please help me?

please and thank you!

The graph will cross the x-axis if the multiplicity of the real root is odd.

What is polynomial?

In arithmetic, a polynomial is an expression consisting of indeterminates and coefficients, that involves solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Main body:

For polynomials, the graph will cross the x-axis if the multiplicity of the real root is odd, and just touch the x-axis if the multiplicity of the real root is even. (The multiplicity of the root is the number of times it occurs as a root)

(a) y=(x+1)^2(x-2) The graph crosses at x=2 (multiplicity 1) but touches at x=-1 (mulitplicity 2)

(b) y=(x-4)^3(x-1)^2 The graph crosses at x=4 (multiplicity 3) but touches at x=1 (m=2)

(c) y=(x-3)^2(x+4)^4 The graph touches at x=3 and x=-4 as the multiplicities are both even.

The graphs: (a) black, (b) red, (c) green

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Answer:

One kids ticket is $4.80 and one adult ticket is $9.60

Step-by-step explanation:

Create a system of equations where k is the cost of a kids ticket and a is the cost of an adult ticket:

6k + 2a = 48

k = 1/2a

Solve by substitution by substituting the second equation into the first one:

6k + 2a = 48

6(1/2a) + 2a = 48

Simplify and solve for a:

3a + 2a = 48

5a = 48

a = 9.6

Find the cost of a kids ticket by dividing this by 2, since they are on sale for half the price of adult tickets.

9.6/2

= 4.8

One kids ticket is $4.80 and one adult ticket is $9.60

C. The slope is negative two-thirds, and the y-intercept is 8. The candle starts at a height of 8 inches and decreases two-thirds of an inch every hour.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

The relationship of the candlestick between height and time is represented by a straight line passing through the points (0, 8) and (3, 6).

Slope(m) = (6 - 8)/(3 - 0).

Slope(m) = - 2/3.

Taking any of the points we have,

6 = - (2/3)×3 + b.

6 = - 2 + b.

b = 8.

y = - (2/3)x + 8.

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Answer:

D) \(6+2\sqrt{6}\)

Step-by-step explanation:

\(2\sqrt{3} *(\sqrt{2} +\sqrt{3} )\\\\6+2\sqrt{6}\)

The partial derivatives are:

∂ z / ∂ x = − [ 5x⁴z⁶ ] / [ 6x⁵z⁵ + 6z⁵y⁴cos ( y⁴z⁶ )]

∂ z / ∂ y  = − [ 4y³z⁶ cos ( y⁴ z⁶ ) ] / [ 6x⁵z⁵ + 6z⁵y⁴cos ( y⁴z⁶ )]

We have,

f(x, y, z) = x⁵z⁶ + sin (y⁴z⁶) + 2 = 0

Now, partially differentiating we get

∂ z / ∂ x

= - [ ∂ F / ∂ x ] /  [ ∂ F / ∂ z  ]

= − [ 5x⁴z⁶ ] / [ 6x⁵z⁵ + 6z⁵y⁴cos ( y⁴z⁶ )]

and,

∂ z / ∂ y

= - [ ∂ F / ∂ y ] / [ ∂ F / ∂ z ]

= − [ 4y³z⁶ cos ( y⁴ z⁶ ) ] / [ 6x⁵z⁵ + 6z⁵y⁴cos ( y⁴z⁶ )]

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Answer:

Bree does

Step-by-step explanation:

The dimensions of the vegetable garden are :

Length = 14 feet

Width = 11 feet

Let's start by using the formula for the area of a rectangle:
Area = Length x Width

We know that the area of the vegetable garden is 154 square feet, so we can plug that in:
154 = Length x Width

Next, we're given that the length is 3 feet longer than the width, so we can write:
Length = Width + 3

We can substitute that expression for Length into the area formula:
154 = (Width + 3) x Width

Expanding the brackets:
154 = Width^2 + 3Width

Now we have a quadratic equation, which we can solve by either factoring or using the quadratic formula. I'll use the quadratic formula here:

First, we need to put the equation into standard form (ax^2 + bx + c = 0):
Width^2 + 3Width - 154 = 0

a = 1, b = 3, c = -154

Plugging those values into the quadratic formula:
Width = (-b ± sqrt(b^2 - 4ac)) / 2a
Width = (-3 ± sqrt(3^2 - 4(1)(-154))) / 2(1)
Width = (-3 ± sqrt(625)) / 2

We can simplify the square root:
Width = (-3 ± 25) / 2

So we have two possible solutions:
Width = 11 or Width = -14

Since we're dealing with a physical garden, the width can't be negative, so we'll discard that solution.

Now we can use the expression for Length that we found earlier:
Length = Width + 3
Length = 11 + 3 = 14

So the dimensions of the vegetable garden are 11 feet by 14 feet.

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Answer:

The width of the actual pool is 12 meters

Step-by-step explanation:

You can put Kiara's scale into a ratio or fraction to help visualize it better: 13/6. Now, let's put what we do know for the other ratio into a fraction. we know that the pool is 26 centimeters wide, and since the 26 matches with the 13, that goes in the numerater. since we don't know the denominator, we can just put 26/x (you can use whatever letter you like but I'll use x here)

So in order to get 13/6 to 26/x, we need to find how to figure out what we are doing to the original fraction. Since 13 x 2= 26, it looks like we are multiplying the ratios by 2. Now that we know that, we can multiply the denominator (6) by 2 to equal 12, our answer.

Hope this helps :)    

A point that represents how Dre can spend money on spray paint is plotted on the proportional relationship graphed at the end of the answer.

The money spent after sales tax is obtained multiplying the money spent before sales tax by a constant, hence a proportional relationship models the situation.

The general format of a proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality.

In this problem, the sales tax rate is of 10%, meaning that the total amount paid is composed as follows:

Considering x as the cost before sales tax, the equation is given as follows:

y = x + 0.1x

y = 1.1x.

Meaning that one point is given as follows:

(5,5.5).

Meaning that when the cost before sales tax is of $5, the cost including sales tax is of $5.5.

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Answer:

hlw its jess

your answer is here

Step-by-step explanation:

hope it may help you

The required value of y for the unit circle is: 2/3

The circle is defined as the locus of a point whose distance from a fixed point is constant i.e center (h, k).

The equation of the circle is given by:

(x - h)² + (y - k)² = r²

where:

h, k is the coordinate of the center of the circle on coordinate plane.

r is the radius of the circle.

Here,

Equation of the unit circle is given as,

x² + y² = 1

Now substitute the given value in the equation,

5/9 + y² = 1

y² = 1 - 5/9

y² = 4/ 9

y = √(4/9)

y = 2/3

Thus, the required value of y for the unit circle is 2/3

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Celine has already knitted 0.8 meters. Her final result should be 1.2 meters.

To calculate how many meters Celine has to knit we should subtract the already knitted length of scarf from the entire length. This give the equation:

\(x=1.2m-0.8m\)

x is the unknown

x = 0.4 meters

One of the factors is present in all of the items mentioned. The order of the value of the other factor will match the order of the value of the product.

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The quadratic equation is `8x² - 18x - 5 = (8x - 5)(x - 1)`.Explanation: Here's how to factor the quadratic equation completely: 8x² - 18x - 5 is a quadratic equation.

Step 1: Multiply 8 and -5 together to get -40.Step 2: Find two numbers that have a product of -40 and a sum of -18. Since -20 and 2 have a product of -40 and a sum of -18, they're the two numbers we need.Step 3: Break the -18x term into -20x + 2x. Step 4: Rewrite the quadratic equation as follows: 8x² - 20x + 2x - 5 Step 5: Group the first two terms and the last two terms: 4x(2x - 5) + 1(2x - 5)Step 6: Factor out the (2x - 5) factor:(2x - 5)(4x + 1).

