A mining company is mining silver. The relationship between the mass of the material mined in metric tons and the number of carts required to transport the material is given by the function V(n) = 0.5n. Additionally, the relationship between the amount of silver and the material mined is given by the function G(V) = 0.00001V.
Which function can be used to determine the mass of silver in metric tons as a function of the number of carts required to transport the materials out of the mine?
A)G(V(n))
B)V(G(n))
C)n(G(V))
D)n(V(G))

As there is the highest degree 4 there are four zeros .

Using calculator

the roots are(attached)

The graph is also attached

Answer:

a) 4 roots

b) x = 1 and x = -3

[tex]\textsf{c)} \quad x=1, \quad x=-3, \quad x=\dfrac{-1 + \sqrt{3}i}{2}, \quad x=\dfrac{-1 - \sqrt{3}i}{2}[/tex]

d) see attached

Step-by-step explanation:

Given function:

[tex]f(x)=x^4+3x^3-x-3[/tex]

Part (a)

From inspection of the function, the highest exponent of the polynomial is 4.  Therefore, it is expected that the polynomial will have 4 roots.

Part (b)

To find the rational roots, find values of x where [tex]f(x)=0[/tex]

[tex]f(1)=(1)^4+3(1)^3-1-3=0[/tex]

[tex]f(-3)=(-3)^4+3(-3)^3-(-3)-3=0[/tex]

Therefore, the rational roots are: x = 1 and x = -3

Part (c)

As there are only 2 rational roots, the other 2 roots must be complex roots. To find these, first factor the polynomial using the 2 rational roots found in part (b):

[tex]\implies f(x)=(x-1)(x+3)(x^2+bx+1)[/tex]

[tex]\implies f(x)=(x^2+2x-3)(x^2+bx+1)[/tex]

[tex]\implies f(x)=x^4+bx^3+x^2+2x^3+2bx^2+2x-3x^2-3bx-3[/tex]

[tex]\implies f(x)=x^4+(2+b)x^3+(2b-2)x^2+(2-3b)-3[/tex]

Compare coefficients to find b:

[tex]\implies (2+b)x^3=3x^3[/tex]

[tex]\implies b=1[/tex]

Therefore the fully factored function is:

[tex]\implies f\:\!(x)=(x-1)(x+3)(x^2+x+1)[/tex]

Therefore:

[tex](x^2+x+1)=0[/tex]

To find the complex roots, use the quadratic formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

[tex]\implies x=\dfrac{-1 \pm \sqrt{1^2-4(1)(1)}}{2(1)}[/tex]

[tex]\implies x=\dfrac{-1 \pm \sqrt{-3}}{2}[/tex]

[tex]\implies x=\dfrac{-1 \pm \sqrt{3}\sqrt{-1}}{2}[/tex]

[tex]\implies x=\dfrac{-1 \pm \sqrt{3}i}{2}[/tex]

Therefore, all the roots of the function are:

[tex]x=1, \quad x=-3, \quad x=\dfrac{-1 + \sqrt{3}i}{2}, \quad x=\dfrac{-1 - \sqrt{3}i}{2}[/tex]

Part (d)

End behaviors:

As the degree of the function is even and the leading coefficient is positive, the end behaviors are:

[tex]\textsf{As } x \rightarrow - \infty, \:\: f(x) \rightarrow + \infty[/tex]

[tex]\textsf{As } x \rightarrow + \infty, \:\: f(x) \rightarrow + \infty[/tex]

y-intercept

Substitute x = 0 into the function:

[tex]f\:\!(0)=(0)^4+3(0)^3-(0)-3=-3[/tex]

Therefore, the y-intercept is (0, -3)

To find the approximate x-coordinates of the turning points (stationary points), differentiate the function, set it to zero, then solve for x:

[tex]f'\:(x)=4x^3+9x^2-1[/tex]

[tex]\implies 4x^3+9x^2-1=0[/tex]

Using a calculator, x ≈ -2.2, x ≈ -0.4, x ≈ 0.3

Therefore the approximate coordinates of the turning points are:

(-2.2, -9.3),  (-0.4, -2.7)  and (0.3, -3.2)

We don't need to plot these points, they merely help us with the approximate shape of the curve.

