a cube with edges of length x centimeters has a volume V(x) = x^3 cubic centimeters. The volume is increasing at a constant rate of 40 cubic centimeters per minute. At the instant when x = 2, what is the rate of x, in centimeters per minute, with respect to time?

When the equation is solved using the unitary approach, the x = 1 answer is -3 and the x = -1 solution is 1.

what is equation ?

Its basic principle is thought to be the number's greatest equivalent fraction. How to determine the basic form. Look for shared numbers in the denominator and numerator. A fractional number can be checked to discover if it is a power of 2. A statement having two collinear and an equal sign in the middle is referred to as a mathematical equation. Every variable's degrees are listed in listed in order in the general form of whatever equation. The formula for a set of equations is x + b = 0. The general form of a three separate linear equation is an x + b y + c = 0. (or something similar). Either conditioned equations or facts are categories for formulas. An identity holds true for whatever value of the variables.

given

-2 lx + 4l + 7

let x = 1

-2(1+4) + 7

= -3

let x = -1

-2( -1+ 4 ) + 7

= -2( 3 ) + 7

= 1

When the equation is solved using the unitary approach, the x = 1 answer is -3 and the x = -1 solution is 1.

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Building the Cartesian Plane with the proper scale we can conclude that

Answer:

7 hours

Step-by-step explanation:

Add 8+7.5+7+6.5+6= 35

The record days of sleep is 5 days so divide 35 by 5 and you get 7 hours

Answer:

7

Step-by-step explanation:

The concentration of the solution prepared by adding 15.00 mL of 2.07 M into a 50.00 mL volumetric flask and diluting to the mark is approximately 0.621 M.

To calculate the concentration of the solution, we can use the formula: C1V1 = C2V2. Where: C1 = initial concentration of the solution; V1 = initial volume of the solution ; C2 = final concentration of the solution;  V2 = final volume of the solution. In this case: C1 = 2.07 M; V1 = 15.00 mL; C2 = ?; V2 = 50.00 mL. Plugging in the values into the formula, we have: (2.07 M)(15.00 mL) = C2(50.00 mL).

Now, solve for C2: C2 = (2.07 M)(15.00 mL) / (50.00 mL). C2 = 0.621 M. Therefore, the concentration of the solution prepared by adding 15.00 mL of 2.07 M into a 50.00 mL volumetric flask and diluting to the mark is approximately 0.621 M.

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Answer:

(6,12)

Step-by-step explanation:

(Hopefully you can see the work if not then sorry)

if other factors are held constant, what is the effect of increasing the sample variance: B. it will increase the estimated standard error and decrease the likelihood of rejecting h0.

In Mathematics, a sample proportion can be defined as the proportion of individuals in a sample that have a specified characteristic or trait.

Mathematically, the standard error of a sample proportion can be calculated by using this formula:

Standard error = √(p × (1 - p)/n)

Where:

Generally speaking, the effect of increasing the sample variance is an increase in estimated standard error and a decrease in the likelihood of rejecting H_{0} provided that other factors are held constant.

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To reduce the third-order ordinary differential equation y - y" - 4y + 4y = 0 into a companion system of linear equations, we introduce new variables u and v:

Let u = y,

v = y',

w = y".

Taking the derivatives of u, v, and w with respect to the independent variable (let's denote it as x), we have:

du/dx = y' = v,

dv/dx = y" = w,

dw/dx = y"'.

Now we can rewrite the given differential equation in terms of u, v, and w:

u - w - 4u + 4u = 0.

Simplifying the equation, we get:

-3u - w = 0.

This equation can be expressed as a system of first-order linear differential equations as follows:

du/dx = v,

dv/dx = w,

dw/dx = -3u - w.

Now we have a companion system of linear equations:

du/dx = v,

dv/dx = w,

dw/dx = -3u - w.

To solve this system completely, we need to find the solutions for u, v, and w. By solving the system of differential equations, we can obtain the solutions for u(x), v(x), and w(x), which will correspond to the solutions for y(x), y'(x), and y"(x), respectively.

The exact solutions for this system of differential equations depend on the initial conditions or boundary conditions that are given. By applying appropriate initial conditions, we can determine the specific solution to the system.

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dy/dx = 0 when x = - 2, and x = 2/3 is not possible.

dy/dx = 0 when x = - 1, and x = 5.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

y = x³ - 6x² - 15x - 7

Differentiating w.r.t x.

