Consider the quadratic expression given below.

4x^2 + 8x - 60

Factor the following expression completely.

Answer:

15000 pay on the ship for me

Answer:

3, 6, 9, 12, 15

1, 10, 19, 28,37,46

3, 9, 27, 81. 243, 729

Step-by-step explanation:

1. keep adding 3

2. keep adding 9

3. keep multiplying by 3

The two points are t = 10.095, and t = 0.216 in time when the object is 167 feet above the ground.

The quadratic function is defined as a function containing the highest power of a variable is two.

The projectile is shot vertically up into the air with an initial velocity of 165 feet per second from an initial height of 132 feet off the ground, then the height of the projectile,

h, in feet, t seconds after its shot is given by the equation:

h = -16t² + 165t + 132

To determine the two points in time when the object is 167 feet above the ground.

Substitute the value of h = 167 in the above equation,

167 = -16t² + 165t + 132

16t² - 165t - 132 + 167 = 0

16t² - 165t + 35 = 0

Compare the given function to the standard quadratic function f(x) = ax² + b x + c.

We get a =16, b = -165 and c = 35

Using the quadratic formula to solve the above quadratic function

\(t = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\)

\(t=\frac{-\left(-165\right)\pm \sqrt{\left(-165\right)^2-4\cdot \:16\cdot \:35}}{2\cdot \:16}\)

\(t=\frac{-\left(-165\right)\pm \sqrt{24985}}{2\cdot \:16}\)

\(t=\frac{-\left(-165\right)+\sqrt{24985}}{2\cdot \:16},\:t=\frac{-\left(-165\right)-\sqrt{24985}}{2\cdot \:16}\)

\(t=\frac{165+\sqrt{24985}}{32},\:t=\frac{165-\sqrt{24985}}{32}\)

t = 10.095, t = 0.216

Hence, the two points are t = 10.095, and t = 0.216 in time when the object is 167 feet above the ground.

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If the length is Fraction 2 over 3 unit and the width is Fraction 1 over 3 unit The perimeter of the rectangle is 2 units.

First, substitute l = 2/3 and w = 1/3 in the expression for the perimeter of the rectangle:

P = 2(l + w)

P = 2(2/3 + 1/3)

P = 2(1)

P = 2

A rectangle is a four-sided flat shape with four right angles. It is a type of quadrilateral, which means it has four sides.

The perimeter of a rectangle is the total distance around the outside of the rectangle. It is calculated by adding up the length of all four sides of the rectangle. The formula for the perimeter of a rectangle is:

Perimeter = 2(length + width)

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The combinations of partial quotients that can be used to find the quotient of 84÷4 are given as follows:

What is the partial quotient method?

when a division is done applying the partial quotient method, consecutive subtractions are done with n groups of the divisor. Each partial quotient is the number of groups of each term and the final quotient is the sum of the partial quotients.

The final quotient of 84÷4 as follows:

84÷4 =21

hence the sum of quotients is 21.

The possible combinations are only two.

The other combinations are incorrect.

Answer:

93mL 98mL

Step-by-step explanation:

First add the mL. There are 78mL, so it cannot become a liter. Then add the liters.

Answer:

{x:x is having odd number}

Answer:

I am pretty sure  it is dependent  

Let me know if it is wrong.

patternpatternGreat!

The patteren is 1, 4, 9, 16,...

All these numbers are square numbers, which means

1 * 1 = 1

2 * 2 = 4

3 * 3 = 9

4 * 4 = 16

That means

1st term = 1^2

2nd term = 2^2

3rd term = 3^2

4th term = 4^2

so

nth term = n^2

The conjecture is

The pattern is 100%, 93%, 86%, ...........

Since 93% - 100% = -7%

Since 86% - 93% = -7%

Then this pattern is decreases by 7%

So it is an arithmetic sequence

Its rule is:

Where a is the first term

d is the constant difference

n is the position of the number

Since a = 100%

Since d = -7%

Let us substitute these values in the rule

Simplify it

an = 100% + (n)(-7%) + (-1)(-7%)

an = 100% + (-7n%) + (7%)

Add the like terms

an = (100% + 7%) - 7n%

an = 107% - 7n%

Let us check the rule

What is the 3rd term

n = 3

a3 = 107% - 7(3)%

a3 = 107% - 21%

a3 = 86% which is true

Answer:

B... Because indicates the direction of gravity because its direction is downward

Answer:b

Step-by-step explanation:

Answer:

Step-by-step explanation:

large necklace; $5.70

$4.60 x 6= $27.60

$33.30 total

Answer:

2,-3

Step-by-step explanation:

hope this helps :)

Answer:

11x + 4y - y^2

Step-by-step explanation:

You plus the same variables, in this time you got 9x and 2x so it's 11x!

