Check all that apply.
x2 - 4 = 0
A. X = 4
B. X = -2
C. x = 1
D. X = -4
E. X = 2
F. x = -1

The algebraic expression for the weigh of both baskets where each one contains pumpkins and carrots in kilos is equals to the 7x + 2, in kilos.

We have two baskets where each one contains pumpkins and carrots. We have to determine the both baskets weigh together in kilos. Let's assume that

The number of pumpkins in second basket = x kilos

Now, according to first scenario, first basket contains the pumpkins twice as many kilos of pumpkin as in the second basket. That is the number of pumpkins in first basket = 2x kilos

In second case, the second basket there are three more kilos of carrots than there are kilos of pumpkin in the first. So, the number of carrots in second basket

= (3 + 2x ) kilos

In third case, the first basket has 4 kilos less carrot than the second, that is x

=( ( 3 + 2x) - 4 ) kg

Now, weigh of first basket = carrots + pumpkins = (2x + 2x - 1) kilos

= (4x - 1 ) kilos

Weigh of second basket = carrots + pumpkins = (3 + 2x) kilos + x kilos

= (3 + 3x) kilos

So, weigh of both baskets together

= (4x - 1 ) kilos + (3 + 3x) kilos

=( 7x + 2 ) kilos.

Hence, required expression is 7x + 2.

For more information about algebraic expression,

https://brainly.com/question/4344214

#SPJ4

Complete question:

You have two baskets. Each contains pumpkins and carrots. In the first basket there are twice as many kilos of pumpkin as in the second, and in the second there are three more kilos of carrots than there are kilos of pumpkin in the first. The first basket has 4 kilos less carrot than the second. How many kilos do both baskets weigh together? Represent it algebraically

The output when three workers are hired is 5 units..

To find the output when three workers are hired, we need to first determine the total cost and then use the marginal cost to calculate the output.

Find the total cost when three workers are hired.
Average total cost (ATC) = Total cost (TC) / Output (Q)
$50 = TC / Q
Since fixed cost (FC) is $130 and the marginal cost (MC) is $40 per worker, the total cost can be found by adding the fixed cost and the cost of the three workers.
TC = FC + 3(MC)
TC = $130 + 3($40)

Calculate the total cost.
TC = $130 + $120
TC = $250

Use the total cost and average total cost to find the output.
$50 = $250 / Q
Q = $250 / $50
Q = 5

Therefore, the output when three workers are hired is 5 units.

Learn more about "marginal cost": https://brainly.com/question/17230008

#SPJ11

In a long-run equilibrium in a perfectly competitive market structure, the following statement is true: Price equals the minimum average total cost (ATC).

In a perfectly competitive market, firms are price takers, meaning they have no control over the market price. In the long run, firms have the flexibility to adjust their inputs and make changes to their production processes.

In a long-run equilibrium, firms aim to maximize their profits. They will continue to adjust their production levels until they reach the point where their marginal cost (MC) equals the market price (P) and their average total cost (ATC) is minimized.

When a firm is producing at the long-run equilibrium, the price they receive for each unit of output is equal to the minimum average total cost. This condition ensures that the firm is covering all of its costs and earning normal profits in the long run.

If the price exceeds the minimum ATC, firms would have an incentive to increase production and if the price falls below the minimum ATC, firms would face losses and might consider exiting the market. Therefore, in a long-run equilibrium in a perfectly competitive market structure, the firm operates efficiently by producing at the minimum average total cost.

Learn more about marginal cost  here:

https://brainly.com/question/28932883

#SPJ11

==========================================================

Explanation:

We have five slots which we can label A,B,C,D,E

We start at 8 and count down by 1 each time until all slots are accounted for. Then multiply out those items: 8*7*6*5*4 = 6720

--------------

Another approach is to use the nPr permutation formula.

Plug in n = 8 and r = 5.

\(n P r = \frac{n!}{ (n-r)! }\\\\8 P 5 = \frac{8!}{ (8-5)! }\\\\8 P 5 = \frac{8!}{ 3! }\\\\8 P 5 = \frac{8*7*6*5*4*3!}{ 3! }\\\\8 P 5 = 8*7*6*5*4\\\\8 P 5 = 6720\\\\\)

In the second to last line, the "3!" factorial terms cancel out.

We have the string 8*7*6*5*4 show up again to help reinforce the previous section.

