find the solution set 2x+1+2=4

Answer:

p = 8

Step-by-step explanation:

Divide -5 to both sides

-5p = -40

5p = 40

p = 8

So p = 8

The volume of the metal tank is 0.15 cubic meters.

To calculate the volume of a cuboid, you multiply its three dimensions: length, width, and height.

The internal measurements of the metal tank are given as:

Length = 1 m

Width = 0.3 m

Height = 0.5 m

To find the volume, you simply multiply these dimensions together:

Volume = Length × Width × Height

Substituting the given values:

Volume = 1 m × 0.3 m × 0.5 m

Volume = 0.15 cubic meters

A cuboid's volume is determined by multiplying its three dimensions, which are length, width, and height.

The metal tank's inside dimensions are as follows:

length is 1 m.

Height = 0.3 m

Height: 0.5 meters

Simply multiplying these dimensions together yields the volume:

Volume equals length, width, and height

replacing the specified values:

Volume = 0.3 + 0.5 + 1 m

0.15 cubic meters of volume.

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Answer:

6

Step-by-step explanation:

What is the evaluation of 2 - 5 + 9?

2 - 5 = -3

-3 + 9 = 6

So, the answer is 6

The equation of the best fit line is (b) y = -0.98x + 0.8

from the question, we have the following parameters that can be used in our computation:

The graph

Using the least squares, we have the following summary

The regression equation is

y = mx + b

Where

m = SP/SSX = -10.6/10.8 = -0.98148

b = MY - bMX = 0.6 - (-0.98*0.2) = 0.7963

So, we have

y = -0.98x + 0.8

Hence, the equation is y = -0.98x + 0.8

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The overall score that would be received obtained as the product of weight and grade is 1.5

The overall score is the product of the Weight and grade value received .

(0.25 * 2) + (0.25 * 0) + (0.3 * 2) + (0.2 * 2)

0.5 + 0 + 0.6 + 0.4 = 1.5

Therefore, the overall score which would be received by the school is 1.5

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Derek should drill E 5.14 feet up to wall from C.

If a line is drawn parallel to any one side of a triangle so that it intersects the other two sides in two distinct points, then the other two sides of the triangle are divided in the same ratio.

Using the triangle proportionality theorem,

Therefore,

let

EC = x

4 / 3 = x / 9 - x

cross multiply

4(9 - x) = 3x

36 - 4x = 3x

36 = 3x + 4x

36 = 7x

divide both sides of the equation by 7

x = 36 / 7

x = 5.14 feet up the wall from C

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Answer:

D. 188

Step-by-step explanation:

Because the water tank's dimensions are 6 feet by 4 feet by 7 feet, this means that the areas of the three pairs of opposite faces are:

So, the total surface area of the water tank is 2 * (24 + 42 + 28) = 188 square feet.

Answer: 4000

Step-by-step explanation:

Each person received 1/4 gallon of water.

To determine how much water each person received, we can divide the total amount of water (3/4 gallon) equally among the three hikers.

Since there are three hikers, we need to divide the total amount of water by 3.

Dividing 3/4 gallon by 3, we perform the following calculation:

(3/4 gallon) ÷ 3 = (3/4 gallon) × (1/3) = (3/12) gallon

So, each person received 3/12 gallon of water.

To simplify the fraction, we can divide the numerator and denominator by their greatest common divisor, which is 3 in this case:

(3/12 gallon) ÷ 3/3 = (3/12) gallon × (1/3) / (1/3) = (1/4) gallon

Therefore, each person received 1/4 gallon of water.

As a decimal, 1/4 gallon is equal to 0.25 gallons.

Hence, each person received 0.25 gallons of water.

In conclusion, each person in the hiking group received 1/4 gallon or 0.25 gallons of water at the rest area.

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Rearranging the Future Value formula to highlight the present value is [tex]P = F/(1+r)^t[/tex].

The present value refers to the future value discounted at an interest rate.

The present value is the multiplication of the future value by the discount factor.  It can also be found by dividing the future value by the compounding factor.

Where the future value formula is:

[tex]F = P(1+r)^t[/tex]

Where F = Future value, P = Present value, r = interest rate, and t = time.

The present value formula can be rearranged from the future value formula as follows:

[tex]P = F/(1+r)^t[/tex]

Thus, the future value formula rearranged to highlight the present value changes from [tex]F = P(1+r)^t[/tex] to [tex]P = F/(1+r)^t[/tex].

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The range of the quadratic function g(x) = 3x² - 24x + 44 is [-4, ∝)

From the question, we have the following parameters that can be used in our computation:

g(x) = 3x² - 24x + 44

The vertex (x) is calculated as

x = 24/(2 * 3)

x = 4

So, we have

g(4) = 3 * 4² - 24 * 4 + 44

g(4) = -4

The leading coefficient is positive

So, we have

g(4) ≥ -4

As an interval, we have

[-4, ∝)

Hence, the range is [-4, ∝)

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The probability of losing the game is 0.9399. So, the answer is 0.9399.

