Question 4 Use the Rational Zero Theorem to list all possible rational zeros for the given function. f(x)=-2x^(3)+x^(2)-4x+6

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[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{5}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(~~5 - 2~~)^2 + (~~5 - 1~~)^2} \implies AB=\sqrt{( 3 )^2 + ( 4 )^2} \\\\\\ AB=\sqrt{ 9 + 16 } \implies AB=\sqrt{ 25 }\implies AB=5[/tex]

Answer:

The equation y=225x represents a proportional relationship between the number of hours the field is being rented and the total cost. This means that as the number of hours increases, the total cost will increase proportionally. Therefore, statement D) "The equation shows a proportional relationship, but not a linear relationship" is true based on the given equation.

All the roots of all the polynomials in {f1, ..., fn}.

(a) Let E be an intermediate field of the extension K⊂F and assume that E=K(u1,…,ur) where the ui are (some of the) roots of fεK [x]. Then F is a splitting field of f over K if and only if F is a splitting field of f over E.

(b) We can extend part (a) to splitting fields of arbitrary sets of polynomials by first noting that the field E must contain the coefficients of all the polynomials in the given set. This implies that for a given set of polynomials {f1, ..., fn}, the field F is a splitting field over K if and only if it is a splitting field over E, where E is the smallest field containing the coefficients of {f1, ..., fn}. In other words, F must contain all the roots of all the polynomials in {f1, ..., fn}.

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The distance between London and Cardiff is approximately 241.4 kilometers.

A conversion factor is a ratio in mathematics that is used to change a quantity's unit of measurement. We may represent the same quantity in many units thanks to this link between the two units of measurement. For instance, 1 mile equals 1.60934 kilometres, thus we may multiply the number of miles by this conversion ratio to find the corresponding distance in kilometres. In science, engineering, and daily life, conversion factors are frequently employed to translate units of length, volume,

We know that,

1 mile = 1.60934 kilometers

Thus,

150 miles x 1.60934 kilometers/mile = 241.4 kilometers

Hence, the distance between London and Cardiff is approximately 241.4 kilometers.

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The equation representing filling y in x seconds is given as;

y = 0.8x. Option B

Algebraic expressions are defined as expressions that are composed of terms, variables, constants, coefficients and factors.

They are expressions that are also identified with some mathematical operations, they are;

From the information given, we have that;

24 jars are filled in 30 seconds

Then, for y number of jars of honey, we have x seconds

cross multiply the values, we have;

y = 24x /30

divide the values

y = 0. 8x

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The solution for d in the one-variable equation as required to be determined is; d = 9.

As evident in the task content; the given equation is;

3/4d - 11 = 1/4d - 6½

¾d - 11 = ¼d - 13/2

Therefore, we have that;

¾d - ¼d = 11 - 13/2

½d = 9/2

d = 9

Ultimately, the value of d which holds true for the given equation is; 9.

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Answer:

Step-by-step explanation:

Answer:

Your score is -9.

Step-by-step explanation:

Answer:

18cm^2

Step-by-step explanation:

3×2=6cm^2

2×6=12cm^2

6+12=18cm^2

Therefore , the solution of the given problem of function comes out to be Nolan dropped the ball from a height of 12 units at the beginning.

The study of mathematics includes numbers, symbols, and their parts, as well as anatomy, building, and both actual and hypothetical geographic locations. The relationships between different components, each of which has a corresponding result, are described by a function. A function is made up of a variable of distinct components that, when put together, produce specific results for each input.

Here,

Assume that h represents the original height at which Nolan threw the ball. The object bounces once and rises to a height of 4, so after the bounce it has a height of h + 4.

=> h = k f(1) (1)

where k is a constant that denotes how much energy the object retains after each bounce.

=> h = k(4) (4)

The knowledge that the ball returns to a height of 4 on the first bounce must be used to determine the value of k:

=> 4 = k f(1) (1)

=> 4 = k (4/3)

=> k = 3

When we put this number of k back into the equation as a replacement for h, we get:

=> h = k(4) = 3(4) = 12

Nolan dropped the ball from a height of 12 units at the beginning.