Answer:

11x + 4y - y²

Step-by-step explanation:

9x + 4y + 2x - y²

combine like terms

11x + 4y - y²

For a clinical trial (study) on the mean GPA of night students, the appropriate null and alternative hypotheses would be given by:

A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.

For a clinical trial (study) on the mean GPA of night students, the appropriate null and alternative hypotheses would be given by:

In conclusion, we can infer and logically deduce that this test would be right-tailed.

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y = 1.5x + 0.5 is the equation of the line passing through the coordinate points

The formula for finding the equation of a line in slope-intercept form is expressed as:

y =mx + b

where:

m is the slope

b is the intercept

Determine the slope

slope = 5-2/3-1

slope = 3/2

slope = 1.5

Determine the y-intercept

y = mx + b

5 = 1.5(3) + b

5 = 4.5 + b

b = 0.5

Hence the required equation of the line passing through ( 1,2) and (3,5) is

y = 1.5x + 0.5

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Complete question

What's the equation of a line that passes through (1,2) (3,5)?

Answer:

Option B

Step-by-step explanation:

Well, now that I found out the prices per ounce, it has to be option B. Here is my reasoning:

Option A, when you do 2.98÷15.5, you get 0.19225...

Option B, is a different story. When you do the same process, it amazingly comes out to 0.1785...(this means that Option B is 0.2 cents (rounded) cheaper per unit, then Option A.

So its option B

Your welcome.

The derivative of f(x) function is given by f'(x) = (3x + 1)² (x - 4) (x²+ 1)³ · sin(x) · (12/(3x + 1) + 1/(x - 4) + 6x/(x² + 1) + cos(x)/sin(x)).

To find the derivative of the function f(x) = (3x + 1)² (x - 4) (x² + 1)³· sin(x) using logarithmic differentiation, we follow these steps:

Take the natural logarithm of both sides of the equation: ln(f(x)) = ln((3x + 1)² (x - 4) (x² + 1)³ · sin(x)).

Use the properties of logarithms to simplify the expression:

ln(f(x)) = 4ln(3x + 1) + ln(x - 4) + 3ln(x² + 1) + ln(sin(x)).

Differentiate both sides of the equation with respect to x using the chain rule and product rule:

(1/f(x)) · f'(x) = 4(1/(3x + 1)) · 3 + (1/(x - 4)) + 3(1/(x² + 1)) · 2x + (1/sin(x)) · cos(x).

Simplify the right-hand side of the equation:

f'(x)/f(x) = 12/(3x + 1) + 1/(x - 4) + 6x/(x² + 1) + cos(x)/sin(x).

Multiply both sides of the equation by f(x) to isolate f'(x):

f'(x) = f(x) · (12/(3x + 1) + 1/(x - 4) + 6x/(x² + 1) + cos(x)/sin(x)).

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Express the weight W of a bearing in terms of its surface area:To express the weight W in terms of the surface area A, we can rearrange the equation for surface area A = 4πr^2 to solve for r in terms of A:

A = 4πr^2

r^2 = A / (4π)

r = √(A / (4π))

Now substitute this value of r into the weight formula W = (4/3)πp(r^3):

W = (4/3)πp(√(A / (4π)))^3

Simplifying further:

W = (4/3)πp(A^(3/2)) / (4^(3/2)π^(3/2))

W = (4/3)πp(A^(3/2)) / (4^(3/2)π^(3/2))

W = (4/3)πp(A^(3/2)) / (4√π)

W = (4/3)√πp(A^(3/2)) / 4√π

W = (1/3)√(πp)(A^(3/2))

Therefore, the weight W of a bearing in terms of its surface area A is (1/3)√(πp)(A^(3/2)).

