A 4 inch hole has been bored thru a 6 man nah cube.

Answer:

\(y = \frac{5}{2} x^{2}\)

Step-by-step explanation:

When you scale a parabola vertically, you multiply the \(x^{2}\) by what you are scaling it vertically by.

For example, say you have  \(y = 8x^{2}\). That means that  \(y = x^{2}\) was scaled vertically by a factor of 8.

I hope this helps!

By solving the given equation x/7 - 6 = - x/6 + 5 we get x value = 462/13.

What is called the equation?

Given that :

     x/7 - 6 = - x/6 + 5

Multiply the denominators with numerator on both sides

                x / 7 - 6(7) = - x / 6 + 5(6)

                  x - 42 / 7 = - x + 30 / 6

Multiply both denominators with numerator on both sides

                  6 (x - 42) = 7 (- x + 30)

Multiply 6 and 7 inside the bracket

                   6x - 252 = - 7x + 210

Separate x terms and constant terms

                    6x + 7x = 210 + 252

                           13x = 462

                              x = 462 / 13

Therefore, x = 462 /13

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Answer:

y < 4x - 2

Step-by-step explanation:

Answer:

y < 4x - 2

Step-by-step explanation:

Determine the equation of the line:

A solid line means the signs ≤ or ≥ should be used (inclusive boundary)

A dotted line means the signs < or > should be used (non inclusive boundary).

> is points above the boundary line

< is points below the boundary line

Therefore, the grey shaded area is y < 4x - 2

Answer:

If the track is in the shape of a circle, then we can use the formula for the area of a circle to calculate the approximate area inside the track.

The formula for the area of a circle is:

A = πr^2

where A is the area and r is the radius of the circle.

To find the radius of the circle, we can use the formula for the circumference of a circle:

C = 2πr

where C is the circumference of the circle.

We know that the circumference of the circle is 650 yards. So we can solve for the radius by rearranging the formula:

r = C/(2π) = 650/(2π) ≈ 103.4 yards

Now we can use the formula for the area of a circle to find the approximate area inside the track:

A = πr^2 ≈ 3.14 × (103.4)^2 ≈ 33,608 square yards

Therefore, the approximate area inside the track is about 33,608 square yards.

Step-by-step explanation:

A. The equation to represent the profit is P(x) = -150x² + 4x + 900.

B. The degree is 2, the leading coefficient is -150, the leading term is -150x², and the constant is 900.

C. The profit polynomial can be factored as P(x) = (25x + 16)(-6x + 100).

D. We get:

x = (-4 ± √(4² - 4(-150)(900))) / (2(-150))

= (-4 ± √(16 + 540000)) / (-300)

= (-4 ± √540016).

a. The equation to represent the profit is given by P(x) = R(x) - C(x). We can substitute the given equations for R(x) and C(x) into this equation to find the profit equation.

P(x) = (7x + 300x² + 900) - (3x + 450x²)

Simplifying the equation further, we get:

P(x) = 7x + 300x² + 900 - 3x - 450x²

Combining like terms, we have:

P(x) = (7x - 3x) + (300x² - 450x²) + 900

P(x) = 4x - 150x² + 900

Therefore, the equation to represent the profit is P(x) = -150x² + 4x + 900.

b. To identify the degree, leading coefficient, leading term, and constant of the profit equation, we examine the highest power of x, the coefficient of that term, and the constant term.

Degree: The degree of the polynomial is the highest power of x. In this case, the degree is 2.

Leading coefficient: The leading coefficient is the coefficient of the term with the highest power of x. In this case, the leading coefficient is -150.

Leading term: The leading term is the term with the highest power of x. In this case, the leading term is -150x².

Constant: The constant term is the term without any x. In this case, the constant term is 900.

Therefore, the degree is 2, the leading coefficient is -150, the leading term is -150x², and the constant is 900.

c. To factor the profit polynomial P(x) = -150x² + 4x + 900, we look for factors that will multiply to give the product of the leading coefficient and the constant term, while also adding up to give the coefficient of the linear term (4x). In this case, we can factor the polynomial by splitting the linear term:

P(x) = -150x² + 4x + 900

      = -150x² - 96x + 100x + 900

      = -6x(25x + 16) + 100(25x + 16)

      = (25x + 16)(-6x + 100)

Therefore, the profit polynomial can be factored as P(x) = (25x + 16)(-6x + 100).

d. To determine the values where the company will break even, we set the profit equation P(x) = 0 and solve for x.

