According to the fundamental theorem of algebra, how many zeros does the function f(x) = 3x4 + x + 2 have? (2 points) 1 2 3 4.

The volume of the right cone is 7 units.

The radius of a cone can be found as follows:

The volume of the right cone is 245π unit³. The height of the right cone is 15 units.

Therefore,

volume of a right cone = 1 / 3 πr²h

where

Hence,

volume of the right cone = 245π

h = 15 units

Hence,

245π = 1 / 3 × π × r²  × 15

divide both sides by π

245 = 15 / 3 r²

245 = 5r²

r² = 245 / 5

r = √49

r = 7 units

Therefore,

radius of the cone = 7 units

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The solution set for inequality 3|x + 1| < 9 is option(C).

What is inequality?

A relationship between two expressions or values that is not equal to each other is known as an "inequality" in mathematics. The "not equal symbol (≠)" is typically used to indicate that two values are not equal that is there is inequality.

The equals sign in the equation-like statement 5x - 4 > 2x + 3 has been replaced by an arrowhead. This is a prime instance of inequality. This indicates that the left half, 5x - 4, is larger than the right part, 2x + 3, in the equation.

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Answer:

B.

Step-by-step explanation:

635/100 = 127/20

=>6 3/10

The length of diagonal falls between 4 and 5.

Given,

Length of diagonal = [tex]\sqrt{18}[/tex]

                                = 4.24

which is between whole numbers 4 and 5 and closer to 4.

Hence, The length of diagonal falls between 4 and 5 and closer to 4.

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Answer:

Step-by-step explanation:

The distance from coordinates Point p (5, 7) to coordinates (–2, 1) and (4, 1) in line n are  9.21 units and 6.08 units respectively.

The distance between two points is defined as the length of the line segment between two places representing their distance.

Line n contains points (–2, 1) and (4, 1). Point p has coordinates (5, 7).

The distance from coordinates p (5, 7) to coordinates (–2, 1) in line n will be

⇒ √[(-2-5)² + (1-7)²]

⇒ √[(-7)² + (-6)²]

⇒ √[49 + 36]

⇒ √85

⇒ 9.21 units

The distance from coordinates p (5, 7) to coordinates (4, 1) in line n will be

⇒ √[(4-5)² + (1-7)²]

⇒ √[(-1)² + (-6)²]

⇒ √[1 + 36]

⇒ √37

⇒ 6.08 units

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The quadrilateral above is a parallelogram.

A parallelogram is a quadrilateral with opposite sides equal to each other. Opposite sides of a parallelogram is parallel to each other.

The sum of angles in a parallelogram is 360 degrees.

Opposite angles of a parallelogram is congruent to each other.

Adjacent angles of a parallelogram sum up to 180 degrees. This means adjacent angles are supplementary.

Let's check if the Known adjacent angles of the quadrilateral is supplementary.

Therefore,

105 + 75 = 180 degrees.

Hence, the quadrilateral is a parallelogram.

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(1) The explicit formula and the 21st term for the first sequence are:

aₙ = 10 - 5n and a₂₁ = -95

(2) The explicit formula and the 21st term for the second  sequence are:

aₙ = 1.5n + 1.5 and a₂₁ = 33

A sequence in which the difference between any two consecutive terms is the same is known as an arithmetic sequence.

(1)

The given sequence is 5, 0, -5, -10,...

Note the difference between two consecutive terms of the sequence is the same, which is -5.

Therefore, the sequence is an arithmetic sequence with a common difference of d = -5.

The [tex]n^{th}[/tex] term of an arithmetic sequence is given by:

aₙ = a₁ + (n-1)d

Substitute a₁ = 5 and d= -5 into the equation,

aₙ = 5+ (n-1)(-5)

   = 5 - 5n + 5

aₙ = 10 - 5n

To find the 21st term, substitute n = 21 into the above equation,

a₂₁ = 10 - 5n

a₂₁ = 10 - 5(21)

a₂₁ = 10 - 105

a₂₁ = -95

Hence, the explicit formula and the 21st term for the first sequence are:

aₙ = 10 - 5n and a₂₁ = -95

(2)

The given sequence is 3, 4.5, 6, 7.5, 9,...

Note that the difference between two consecutive terms is 1.5, therefore, the sequence is an arithmetic sequence with a common difference of

d = 1.5.