The probability of losing the game is 0.9399. To determine the probability of losing, we must subtract the probability of winning from 1.

The probability of losing is equal to the complement of the probability of winning, and the complement of an event is the probability of the event not occurring.

Therefore, we will calculate the probability of the event not winning.  

We know that the probability of winning a two-spot Keno game is 0.0601.

This means that the probability of not winning is 1 - 0.0601 = 0.9399.

Therefore, the probability of losing the game is 0.9399. So, the answer is 0.9399.

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To convert a number from base 7 to base 10, we multiply each digit of the base 7 number by the corresponding power of 7 and sum the results.

In the base 7 number system, the digits range from 0 to 6.

To convert 36 in base 7 to base 10:

Identify the place value of each digit: The rightmost digit is in the ones place, and the leftmost digit is in the sevens place.

Multiply each digit by the corresponding power of 7:

3 * 7^1 + 6 * 7^0

Perform the calculations:

3 * 7 + 6 * 1

21 + 6

Add the results together:

27

Therefore, 36 in base 7 is equal to 27 in base 10.

The interval that contains the scalar for this problem is given as follows:

Between -1 and 0.

When a vector is multiplied by a scalar, each component of the vector is multiplied by the scalar.

For this problem, we have that the direction of the vector u changed when it was multiplied by the scalar, hence the scalar is a negative number.

As vector v is smaller than vector u, the scalar has an absolute value that is less than 1, hence the number is between -1 and 0.

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The exponential function that models a 15% decay is: y = (0.85)^t^(1/2)

To find the base that could be written in the blank to make the exponential function model a 15% decay, we can start by understanding the nature of exponential decay.

The general formula for exponential decay is given by:

y = A(1 - r)^t

Where:

y represents the final amount or value after time t.

A is the initial amount or value.

r is the decay rate (expressed as a decimal).

t is the time.

In this case, we want to find the decay rate (r) that corresponds to a 15% decay. A 15% decay means that the final amount is 85% of the initial amount. So, we can write the equation as:

y = A(1 - 0.15)^t

Simplifying further:

y = A(0.85)^t

Comparing this equation to the given form y = (_)t^(1/2), we see that the base in the blank must be 0.85.

Therefore, the exponential function that models a 15% decay is:

y = (0.85)^t^(1/2)

This equation represents a scenario where the initial value or amount (A) is being reduced by 15% over time (t), with the exponent of 1/2 indicating that the decay occurs at a square root rate.

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The derivative of the function [tex]y = x^2sin^4(x) + xcos^(-5)(x)[/tex]is given by [tex]2xsin^4(x) + 4x^2sin^3(x)cos(x) - sin(x)/(cos(x))^5.[/tex]

To find the derivative of the function [tex]y = x^2sin^4(x) + xcos^(-5)(x)[/tex], we will apply the product rule and chain rule.

Let's break down the function into its individual components for differentiation:

[tex]f(x) = x^2sin^4(x) + xcos^(-5)(x)[/tex]

Derivative of[tex]x^2sin^4(x):[/tex]

Applying the product rule, we differentiate x^2 and sin^4(x) separately.

[tex]d/dx (x^2sin^4(x)) = (2x)(sin^4(x)) + (x^2)(4sin^3(x)cos(x))[/tex]

Simplifying further:

[tex]= 2xsin^4(x) + 4x^2sin^3(x)cos(x)[/tex]

Derivative of xcos^(-5)(x):

Here, we will apply the chain rule as cos^(-5)(x) is a composite function.

Let u = cos(x), then the function can be rewritten as:

[tex]f(x) = x/u^5[/tex]

Using the chain rule, the derivative is given by:

d/dx (x/u^5) = (1/u^5)(du/dx)

To find du/dx, we differentiate cos(x) with respect to x:

du/dx = -sin(x)Substituting back into the equation:

[tex]d/dx (x/u^5) = (1/u^5)(-sin(x))[/tex]

Now, substituting u = cos(x) back into the equation:

[tex]= -sin(x)/(cos(x))^5[/tex]

Combining the derivatives of both components, we get:

[tex]f'(x) = 2xsin^4(x) + 4x^2sin^3(x)cos(x) - sin(x)/(cos(x))^5[/tex]

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1. The quadratic function for the Area in terms of x: A(x) = 24x.

2. The cross-sectional area is maximized when the depth of the gutter is 0.

3. The maximum cross-sectional area is square inches 0.

To determine the depth of the gutter that maximizes its cross-sectional area and allows the greatest amount of water to flow, we need to follow a step-by-step process.

