

Answer:

Option 2 is correct

[tex]g(x) = (\frac{1}{2})5^{(x+3)}+2[/tex]

Step-by-step explanation:

We can se ethat the given function is an exponential function.

The function is:

5^x

In order to compress the function the original function is multiplied a constant.

As the function is compressed by a factor of 1/2

The function will become:

g(x) = 1/2 * 5^x

Now the function is shifted to left which is a horizontal shift. For horizontal shift of n units, n is added to the power so the function will become:

[tex]g(x) = \frac{1}{2}5^{x+3}[/tex]

Then the function is shifted upwards two units, the vertical shhift is added to the whole function so the function will become:

[tex]g(x) = (\frac{1}{2})5^{(x+3)}+2[/tex]

Hence, Option 2 is correct ..

Answer:

8:7 and 64:49

Step-by-step explanation:

If the widths of two similar rectangles are 16 cm and 14 cm, the ratio of the areas are 8:7 and 64:49.

Answer:

Yes, the number of mosquito bites can be represented as a function of the amount of repellent used.

Step-by-step explanation:

Let x represents the number of cans of repellent and y represents the number of mosquitos,

If f be the relation from x to y,

Then by the given table,

f(x) = { (0, 11), (1, 8), (5, 2), (4,5), (2, 9), (3, 6)}

∵ If for each input in a relation has exactly one output, the relation is called a function.

Here, for each value of x there is exactly one value of y,

Hence, f(x) is a relation from x to y,

That is, the number of mosquito bites can be represented as a function of the amount of repellent used.

Answer:

{3,23,39}

Step-by-step explanation:

I think that thing inside the box says 4x-5.

The numbers we are putting in are 2,7, and 11.

So when we put 2 in we get 4(2)-5 which is 8-5=3.

When we put 7 in we get 4(7)-5 which is 28-5=23.

When we put 11 in we get 4(11)-5 which is 44-5=39

So the answer is {3,23,39}.

Answer:

If parabolas open down, then their vertices are at a maximum point, whereas if parabolas open up, their vertices are at a minimum point.

I hope this was the answer you were looking for, and as always, I am joyous to assist anyone at any time.

To find the max/min of a function, find where the function's first derivative is zero. Check those points with the second derivative: a positive value indicates a minimum and a negative value indicates a maximum.

To find the maximum or minimum of a function, you should first understand that these points occur where the derivative of the function is zero, which corresponds to the points with a flat tangent line (no slope). To derive this, differentiate the function and mark all the points where the derivative equals zero. These are potential maximum or minimum points, also known as extrema.

However, it's also important to note that a zero derivative does not always mean a maximum or minimum is present. To confirm this, you need to perform the second-derivative test. If after differentiating the first derivative you get a positive value, the original function has a minimum at that point. If it's negative, the function has a maximum.

For example, let's take the function f(x) = x². The derivative f'(x) = 2x, and setting this to zero gives us x = 0 as the only point whose derivative equals zero. Further, the second derivative, f''(x), equals 2, which is positive, indicating a minimum occurs at x = 0.

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Answer:

8.45 kilometers

Step-by-step explanation:

Given

The distance from library to post office = 5.25 miles

We are given that one mile is equal to 1.61 kilometers

So to find the distance from the library to post office in kilometers we have to multiply 5.25 with 1.61

So,

The distance from library to post office in kilometers = 5.25*1.61

8.4525

Rounding off to nearest hundredth

8.45 kilometers ..

Answer:

40,320

Step-by-step explanation:

First you have 8 movies to watch.

A day passes you have 7 left, then another day passes you have 6 left...

You do this until you have 1 movie left because by then you'd have watched 7 movies in 7 days of a week.

Take the product: 8 * 7 * 6 * 5...*2*1 = 8! = 40,320

Answer: C. 40,320

Step-by-step explanation:

Given : The total number of movies = 8

Also, in one week if you watch one movie a day , then the number of possible movies you can watch in next week must be 7.