Answer:

45.6 x 10^3

Step-by-step explanation:

76 can be expressed as 7.6 x 10^1.

Now, you can multiply the two values together.

7.6 x 6.0 is 45.6.

Then, add the two exponents together:

1 + 2 = 3

45.6 x 10^3

Answer:

6 and 11

Step-by-step explanation:

n1 = n + 5

ns^2 = 3 + 3nb

6^2 = 3 + 3(11)

36 = 3 + 33

11 = 6 + 5

Answer:

2: 86

3:64

4: 77

6: 3

7:12

8: O=110 X:110

Step-by-step explanation:

Number 2 shows what is called a central angle. Central Angles are equivalent to the ark length

Number 3 shows an Inscribed angle. These angles are half of the ark but in your question, it is twice the angle measurement

Number 4 you want to divide the ark length by two when the angle is not given. And when the angle is given you want to mutilate by two

Number 6 is Overlapping Ark which means they are both congruent to each other because the ark is equivalent to each other.

Number 7 is x=12 because 5x+12 is twice the measure of 3x

Number 8 o=110 because a circle has 360 degrees so you want to add them up and then subtract that from 360. x is also 110 degrees because it is a central angle, which is the same amount of degrees as the ark length.

The distance between a and b is 5 units.

An equilateral triangle has three sides that have the same length. The triangle is defined as the plane two-dimensional figure with three sides having the sum of the three angles of 180 degrees.

Since the figure is missing in the question so I have attached the figure of the points on the graph for better understanding.

The given coordinates are as follows:-

a (-3, 2)

b (-6, -2)

c (0, -2)

Use the distance formula,[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] , to find ab.

ab  = √[(−6−(−3))² + (−2−2)²]

ab  = √25

ab  = 5 units

Therefore the distance between A and B is 5 units.

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Answer:

y= -4x/9+4

Step-by-step explanation:

4x+9y=36 (move 4x)

9y=-4x+36 (divide by 9)

y= -4/9x+36/9

y= -4x/9+4

Answer:

1. 84º

Step-by-step explanation:

1. CEB = 180º - 96º

  CEB = 84º

you do the rest

Answer:

Step-by-step explanation:

Answer:

∠ECB

Step-by-step explanation:

The angle which is vertical to ∠HCI is ∠ECB.

A vertical angle has the equal angle measure to the angle opposing it.

Hence, our answer is understood.

Answer:

70

Step-by-step explanation:

using the Pythagorean theorem we see that the side length is 29, meaning the perimeter is 70

Answer:

The line would be a solid line.

Step-by-step explanation:

To draw inequality graphs, solid lines represent [tex]\geq or \leq[/tex] and dotted lines show > or <. Hope this helps.

Answer: 40.69°

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Answer:

[tex]\pi * 9[/tex] or 28.28

Step-by-step explanation:

With the equation of [tex]A = \pi * r^2[/tex], We find that the r - (radius) = 3, so it would be [tex]\pi *3^2\\[/tex] or [tex]\pi * 9[/tex]

Hope This Helps!

Answer:

the graph has a minimum

Step-by-step explanation:

the minimum is -9

Answer:

the graph has a minimum & the vertex is located at (-1,-9)

Step-by-step explanation:

Minimum is where its like at the bottom opening down. And the vertex is the x value of the minimum point. Maximum is the opposite where the curve is facing upwards and is the highest point where the vertex is the x value of the maximum or highest point.

Answer:

1=6

Step-by-step explanation:

Divide both sides of the equation by the same term

1=6

Answer:

hope u understand...........

The phrase in the excerpt that is most similar to the modern language used in writing is "You are here to enjoy every moment".

It corresponds to a language that is in current use in society, being a term used to differentiate a language that is still used for communication from a language that is not used anymore today, such as Latin.

Therefore, the phrase relates to the values ​​of modern society with regard to the use of words and the message that the author wants to convey to readers.