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For 175÷2, the quotient is 87 and remainder is 1

When dividing 175 by 2, we can use long division to find the quotient and remainder.

First, we will divide 2 into the first digit, 1. Since 2 does not go into 1, we will move to the next digit, 7. 2 goes into 7 three times, so we will write 3 above the 7.

Next, we will multiply 3 by 2 to get 6, and subtract this from 7 to get a remainder of 1.

We will then bring down the next digit, 5, and divide 2 into 15. 2 goes into 15 seven times, so we will write 7 above the 5.

Finally, we will multiply 7 by 2 to get 14, and subtract this from 15 to get a remainder of 1.

Therefore, the quotient is 87 and the remainder is 1.

The final answer is:

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Answer:

14.75 + 18.75x ≤ 425

Step-by-step explanation:

Total amount they have is $425

Parking for the entire group = $14.75

If x is the number of persons in the group, the cost of x tickets at $18.75 per head
= 18.75x

The total cost incurred
= Parking Cost + Ticket Cost

= 14.75 + 18.75x

This has to be less than equal to 425

So the inequality is

14.75 + 18.75x ≤ 425

i cannot make out the given answer choices clearly, it appears the constant 425 is on the left side in each answer choice - choose the one which is closest to the given answer

Answer:

It is not clear what you mean by "pre-image" in this context. However, based on the given information, we can say that the second triangle is a dilation of the first triangle.

A dilation is a transformation that changes the size of an object, but not its shape. In this case, the second triangle has the same shape as the first triangle, but its sides are scaled up by a factor of 8/3, which is greater than 1. Therefore, the second triangle is an enlargement (or a magnification) of the first triangle.

Answer: Your welcome!

Step-by-step explanation:

The transformation of the triangle is a reduction. This is because the side of the triangle that was 3 cm has been reduced to 8 cm, while the other two sides have stayed the same. This reduction has resulted in the triangle being smaller than the original triangle.

All of Four table shows the proportionality.

Proportionality refers to any relationship that always has the same ratio. For example, the amount of apples in a crop is proportionate to the number of trees in the orchard, with the proportionality ratio being the average number of apples per tree.

To the proportionality we have to find the rate change of each table

Table 1:

Rate of change

= (4-2)/ (4-0)

= 2/4

= 0.5

Again, (6-4)/ (8-4)

= 2/4

= 0.5

As, the rate of change is constant then the table shows the proportionality.

Table 2:

Rate of change

= (1-0)/ (2-0)

= 1/2

= 0.5

Again, = (2-1)/ (4-2)

= 1/2

= 0.5

As, the rate of change is constant then the table shows the proportionality.

Table 3:

Rate of change

= (3-1)/ 5-0)

= 2/5

= 0.4

Again, (5-3)/ (10-5)

= 2/ 5

= 0.4

As, the rate of change is constant then the table shows the proportionality.

Table 4:

Rate of change

= (7-3)/ (3-0)

= 4/3

Again, (11-7)/ (6-3)

= 4/3

As, the rate of change is constant then the table shows the proportionality.

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Answer: if there is a none of the above answer I would choose that otherwise your best bet might be A.  

Answer:

  27 cm

Step-by-step explanation:

You want the distance from the vertex of an ellipse to the opposite focus if the semi-major axis is 15 cm, and the minor axis is 18 cm.

The square of the distance from the center to either focus is the difference of the squares of the semi-axes. The semi-minor axis is half the  diameter of the ellipsoid.

  c² = 15² -(18/2)² = 225 -81 = 144

  c = √144 = 12 . . . . . cm

The distance from the vertex (V) to the opposite focus is the distance from vertex to center plus the distance from center to focus:

  15 cm +12 cm = 27 cm

The kidney stone should be located 27 cm from the vertex for greatest effect.

The inverse of f(x)=−8x+9 is y = (-x + 9)/8.

The inverse of a function is found by switching the x and y variables and solving for y. This is done to find the function that will undo the original function.

To find the inverse of f(x)=−8x+9, we will follow these steps:

1. Switch the x and y variables: x = -8y + 9
2. Solve for y by isolating the y variable on one side of the equation:
x - 9 = -8y
(x - 9)/-8 = y
3. Simplify the equation by dividing the numerator and denominator by -1:
y = (-x + 9)/8

Therefore, the inverse of f(x)=−8x+9 is y = (-x + 9)/8.