P(x) = -150x² + 4x + 900

Setting P(x) = 0, we have:

-150x² + 4x + 900 = 0

This is a quadratic equation, and we can solve it using factoring, completing the square, or the quadratic formula. However, since factoring is not straightforward in this case, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For the equation -150x² + 4x + 900 = 0, we have:

a = -150, b = 4, c = 900

Substituting these values into the quadratic formula, we get:

x = (-4 ± √(4² - 4(-150)(900))) / (2(-150))

  = (-4 ± √(16 + 540000)) / (-300)

  = (-4 ± √540016)

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Answer:

The answer is :

8

.......

Answer:

x ≥ 6

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

-3x ≤ -18

Step 2: Solve for x

Answer:

x = 4

Step-by-step explanation:

5x - 4 = 4x

- Subtract 5x from both sides of the equation.

-4 = -1x

- Divide -1 to isolate the x variable

x = 4

Answer:

x = 4

Step-by-step explanation:

\(5x - 4 = 4x \\ 5x = 4x + 4 \\ 5x - 4x = 4 \\ \)

\(\boxed{\bold{Answer:{\boxed{\bold{\green{x = 4}}}}}}\)

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Answer: f(-5)=-11 g(-3)=-52

Step-by-step explanation:

The required rate of return (or minimum acceptable rate of return) is 20 percent. If the net cash flows are $15,000 per year for ten years, the total cash flow is $150,000. The project's cost is $47,500. We can now apply the net present value formula to determine whether or not the project is feasible.

Net Present Value (NPV) = Cash flow / (1 + r)^n - Cost Where, r is the discount rate, n is the number of years, and Cost is the initial outlay.

Net Present Value = 150000 / (1 + 0.20)^10 - 47500

Net Present Value = $67,482.22

Since the NPV is positive, the project is feasible. When calculating net present value, it's important to remember that a positive NPV implies that the project is expected to generate a return that exceeds the cost of capital, whereas a negative NPV indicates that the project is expected to generate a return that is less than the cost of capital, and as a result, it should be avoided.

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The total number of bacteria in the dish is 31457280

The expression is given as:

Total = (32)^4 * 30

Start by evaluating the exponent

Total = 1048576 * 30

Next, evaluate the product

Total = 31457280

Hence, the total number of bacteria in the dish is 31457280

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Answer:

A (3^8)

Step-by-step explanation:

I have this question on my test. I'm just assuming the person didn't put ^.

(3^2)^4 times 3^0

Solving a system of equations we can see that each pair of pants costs €82.94 and each coat costs €26.37

Let's define the variables:

x = cost of a pant

y = cost of a coat.

First, we know that:

3x + 2y = 245

And then there are discounts of 20% and 5%, and the cost of one of each is 100.75, then:

0.8x + 0.95y = 100.75

Then we have a system of equations:

3x + 2y = 245

0.8x + 0.95y = 100.75

We can isolate x on the second equation to get:

x = (100.75 - 0.96y)/0.8

x = 125.9 - 1.2y

Replace that in the other equation:

3*(125.9 - 1.2y) + 2y = 245

Solving for y:

3*125.9 - 3*1.2y + 2y = 245

y*(2 - 3*1.2) = 245 - 3*125.9

y = (245 - 3*125.9)/(2 - 3*1.2)

y = 82.94

Then the value of x is:

x = 125.9 - 1.2*82.94

x = 26.37

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The centripetal force is the force that acts on an object moving in a circular path, directing it towards the center of the circle. option a.

When a car is driving around a curve, the centripetal force is provided by the frictional force between the tires and the road. This force acts inwards, towards the center of the circle, and is responsible for keeping the car moving in a circular path.

The centripetal force is always perpendicular to the direction of motion, so option (b) and (d) can be eliminated.

Additionally, there is no force that acts away from the center of the circle, so option (c) can also be eliminated. Option (e) is not applicable since the question is asking about the direction of the force, not its orientation.

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The recursive rule for the given sequence 1, 3, 4, 7, 11 ... is aₙ₊₁ = aₙ + aₙ₋₁.

The next two term of the sequence 1, 3, 4, 7, 11, is equal to 18 , 29.

Recursive rule for the sequence 1, 3, 4, 7, 11, ...... is represented by :

Let us consider before 1 it is 0.

Next term is sum of previous two terms :

0 + 1 = 1

1 + 3 = 4

3 + 4 = 7

4 + 7 = 11

Recursive rule for the given sequence is equal to :

3rd = 2nd + 1st term

4th term = 3rd term + 2nd term .....

aₙ₊₁ = aₙ + aₙ₋₁

Next two terms for the above sequence is equal to:

7 + 11 = 18

11 + 18 = 29

Therefore, the recursive formula to represents the sequence 1, 3, 4, 7, 11 is equal to aₙ₊₁ = aₙ + aₙ₋₁ and next two terms are 18, and 29.

The above question is incomplete, the complete question is:

Write a recursive rule for the sequence. Then write the next two term of the sequence. For 1,3,4,7,11

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Answer:

Step-by-step explanation:

The monthly interest rate is the annual rate (APR) divided by 12.