Express the bearing's surface area A in terms of its weight:

To express the surface area A in terms of the weight W, we rearrange the weight formula W = (4/3)πp(r^3) to solve for r in terms of W:

W = (4/3)πp(r^3)

r^3 = (3W) / (4πp)

r = (3W / (4πp))^(1/3)

Now substitute this value of r into the formula for surface area A = 4πr^2:

A = 4π((3W / (4πp))^(1/3))^2

A = 4π((3W / (4πp))^(2/3))

Therefore, the surface area A of a bearing in terms of its weight W is 4π((3W / (4πp))^(2/3)).

c. For steel, p = 7.85 g/cm^3. What is the surface area of a bearing weighing 0.62 g?

Given: W = 0.62 g, p = 7.85 g/cm^3.

To find the surface area A, we need to substitute the given values into the formula for surface area derived in part (b):

A = 4π((3W / (4πp))^(2/3))

Substituting the values:

A = 4π((3(0.62) / (4π(7.85)))^(2/3))

Simplifying further:

A = 4π((0.186 / 31.02)^(2/3))

A = 4π(0.00599051^(2/3))

A = 4π(0.0864001)

A ≈ 1.087 cm^2

Therefore, the surface area of a bearing weighing 0.62 g is approximately 1.087 cm^2.

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Answer:

C

Step-by-step explanation:

The positions through which the equation of f^-1(x) travels are: (4, 1), (6, 4)

A mathematical statement called an equation is comprised of two expressions joined together with the equal sign.

A formula would just be 3x - 5 = 16, for instance.

When this equation is solved, we observe that the value of the variable x is 7.

So, (1, 4) and (4, 6) are points through which the equation of f(x) goes.

If the f (x) equation contains (x, y).

Therefore, the f^-1(x) equation is as follows: (y, x).

Here, the f (x) equation passes through the following points: (1, 4) and (4, 6).

So, (4, 1) and (6, 4) are the points through which the equation of f^-1(x)  goes through.

Therefore, the positions through which the equation of f^-1(x) travels are:

(4, 1), (6, 4)

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Correct question:
If the equation of f(x) goes through (1,4) and (4,6), what points does f^-1(x) go through?

Answer:

100⁰

because this is a quadrilateral inscribed in the circle

=> x + 80 = 180

<=> x = 180 - 80 = 100⁰

Answer:

x = 6

Step-by-step explanation:

Coach ticket = $180

first class ticket = $1020

people = 8

Let x be number of coach tickets

Then number of first class tickets = (8 - x)

x * 180 + (8 - x) * 1020 = 3120

180 X + 8 * 1020 - 1020 x = 3120

180 x + 8160 - 1020 x = 3120

180 x - 1020 x = 3120 -8160

- 840 x = - 5040

840 x = 5040

x = 6

So 6 coach class tickets and 2 first class tickets

Answer:

She bought 8 coach tickets

And 5 first class tickets

Step-by-step explanation:

390 x 8 = 3,120

1000 x 5 = 5,000

3,120 + 5,000 = 8,120

Answer:

(c)the sum of the GP.?

Step-by-step explanation:

Overloading in object-oriented programming enables class methods with different parameter lists and return types to perform distinct tasks based on input parameters, improving readability and reducing code complexity.

In the object-oriented model, if class methods have the same name but different parameter lists and/or return types, they are said to be Overloaded.

In object-oriented programming (OOP), overloading refers to the ability of a function or method to be used for a variety of purposes that share the same name but have different input parameters (a parameter is a variable that is used in a method to refer to the data that is passed to it).In object-oriented programming, method overloading allows developers to use the same method name to perform distinct tasks based on the input parameters. The output of the method is determined by the input parameters passed. This enhances the readability of the program and makes it easier to use because it minimizes the number of method names used for distinct tasks.The overloaded method allows the same class method to be used to execute a variety of operations.

It's a great feature for developers because it lets them write fewer lines of code. Overloaded methods are commonly employed when the same task can be completed in multiple ways based on the input parameters.

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The graph of the linear equation 3x + 6y = 18 is a straight line passing through the points (6, 0) and (0, 3), with the x-intercept at (6, 0) and the y-intercept at (0, 3).

The given linear equation is 3x + 6y = 18.

To sketch the graph, we need to find the x-intercept and y-intercept, if they exist.

To find the x-intercept, we set y = 0 and solve for x:

3x + 6(0) = 18

3x = 18

x = 6

So, the x-intercept is (6, 0).

