A passenger train and a freight train leave cities 260 mi apart and travel toward each other. The passenger train is traveling
15 mph faster than the freight train. Find the speed of each train if they pass each other after 4 hr.

Answer:

To calculate the cost of painting the top surface of 20 engine parts, we need to find the surface area of one engine part and then multiply it by 20.

To find the surface area, we need to find the length of the curved surface. We can do this by using the Pythagorean theorem to find AB and then use that to find the circumference of the curved surface.

AB^2 = BO^2 + AO^2 = 9 + 36 = 45

AB = sqrt(45) = 3 sqrt(5)

Circumference = 2 * pi * AB = 2 * pi * 3 sqrt(5) = 6 pi sqrt(5)

Using the fact that the reflex angle BÔC is 240 degrees, we can find the length of the curved surface:

240° / 360° = 2/3 of the circumference

Curved surface length = 2/3 * 6 pi sqrt(5) = 4 pi sqrt(5)

Finally, we can find the surface area of one engine part:

Surface area = (2 * 6 * 3) + (4 pi sqrt(5) * 6) = 36 + (24 pi sqrt(5))

To paint 20 engine parts, the cost would be:

20 * surface area * 15p = 20 * 36 + 20 * 24 pi sqrt(5) * 15p = 720 + (24 * 20 * 15 * pi * sqrt(5)) p = 720 + 720 pi sqrt(5) p

Since 1 pound is equal to 100 pence, the cost in pounds would be:

720 + 720 * pi * sqrt(5) / 100 = 720 + 720 * 0.177 / 100 = 720 + 1.264

So, the cost to paint the top surface of 20 engine parts would be 721.264 pounds.

Answer:

Step-by-step explanation:

Answer:

x = 2/3

y = 5

Step-by-step explanation:

6x + y = 9

3x -4y = -18

Times the second equation by -2

6x + y = 9

-6x + 8y = 36

9y = 45

y = 5

Now put 5 in for y and solve for x

6x + 5 = 9

6x = 4

x = 2/3

Let's check

6(2/3) + 5 = 9

4 + 5 = 9

9 = 9

So, x = 2/3 and y = 5 is the correct answer.

The number 0.54227406110177, is non- repeating and non- terminating, so, that is an irrational number.

We have to determine that the number 0.54227406110177, is rational or irrational.

There is infinite numbers of rationals or irrationals between two real numbers. Rational number is of form p/q where q≠0 and p and q are integers. For example 1/2 , 1/4 are rationals. To identify if a number is rational or not, check the following conditions :

The numbers which are not rational numbers are called irrationals. Here, see the number 0.54227406110177, no repetition of numbers in decimal form and non- terminating. So, it not a rational number. Hence, it is an irrational.

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The polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. -5, -1, 2 is,

⇒ f (x) = x³ + 4x² - 7x - 10

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

For a polynomial,

A leading coefficient = 1,

And, the given zeros = -5, -1, 2

Now, We know that;

The standard polynomial is given by:

⇒ f (x) = a (x - p) (x - q) ...

Where, 'a' is leading coefficient and p, q, .. are zeroes.

Here, A leading coefficient = 1,

And, the given zeros = -5, -1, 2

Hence, The polynomial is,

⇒ f (x) = 1 (x - (-5)) (x - (- 1)) (x - 2)

⇒ f (x) = (x + 5) (x + 1) (x - 2)

⇒ f (x) = (x + 5) (x² - 2x + x - 2)

⇒ f (x) = (x + 5) (x² - x - 2)

⇒ f (x) = x³ - x² - 2x + 5x² - 5x - 10

⇒ f (x) = x³ + 4x² - 7x - 10

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Check the picture below.

The zeros of the equation x² - 4x + 4 = 0 is 2.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

A quadratic equation,

x² - 4x + 4 = 0.

To find the zeros:

Solving further,

x² - 4x + 4 = 0.

x² - 2x -2x + 4 = 0.

x(x - 2) -2(x - 2) = 0.

(x - 2)² = 0.

x  = 2.

Hence, 2 is zeros.

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The complete question:

Solve the quadratic equation and find the zeros.

The equation,

x² - 4x + 4 = 0.

The best measure of variability is the standard deviation.