  19%/12 ≈ 1.5833%

The loan will be paid in fewer than 91 months, because Zach will be paying at least $10 per month on his current balance of $910. The attached spreadsheet shows it will take 73 payments to pay off the loan.

We need to solve the algebraic expression:

-2(x+8) + 6(5 + (_)x) = 10x + 14

Expanding the operations and grouping similar terms:

-2x -16 + 30 + 6(_)x = 10x + 14

-2x + 6(_)x -16 + 30 = 10x + 14

To solve this, we need to equaling each similar term at both sides of the equation:

-2x + 6(_)x = 10x [1]

-16 + 30 = 14 [2]

14 = 14

We need to solve the following equation:

-2x + 6(_)x = 10x

We can rewrite the previous equation as follows:

-2 + 6x = 10

6x = 10 + 2

x = (12/6)

x = 2

Checking the previous result, we have:

-2 + 6(2) = 10

-2 + 12 = 10

10 = 10

Then the value for the blank in the question is 2.

Checking equation [1]:

-2x + 6(2)x = 10x

-2x + 12x = 10x

10x = 10x

Therefore, we have then:

10x + 14 = 10x + 14

The answer is

A.(2,2)

The new coordinates of point J' of the quadrilateral J' K’ L’ M’ is option (D) (6,4) is the correct answer.

Dilation is a kind of transformation in which an object is resized based on a scale factor. Dilation is the process of enlarging or reducing the size of a geometrical object without changing its shape.

For the given situation,

Quadrilateral JKLM is dilated by a scale factor of 2 with a center of dilation at the origin to form quadrilateral J' K’ L’ M’.

To dilate the figure by a factor of 2, we need to multiply the x and y-value of each point by 2.

Here the coordinates of J is (3,2).

The dilation factor is 2, so multiply both the x and y value by 2.

Thus x value is

\(3(2)=6\)

and y value is

\(2(2)=4\)

Hence we can conclude that the new coordinates of point J' of the quadrilateral J' K’ L’ M’ is option (D) (6,4) is the correct answer.

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Answer:

12 jugs
Step-by-step explanation:

(\(\frac{21}{5} \\\\\))  divided by  (\(\frac{3}{8}\)) find a common denominator between 5 and 8 which is 40. Multiply the left side top and bottom by 8 and then multiply the right side by 5 top and bottom to get \(\frac{168}{40}\) divided by \(\frac{15}{40}\) and get 11.2 however you cant purchase .2 of a jug so round up and you get 12 jugs.

Answer:1386cm2

Step-by-step explanation:

Answer:

72 you just need to keep multiplying

Step-by-step explanation:

3x4. 2x3

12 x 6

72

Answer:

x=−2y+18

Step-by-step explanation:

if you want to graph it then click on the screenshot

(ps tell me if this helped)

The steady-state amplitude is X = 2/√(29) and the steady-state phase is φ = -tan^(-1)(10/√29), the steady-state response xss(t) lags the input.

The steady-state response of the given system is a sinusoidal function with amplitude X and phase φ. Using the formula for steady-state response, we can find the values of X and φ for the given system. The output is said to lag the input if the phase is negative, which is the case here. We can plot the input and output versus time on the same graph to visualize the lag.

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Answer: the answer is 0.98.

Step-by-step explanation:

the equation 8/100 + 9/10 = 0.98.

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Answer:

0.565 m^3 to the nearest thousandth.

Step-by-step explanation:

The volume of the cylinder = π r^2 h

Here the radius r = 1/2 diameter

= 1/2 * 3 = 1.5 m

8 cm = 0.08 m.

So the volume = π (1.5)^2 * 0.08

= 0.565 m^3 to the nearest thousandth.

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

perseveration

Step-by-step explanation:

The term you are looking for is "perseveration."

When the patient recovery time from a specific surgical procedure is normally distributed, with a mean of 5.2 days and a standard deviation of 2.3 days, the probability of spending more than 2 days in recovery will be 0.61.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. Information about the likelihood that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is used in epidemiology to comprehend the connection between exposures and the risk of health effects.

Here,

z=(X-μ)/σ

X=2

μ=5.2

σ=2.3

Z=(2-5.2)/2.3

Z=-1.39

-1.39+1

=0.39

1-0.39=0.61

The probability of spending more than 2 days in recovery will be 0.61 when the patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.2 days and a standard deviation of 2.3 days.

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Answer: x_>6

Step-by-step explanation:

Answer:

Length in feet = X - 80

Step-by-step explanation:

A = width x length

A/width = length

(x^2 -100x + 1600) /( x - 20) = length

(x - 20) (x - 80) / (x - 20) = length

x - 80 = length

x - 80 = length