Now, the number of ways to watch 8 movies taking 7 movies from is given by permutations :-

[tex]^8P_7=\dfrac{8!}{(8-7)!}\\\\=\dfrac{8!}{1!}=8\times7\times6\times5\times4\times3\times2\times1\\\\=40,320[/tex]

Answer:

(x + 2)^2 + (y - 1)^2 = 2^2

Step-by-step explanation:

The equation of this circle is

(x + 2)^2 + (y - 1)^2 = r^2, and we are to determine the values of r^2 and r by substituting -4 for x and 1 for y:

(-4 + 2)^2 + (1 - 1)^2 = r^2, or:

(-2)^2                        =  r^2, or

4 = r^2

Then r = 2.

The desired equation is:

(x + 2)^2 + (y - 1)^2 = 2^2

Answer:

6

Step-by-step explanation:

=81−43+(9)(2)−50

=38+(9)(2)−50

=38+18−50

=56−50

=6

Answer:

6.

Step-by-step explanation:

81-86÷2+(9×2)-50

work out the parentheses first;

= 81 - 86 / 2 + 18 - 50

Now the division:

= 81 - 43 + 18 - 50

= 38 + 18 - 50

= 56 - 50

= 6.

Answer:

Let's evaluate each rental shop:

For one hour, the cost is $5 + $1.5 = $6.5. For ten hours the total cost is: $5 + 10×$1.5 = $20

For one hour, the cost is $6 + $1.25 = $7.25. For ten hours the total cost is: $6 + 10×$1.25 = $18.5

If Clara and her brother are thinking about renting a bike for an hour, Bargain Bikes is the best option. On the other hand, if they want to rent it fr several hours Frugal Wheels is the best option.

Answer:

5xy^2(y + 3x^2 - 6x).

Step-by-step explanation:

5xy^3 + 15x^3y^2 − 30x^2y^2

The GCF is 5xy^2 so dividing through by this we get the factors:

= 5xy^2(y + 3x^2 - 6x).

Answer:

[tex]5xy^2(y+ 3x^2- 6x)[/tex]

Step-by-step explanation:

[tex]5xy^3 + 15x^3y^2 - 30x^2y^2[/tex]

To factor out an expression, factor out GCF

[tex]5xy^3= 5 \cdot x \cdot y \cdot y \cdot y[/tex]

[tex]15x^3y^2= 5 \cdot 3 \cdot x \cdot x \cdot x \cdot y \cdot y[/tex]

[tex]30x^2y^2= 5 \cdot 2 \cdot 3 \cdot x \cdot x \cdot y \cdot y[/tex]

GCF  is 5 times x times y time y

GCF is 5xy^2. Factor out GCF

[tex]5xy^3 + 15x^3y^2 - 30x^2y^2[/tex]

[tex]5xy^2(y+ 3x^2- 6x)[/tex]

Final answer:

The two-digit number in question is 96, as it has one digit as 9 and is divisible by 6.

Explanation:

The student is asking to find a two-digit number where one of the digits is 9, and the number is divisible by 6 without any remainder. To solve this, we need to remember that for a number to be divisible by 6, it must be divisible by both 2 and 3. A two-digit number is divisible by 2 if its last digit is even.

Since one of the digits is 9 (an odd number), the other digit must be even, so our options for the two-digit numbers with a 9 are 90, 92, 94, 96, and 98. To be divisible by 3, the sum of the digits must be divisible by 3. Out of our options, only 96 has a sum of digits (9 + 6) that is divisible by 3. Therefore, the number we are looking for is 96.

Answer:

True

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

1st mean: 65

2nd mean: 106.5

Answer:

The function is odd because it is symmetric about the origin.

Step-by-step explanation:

we know that

A function f(x) is even when

f(x)=f(-x) ----> the function is symmetry about the y-axis

A function is odd when

-f(x)=f(-x) ---> the function is symmetry about the origin

In this problem we have

f(x)=-5x

Verify if the function is even

For x=1 ----> f(1)=-5(1)=-5

For x=-1 ---> f(-1)=-5(-1)=5

so

f(x) is not equal to f(-x)

therefore The function is not even

Verify if the function is odd

we have

f(1)=-5

f(-1)=5

so

-f(1) is equal to f(-1)

-f(x)=f(-x)

therefore

The function is odd because it is symmetric about the origin.