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Answer:

b

Step-by-step explanation:

Answer:

[tex]y=\frac{2}{3}x+4[/tex]

Step-by-step explanation:

Calculate the slope by using rise over run to get 2/3x

The Y Intercept is 4

For the first statement the converse is two angles are equal if the two angles are both obtuse, for second "x = -5 if the equation is  3 - 2x = 13" for third Two angles are not equal if 2 angles are supplementary.

A conditional statement with the antecedent and effect reversed is known as a converse statement.

We have statement:

1. If two angles are both obtuse, the two angles are equal.

Converse: The two angles are equal if the two angles are both obtuse.

2. If 3 - 2x = 13, then x = -5.

Converse: x = -5 if the equation is  3 - 2x = 13

3. If 2 angles are supplementary, then they are not equal.

Converse: Two angles are not equal if 2 angles are supplementary.

Thus, for the first statement the converse is two angles are equal if the two angles are both obtuse, for second "x = -5 if the equation is  3 - 2x = 13" for third Two angles are not equal if 2 angles are supplementary.

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Answer:

B

Explanation:

There are 19 rectangles and 8 circles

19

+8

27 so it would be 27/47

Answer:

It would be 70

Step-by-step explanation:

hope this helped :)

Answer:

(-3, -1.5)

Step-by-step explanation:

Given:

[tex]\boxed{\text{Midpoint of a line segment:} \ \huge\text(\dfrac{x_1 + x_2}{2} ,\dfrac{y_1 + y_2}{2} \text)}[/tex]

Substitute the endpoints of the line segment in the midpoint:

[tex]\implies \huge\text[\dfrac{-2 + (-4)}{2} ,\dfrac{6 + (-9)}{2} \text][/tex]

Simplify the coordinates in the midpoint:

[tex]\implies \huge\text[\dfrac{-2 - 4}{2} ,\dfrac{6 - 9}{2} \text] \implies \huge\text[\dfrac{-6}{2} ,\dfrac{-3}{2} \text]\implies \huge\text[-3 ,-1.5 \text][/tex]

Thus, the coordinate of the midpoint is (-3, -1.5)

Answer:  Other animals

Step-by-step explanation:

Answer:

9c² -30c + 25

Step-by-step explanation:

Perfect square trinomial: (a - b)² = a² - 2ab + b²

(3c - 5)²

(3c)² -2(3c * 5) + 5²

9c² -2(15c) + 5²

9c² -30c + 25

Final answer: 9c² -30c + 25

Hope this helps!

Hi!

Given:

[tex](3c-5)^2[/tex]

As this is squared, we are simply multiplying the given expression by itself, like so:

[tex](3c-5)(3c-5)[/tex]

Now, we can use the Distributive Property to solve, using the FOIL Method:

[tex](3c-5)(3c-5)[/tex]

[tex]9c^2-15c-15c+25[/tex]

Combine like terms:

[tex]9c^2-30c+25[/tex]

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The measure of minor arc BC is equal to ∠BPC which is 147 degrees.

An equation is an expression that shows the relationship between two or more variables and numbers.

From the diagram:

4k + 159 = 2k + 153 (vertical opposite angles are equal)

4k + 159 = 2k + 153

k = -3

Arc Bc = 4k + 159 = 4(-3) + 159 = 147

The measure of minor arc BC is equal to ∠BPC which is 147 degrees.

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Answer: 147 :)

Step-by-step explanation:

khan academy

Answer:

1/2

Step-by-step explanation:

number of required outcome ÷number of possible outcomes

1/2

Answer:

Irrational

Step-by-step explanation:

If the number goes on and on it’s irrational

Hope this helps! ;-)

Answer:

It is not rational because the square root of 3 is not a fraction nor a repeating decimal.

The volume of the stump in cubic inches is 18095.6  if the Ashley measures its height as 1.2 ft and its radius as 20 in.

In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the volume of the cylinder is given by:

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

We have h = 1.2 ft = 1.2×12 = 14.4 inches

r = 20 inches

[tex]\rm V = \pi (20)^2 \times 14.4[/tex]

After calculating, we get:

V = 18095.57 ≈ 18095.6 cubic inches

Thus, the volume of the stump in cubic inches is 18095.6  if the Ashley measures its height as 1.2 ft and its radius as 20 in.

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Answer:

Step-by-step explanation:

2