The correct answer is options B, C, D and E, that is, B. A + A⁻¹ is invertible, C. (In + A) (In + A⁻¹) = 2In + A + A⁻¹, D. A⁶ is invertible and E. (A + A⁻¹)⁹ = A⁹ + A⁻⁹.

Given below are the solutions to the provided mathematical expressions:A.  This expression is incorrect.

The correct expression should be (A + B)² = A² + 2AB + B²B.  We can see that A + A⁻¹ = A(A⁻¹) + A(A⁻¹) = I. Therefore, A + A⁻¹ is invertible.C. Given (In + A) (In + A⁻¹) = In² + InA⁻¹ + AIn + AA⁻¹ = 2In + A + A⁻¹D. If A⁶ is invertible, it means that (A⁶)⁻¹ exists. Let's assume that A⁶ is not invertible.

Therefore, we cannot find the inverse of A⁶. It means (A⁶)⁻¹ does not exist. This is contradictory. Hence A⁶ is invertible.E.  We can see that (A + A⁻¹)² = A² + A⁻² + 2I. Let's replace (A + A⁻¹)² by (A + A⁻¹) × (A + A⁻¹)⁸(A + A⁻¹)⁹= (A + A⁻¹)² × (A + A⁻¹)⁷= (A² + A⁻² + 2I) × (A + A⁻¹)⁷= A⁹ + A⁻⁹ + 9(A⁷ + A⁻⁷) + 36(A⁵ + A⁻⁵) + 84(A³ + A⁻³) + 126(A + A⁻¹) Here, we have used binomial expansion for (A + A⁻¹)⁸.F.  

If AB = BA, it means that A and B are commutative. This doesn't necessarily imply that A and B are invertible. So, option F is incorrect.Solution: In this problem, options A, B, C, D and E are provided to us, and we need to find out the correct option(s) out of them.

Hence, the correct option(s) is(are) as follows:B. A + A⁻¹ is invertibleC. (In + A) (In + A⁻¹) = 2In + A + A⁻¹D. A⁶ is invertibleE. (A + A⁻¹)⁹ = A⁹ + A⁻⁹

Thus, the correct answer is options B, C, D and E, that is, B. A + A⁻¹ is invertible, C. (In + A) (In + A⁻¹) = 2In + A + A⁻¹, D. A⁶ is invertible and E. (A + A⁻¹)⁹ = A⁹ + A⁻⁹.

To know more about invertible visit:

brainly.com/question/14693755

#SPJ11

Answer:

x = 2

Step-by-step explanation:

3(x - 4) = 2x - (6 + x)​ first get rid of parenthesis

3(x - 4) = 3x - 12 and

2x - (6 + x) = 2x - 6 - x

3x - 12 = 2x - 6 - x

3x - 12 = x - 6 export like terms to the same side

3x - x = 12 - 6

2x = 6 divide both sides by 2

x = 3

The simplest form of the given expression ( x⁴ )⁸ exists x³².

Expression in Math exists described as the collection of numbers variables and functions by utilizing characters like addition, subtraction, multiplication, and division.

The given expression will be simplified as:-

( x⁴ )⁸ = x ⁴ ⁽⁸⁾

( x⁴ )⁸ = x ³²

Therefore the simplest form of the given expression exists as x³².

To learn more about expression refer to:

brainly.com/question/723406

#SPJ4

Answer: 1.43 meters

Step-by-step explanation:

subtract 7.52 from 8.92 and that's the difference so that is how far she would have to jump to tie the record

Answer:

y = -14x + 61

Step-by-step explanation:

y = mx + b

First, we can find the slope by reading the question and plugging in the slope of -14 into a slope-intercept formula.

y = (-14)x + b

Now, we need to find the "b" value. We can plug anything we want in for x and y here, but we want the equation for the line that passes through the the point (4,5). Plug in 4 into the x value and 5 into the y value, and solve for b.

5 = (-14)(4) + b

(Flip the equation, so we can solve for b.)

b = 5 - (-14) (4)

(Multiply.)

b = 5 - -56

(Substitute the double minus for a plus sign and add.)

b = 5 + 56

b = 61

Now, plug in your "b" value into our original equation.