Answer:

The function is odd because it is symmetric about the origin.

Step-by-step explanation:

Answer:

Graph C is your answer

Step-by-step explanation:

Draw the following graph using the easy coordinates, those are were y axis is zero, and the other were x axis is 0:

[tex]y=-2x+2[/tex]

First point is (1,0) and the other (0,2)

The entire region that belongs to your graph is greater than drawn line.

Draw another graph using the same easy coordinates.

[tex]y=2x-1[/tex]

First point is (0.5,0) and the other (0,-1)

The entire region that belongs to your graph is lesser than the drawn line.

When you merge those graphs into one, you can clearly see that they correspond to the C answer.

Answer:

Graph A.

Step-by-step explanation:

The given inequalities are

[tex]y>-2x+2[/tex]

[tex]y<2x-1[/tex]

The related equation of given inequalities are

[tex]y=-2x+2[/tex]

[tex]y=2x-1[/tex]

The slope of line (1) is -2 and the y-intercept is 2.

The slope of line (2) is 2 and the y-intercept is -1.

Both related lines are dotted line because the points on the line are not included n the solution set.

Check each inequality by (0,0).

[tex]0>-2(0)+2\Rightarrow 0>2[/tex] False statement

[tex]0<2(0)-1\Rightarrow 0<-1[/tex] False statement

So, (0,0) is not included in the shaded area of any of these two inequities.

Therefore, graph A shows the solution to the system of linear inequalities.

Answer:

For every real number x, C expresses the solution to the inequality

Final answer:

To find the solution to the inequality x + 3 < 1, subtract 3 from both sides to get x < -2. The number line would have an open circle at -2 and be shaded to the left, indicating all numbers less than -2.

Explanation:

To solve the inequality x + 3 < 1, we need to find the value of x that makes the inequality true. We start by subtracting 3 from both sides of the inequality:

The number line for this inequality would have an open circle at -2 (since -2 is not included in the solution) and shade to the left of -2 to show that all numbers less than -2 are included. The reason we shade to the left is because those are the numbers that are less than -2, thus satisfying the inequality.

Answer: 25200

Step-by-step explanation:

I hope that this is helpful, I'm bad at explaining answers so i wont. XD

Answer:

(3x^2+5)(x+3)

Step-by-step explanation:

The given expression is:

3x3 + 9x2 + 5x + 15

First of all group the first two terms and last two terms:

(3x3 + 9x2) + (5x + 15)

Now factor out the greatest common factor from each group:

3x^2(x+3)+5(x+3)

(3x^2+5)(x+3)

Thus the factors of 3x3 + 9x2 + 5x + 15 are:

(3x^2+5)(x+3) ....

Answer:(3x^2 + 5)(x + 3)

Step-by-step explanation:

B.

Answer:

The simplest form is 1/r^7 + 1/s^12

Step-by-step explanation:

The given expression is r^-7+s^-12.

Notice that the exponents of both the base are negative

So, we will apply the rule which is:

a^-b = 1/a^b

Which means that to change the exponent into positive we will write it as a fraction:

r^-7+s^-12.

= 1/r^7 + 1/s^12..

Therefore the simplest form is 1/r^7 + 1/s^12....

Answer:

The simplest form is 1/r^7 + 1/s^12

Step-by-step explanation:

Answer: is there anyway U can give me a more zoomed in pic

Step-by-step explanation:

Answer:

(a + 6b)(a - 4b)

Step-by-step explanation:

You want your midst term to result in 2ab, NOT -2ab.

I am joyous to assist you anytime.

Answer:

-2 >-4

This is true, so it is a solution

Step-by-step explanation:

2x+1> x-3

Subtract x from each side

2x-x+1> x-x-3

x +1 > -3

Subtract 1 from each side

x+1-1 >-3-1

x > -4

x =-2   Substitute this into the inequality

-2 >-4

This is true, so it is a solution