please help 50 points

Factor the expression completely over the complex numbers. y^4+14y^2+49

Answer:

28π and 196π

10π and 25π

2500π

A = C/4π

Step-by-step explanation:

The circumference of a circle is the distance around the edge of the circle. To find the circumference, we use the formula C = 2πr. The area of the circle is the amount inside the circle and is found using A = πr². Substitute the relevant values in each situation into the formulas to find the circumference and area.

if the radius of a circle is 14 units, what is its circumference? what is its area?

Substitute r = 14.

C = 2πr = 2π(14) = 28π

A = πr² = π(14)² = 196π

if a circle has diameter 10 units, what is its circumference? what is its area?

Substitute r = 5.

C = 2πr = 2π(5) = 10π

A = πr² = π(5)² = 25π

if a circle has circumference 100π units, what is its area?

Substitute C = 100π to find the radius. Then substitute the radius into the are formula.

C = 2πr

100π=2πr

100 = 2r

50 = r

A = πr² = π(50)² = 2500π

if a circle has circumference c, what is its area in terms of c?

Cole the circumference formula for r. Then substitute the expression into the area formula.

C = 2πr

r = C / 2π

A = πr² = π(C/2π)² = πC/4π² = C/4π

1. Circumference: [tex]\(28\pi\)[/tex]units, Area: [tex]\(196\pi\)[/tex] square units.

2. Circumference: [tex]\(10\pi\)[/tex]units, Area: [tex]\(25\pi\)[/tex]square units.

3. Area: [tex]\(2500\pi\)[/tex]square units.

4. Area: [tex]\(\frac{C^2}{4\pi}\)[/tex]  square units.

Let's go through each question one by one, using the formulas for the circumference and area of a circle.

1. If the radius of a circle is 14 units, what is its circumference? What is its area?

  - The circumference [tex]\( C \)[/tex] of a circle is given by the formula:

[tex]\[ C = 2\pi r \][/tex]

    where [tex]\( r \)[/tex] is the radius.

    Given [tex]\( r = 14 \)[/tex] units, we have:

[tex]\[ C = 2\pi \times 14 = 28\pi \text{ units} \][/tex]

  - The area [tex]\( A \)[/tex]of a circle is given by the formula:

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

    Given [tex]\( r = 14 \)[/tex] units, we have:

[tex]\[ A = \pi \times 14^2 = \pi \times 196 = 196\pi \text{ square units} \][/tex]

2. If a circle has diameter 10 units, what is its circumference? What is its area?

  - The diameter [tex]\( d \)[/tex] is related to the radius by [tex]\( d = 2r \)[/tex]. Therefore, the radius [tex]\( r \)[/tex] is:

[tex]\[ r = \frac{d}{2} = \frac{10}{2} = 5 \text{ units} \][/tex]

  - Using the circumference formula [tex]\( C = 2\pi r \):[/tex]

[tex]\[ C = 2\pi \times 5 = 10\pi \text{ units} \][/tex]

  - Using the area formula [tex]\( A = \pi r^2 \):[/tex]

[tex]\[ A = \pi \times 5^2 = \pi \times 25 = 25\pi \text{ square units} \][/tex]

3. If a circle has circumference [tex]\( 100\pi \)[/tex] units, what is its area?

  - Given the circumference [tex]\( C = 100\pi \),[/tex] we can find the radius [tex]\( r \)[/tex] using the formula [tex]\( C = 2\pi r \):[/tex]

[tex]\[ 100\pi = 2\pi r \][/tex]

    Dividing both sides by [tex]\( 2\pi \):[/tex]

[tex]\[ r = \frac{100\pi}{2\pi} = 50 \text{ units} \][/tex]

  - Using the area formula [tex]\( A = \pi r^2 \):[/tex]

[tex]\[ A = \pi \times 50^2 = \pi \times 2500 = 2500\pi \text{ square units} \][/tex]

4. If a circle has circumference [tex]\( C \),[/tex] what is its area in terms of [tex]\( C \)[/tex]

  - Given the circumference [tex]\( C \),[/tex] we can express the radius [tex]\( r \)[/tex] in terms of [tex]\( C \)[/tex] using the formula [tex]\( C = 2\pi r \):[/tex]

[tex]\[ r = \frac{C}{2\pi} \][/tex]