Note that we do not need to use parentheses around the denominator since it is a single term. We also do not need to use the term "inverse" in our answer since we are simply finding the inverse of the function. The terms "denominator" and "parentheses" are also not needed in our answer since they do not apply to this specific problem.

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Taking into account the definition of molarity, the mass of MgBr₂ in 215 mL of a 0.350 M solution of MgBr₂ is 13.85 grams.

Molarity is a measure of the concentration of a solution expressed in the number of moles dissolved per liter of solution.

This is, the molarity indicates the number of moles of solute that are dissolved in a given volume.

The molarity of a solution is calculated by dividing the moles of solute by the volume of the solution:

molarity= number of moles of solute÷ volume

Molarity is expressed in units moles/L.

The molar mass of substance is a property defined as the amount of mass that a substance contains in one mole.

In this case, you have:

Replacing in the definition of molarity:

0.350 M= number of moles of solute÷ 0.215 L

Solving:

0.350 M× 0.215 L= number of moles of solute

0.07525 moles= number of moles of solute

Being the molar mass of MgBr₂ 184.11 g/mole, the mass of the compound is calculated as:

mass of MgBr₂= 0.07525 moles× 184.11 g/mole

mass of MgBr₂= 13.85 grams

Finally, the mass of MgBr₂ is 13.85 grams.

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The intersection point of ℓ and Q is (1, 1, 2.5) is not in any of the option.

To find the intersection point of ℓ and Q, we need to find a point that lies on both the line and the plane. We can do this by finding the equation of the line and the equation of the plane, and then solving for the point where they intersect.

First, let's find the equation of the line ℓ. We can use the formula for a line passing through two points:

(x - x1) / (x2 - x1) = (y - y1) / (y2 - y1) = (z - z1) / (z2 - z1)

Plugging in the points (1, 1, 1) and (2, 0, 1), we get:

(x - 1) / (2 - 1) = (y - 1) / (0 - 1) = (z - 1) / (1 - 1)

Simplifying, we get:

x - 1 = -y + 1 = 0

So the equation of the line is x + y = 2.

Next, let's find the equation of the plane Q. We can use the formula for a plane passing through three points:

| x - x1  y - y1  z - z1 |
| x2 - x1  y2 - y1  z2 - z1 | = 0
| x3 - x1  y3 - y1  z3 - z1 |

Plugging in the points (0, 0, 0), (1, 2, 2), and (1, 0, 1), we get:

| x   y   z |
| 1   2   2 | = 0
| 1   0   1 |

Expanding the determinant, we get:

x(2 - 0) - y(2 - 1) + z(0 - 2) = 0

Simplifying, we get:

2x - y - 2z = 0

So the equation of the plane is 2x - y - 2z = 0.

Now we can solve for the intersection point of the line and the plane by substituting the equation of the line into the equation of the plane:

2(x + y) - y - 2z = 0

2x + 2y - y - 2z = 0

2x + y - 2z = 0

Since x + y = 2, we can substitute 2 for x + y:

2(2) + y - 2z = 0

4 + y - 2z = 0

y - 2z = -4

Now we can solve for y in terms of z:

y = 2z - 4

And substitute this back into the equation of the line:

x + (2z - 4) = 2

x = 2 - 2z + 4

x = 6 - 2z

Now we have two equations with two unknowns:

y = 2z - 4
x = 6 - 2z

We can solve for z by setting the two equations equal to each other:

2z - 4 = 6 - 2z

4z = 10

z = 2.5

And then solve for x and y:

y = 2(2.5) - 4 = 1
x = 6 - 2(2.5) = 1

So the intersection point of ℓ and Q is (1, 1, 2.5).

The correct answer is none of the options given.

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The height (in inches) of a triangle with an area of 720 square inches and base of 32 inches is 45 inches.

The height of a triangle can be found using the formula for the area of a triangle: A = (1/2)bh, where A is the area, b is the base, and h is the height.

In this case, we are given the area (720 square inches) and the base (32 inches) and are asked to find the height.