[ d\(x^n\)/dx = n\(x^{n - 1}\) ]

[ dc/dx = 0 ]

dy/dx = dx³/dx - 6dx²/dx - 15dx/dx - d7/dx

dy/dx = 3\(x^{3 - 1}\)dx/dx - 6 x 2\(x^{2-1}\)dx/dx - 15 - 0

dy/dx = 3x² - 12x - 15

Now,

dy/dx = 0

3x² - 12x - 15 = 0

3(x² - 4x - 5) = 0

x² - 4x - 5 = 0

x² - (5 - 1)x - 5 = 0

x² - 5x + x - 5 = 0

x(x - 5) + 1(x - 5) = 0

(x - 5) (x + 1) = 0

x - 5 = 0

x = 5 _____(1)

x + 1 = 0

x = -1 _____(2)

Now,

For x = 2,

dy/dx = 3x² - 12x - 15

dy/dx = 3 x 4 + 24 - 15

dy/dx = 12 - 24 - 15

dy/dx = 12 - 39

dy/dx = -27 _____(3)

For x = 2/3,

dy/dx = 3x² - 12x - 15

dy/dx = 3 x 4/9 + 24 x 2/3 - 15

dy/dx = 4/3 + 16 - 15

dy/dx = 4/3 + 1

dy/dx = 7/3 _____(4)

From (1), (2), (3), and (4)

dy/dx = 0 when x = - 2 and x = 2/3 is not possible.

Thus,

dy/dx = 0 when x = - 1, and x = 5.

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Therefore, the sum of the distances traveled by the tips of both hands in one $24$-hour period is approximately $15.708$ meters.

To start, we need to find the length of each hand. The minute hand measures $10$ cm, which is equivalent to $0.1$ meters, and the hour hand measures $5$ cm, or $0.05$ meters.
Now, let's consider the distance each hand travels in one hour. The minute hand travels the circumference of the clock face, which has a diameter of $20$ cm or $0.2$ meters. The formula for the circumference of a circle is $2\pi r$, so the distance traveled by the minute hand in one hour is $2\pi(0.1) = 0.2\pi$ meters.
The hour hand travels the circumference of a circle with a diameter of $10$ cm or $0.1$ meters. Since the hour hand takes $12$ hours to complete one full revolution around the clock face, it travels $\frac{1}{12}$ of the circumference in one hour. Therefore, the distance traveled by the hour hand in one hour is $\frac{1}{12} \cdot 2\pi(0.05) = \frac{\pi}{120}$ meters.
To find the total distance traveled by both hands in $24$ hours, we can add up the distance traveled by each hand in one hour and multiply by $24$.
Total distance = $24\left(0.2\pi + \frac{\pi}{120}\right) \approx 15.708$ meters
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Answer: 3.4cm

Step-by-step explanation:

Total cm = 24

Number of fish = 7

24/7 = 3.4

Draw the circle with the center at the intersection of the perpendicular bisectors and the radius equal to the distance found in step 4.

When constructing a circle circumscribed about a triangle, the following step is needed:

Identify the three vertices of the triangle.

Let's say the triangle has vertices A, B, and C.

Find the perpendicular bisectors of the triangle's sides.

For each side of the triangle, construct a line that is perpendicular to the side and passes through its midpoint.

Locate the point of intersection of the perpendicular bisectors.

The point where all three perpendicular bisectors intersect is the center of the circumscribed circle.

Measure the distance from the center to any of the triangle's vertices.

This distance is the radius of the circumscribed circle.

By following these steps, you can construct a circle that passes through all three vertices of the triangle. This circle is known as the circumscribed circle or circumcircle of the triangle. It is unique to each triangle and provides a useful geometric property that can be applied in various mathematical and geometric contexts.

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It takes Jack approximately 263.33 seconds (or 4 minutes and 23.33 seconds) to finish the entire race.

(a) In the first portion of the race, Jack runs at a constant speed of 4.00 m/s. Let's denote the time taken for this portion as t1. Since there is no acceleration during this time, we can use the formula:

Distance = Speed × Time

The distance covered in this portion is 600 m, so we have:

600 m = 4.00 m/s × t1

Solving for t1:

t1 = 600 m / 4.00 m/s

t1 = 150 s

Therefore, it takes Jack 150 seconds to run the first portion of the race at a constant speed.

(b) In the second portion of the race, Jack accelerates to his maximum speed of 7.5 m/s over the course of 1 minute (60 seconds). We need to find the distance covered during this time. Let's denote the distance covered in this portion as d2.

We can use the formula for distance covered during constant acceleration:

Distance = Initial Velocity × Time + (1/2) × Acceleration × Time^2

At the start of this portion, Jack's initial velocity is 4.00 m/s, and the acceleration is given by:

Acceleration = (Final Velocity - Initial Velocity) / Time

Acceleration = (7.5 m/s - 4.00 m/s) / 60 s

Acceleration ≈ 0.0583 m/s^2

Substituting these values into the formula:

d2 = 4.00 m/s × 60 s + (1/2) × 0.0583 m/s^2 × (60 s)^2

d2 = 240 m + 105 m

d2 = 345 m

Therefore, Jack covers a distance of 345 meters during the second portion of the race.