  - Using the area formula [tex]\( A = \pi r^2 \)[/tex] and substituting [tex]\( r = \frac{C}{2\pi} \):[/tex]

[tex]\[ A = \pi \left( \frac{C}{2\pi} \right)^2 = \pi \left( \frac{C^2}{4\pi^2} \right) = \frac{\pi C^2}{4\pi^2} = \frac{C^2}{4\pi} \][/tex]

Answer:

10

Step-by-step explanation:

We'll note the numbers as [tex]x_{n}, x_{n+1} ...[/tex]

[tex]x_1 + x_2 + x_3 + x_4 = 20\\Avg = 5\\\frac{x_1 + x_2 + x_3 + x_4 + x_5 }{5} = 6 = \frac{20 + x_5}{5}\\ 4 + \frac{x_5}{5} = 6\\\\frac{x_5}{5} = 2\\\x_5 = 10[/tex]

Answer:

10.

Step-by-step explanation:

The average of the 5 numbers =

(20 + x) / 5 = 6  where x is the 5th number.

20 + x = 30

x = 10

The fifth number is 10.

Answer:

Brenda

Step-by-step explanation:

You can divide the number of pages by the number of minutes to find the amount of minutes it takes to read 1 page. For Arnold, 3 pages / 7 minutes = 1 page per approximately 0.43 minutes. For Brenda, 8 pages / 14 minutes = 1 page per approximately 0.57 minutes. Brenda reads slightly faster since 0.57 > 0.43

Answer: second option.

Step-by-step explanation:

By definition, you know that:

[tex]b^0=1[/tex]

You can see in the graph that the interception with the y-axis is at -1.

Therefore, in that point: x=0 and y=-2

Substitute into the function and solve for a:

[tex]-1=a(b)^0\\-1=a(1)\\a=-1[/tex]

Now, choose any point of the function and substitute this point and the value of a into the function and solve for b. Then you obtain:

Point (2,-4)

[tex]-4=-1(b)^2\\\frac{-4}{-1}=b^2\\b=\sqrt{4}\\b=2[/tex]

Answer:

Its B

Step-by-step explanation:

Because it is

On edge

1/8 chance since there are 8 numbers from 5 to 12 and 1 is only one number so 1/8

➷ cos38 = 79/x

x = 79/cos38

x = 100.2524

The correct option would be 100.25

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

100.25

Step-by-step explanation:

Using the cosine ration in the right triangle, then

cos38° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{79}{x}[/tex]

Multiply both sides by x

x × cos38° = 79 ( divide both sides by cos38° )

x = [tex]\frac{79}{cos38}[/tex] ≈ 100.25

The volume of the cylinder is 25295.26 cubic meters.

To find the volume of a cylinder, we can use the formula V = π * r^2 * h, where r is the radius and h is the height. Given that the diameter is 34 m, the radius is half of that, which is 17 m. The height is given as 27 m.

Plugging in the values into the formula, we get V = 3.14 * (17^2) * 27. Evaluating this expression, we find that the volume of the cylinder is 25295.26 cubic meters.

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The volume of a cylinder is 25295.26 cubic meters.

To find the volume of a cylinder, use the formula V = πr^2h, where V represents the volume, π is a constant approximately equal to 3.14, r is the radius of the cylinder, and h is the height of the cylinder.

In this case, the diameter of the cylinder is given as 34 m, so the radius is half of the diameter, or 17 m.

The height of the cylinder is given as 27 m. Substitute these values into the formula to calculate the volume.

V = 3.14 × (17^2) × 27

= 25295.26 cubic meters.

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Moving the decimal point left or right works in the metric systems because; The metric system is based on powers of 10.

It follows from the task content that the reason for moving the decimal point left or right in metric system conversions be identified.

It follows from metric system conversions that;

Based on the aforementioned, it can be concluded that the measurements conversion in the metric system is such that the decimal point is moved left or right.

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choice D is the correct solution

PARALLEL slopes always have the same slope no matter what because they are parallel

The equation of the line that is parallel to y = 5x-4 and passes through the point (3, 4) is y = 5x - 11 because it has the same slope, 5, as the given line depicting parallelism and it passes through the specified point.

In Mathematics, two lines are parallel if their slopes are equal. In this case, the given line is y = 5x - 4, and its slope is 5. To find an equation of a line that is parallel to this line and passes through a specific point, we use the point-slope form of a line, which is y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the point through which the line passes.