Player A is the most consistent, with an IQR of 1.5.

The correct option is C.

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.

Given:

The table shows the number of goals made by two hockey players.

Player A:

2, 3, 1, 3, 2, 2, 1, 3, 6

Mean = 2.56

S.D. = 1.51

Player B:

1, 4, 5, 1, 2, 4, 5, 5, 11

S.D. = 3.03

The best measure of variability is the standard deviation.

Player A is the most consistent, with an IQR of 1.5.

Therefore, the best measure of variability is the standard deviation.

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Answer:1.5

Step-by-step explanation:

The amount deposited in the Patricia retirement savings plan are:

Amount deposited in the twentieth year is $1150.

Total amount deposited in time span of twenty years is $13,500.

Amount deposited by Patricia in the first year ' a₁ ' = $200

Difference between the amount deposited in the subsequent year is

'd' = $50

Amount deposited during 20th year

Let 'n' be the 20th year

The above situation represents it is arithmetic progression problem

nth term of A.P. is :

aₙ = a₁ + ( n - 1 ) d

Substitute the value we get,

a₂₀ = 200 + ( 20 - 1 ) 50

⇒ a₂₀ = 200 + 19 × 50

⇒ a₂₀ = 200 + 950

⇒ a₂₀ = $1150

Total amount deposited in twenty years

S₂₀ = (n/2) [ 2 a₁+ ( n - 1 )d ]

Substitute the value we get,

⇒S₂₀ = ( 20 /2 ) [ 2(200 ) + 19 × 50 ]

⇒ S₂₀ = 10 [ 400 + 950 ]

⇒S₂₀ = $13,500

Therefore, the amount deposited in the twentieth year is $1150 and total amount deposited in twenty years is $13,500.

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Answer:

Below

Step-by-step explanation:

12 + 3s + 9s + 2 =

(3s+9s) + (12+2) =

12s + 14           ( or   2 (6s+7)   )

Answer:

$55.44 is the price of the sunglasses

Step-by-step explanation:

Price Of Sunglasses = $56

10% Discount = $5.6

So, $56-$5.6 = $50.4 <------ Applying Discount

10% of $50.4 = $5.04 <------ Price of Processing Fee for Discounted Price

$50.4+$5.04 = $55.44 <------ Total Price

The discounted price is $50.4 and we take 10% of that [discounted price] and we add it to the discounted price. 10% of that is $5.04. = $55.44

Answer:

$55.44

Step-by-step explanation:

56 - 56(0.10) = 50.40  price with 10% off

50.40 + 50.40(0.10) = 55.44   10% processing fee added to discounted price

The missing values are derived from the graph as follows:

3 ) 7, 14, 21, 28, 35

4) 3, 7, 10, 14, 17

5) 1, 21, 10, 49, 19

In mathematics, a graph is defined as a graphical representation or diagram that organizes facts or values. The graph's points frequently reflect the relationship between two or more objects.

In order to solve for the above values, the best way is to spot the function that exists in the graph which is given as:

F(y) = 3.5x

In the first table, where x = 2

y= 3.5 *2

= 7

This iteration goes on and on and is consistent for all the values.

In the second table,

Where F(y) is known, for example 10.5, then x is derived as:

10.5 = 3.5x (divide both sides by 3.5)

x = 3

This iteration goes on and on and is consistent for all the values.

In the third table, we simply swap the values back and forth using the function F(y) = 3.5x to derive all values.

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The column vectors of the given matrix is linearly dependent as determinant is equal to zero.

To find the column vectors of the matrix is linearly independent or linearly dependent.

Value of the determinant is equal to zero it implies linearly dependent.

And if determinant is not zero it is linearly independent.

Let 'A' be the given matrix is:

A = [tex]\left[\begin{array}{ccc}1&0&5\\-2&1&-6\\0&2&8\end{array}\right][/tex]

Determinant of A

= 1 ( 8 - (-12)) - 0( -16 -0 ) + 5 (-4 -0 )

= 1 (20 ) - 0  -20

= 20 -20

= 0

Here det(A) = 0

Therefore, the column vectors of the matrix is linearly dependent as det(A) = 0.