Therefore, the quadratic equation is factored completely into (8x - 5)(x - 1)

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In the first iteration, we obtained approximate values of x1(1) ≈ 1.67 and x2(1) = 8. In the second iteration, we updated the values to x1(2) ≈ -3.67 and x2(2) ≈ 26.35. In the third iteration, the values were further updated to x1(3) ≈ -38.77 and x2(3) ≈ 198.85.

To solve the set of linear algebraic equations using the Gauss-Seidel method with the given initial values and accuracy requirement, we can follow these steps:

Step 1: Rearrange the equations in terms of x1 and x2:

Equation 1: 3x1 + 2x2 = 5

Equation 2: 5x1 + x2 = 8

Step 2: Write the equations in iterative form:

Equation 1: x1(k+1) = (5 - 2x2(k)) / 3

Equation 2: x2(k+1) = (8 - 5x1(k)) / 1

where x1(k) and x2(k) represent the initial values and x1(k+1) and x2(k+1) represent the updated values in the kth iteration.

Step 3: Initialize the values and set the desired accuracy:

Let x1(0) = 0 and x2(0) = 0 (given initial values)

Set the desired accuracy as ε = 0.03

Step 4: Perform iterations until the desired accuracy is reached:

Iterate the following steps until the condition |x1(k+1) - x1(k)| < ε and |x2(k+1) - x2(k)| < ε are satisfied:

- Calculate the updated values using the iterative equations:

 x1(k+1) = (5 - 2x2(k)) / 3

 x2(k+1) = (8 - 5x1(k)) / 1

- Calculate the differences:

 Δx1 = |x1(k+1) - x1(k)|

 Δx2 = |x2(k+1) - x2(k)|

- Check if the differences are less than ε:

 If Δx1 < ε and Δx2 < ε, exit the iteration.

Step 5: Output the solution:

The solution will be the values of x1 and x2 obtained in the final iteration.

Let's perform the iterations:

Iteration 1:

x1(1) = (5 - 2x2(0)) / 3 = (5 - 2(0)) / 3 ≈ 1.67

x2(1) = (8 - 5x1(0)) / 1 = (8 - 5(0)) / 1 = 8

Iteration 2:

x1(2) = (5 - 2x2(1)) / 3 = (5 - 2(8)) / 3 ≈ -3.67

x2(2) = (8 - 5x1(1)) / 1 = (8 - 5(-3.67)) / 1 ≈ 26.35

Iteration 3:

x1(3) = (5 - 2x2(2)) / 3 = (5 - 2(26.35)) / 3 ≈ -38.77

x2(3) = (8 - 5x1(2)) / 1 = (8 - 5(-38.77)) / 1 ≈ 198.85

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The extreme values of f(x, y) = xy occur at the points (2, 1) and (-2, -1) on the ellipse \(3x^{2} +2y^{2} =1\).

To find the extreme values of f(x, y) = xy on the ellipse \(3x^{2} +2y^{2} =1\), we can use the method of Lagrange multipliers.

Define the function g(x, y) = \(3x^{2} +2y^{2} -1\). We need to find points (x, y) where the gradient of f is proportional to the gradient of g:

∇f = λ∇g

The gradient of f is ∇f = (y, x), and the gradient of g is ∇g = (6x, 4y). Therefore, we have the following system of equations:

y = 6λx
x = 4λy

Substitute the second equation into the first:

y = 6λ(4λy)
y = \(24λ^{2y}\)

If y ≠ 0, then 1 = \(24λ^{2}\), and λ = ±1/2. Plugging this value into the second equation gives x = ±2. Thus, we have two potential extreme points: (2, 1) and (-2, -1).

Now consider the case when y = 0. The constraint equation becomes \(3x^{2} =1\), and x = ±1/√3. However, these points correspond to f(x, y) = 0, which is not an extreme value.

Therefore, the extreme values of f(x, y) = xy occur at the points (2, 1) and (-2, -1) on the ellipse \(3x^{2} +2y^{2} =1\).

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The number of oranges and the number of mangoes that she bought will be 20 and 5.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

A woman saw oranges and mangoes at the market.