FINAL ANSWER:

y = -14x + 61

Answer:

2

Step-by-step explanation:

Given

< x₁, y₁ > and < x₂, y₂ > , then

the dot product is calculated as

x₁ x₂ + y₁ y₂

Given u = < 7, 4 > and v = < 2, - 3 > , then

u • v

= (7 × 2 ) + (4 × - 3 )

= 14 + (- 12)

= 14 - 12

= 2

Answer:

84500 is the correct answer

Answer:

40182 delta math

Step-by-step explanation:

Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.

Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.

First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.

Next, we can find the vertex using the formula:

Vertex = (-b/2a, f(-b/2a))

where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:

Vertex = (-b/2a, f(-b/2a))

= (-6/(2*-1), f(6/(2*-1)))

= (3, -14)

So the vertex of the parabola is at the point (3,-14).

Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.

Know more about quadratic function here;

https://brainly.com/question/18958913

#SPJ11

Answer:

v=424.1cm³

Step-by-step explanation:

v=πr²h

v=π×3²×15

v=424.1150082

∴v=424.1cm³

Jamar's first step is correct. He should continue to factor the expression. Then the correct option is A.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

Jamar is attempting to factor the expression 15x² – 16x – 15.

In his first step, he rewrites the expression as 15x² – 25x + 9x – 15.

Jamar's first step is correct. He should continue to factor the expression.

Then the correct option is A.

More about the factorization link is given below.

https://brainly.com/question/6810544

#SPJ1

Answer: 1887

Step-by-step explanation:

Multiply the numbers:

(2.75 x 10) = 27.5

(8 x 10) = 80

Subtract the numbers:

(27.5 - 2) = 25.5

(80 - 6) = 74

Multiply

74 x 25.5

Answer

1887

The next four terms in the geometric sequence are 500, 100, 20 and 4

Sequence is a set or series of related items or events in a particular order. It can refer to a number of different things, such as a set of numbers, a set of events, or a set of objects. In mathematics, a sequence is a series of numbers or other mathematical objects that follow a particular pattern.

In the given problem, the sequence is;

312,500, 62,500, 12,500, 2,500

This is most likely a geometric sequence and we have to find the common ratio.

r = 62500 / 312500 = 0.2 or 2500 / 12500 = 0.2

The common ratio is 0.2

The next term will be the 5th term

Tₙ = arⁿ⁻¹

T₅ = ar⁴

a = first term = 312500

T₅ = 312500(0.2)⁴

T₅ = 500

The next term is 6th term

T₆ = ar⁵

T₆ = 312500(0.2)⁵

T₆ = 100

T₇ = ar⁶

T₇ = 312500(0.2)⁶

T₇ = 20

T₈ = 312500(0.2)⁷

T₈ = 4

Learn more on sequence here;

https://brainly.com/question/6561461

#SPJ1

The Fourier series of the odd-periodic extension of  the Fourier series of the even-periodic extension of the function\(f(x) = 1+ 2x\). for x Here, we have\(f(x) = 1+ 2x for x€ (0, 2)\) We are going to find the Fourier series of the even periodic extension.

Determine the fundamental period of\(f(x)T = 4\) Step 2: Determine the coefficients of the Fourier series. The Fourier series of the even-periodic extension of\(f(x) = 1+ 2x.\) for x is given by: The Fourier series representation is unique.

To know more about Fourier series visit:

https://brainly.com/question/30763814

#SPJ11

Answer:

Step-by-step explanation:

i think 1

Answer:

I think 10

Step-by-step explanation:

Answer:

John is 9

Step-by-step explanation:

(9*3)-5=22+9=31

Answer:

171

Step-by-step explanation:

1140 * 15

Answer:

113.04

Step-by-step explanation:

All you have to do is substitute the r in the equation.

And of course pi is equal to 3.14

V = 4/3(3.14)3^3

That gives you a volume of around 113.04

Answer:

3 centimeters is greater

Step-by-step explanation:

A millimeter is 10 times smaller than a centimeter

Therefore ,the collar remain effective for 26.44 days.

In mathematics, there are numerous ways to use the word "order." It most frequently refers to the quantity of elements in (for example, conjugacy class order, graph order, group order, etc.) or describes the biggest term (for example, curve order, surface order, or polynomial order) that appears in a mathematical object.

Here,

=>Rate of evaporation=k=dr/dt

=> amount still present=R.

Thus ,It's a first order reaction.

So, half life=0.693/k.

20=0.693/k.

=> k=0.0346

Now,

60% of active ingredient has been evaporated.

So, 40% left.