The [tex]n^{th}[/tex] term of an arithmetic sequence is given by:

aₙ = a₁ + (n-1)d

Substitute a₁ = 3 and d= 1.5 into the equation,

aₙ = 3 + (n-1)1.5

aₙ = 3+1.5n-1.5

aₙ = 1.5n+1.5

To find the 21st term, substitute n = 21 into the above equation,

a₂₁ = 1.5(21) + 1.5

a₂₁ = 31.5 + 1.5

a₂₁ = 33

Hence, the explicit formula and the 21st term for the second  sequence are:

aₙ = 1.5n + 1.5 and a₂₁ = 33

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Using inequality the number of 105  of 120-kilogram crates that can be loaded into the shipping container.

What is inequality?

A difference between two values indicates whether one is smaller, larger, or simply not equal to the other. In mathematics, the term "inequality" refers to a relationship between two expressions or values that is not equal to one another.

The greatest weight that container can hold = 27500

Shipment weight already  in the container =14900

Amount of weight that may be loaded = 27500 - 14900 = 12600

Weight of each crates = 120 kg

Let x be the maximum number of 120 kg crates that can be loaded to the container then,

Weight of 'x' number of 120 kg crates = 120x

Therefore, the required inequality is as follows

=>120x< 12600

(since the maximum amount of weight of crates that can be put in the container should be less than or equal to the total weight of the maximum number of crates that can be loaded into the container).

Then the inequality is ,

=> x [tex]\leq \frac{12600}{120}[/tex]

=> x ≤ 105.

Thus, a maximum of 105 crates can be loaded into the container.

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Answer:

f = -8

Step-by-step explanation:

We know the slope formula is:

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

Because we already know the slope and three other points, we can let point f represent y2 and solve for it:

[tex]\frac{1}{8}=\frac{f-(-6)}{-8-8}\\ \frac{1}{8}=\frac{f+6}{-16}\\ -2=f+6\\ -8=f[/tex]

Expressing the complex number 2i(i +3) in a + bi form gives -2 + 6i

Complex numbers are numbers that are expressed as a + ib,

where a and b are real numbers and i is an fictitious number called "iota."

i has the value (-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Real number) and the imaginary number 3i.

The multiplication of 2i(i + 3)

= 2i^2  + 6i

= -2 + 6i

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Answer A, B, D

Step-by-step explanation:

The distance between the point (-3,3) and (a, b) is;

⇒ d = √(a + 3)² + (b - 3)²

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Two points are,

(-3,3) and (a, b)

Now,

The distance between the point (-3,3) and (a, b) is;

d = √(a - (-3))² + (b - 3)²

d = √(a + 3)² + (b - 3)²

Thus, The distance between the point (-3,3) and (a, b) is;

⇒ d = √(a + 3)² + (b - 3)²

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Answer:

the answer is because u need trust me6

The number of laddus who were there at the beginning Rohan has is 48.

Here we have to find the number of laddu Rohan at the beginning.

Let x be the number of laddu Rohan have.

He gave on the first day = x × 1/3= x/3

The leftover laddu = x - x/3

= 2x/3

Laddu is given on the second day = 2x/3 × 1/4

= x/6

Here we know that the laddu given by Rohan is 8,

So

x/6 = 8

x = 48

Therefore we get the number of laddu Rohan has 48.

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If the faculty went on a weight watchers diet plan and now weight an average of 185 pounds in 2021.  The faculty's average weight loss per year : 185 pounds and 155 pounds.

First step is to find the difference between the initial weight and the final weight

Difference = Initial weight - Final weight

Difference = 215 pounds - 185 pounds

Difference = 30 pounds

Now let find the lost per year

2018

Lost per year = 215 pounds - 30 pounds

Lost per year = 185 pounds

2021

Lost per year = 185 pounds - 30 pounds

Lost per year = 155 pounds

Therefore the loss is 185 and 155 pounds.

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Answer:

5

Step-by-step explanation:

-3x

2y

-6

12

-4y

The total cost to the nearest cent = 2675 cents.

Given that:

The cost of backpack = $25

Tax = 7%

To calculate the total cost, we can also approach the problem in two ways:

1). Multiply the amount by 7% ($25 x 0.07 = $1.75, rounded up to the nearest cent at 175 cents or $1.75). This will tell us how much tax we will have to pay. Add this to the cost to get the total amount one has to pay (25 + 1.75 = $26.75 or 2675 cents).