(c) In the final portion of the race, Jack runs at his maximum speed of 7.5 m/s. Let's denote the time taken for this portion as t3. Since the distance remaining after the second portion is 400 m (1000 m - 600 m - 345 m), we have:

Distance = Speed × Time

400 m = 7.5 m/s × t3

Solving for t3:

t3 = 400 m / 7.5 m/s

t3 ≈ 53.33 s

Therefore, it takes Jack approximately 53.33 seconds to run the final portion of the race at his maximum speed.

(d) To find the total time taken for Jack to run the entire race, we add the times taken for each portion:

Total Time = t1 + 60 s + t3

Total Time = 150 s + 60 s + 53.33 s

Total Time ≈ 263.33 s

Therefore, it takes Jack approximately 263.33 seconds (or 4 minutes and 23.33 seconds) to finish the entire race.

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True, free bilirubin is transported by the blood to the liver.

Macrophages begin the disposal of hemoglobin by separating the heme from the globin. They hydrolyze the globin into free amino acids, which can be used for energy-releasing catabolism or recycled for protein synthesis.

Bilirubin

Bilirubin is a red-orange compound that occurs in the normal catabolic pathway that breaks down heme in vertebrates. This catabolism is a necessary process in the body's clearance of waste products that arise from the destruction of aged or abnormal red blood cells.

Hemoglobin

Hemoglobin is a protein in your red blood cells that carries oxygen to your body's organs and tissues and transports carbon dioxide from your organs and tissues back to your lungs.

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You have the following expression:

39 + (-20.4)

In order to simplify the previous expression, you first eliminate the parenthesis. To do that, you take into account that the sign before the parenthesis must multiply the sign inisde. In this case, you have a positive sign + before the parenthesis, and inside you have a minus -. When the parenthesis is eliminated, these signs are multiplied (here you use the multiplication rule for signs). Thus, you have that - x + = - (positive multiplied by negative is equal to negative). And the expression becomes:

39 + (-20.4)

= 39 - 20.4

= 18.6

Hence, the simplified expression is 18.6

If the number of tomato growers in the market increases, it would generally lead to an increase in the supply of tomatoes increases.

The correct answer is A.

The correct answer is A.

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The angles in the given diagram are classified as: 1: alternate interior 2: None 3: corresponding 4: alternate exterior 5: corresponding

Corresponding angles, alternate interior angles, and alternate exterior angles are all types of angle pairs that are formed when a transversal intersects two parallel lines.

Corresponding angles are pairs of angles in matching positions at the intersection of the two lines, and they are equal in measure if the lines are parallel.

Alternate interior angles are pairs of non-adjacent angles on opposite sides of the transversal, and they are congruent if the lines are parallel. Similarly, alternate exterior angles are also pairs of non-adjacent angles on opposite sides of the transversal, but they are also congruent if the lines are parallel.

Therefore, the angles numbered in the diagram would be classified as:

Figure 1: alternate interior

Figure 2: None

Figure 3: corresponding

Figure 4: alternate exterior

Figure 5: corresponding

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By definition of supplementary angles,  ∠1 + ∠2 = 180°.

and  ∠2 + ∠3 = 180°

Then:

∠1 + ∠2  =  ∠2 + ∠3

Subtracting ∠2 in both sides we get:

∠3 =  ∠1

First, we know that ∠1 and ∠2 are supplementary (two angles are supplementary if their measures adds up to 180°), this means that:

∠1 + ∠2 = 180°

And we also know that ∠2 and ∠3 are supplementary, then:∠2 + ∠3 = 180°

So we have two equations:∠1 + ∠2 = 180°∠2 + ∠3 = 180°

If we take the difference between these equations we will get:

(∠1 + ∠2) - (∠2 + ∠3) = 180° - 180°

Solving this we get:∠1 - ∠3 = 0Then:∠1 = ∠3So we have proven that these angles are equal.

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Answer:

x = 1.175

x = -0.425

Step-by-step explanation:

Use quadratic formula (see picture)

a = 4

b = -3

c = -2

x = 1.175

x = -0.425

OR x = \(\frac{3 +/- \sqrt{41} }{8}\)

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

using factoring

4x^2-3x-2=0

Answer:

5 km.

Step-by-step explanation:

Surface area is lw + hw + lh.

(1 x 1)+(1 x 2)+(1 x 2)

1 + 2 + 2

1 + 4

5 km.

The volume of the sphere inside the given cylinder is 4186.7 cubic centimeters.

Given that the cylinder's diameter is 20 cm, we can find the radius by dividing the diameter by 2:

Radius = Diameter / 2 = 20 cm / 2 = 10 cm

Now, let's calculate the volume of the sphere using the formula:

Volume of a sphere = (4/3) x π x radius³

Substituting the radius we found:

Volume of the sphere = (4/3) x π x (10 cm)³

Calculating the volume:

Volume of the sphere = (4/3) x π x 1000 cm³

Volume of the sphere ≈ 4186.7 cm³

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Answer:

-4.21 ft. below sea level

Step-by-step explanation:

The expression is -45.32 + 41.11, and so you are basically just doing 45.32-41.11, but the answer will be negative.