Replace m with 5 (the slope of the given line), and (x1, y1) with (3, 4) (the point through which the line passes), and we have y - 4 = 5(x - 3). Distributing and simplifying, we get y = 5x - 15 + 4 = 5x -11. Therefore, the equation of the line that is parallel to y = 5x - 4 and passes through the point (3, 4) is y = 5x - 11.

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Answer:

b: [tex] x= 8 \sqrt7 y= 4 \sqrt{21} [/tex]

Step-by-step explanation:

Euclid 1st theorem:

[tex] x^2 = 16 * (16+12); y^2 = 12*(12+16) [/tex]

Calculation is trivial

Answer:

sqrt(sqrt(x))

Step-by-step explanation:

A quartic root of is written mathematically as . THe quartic root of 16 is 2 since 2*2*2*2 = 16. However, a quartic root can also be defined as the square root of a square root. For example the √16 = 4 and the √4 = 2. This is the same response as taking the quartic root. This means you can write it as the sqrt(sqrt(x)). In the example, it would be sqrt(sqrt(16)) = sqrt(4) = 2.

The quartic root of a variable x can be calculated using the expression Math.sqrt(Math.sqrt(x)), which calls the square root function twice. This computes the square root of x, then computes the square root of the result, yielding the quartic root.

In order to compute the quartic root of a variable x, we call the Math.sqrt() method twice in a nested manner. The quartic root is essentially the square root of a square root, hence the need for the double call. The appropriate expression in this case would be:

Math.sqrt(Math.sqrt(x))

This expression first computes the square root of x and then computes the square root of the result, which gives us the quartic root of x. As a result, if x is 16.0, the result of this expression would be 2.0, and if x is 81.0, the result would be 3.0.

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Answer:

option a

[tex]log\frac{x^{5} }{(x-8)^{6} }[/tex]

Step-by-step explanation:

Given in the question an expression

5logx - 6log(x-6)

To solve this question we will apply two of the logarithm property

1) power rule

alogx = log[tex]x^{n}[/tex]

log[tex]x^{5}[/tex] - log[tex](x-8)^{6}[/tex]

2) substraction rule

The log of a quotient is the difference of the logs

loga (x/y) = loga x - loga y

[tex]logx^{5}- log(x-8)^{6}[/tex]

log[tex]\frac{x^{5} }{(x-8)^{6} }[/tex]

Answer:

a edge

Step-by-step explanation:

Answer:

  3 ft by 7 ft

Step-by-step explanation:

Try the solutions and find the one that works.

  3.5 × 6 — area OK, perimeter = 19 ft

  4 × 6 — area = 24 ft², perimeter OK

  3 × 7 — area OK, perimeter OK

  3.5 × 7 — area 24.5 ft², perimeter 21 ft

___

The perimeter is the sum of the four side lengths; the area is the product of two adjacent side lengths.

distributive property because u need to mulptiply the number outside with the parentheses

Answer:

A)Distributive property

Step-by-step explanation:

This is because you need to multiply

Answer:

Graphic attached

Step-by-step explanation:

The oblique asymptote of the function has the shape of a line of the form

[tex]y = mx + b[/tex]

We need to find the slope m and the intercept b.

The oblique asymptote is found by these two limits:

[tex]m = \lim_{x \to \infty}\frac{f(x)}{x}\\\\b = \lim_{x \to \infty}[f(x) - mx][/tex]

If [tex]f(x) = \frac{(2x+3)(x-6)}{(x+2)(x-1)}[/tex] then:

[tex]m = \lim_{x \to \infty} \frac{\frac{(2x+3)(x-6)}{(x+2)(x-1)}}{x}\\\\m = \lim_{x \to \infty} \frac{2x^2-9x-18}{x^3 +x^2 -2x}\\\\m = 0[/tex]

The slope is 0. Therefore the function has no oblique asymptote.

Horizontal asymptote:

[tex]y = 2[/tex]

Vertical asymptote

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

Answer:

Step-by-step explanation:

0.3. x + 18.3

The data for tree 1 is an illustration of a linear equation.