To find the y-intercept, we set x = 0 and solve for y:

3(0) + 6y = 18

6y = 18

y = 3

So, the y-intercept is (0, 3).

Now, let's plot the points (6, 0) and (0, 3) on a coordinate plane.

The x-axis represents the values of x, and the y-axis represents the values of y.

We can label the axes accordingly.

The x-intercept is at (6, 0), and the y-intercept is at (0, 3).

Since the equation is linear, we can draw a straight line passing through these two points.

By connecting the x-intercept and y-intercept with a straight line, we obtain the graph of the linear equation 3x + 6y = 18.

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False claims do not have to engage with previous theories in order to be effective. So it must contradict previous theories. So the option d is correct.

A tentative, verifiable explanation for a natural world phenomenon is what is known as a scientific hypothesis. The scientific method's foundational element is it.

It's sometimes referred to as a "informed guess" that was made using past knowledge and observation. Despite the fact that this is true, a hypothesis is a better guess.

Creating a hypothesis calls for active observation and background research, in contrast to making a "informed guess," which implies a random prediction based on one's expertise. A hypothesis is predicated on the fundamental tenet that no outcome is predetermined.

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Answer:

Step-by-step explanation:

The possibility of answers are endless :)

Driver D ) 144.9 , 144.953 , 145.123

Literally any number between 144.809 and 145.155 would work

Answer:

144.982

Step-by-step explanation:

145.155+144.809=289.964

289.964/2=144.982

a) The break-even points for the given cost and revenue functions are approximately x = 16.526 and x = 6.474.

b) The break-even points for the given cost and revenue functions are approximately x = 12.225 and x = 62.775.

c) The maximum profit for the given cost and revenue functions is approximately $843.75.

a) To find the break-even points, we need to determine the values of x where the total costs (C(x)) equal the total revenues (R(x)). We set C(x) = R(x) and solve for x:

C(x) = R(x)

1760 + 8x + 0.6x² = 100x - 0.4x²

Combining like terms and rearranging the equation, we get:

1x² - 92x + 1760 = 0

Solving this quadratic equation, we find two solutions for x:

x ≈ 16.526

x ≈ 6.474

b) Similarly, we set C(x) = R(x) and solve for x:

900 + 25x = 100x - x²

Rearranging the equation, we get:

x² - 75x + 900 = 0

Solving this quadratic equation, we find two solutions for x:

x ≈ 12.225

x ≈ 62.775

c) To find the maximum revenue, we need to determine the vertex of the revenue function R(x) = 100x - x². The x-coordinate of the vertex is given by x = -b / (2a), where a and b are the coefficients of the quadratic equation.

In this case, a = -1 and b = 100. Plugging in the values, we get:

x = -100 / (2 * -1) = 50

Substituting this value back into the revenue function, we find:

R(50) = 100(50) - (50)² = 5000 - 2500 = 2500

Therefore, the maximum revenue for the given cost and revenue functions is $2500.

To find the maximum profit, we need to subtract the total costs from the total revenues. Given that the cost function is C(x) = 900 + 25x, the profit function is P(x) = R(x) - C(x). Substituting the revenue and cost functions, we have:

P(x) = (100x - x²) - (900 + 25x)

P(x) = -x² + 75x - 900

To find the maximum profit, we need to determine the vertex of the profit function. Using the same formula as before, we find:

x = -75 / (2 * -1) = 37.5

Substituting this value back into the profit function, we find:

P(37.5) = -(37.5)² + 75(37.5) - 900 ≈ 843.75

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(a) The graph of the linear functions is as attached.

(b) The equation of the linear function in slope-intercept form is; y = x

(c) The equation of the transformed function in slope-intercept form is;

y = x + 2 and y = x - 3

Functions are defined as the relationship between sets of values. For example, in the function; y = f(x), for every value of x there exists a set of y values.

x is the independent variable.

y is the dependent variable.

If the linear function is; y = x,

The equation of the transformation in slope-intercept form is given as;

For translation of 2 units up, we have;

y = x + 2

For a translation of 3 units down, we have;

y = x - 3

Thus, the required graph has been attached and the solution is determined.

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Step-by-step explanation:

Sum of angles in a triangle = 180°.

=> s° + (s/7 + 3)° + (s/7 - 3)° = 180°

=> 9/7 * s° = 180°

=> s° = 180° * (7/9) = 140°

Hence the value of s is 140.