First, we can plug in the given values into the formula:

720 = (1/2)(32)(h)

Next, we can simplify the equation by multiplying both sides by 2:

1440 = 32h

Finally, we can solve for the height by dividing both sides by 32:

h = 45 inches

Therefore, the height of the triangle is 45 inches.

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Answer:

832

Step-by-step explanation:

The first step is to add 1 + 0.65 which is 1.65. Then you do 1.65 times itself 7 times which equals 33. You multiply 33 • 25 which is 832.

The probability that the distance between them is more than the radius of the circle is given as follows:

0.5 = 50%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

For the circle, we have that the radius is the distance between any point on the circumference of the circle, and the center.

The largest distance is the diameter, which is the distance between two points on the circumference of the circle, passing through the center.

The diameter is twice the radius, hence the probability is given as follows:

p = r/2r

p = 1/2

p = 0.5 = 50%.

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Shape A is Convex and Hexagon.

Shape B is Concave and Hexagon.

Shape C is Convex and Pentagon.

Shape D is Concave and Hexagon.

Shape E is Concave and Pentagon.

Shape F is Convex and Pentagon.

Polygons are closed figures which has at least three set of line segments joined together.The polygon with the least number of sides is a triangle.

As per the given data:

The shape of the figures is given.

The shapes can be classified as:

Concave, Convex, Hexagon, Pentagon.

Concave polygons are the one with alteast one of the vertices pointing inwards toward the shape.

Convex polygons are the one with all the vertices pointing outwards from the shape.

A Hexagon can be defined as a closed two-dimensional polygon with six sides.

A Pentagon can be defined as a closed two-dimensional polygon with five sides.

Consider the shape A:

It has 6 sides and all vertices pointing outwards.

Shape A is Convex and Hexagon.

Consider the shape B:

It has 6 sides and some vertices pointing inwards.

Shape B is Concave and Hexagon.

Consider the shape C:

It has 5 sides and all vertices pointing outwards.

Shape C is Convex and Pentagon.

Consider the shape D:

It has 6 sides and one vertice pointing inwards.

Shape D is Concave and Hexagon.

Consider the shape E:

It has 5 sides and one vertice pointing inwards.

Shape E is Concave and Pentagon.

Consider the shape F:

It has 5 sides and all vertices pointing outwards.

Shape F is Convex and Pentagon.

Hence, Shape A is Convex and Hexagon. Shape B is Concave and Hexagon. Shape C is Convex and Pentagon. Shape D is Concave and Hexagon. Shape E is Concave and Pentagon. Shape F is Convex and Pentagon.

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The system of equations are solved and the value of x and y are 6/5 and -14/5 respectively

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

y = x - 4   be equation (1)

y = 6x - 10   be equation (2)

On simplifying , we get

x - 4 = 6x - 10

Subtracting x on both sides , we get

5x - 10 = -4

Adding 10 on both sides , we get

5x = 10 - 4

5x = 6

Divide by 5 on both sides , we get

x = 6/5

So , the value of y = ( 6/5 ) - 4

y = -14/5

Hence , the value of x and y are 6/5 and -14/5 respectively and the equations is solved

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Answer:

Alice paid for the 4 packs of cards with 4 x $2 = $8.

She used 3 ten dollar bills, which is 3 x $10 = $30.

Therefore, the cost of the 2 jigsaw puzzles is:

Total cost of the purchase - Cost of the packs of cards

= ($30 + $4 change) - $8

= $26

So, the total cost of the 2 jigsaw puzzles was $26.

The answer is (D) $26.

Answer:

C. $22

Step-by-step explanation:

You have $30, then you multiply 4x2=8(Price of the Cards)

next subtract the $8 from $30 (30-8)

Your final answer is 22

Answer:

We can use the properties of logarithms to simplify this expression:

log2(9x^10/y²) = log2(9) + log2(x^10) - log2(y²)

Now we can apply the power rule of logarithms to the second term:

log2(x^10) = 10 log2(x)

Substituting back into the original expression:

log2(9x^10/y²) = log2(9) + 10 log2(x) - log2(y²)

This is the simplified form of the expression.

[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{let's use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_3(3^{2x+1})\implies 2x+1[/tex]