The linear equation that fits the data for tree 1 is: [tex]\mathbf{y = 0.3x + 18.3}[/tex]

From the complete question, we have the following points

[tex]\mathbf{(x_1,y_1) = (1,18.6)}[/tex]

[tex]\mathbf{(x_2,y_2) = (3,19.2)}[/tex]

First, we calculate the slope (m)

[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]

So, we have:

[tex]\mathbf{m = \frac{19.2 - 18.6}{3 -1}}[/tex]

[tex]\mathbf{m = \frac{0.6}{2}}[/tex]

[tex]\mathbf{m = 0.3}[/tex]

The equation is then calculated as:

[tex]\mathbf{y = m(x - x_1) + y_1}[/tex]

So, we have:

[tex]\mathbf{y = 0.3(x - 1) + 18.6}[/tex]

[tex]\mathbf{y = 0.3x - 0.3+ 18.6}[/tex]

[tex]\mathbf{y = 0.3x + 18.3}[/tex]

Hence, the linear equation that fits the data for tree 1 is: [tex]\mathbf{y = 0.3x + 18.3}[/tex]

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1+y (greater than or equal to symbol) 6

Answer:

The number of goats in the farm is [tex]74[/tex]

The number of sheep in the farm is [tex]63[/tex]

Step-by-step explanation:

Let

x----> the number of goats in the farm

y----> the number of sheep    

we know that

[tex]x+y=137[/tex] ----> equation A

[tex]x=y+11[/tex] -----> equation B

substitute the equation B in equation A and solve for y

[tex](y+11)+y=137[/tex]

[tex]2y=137-11[/tex]

[tex]2y=126[/tex]

[tex]y=126/2=63[/tex]

Find the value of x

[tex]x=63+11=74[/tex]

therefore

The number of goats in the farm is [tex]74[/tex]

The number of sheep in the farm is [tex]63[/tex]

right isosceles

rs:34&rs=rt+st

rt:17

st:17

ab=[(x(a)-x(b))+(y(a)+y(b))]

Answer:

Isosceles.

Step-by-step explanation:

We are going to check it with the distance formula

d(R,T) = [tex]\sqrt[2]{(3-4)^{2}+(-3-1)^{2}}[/tex]

= [tex]\sqrt[2]{(-1)^{2}+(-4)^{2}}[/tex]

= [tex]\sqrt[2]{1+16}[/tex]

=  [tex]\sqrt[2]{17}[/tex].

d(T,S) = [tex]\sqrt[2]{(4-8)^{2}+(1-0)^{2}}[/tex]

= [tex]\sqrt[2]{(-4)^{2}+(1)^{2}}[/tex]

= [tex]\sqrt[2]{16+1}[/tex]

=  [tex]\sqrt[2]{17}[/tex].

d(S,R) = [tex]\sqrt[2]{(8-3)^{2}+(0-(-3))^{2}}[/tex]

= [tex]\sqrt[2]{(5)^{2}+(3)^{2}}[/tex]

= [tex]\sqrt[2]{25+9}[/tex]

=  [tex]\sqrt[2]{34}[/tex].

Then, as the triangle has two sides with the same length, the triangle is isosceles.

the scale factor is 2.

because

if you look at the length AL in the smaller shape, it is 2 squares.

now if you look at the length AL in the enlarged shape, it is 4 squares.

to find the scale factor, do 4 ÷ 2 which is 2.

therefore the scale factor is 2

Answer:

The correct option is 2. The scale factor is 2.

Step-by-step explanation:

The coordinates of preimage are A(1,2), T(0,0), K(4,1) and L(3,2).

The coordinates of image are A'(2,4), T'(0,0), K'(8,2) and L'(6,4).

If a figure dilated by scale factor k with center at origin then the rule of dilation is

[tex](x,y)\rightarrow (kx,ky)[/tex]

[tex]A(1,2)\rightarrow A'(2,4)[/tex]

[tex]k=\frac{\text{x coordinate of image}}{\text{x coordinate of preimage}}[/tex]

[tex]k=\frac{2}{1}[/tex]

[tex]k=2[/tex]

Therefore the scale factor is 2 and the correct option is 2.

First you need to rewrite the equation in the form y = mx +b:

2y = x-4

Divide all terms by 2:

2y / 2 = x/2 - 4/2

Simplify:

y = 1/2x - 2

The slope of the line is 1/2.

A perpendicular line has a slope of the negative reciprocal, which would be -2.