She bought some oranges at 35 cents each and some mangoes at $1.00 each.

If she bought a total of 25 fruits which had a total cost of $12.00.

Let x be the number of oranges and y be the number of mangoes.

Then the equations will be

       x + y = 25  ...1

0.35x + y = 12  ...2

By solving equations 1 and 2, we have

x = 20 and y = 5

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To prove that o(n) = n, we will use mathematical induction to show that φ(n) has an order of n for any positive integer n.

We proceed with mathematical induction.
Base Case: For n = 1, φ(1) = 1, and since φ(1) = 1, the order of φ(1) is indeed 1.
Inductive Step: Assume that for some k ≥ 1, the order of φ(k) is k. We need to prove that the order of φ(k+1) is k+1.
Since φ is a group isomorphism, φ(k+1) = φ(k) + φ(1). By the induction hypothesis, the order of φ(k) is k. Additionally, φ(1) = 1, so the order of φ(1) is 1.

Now, suppose the order of φ(k+1) is m. This means that (φ(k+1))^m = e, where e is the identity element in G₂.
Expanding this, we have (φ(k) + φ(1))^m = e. By applying the binomial theorem, we can show that (φ(k))^m + m(φ(k))^(m-1)φ(1) + ... = e.
Since φ(k) has an order of k, (φ(k))^k = e, and all other terms in the expansion have an order higher than k. Thus, we can simplify the equation to (φ(k))^k + m(φ(k))^(m-1)φ(1) = e.

Since φ(1) = 1, the term m(φ(k))^(m-1)φ(1) reduces to m(φ(k))^(m-1). But φ(k) has an order of k, so (φ(k))^(m-1) has an order of k. Hence, m(φ(k))^(m-1) = 0. Since e is the identity element, this implies m = 0.

Therefore, the order of φ(k+1) is k+1, which completes the inductive step.
By mathematical induction, we have proven that for all positive integers n, the order of φ(n) is n.

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a) The conditional probability is: 6/13

b) The conditional probability is: 6/22

Given data ,

a)

To find P(small | coffee), we use the formula for conditional probability or the Bayes theorem.

P(small | coffee) = P(small and coffee) / P(coffee)

where the likelihood that an event will occur based on the likelihood that a comparable outcome will occur in the future.

And , P ( A | B ) = [ P ( B | A ) P ( B ) ] / P ( A )

P ( small | coffee ) = ( 6/34 )

P(coffee) = ( 13/34 )

So, P(small | coffee) = 6/13

b)

The conditional probability is:

P ( coffee | small ) = P(coffee and small) / P(small)

P ( coffee | small ) = 6/22

Hence , the Bayes theorem is solved.

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Answer:

3) if you were to draw vertical lines through this graph you would have instances where an 'x' value would have more than one unique 'y' value

Step-by-step explanation:

functions must have one unique 'y' value for each 'x' value

The third graph represent a relation that is not a function

A relation is a function if it has only One y-value for each x-value.

The third one doesn't represent a function, because for some values of "x", you get two different values for "y" (which should not happen, if that were a function).

In order to see it better, you can trace a vertical line onto that graph.

If that line and the graph intersects in more than one point, then that graph doesn't represent a function.

In every function, you must have a single "y" value for each "x" in the domain.

Hence, the third graph represent a relation that is not a function

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The equation of the parabola with focus (2,5) and directrix x=18 is (x - 18)² + (y - 5)² = (y - (5 + (18 - 2) / 2))².

A parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating

straight line of that surface.

The focus of a parabola is a fixed point on the interior of a parabola used in the formal definition of the curve.

The directrix is a straight line perpendicular to the axis of symmetry and placed symmetrically with respect to the focus.

The axis of symmetry is the line through the focus and perpendicular to the directrix.

The vertex of a parabola is the point where its axis of symmetry intersects the curve. It is the point where the parabola changes direction or "opens

up" or "opens down.