1. Write a quadratic function for the area in terms of x:

The cross-sectional area of the gutter can be represented as a rectangle with a width of 24 inches and a depth of x. Therefore, the area, A(x), is given by A(x) = 24x.

2. The cross-sectional area is maximized when the depth of the gutter is:

To find the value of x that maximizes the area, we need to find the vertex of the quadratic function. The vertex of a quadratic function in form f(x) = ax² + bx + c is given by x = -b/(2a). In our case, a = 0 (since there is no x² term), b = 24, and c = 0. Thus, the depth of the gutter that maximizes the area is x = -24/(2 * 0) = 0.

3. The maximum cross-sectional area is square inches:

Substituting the value of x = 0 into the quadratic function A(x) = 24x, we get A(0) = 24 * 0 = 0. Therefore, the maximum cross-sectional area is 0 square inches.

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Rise over run is the ratio of the vertical change (rise) to the horizontal change (run) between two points on a line, representing the slope or steepness of the line.

Rise over run is a mathematical concept used to express the steepness or slope of a line.

It is also referred to as the slope or gradient of a line and is commonly denoted by the letter "m."

The rise refers to the vertical change or difference between two points on the line, while the run represents the horizontal change or difference between the same two points.

To calculate the rise over run, we take the difference in the y-coordinates (vertical change) and divide it by the difference in the x-coordinates (horizontal change) between two points on the line.

The resulting value represents the slope or steepness of the line.

For example, if we have two points on a line, (x1, y1) and (x2, y2), the rise over run can be calculated as:

Rise over run (m) = (y2 - y1) / (x2 - x1)

The value of the slope (m) can be positive, negative, or zero, indicating the direction and magnitude of the line.

A positive slope represents an upward trend from left to right, a negative slope represents a downward trend, and a zero slope represents a horizontal line.

Understanding the concept of rise over run is essential in various fields, such as mathematics, physics, engineering, and economics, as it helps in analyzing and interpreting the relationships between variables, rates of change, and the nature of linear functions and lines.

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The inverse of the function y = x³ - 27 is

[tex]y = \sqrt[3]{x - 3} [/tex]

The correct answer choice is option D.

y = x³ - 27

Reduce 27 to a number with cubic power

y = x³ - 3³

y = (x - 3)³

[tex]y = \sqrt[3]{x - 3} [/tex]

Hence, y = x³ - 27 is cubic root of x minus 3.

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We have verified the given identity: 6 cos(x + y)cos(x − y) = 6 cos^2(x) − 6 sin^2(y).

To verify the given identity, let's simplify the expression step by step:

Starting with the left side of the equation:

6 cos(x + y)cos(x − y)

Using the cosine of the sum and difference of angles formula:

6 [cos(x)cos(y) − sin(x)sin(y)][cos(x)cos(y) + sin(x)sin(y)]

Expanding the expression:

6 [cos(x)^2cos(y)^2 − sin(x)^2sin(y)^2]

Using the trigonometric identity cos^2(x) = 1 - sin^2(x):

6 [(1 - sin^2(x))(1 - sin^2(y)) − sin^2(x)sin^2(y)]

Expanding further:

6 [1 - sin^2(x) - sin^2(y) + sin^2(x)sin^2(y) - sin^2(x)sin^2(y)]

Combining like terms:

6 [1 - sin^2(x) - sin^2(y) + 2sin^2(x)sin^2(y)]

Now, let's simplify the right side of the equation:

6 cos^2(x) - 6 sin^2(y)

Using the trigonometric identity cos^2(x) = 1 - sin^2(x):

6 (1 - sin^2(x)) - 6 sin^2(y)

Simplifying further:

6 - 6 sin^2(x) - 6 sin^2(y)

Comparing the simplified expressions on both sides, we can see that they are equal:

6 [1 - sin^2(x) - sin^2(y) + 2sin^2(x)sin^2(y)] = 6 - 6 sin^2(x) - 6 sin^2(y)

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Answer:

  (x, y, z) = (-2, 2, 4)

Step-by-step explanation:

You want the solution to the equations ...

The coefficients of these equations can be written as an augmented matrix. The reduced row-echelon form of that matrix gives the solutions to the equations:

  (x, y, z) = (-2, 2, 4)

<95141404393>

Answer:

y = (3/4)x -13

Step-by-step explanation:

First, let's understand what it means when the question asks for the answer in slope-intercept form.

Slope intercept form: y=mx+b

m: Slope

b: Y-intercept

Next, let's write down what was given to us.

m: 3/4

Point on line: (8,-7)

First, let's replace m with 3/4 in our slope intercept form equation.

y=mx+b

y=(3/4)x+b

Now, we know that (8,-7) is a point of the graph. What this means is that when x=8, y must equal -7. Knowing this, lets replace x and y in our slope intercept form equation to solve for b.

y=(3/4)x+b

-7 = (3/4)(8) + b     [Simplify]

-7 = 6 + b     [Subtract 6 from both sides]

-13 = b

Lastly, let's put all the information we have together to write the equation of the line.

y=mx+b

m: Slope / (3/4)

b: Y-intercept / -13

y = (3/4)x -13

To check our answer, I plugged the equation into a grapher and made sure that the line produced had a slope of 3/4 and went through the point (8,-7). Attached is the graph of the line.