Now using the point slope method:

y - y1 = m(x-x1)

Using the given point of (8,-4) and m = -2

you get:

y +4 = -2(x-8)

Simplify:

y +4 = -2x +16

Now subtract 4 from both sides to get the final equation:

y = -2x +12

Answer:

12

Step-by-step explanation:

subtract 25 minus 13 and you get 12 which means 12 students come in cars

We want to find all [tex]f(x)[/tex] such that

[tex](D^2-12D-45)[f(x)]=0[/tex]

We have

[tex](D^2-12D-45)[f]=(D-15)(D+3)[f]=0[/tex]

so that either

[tex](D-15)[f]=0\implies f'-15f=0\implies f(x)=e^{15x}[/tex]

or

[tex](D+3)[f]=0\implies f'+3f=0\implies f(x)=e^{-3x}[/tex]

These solutions are linearly independent; we confirm this by computing the Wronskian:

[tex]W=\begin{vmatrix}e^{15x}&e^{-3x}\\15e^{15x}&-3e^{-3x}\end{vmatrix}=-3e^{12x}-15e^{12x}=-18e^{12x}\neq0[/tex]

We can also confirm that these solutions are correct by substituting the solutions for [tex]f(x)[/tex] in the differential equation:

[tex](D^2-12D-45)[e^{15x}]=225e^{15x}-12(15e^{15x})-45e^{15x}=0[/tex]

[tex](D^2-12D-45)[e^{-3x}]=9e^{-3x}-12(-3e^{-3x})-45e^{-3x}=0[/tex]

The linearly independent functions that are annihilated by the differential operator d2 − 12d - 45 are e^{15x} and e^{-3x}, found by solving the quadratic equation associated with the differential equation.

The differential operator given is d2 − 12d - 45. To find out the linearly independent functions that are annihilated by this operator, we have to solve the homogeneous differential equation d2 − 12d - 45 = 0. This is a second order equation, so we expect two linearly independent solutions.

To find the solutions, we seek the roots of the associated quadratic equation m^2 - 12m -45 = 0. This can be factored into (m-15)(m+3), thus giving roots m = 15 and m = -3.

The general forms of the solutions for these roots are e^{15x} and e^{-3x} respectively. Therefore, the functions e^{15x} and e^{-3x} are linearly independent functions that are annihilated by the given differential operator d2 − 12d - 45.

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Answer:

0.05% means 0.05 per every 100.

Step-by-step explanation:

We find it useful to convert 0.05% to decimal, because if you need to find 0.05% of any number, you can simply multiply that number with 0.0005.

hope this helps!!!!!

The value of 0.05% written as a decimal is 0.0005.

To write 0.05% as a decimal, you need to divide the percentage value by 100.

A decimal number is a number that uses the base-10 numbering system. It is a way of representing numbers using the digits 0-9 and a decimal point. Each digit in a decimal number represents a specific place value, which is a power of 10.

The digits to the left of the decimal point represent whole numbers, and the digits to the right of the decimal point represent fractional parts or decimal fractions.

0.05% divided by 100 is equal to 0.0005.

Therefore, 0.05% written as a decimal is 0.0005.

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Answer:

The answer is five.

Step-by-step explanation:

A pyramid with a square base has one square face and there are four triangle faces, so there are five in total.

I hope this helped! :-)

Number of faces of pyramid with a square base is 5.

Hence option A is correct.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Since we know that

A pyramid having square base have,

Number of square face = 1

Number of triangular face = 4

Hence total face in this triangle is,

= 1+4

= 5

Hence total faces = 5.

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3x+4y-5z=8

1x+0y+2z=-3

4x-3y+0z=6

|`3 4 (-5)`||`x`| |`8`|

| 1 0 2 | |y |=|-3 |

|.4 (-3) 0 .||.z.| |.6.|

Answer:

246.

Step-by-step explanation:

Let the number be 2xy, then

2 + x + y = 2y    and y must be even because the whole number is even.

y = 2 + x .

Now x must be even because y is even.

The only 2 numbers which fit are x = 4 and y = 6 so the number is 246.

Checking: 2+4+6 = 12 and 12 = 2*6.

Answer:

8x³ + 125

Step-by-step explanation:

Cubes:  look for the exponent 3 and for perfect cubes such as 1, 8, 27, ...

8x^3 + 125 is a sum, and 8 is a perfect cube (the cube of 2), and x^3 is a cube, and 125 is a cube.

Thus, the correct answer is 8x^3 + 125 (which is equivalent to

(2x)³ + 5³).