Time taken=T=(2.303/k)log(R/0.4R)

T=(2.303/0.0346)log(5/2)

T=66.56(log5-log2)

T=66.56(0.699-0.301)

T=66.56(0.398)

T=26.44 days.

Therefore ,the collar remain effective for 26.44 days.

To know more about  order , visit

https://brainly.com/question/13073633

#SPJ4

The required breadth of the constructed pond would be 20 meters.

The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.

The perimeter of a rectangle = 2(L+W)

Where W is the width of the rectangle and L is the length of the rectangle

As per the question, the data as:

Length of the park = 40 m

Total cost of fencing = Rs. 36000

Rate of fencing = Rs. 75 per meter

Quantity = Total Cost / Rate

Since the entire cost is Rs. 36000 when the pond is enclosed four times, it represents four times the perimeter.

4 (Perimeter) =  Rs. 36000/Rs. 75 = 480

Perimeter = 480/4 = 120 m

2(L + W) = 120 m

2(40 + W ) = 120 m

80 + 2W = 120 m

2W = 40

W = 20 m

Thus, the required breadth of the constructed pond would be 20 meters.

Learn more about the Perimeter of the rectangle here:

brainly.com/question/15287805

#SPJ1

The question seems to be incomplete the correct question would be:

Rohit constructed a rectangular pond of length 40 m for fish farming. He spent rs.36,000 to fence it with 4 rounds at rs 75 per meter. Find the breadth of the pond.

Answer:

5

5 1/2

6 1/2

Step-by-step explanation:

Let n=1

a1 = 5+(1-1)*(1/6)

a1 = 5

Let n=4

a4 = 5+(4-1)*(1/6)

a4 = 5 +3(1/6)

a4 = 5+1/2 = 5 1/2

Let n=10

a10 = 5+(10-1)*(1/6)

a10 = 5 +9(1/6)

a4 = 5+3/2 = 5 + 1 1/2 = 6 1/2

Answer:

Step-by-step explanation:

Like terms are terms that have the same variable raised to the same exponent. For example, 7z and 2z are like terms because they have the same variable, z, and are raised to the same exponent, 1. 5x² and 10x are not though, because the first one is raised to a power of 2, whereas the latter is only raised to a power of 1. And numbers with different variables, like 7x and 3z, are not either.

Answer: like terms are terms that have the same variables and powers

For example: 3x and 4x are like terms because they both are x and only x. 12xy and 4y would not be like terms because they don’t share the same variable. if it was 5x ² and 8x ² they would be like terms. i hope this helps!

At the instant when the diameter of the dam is 20 m and the water level is 6 m, the rate at which the volume of water in the dam is changing is approximately 8.948 cubic meters per hour.

To determine the rate at which the volume is changing, we need to use the given formula and calculate the derivatives with respect to time. Let's denote the volume as V, the diameter as d, and the water level as h. The formula for the volume of water in the dam is V = 2πh^2(3d - 3h).

We are given that the water level is increasing at a rate of 0.06 m/hr, which means dh/dt = 0.06 m/hr. Additionally, the diameter is increasing at a rate of 0.25 m/hr, which gives us dd/dt = 0.25 m/hr.

We need to find dV/dt, the rate at which the volume is changing. To do this, we can apply the chain rule of differentiation. Taking the derivative of V with respect to time, we have:

dV/dt = (dV/dd) * (dd/dt) + (dV/dh) * (dh/dt)

Now, let's calculate the partial derivatives. Taking the derivative of V with respect to d, we get:

dV/dd = 2πh^2(3 - 3h)

And taking the derivative of V with respect to h, we get:

dV/dh = 2πh(6d - 6h)

Substituting the given values of d = 20 m and h = 6 m into the expressions for dV/dd and dV/dh, we can evaluate these partial derivatives. Plugging in the rates of change dh/dt = 0.06 m/hr and dd/dt = 0.25 m/hr, we can now calculate dV/dt:

dV/dt = (2π(6^2)(3(20) - 3(6)) * 0.25 + (2π(6)(6(20) - 6(6)) * 0.06

Simplifying this expression yields dV/dt ≈ 8.948 cubic meters per hour. Therefore, the rate at which the volume is changing at the instant when d = 20 m and h = 6 m is approximately 8.948 cubic meters per hour.

Learn more about derivatives here:

https://brainly.com/question/25324584

#SPJ11