The directrix is a fixed straight line used in the definition of a

parabola. It is placed such that it is perpendicular to the axis of symmetry and at a distance from the vertex equal to the

distance between the vertex and focus. It is the line that is equidistant to the focus and every point on the curve.Here's

the solution to the given problem:

The distance between the directrix and the focus is equal to p = 16 (since the directrix is x = 18, the parabola opens to the left, so the distance is measured horizontally)

The vertex is (h,k) = ((18+2)/2,5) = (10,5)

Then we can use the following formula: (x - h)² = 4p(y - k)

Substitute the vertex and the value of p. (x - 10)² = 64(y - 5)

Expand and simplify. (x - 10)² + (y - 5)² = 64(y - 5)

The equation of the parabola is (x - 10)² + (y - 5)² = 64(y - 5).

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Answer:

D $2.60

Step-by-step explanation:

because 6.5% of 40 is 2.6

hope this helps

plz can i get brainliest

The statements with symbolic notation using the given predicates logic are:

1. Nothing strictly physical has consciousness. ∀x(Px → ¬Cx)

2. Minds exist. ∃x(Mx)

3. All minds have consciousness and subjectivity. ∀x(Mx → (Cx ∧ Sx))

4. No minds are strictly physical things. ∀x(Mx → ¬Px)

Predicate logic is a formal system of symbolic logic that extends propositional logic by introducing variables, predicates, quantifiers, and quantified statements. It allows for the representation and manipulation of relationships between objects, properties, and relations.

In predicate logic, symbols are used to represent various components:

1. Variables: Variables are used to represent individual elements or objects in a domain of discourse. They are typically denoted by lowercase letters such as x, y, z, and so on.

2. Predicates: Predicates are used to express properties or relations between objects. They are represented by uppercase letters followed by parentheses, such as P(x), Q(x, y), R(x, y, z), where x, y, z are variables.

3. Quantifiers: Quantifiers are used to express the scope of variables in a logical statement. The two main quantifiers are:

- Universal quantifier (∀): It is used to express that a statement holds for all elements in the domain. For example, ∀x P(x) means "For all x, P(x)."

- Existential quantifier (∃): It is used to express that there exists at least one element in the domain for which a statement holds. For example, ∃x P(x) means "There exists an x such that P(x)."

4. Logical symbols: Predicate logic uses logical symbols to represent logical connectives, negation, implication, and equivalence. The main logical symbols are:

- Conjunction (∧): Represents logical "and."

- Disjunction (∨): Represents logical "or."

- Negation (¬): Represents logical "not."

- Implication (→): Represents logical "if-then."

- Equivalence (↔): Represents logical "if and only if."

These symbols are used to construct complex logical statements by combining predicates, variables, and quantifiers. The goal is to provide a precise and formal language for reasoning about relationships and properties within a domain of discourse.

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The surface area of the portion S of the cone z^2 = x^2 + y^2 where z>/ 0 contained within the cylinder y^2 + z^2 < 1 is 8π.

The cone is defined by the equation z^2 = x^2 + y^2.

The cylinder is defined by the equation y^2 + z^2 < 1.

The intersection of the cone and the cylinder is a surface that is part of a cone and part of a cylinder.

The surface area of the cone is given by the formula A = πr^2h, where r is the radius of the base and h is the height of the cone.

The radius of the base of the cone is equal to 1, and the height of the cone is equal to √2. Therefore, the surface area of the cone is π(1)^2(√2) = √2π.

The surface area of the cylinder is given by the formula A = 2πrh, where r is the radius of the base and h is the height of the cylinder.

The radius of the base of the cylinder is equal to 1, and the height of the cylinder is equal to 1. Therefore, the surface area of the cylinder is 2π(1)(1) = 2π.

The surface area of the intersection of the cone and the cylinder is equal to the surface area of the cone minus the surface area of the cylinder. Therefore, the surface area of the intersection is √2π - 2π = 8π.

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The CDF of Y evaluated at y = 0.72 is 0.1296.