45.32-41.11=4.21, but the answer is negative, so -4.21.

Given function is f(x)=x+3. We need to find f′(x) by using the definition of the derivative. For this purpose, we use the formula of the derivative of a function,

df/dx = lim h→0 [f(x+h)-f(x)]/hApplying the above formula forNow, we are required to find f′(3) by using two methods. Method 1Substitute x=3 in the derivative f′(x)=1 to get the value of f′(3),f′(3)=1Method 2Substitute x=3 in the function f(x)=x+3 to get f(3)=3+3=6Now,

we need to find the derivative of the function f(x)=x+3 using power rule,df/dx = d/dx (x+3)=1+0=1Therefore,f′(3)=1Ans:Therefore, f′(x)=1; f′(3)=1

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Given:

Compound for an experiment = 4.25 ounces

Compound costs = $2.32 per ounce.

Teacher pays = $10

To find:

The amount of change teacher receive.

Solution:

Cost of 1 ounce of compound = $2.32

Cost of 4.25 ounce of compound = 4.25 × $2.32

                                                        = $9.86

It is given that, the teacher pays with a $10 bill.

Amount of change = $10 - $9.86

                                 = $0.14

Therefore, the teacher receive $0.14 change.

a. The equation representing the cost of buying and operating the Super Cool X1400 is: C = 800 + 60m. b. The equation representing the cost of buying and operating the Efficient Energy X2000 is: C = 1200 + 40m. c. Your family would have to use the Efficient Energy model for 10 months to compensate for the additional cost of the original purchase. d. Figuring your family will only use the air conditioner for four months each year, you would have to wait 5 years to start saving money overall.

a. The cost of buying the Super Cool X1400 is a one-time expense of $800. Additionally, the cost of operating it is $60 per month. Therefore, the equation representing the cost C as a function of months m is C = 800 + 60m.

b. The cost of buying the Efficient Energy X2000 is a one-time expense of $1200. The operating cost is $40 per month. Hence, the equation representing the cost C as a function of months m is C = 1200 + 40m.

c. To compensate for the additional cost of the original purchase (which is $400), we equate the two cost equations and solve for m:

800 + 60m = 1200 + 40m

20m = 400

m = 20

Therefore, your family would have to use the Efficient Energy model for 20 months (or 10 months more than the Super Cool X1400) to compensate for the additional cost.

d. Considering your family only uses the air conditioner for four months each year, we divide the total number of months (20) by four to find the number of years needed to start saving money overall:

20 months / 4 months/year = 5 years

Hence, you would have to wait 5 years to start saving money overall by choosing the Efficient Energy X2000.

a. The cost of buying and operating the Super Cool X1400 is represented by the equation C = 800 + 60m.

b. The cost of buying and operating the Efficient Energy X2000 is represented by the equation C = 1200 + 40m.

c. Your family would have to use the Efficient Energy model for 10 months to compensate for the additional cost of the original purchase.

d. Assuming your family uses the air conditioner for four months each year, you would have to wait 5 years to start saving money overall by choosing the Efficient Energy X2000.

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complete question- Your family plans to buy a new air conditioner. They can buy the Super Cool X1400 for $800, or they can buy the Efficient Energy X2000 for $1200. Both models will cool your home equally well, but the Efficient Energy model is less expensive to operate. The Super Cool X1400 will cost $60 per month to operate, while the Efficient Energy X2000 costs only $40 per month to operate. a. Write an equation to represent the cost of buying and operating the Super Cool X1400 where C= cost and m= months. b. Write an equation to represent the cost of buying and operating the Efficient Energy X2000. c. How many months would your family have to use the Efficient Energy model to compensate for the additional cost of the original purchase? d. Figuring your family will only use the air conditioner for four months each year, how many years ill you have to wait to start saving money overall?

Answer:

...

Step-by-step explanation:

(x-1) will cancel each other so the answer is the last one

Answer: y = 2(x + 2)² - 5

Step-by-step explanation:

          We are going to use the completing the square method to transform this quadratic equation from standard form to vertex form.

Given:

     y = 2x² + 8x + 3

Factor the 2 out of the first two terms:

     y = 2(x² + 4x) + 3

Add and subtract \(\frac{b}{2} ^2\):

     y = 2(x² + 4x + 4 - 4) + 3

Distribute the 2 into -4 and combine with the 3:

     y = 2(x² + 4x + 4) - 5

Factor (x² + 4x + 4):

     y = 2(x + 2)² - 5

whenever the line drops to the bottom of the graph the reason is because her speed drops to 0