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To find the input horsepower of the engine, we can use the concept of percentage loss. If the engine has a 4% loss of power, it means the output power is 96% (100% - 4%) of the input power.

Let's denote the input horsepower as x. According to the given information:

Output power = 240 HP = 96% of input power

Mathematically, we can represent this as:

0.96x = 240

To solve for x, we divide both sides of the equation by 0.96:

x = 240 / 0.96

Calculating this, we find:

x ≈ 250

Therefore, the input horsepower of the engine is approximately 250 HP.

The inequalities that define the unshaded region for this problem is given as follows:

For the solid line, we have that it has a slope of 4 with an intercept of 0, and the values that are above the line are shaded, hence the inequality is given as follows:

y ≥ 4x.

For the dashed line, we have a line with a slope of 1 and an intercept of -4, and the values that are below the line are shaded, hence the inequality is given as follows:

y < x - 4.

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Bi-monthly and extra principal payments on loans or investments relate to the time value of money by accelerating repayment and reducing overall interest.

Making bi-monthly and extra principal payments on a loan or investment relates to the time value of money by accelerating the repayment process and potentially reducing the overall interest paid.

Bi-monthly payments involve paying half of the monthly amount every two weeks, resulting in 26 payments per year instead of 12. This shorter interval reduces the outstanding balance more frequently, leading to faster interest reduction and loan payoff.

The time value of money concept recognizes that money available today is worth more than the same amount in the future.

Extra principal payments involve paying more than the required amount towards the loan or investment principal. By reducing the principal faster, the interest charged on the remaining balance decreases, thereby saving money in the long run.

The time value of money acknowledges that reducing debt or increasing investment value earlier provides greater financial benefits due to the potential for compounding growth or savings over time.

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a) A function that gives the area of the garden (in square meters) in terms of x is A(x) = 120x - x².

b) The side length that gives the maximum area that the garden can have is x = 60 meters.

c) The maximum area that the garden can have is 3,600 square meters.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths, we have:

360 = 2(x + W)

120 = x + W

W = 120 - x

Therefore, the area of the rectangular garden (in terms of x) is given by this function;

A = LW

A(x) = x(120 - x)

A(x) = 120x - x²

Part b.

For the side length, we would take the first derivative of the area:

A(x) = 120x - x²

A'(x) = dA/dx

A'(x) = 120 - 2x

120 - 2x = 0

x = 120/2

x = 60 meters.

Part c.

W = 120 - x

W = 120 - 60

W = 60 meters.

Therefore, the maximum area can be calculated as follows;

A = xW

A = 60 × 60

A = 3,600 m².

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Complete Question:

Raul has 360 meters of fencing. He will use it to form three sides of a rectangular garden. The fourth side will be along a house and will not need fencing. As shown below, one of the sides has length x (in meters).

(a) Find function that gives the area A(x) of the garden (in square meters) in terms of x. A(x) =

(b) What side length x gives the maximum area that the garden can have? Side length x = meters

(c) What is the maximum area that the garden can have?

Maximum area: square meters

The two numbers that add together to make -4 but subtract to make +8 are 2 and -6.

Two numbers that add together to make -4 but subtract to make +8, we can set up a system of equations.

Let's call the two numbers x and y.

We can set up the following equations:

Equation 1: x + y = -4

Equation 2: x - y = 8

To solve this system of equations, we can use the method of elimination. Adding Equation 1 and Equation 2 eliminates the variable y:

(x + y) + (x - y) = -4 + 8

2x = 4

x = 2

Now, we can substitute the value of x into either Equation 1 or Equation 2 to solve for y.

Let's use Equation 1:

2 + y = -4

y = -6

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Answer:

6 gallons 72-octane

6 gallons 84-octane

Step-by-step explanation:

(84 + 72)/2 = 78

The average octane in 72-octane and 84-octane is 78-octane.

Therefore, you need equal amounts of each.

Answer:

6 gallons 72-octane

6 gallons 84-octane

Answer:

B

Step-by-step explanation:

[tex]\frac{4(x+3)(x+1)}{(x+5)(x-5)}[/tex] ← substitute x = 3 into the expression

= [tex]\frac{4(3+3)(3+1)}{(3+5)(3-5)}[/tex]

= [tex]\frac{4(6)(4)}{8(-2)}[/tex]

= [tex]\frac{96}{-16}[/tex]

= - 6