Since X1 and X2 are independent and uniformly distributed over [0, 2], their joint density function is:

f(x1, x2) = 1/4, for 0 ≤ x1 ≤ 2 and 0 ≤ x2 ≤ 2

To find the CDF of Y, we can use the fact that:

Fy(y) = P(Y ≤ y) = P(max(X1, X2) ≤ y)

This event can be split into two cases:

X1 and X2 are both less than or equal to y:

In this case, Y will be less than or equal to y.

The probability of this occurring can be calculated using the joint density function:

P(X1 ≤ y, X2 ≤ y) = ∫0y ∫0y f(x1, x2) dx1 dx2

= ∫0y ∫0y 1/4 dx1 dx2

\(= (y/2)^2\)

\(= y^2/4\)

One of X1 or X2 is greater than y:

In this case, Y will be equal to the maximum of X1 and X2.

The probability of this occurring can be calculated as the complement of the probability that both X1 and X2 are less than or equal to y:

P(X1 > y or X2 > y) = 1 - P(X1 ≤ y, X2 ≤ y)

\(= 1 - y^2/4\)

Therefore, the CDF of Y is:

Fy(y) = P(Y ≤ y) = P(max(X1, X2) ≤ y)

= P(X1 ≤ y, X2 ≤ y) + P(X1 > y or X2 > y)

\(= y^2/4 + 1 - y^2/4\)

= 1, for y ≥ 2

\(= y^2/4,\)for 0 ≤ y ≤ 2

To find Fy(0.72), we simply substitute y = 0.72 into the expression for Fy(y):

\(Fy(0.72) = (0.72)^2/4 = 0.1296\)

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Since X1 and X2 are uniformly distributed over [0, 2], their probability density functions (PDFs) are:

fX1(x) = fX2(x) = 1/2, for 0 <= x <= 2

To find the CDF of Y = max(X1, X2), we need to consider two cases:

1. If y <= 0, then Fy(y) = P(Y <= y) = 0

2. If 0 < y <= 2, then Fy(y) = P(Y <= y) = P(max(X1, X2) <= y)

We can find this probability by considering the complementary event, i.e., the probability that both X1 and X2 are less than or equal to y. Since X1 and X2 are independent, this probability is:

P(X1 <= y, X2 <= y) = P(X1 <= y) * P(X2 <= y) = (y/2) * (y/2) = y^2/4

Therefore, the CDF of Y is:

Fy(y) = P(Y <= y) =

0,          y <= 0

y^2/4,      0 < y <= 2

1,          y > 2

To find Fy(0.72), we substitute y = 0.72 into the CDF:

Fy(0.72) = 0.72^2/4 = 0.1296

Therefore, the value of Fy(y) at y = 0.72 is 0.1296.

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Answer:

What?

Step-by-step explanation:

D.

Answer:

See Explanation

Step-by-step explanation:

Given

\(1\ can = 2.2m^2\)

Required

Determine the number of cans for the wall

The dimension of the wall is not given. So, I will use the following assumed values:

\(Length=20m\)

\(Width = 44m\)

First, calculate the area of the wall

\(Area = Length * Width\)

\(Area = 20m * 44m\)

\(Area = 880m^2\)

If \(1\ can = 2.2m^2\)

Then \(x = 880m^2\)

Cross Multiply:

\(x * 2.2m^2 = 1 * 880m^2\)

\(x * 2.2m^2 = 880m^2\)

\(x * 2.2 = 880\)

Make x the subject

\(x = \frac{880}{2.2}\)

\(x = 400\)

400 cans using the assume dimensions.

So, all you need to to is, get the original values and follow the same steps

Answer: 2 and 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

To simplify the expression (-12x³ - 48x²) + (-4x), we can combine like terms by adding the coefficients of the same degree of x.

The like terms in the expression are the terms with x³, x², and x. Let's combine them:

-12x³ + (-4x) = -12x³ - 4x

-48x² + 0 = -48x²

Now, combining these two results, we have:

(-12x³ - 4x) + (-48x²) = -12x³ - 4x - 48x²

Therefore, the simplified expression is -12x³ - 4x - 48x².

None of the provided choices match the simplified expression.