2). Multiply the amount by 107%. This includes both steps from 1 in one step. ($25 x 1.07 = $26.75; $26.75 rounded to dollars).

We know that,

1 dollar ($) = 100 cents

Multiply both sides by 26.75

$ 26.75 = 2675 cents.

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The solutions of the given equations are,

(i) [tex]x=\frac{\pi }{2} , x= \frac{5\pi }{2} , x= \frac{9\pi }{2} , x = \frac{13\pi }{2} , x = \frac{17\pi }{2}[/tex]

(ii)  x = 0, x = 2π, x = 4π, x = 6π, x = 8π.

(iii)

[tex]x = cot^-^1(4), x = cot^-^1(4)+\pi , x = cot^-^1(4)+2\pi , x = cot^-^1(4)+3\pi , \\x = cot^-^1(4)+4\pi[/tex]

What is solution of the equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other terms, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transform the equation into an equality.

(i) cosec x = 1      for 0 ≤ x ≤ 360°

Since, the general solution for

cosec x = 1 is, [tex]x = \frac{\pi }{2} +2n\pi[/tex]

The range for the solution is 0 ≤ x ≤ 360°

Hence,

[tex]x=\frac{\pi }{2} , x= \frac{5\pi }{2} , x= \frac{9\pi }{2} , x = \frac{13\pi }{2} , x = \frac{17\pi }{2}[/tex]

(ii) sec x = 2

Since, the general solution for

sec x = 1  is, x = 0 + 2πn

The range for the solution is 0 ≤ x ≤ 360°

Hence,

x = 0, x = 2π, x = 4π, x = 6π, x = 8π.

(iii) cot x = 4

⇒ [tex]x = cot^-^1(4)[/tex]

The range for the solution is 0 ≤ x ≤ 360°

Hence,

[tex]x = cot^-^1(4), x = cot^-^1(4)+\pi , x = cot^-^1(4)+2\pi , x = cot^-^1(4)+3\pi , \\x = cot^-^1(4)+4\pi[/tex]

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Answer:

1. B

2. D

3. A

4. B

5. A

6. C

7. B

8. D

9. B

10. A

Step-by-step explanation:

The integral Value is [tex]\pi[/tex] or 22/7 or 3.14

Integral Value: It is a value which is obtained after integrating.

Triple Integral: Integral function of a three variable over a region in R³ ( real number 3D space) are called triple integral.

            For x = 2,

              x = 2y² + 2z²

equating those two functions, we get,

                         1 = y² + z²

that gives -1≤ y≤ 1 and -(√x/2 -y²) ≤ z≤ (√x/2 - z²) and  2y²≤ x ≤ 2

so after the integration, the form is quite complicated to solve so use the following form instead letting x = 2 and x = 2y² + 2x², so that the integral became

      ∫∫∫ 2y² + 2z² dx dA which becomes

     ff (2 - 2y² - 2z²) da now use polar coordinate where y= 1 cos Ф          and z = 1 sinФ

now, integral becomes

       2 ∫¹₀ (1- r²) r dr dФ

= 4[tex]\pi[/tex] ( r²/2 - r⁴ /4)¹ ₀

= 4[tex]\pi[/tex] ( 1/2 - 1/4)

= 4[tex]\pi[/tex] × 2 - 1/4

= [tex]\pi[/tex]

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For given equation x_(n+1) = ((x_n)^3 - 5)/10,

a) (i) x2 = -0.6

(ii) x3 = -0.5216

b)  the solution to 6 decimal places, x5 = -0.513594

Given equation, x_(n+1) = ((x_n)^3 - 5)/10

also, x1 = -1

a)

(i) we need to find the value of x2

Substitute n = 1 in given equation,

x_(1+1) = ((x1)^3 - 5)/10

x_2 = [(-1)^3 - 5]/10

x_2 = (-1 - 5)/10

x2 = -6/10

x2 = -0.6

(ii) we need to find the value of x3

Substitute n = 2 in given equation,

x_(2+1) = ((x2)^3 - 5)/10

x3 = [(-0.6)^3 - 5]/10

x3 = (-0.216 - 5)/10

x3 = -5.216/10

x3 = -0.5216

b)

We need to find the solution to 6 decimal places.

First we find the value of x4.

Substitute n = 3 in given equation,

x_(3+1) = ((x3)^3 - 5)/10

x4 = [(-0.5216)^3 - 5]/10

x4 = (-0.1419 - 5)/10

x4 = -5.1419/10

x4 = -0.51419

Substitute n = 4 in given equation,

x_(4+1) = ((x4)^3 - 5)/10

x5 = [(-0.51419)^3 - 5]/10

x5 = (-5.13595)/10

x5 = -0.513594

Therefore, for given equation x_(n+1) = ((x_n)^3 - 5)/10,

a) (i) x2 = -0.6

(ii) x3 = -0.5216

b)  the solution to 6 decimal places, x5 = -0.513594

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The value of composition of function (goh) (-3) is [tex]\frac{8}{5}[/tex].

A function that depends on another function is referred to as a composite function. When one function is inserted into another, a composite function is produced. The definition of a composite function is a function made up of two functions, one of which acts as an independent variable for the other function. It can be defined as:

[tex](fog)(x)=f(g(x))\\(gof)(x)=g(f(x))[/tex]

When dealing with the composition of functions, the order of the functions is crucial since (f∘g)(x) is not equivalent to (g∘f)(x).

Finding the composition of function by putting x=h(x) in function g(x),

[tex](goh)(x)=g(h(x))\\\\=\frac{4-x+1}{4-x-2}\\\\=\frac{5-x}{2-x}[/tex]

Now, putting x = -3,

[tex](goh)(-3)=\frac{5-(-3)}{2-(-3)} \\\\=\frac{8}{5}[/tex]

Therefore, the value of composition of function (goh) (-3) is  [tex]\frac{8}{5}[/tex] .

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The equation in point-slope form is y=4x-25.

A line passing through the point (x 1, y1) has a slope of "m," and its point slope form is given by the equation y - y1=m (x - x1).

A horizontal line's equation is of the form y=b when it passes through the points (a, b).

Step 1: Write down the  line's slope, "m," and the coordinates (x 1, y 1) of the point that is given and is on the line.

Step 2: Replace the given values in the calculation for the point slope: y - y1 = m. (x - x1).

Point-slope form is y=mx+b.

To get the equation of the line in standard form, simplify in step three.

Given, m(slope)= 4.

The point is (8,7)= (x1,y1)

y-7=4(x-8)

y-7=4x-32

y=4x-32+7

y=4x-25

Hence, the equation in point-slope form is y=4x-25.

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Answer:

[tex] \huge{ \bold{y - 3 = 7(x +9)}}[/tex]

Step-by-step explanation:

The equation of a line in point-slope form is represented by the formula

[tex]y - y_1 = m(x - x_1)[/tex]

where

(x1, y1) is the point and m is the slope

From the question the point is (-9,3) and m = 7

So we substitute the given variables into the formula and solve

We have

[tex]y - 3 = 7(x - - 9) \\ y - 3 = 7(x + 9)[/tex]

Hope this helps you

Answer:

$35

Step-by-step explanation:

money on clothes is 10%, that means it's $5
you get this by dividing the 50 by 100 to figure out how much 1% is, and then multiply with 10.

money on games is 20%, that means it's $10
again, you figure out how much 1% of 50 is and then multiply by 20 to figure out what 20% is.
50 / 100 = 0.5
0.5 * 20 = 10

So far you spent $5 on clothes, $10 on games, that's $15 in total.
When the rest is spent on books, you need to see how much is left of the $50.
50 - 15 = 35

So you spent $35 on books.

Answer: x=1, y=2

Step-by-step explanIation:

I hope this is right  :)

The numbers form a triangular pattern, but the pattern starts at 1, so 1 is a triangular number.

Hence, The numbers form a triangular pattern, but the pattern starts at 1, so 1 is a triangular number.

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The sentence is true because the expressions are equivalent.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=7x+3. Where:

m= the slope.

b= the constant term that represents the y-intercept

For the given example: m=7 and b=3.

The linear equations are considered equivalent when they are equal.

The given equations are 5y+4−3y = 2y+4. Solving theses equations, you have:

5y+4−3y = 2y+4

2y+4 = 2y+4

Like the both equation present the slope and the constant term equal, the expressions are equivalent.

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