The above question is incomplete, the complete question is:

Are the column vectors of this matrix linearly independent or linearly dependent? show all explanations or computations.

[tex]\left[\begin{array}{ccc}1&0&5\\-2&1&-6\\0&2&8\end{array}\right][/tex]

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Answer: To find the mean hourly wage, you need to sum up the total wages of all employees and then divide by the number of employees. The total hourly wage for 25 phone operators is 25 * $22.85 = $571.25. The total hourly wage for 5 supervisors is 5 * $27.25 = $136.25. The combined total is $571.25 + $136.25 = $707.50. The mean hourly wage for the 30 employees is $707.50 / 30 = $23.58. So, the answer is approximately $23.58.

Step-by-step explanation:

Answer:

rectangular prism has 6 faces, 8 vertices (or corners) and 12 edges.

Step-by-step explanation:

hopefully this is the answer you are looking for.

Answer:

Step-by-step explanation:

Lin counts 5 bacteria under a microscope. She counts them again each day for four days, and finds that the number of bacteria doubled each day—from 5 to 10, then from 10 to 20, and so on.

Is the population of bacteria a function of the number of days? If so, is it linear? The population of bacteria is a function. The relationship is linear.

The two solutions of the quadratic equations are 8,-4 and the negative solution -4

A quadratic equation can be written in the standard form as ax2 + bx + c = 0, where a, b, c are constants and x is the variable. The values of x that satisfy the equation are called solutions of the equation, and a quadratic equation has at most two solutions.

Given here: when 32 subtracted from the square of a number and the result is 4 times the number.

Let x be the number then we have

x²-32=4x

x²-4x-32=0

x²-8x+4x-32=0

x(x-8)+4(x-8)=0

(x-8) (x+4) =0

Thus the two solutions of the quadratic equations are 8,-4

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Answer:

x = 1.523

Step-by-step explanation:

Given
[tex]\quad\quad e^{x-1} = 3^{2-x}[/tex]

we are asked to solve for x

Take natural logs on both sides:
[tex]\ln \left(e^{x-1}\right)=\ln \left(3^{2-x}\right)\\\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)}\\\\\ln \left(e^{x-1}\right)=\left(x-1\right)\ln \left(e\right)\\\\\rightarrow \left(x-1\right)\ln \left(e\right)=\ln \left(3^{2-x}\right)[/tex]substitute on left side of original eqn

[tex]\ln \left(3^{2-x}\right)=\left(2-x\right)\ln \left(3\right)\\\\[/tex]

Therefore we get
[tex]\left(x-1\right)\ln \left(e\right)=\left(2-x\right)\ln \left(3\right)[/tex]

But ln(e) = 1

So we get
[tex]x - 1 = (2-x)\;\ln(3)\\\\[/tex]

So the expression becomes

[tex]x - 1 = (2- x) \ln(3)\\\\x - 1 = 2\ln(3) - x \ln(3)[/tex]

Add [tex]x\ln(3)[/tex] on both sides:

x + x ln(3) - 1 = 2ln(3)

Add 1 to bot sides:
x + x ln(3) = 2ln(3) + 1

x(1 + ln(3)) = 2 ln3 + 1

ln(1 + \ln(3)) = 2.09861

2ln(3) + 1 =3.1972

So we get

x(2.0986) = 3.1972

x = 3.1972/2.0986 = 1.52349

Rounded to 3 decimal places, the answer is 1.523

Answer:

Subtracting an expression is similar to distributing a -1 because it cancels out the numbers in the expression.

Step-by-step explanation:

Step-by-step explanation:

x+4y=0

2x−y=18

​To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

x+4y=0,2x−y=18

Choose one of the equations and solve it for x by isolating x on the left-hand side of the equal sign.

x+4y=0

Subtract 4y from both sides of the equation.

x=−4y

Substitute −4y for x in the other equation, 2x−y=18.

2(−4)y−y=18

Multiply 2 times −4y.

−8y−y=18

Add −8y to −y.

−9y=18

Divide both sides by −9.

y=−2

Substitute −2 for y in x=−4y. Because the resulting equation contains only one variable, you can solve for x directly.

x=−4(−2)

Multiply −4 times −2.

x=8

The system is now solved.

x=8,y=−2

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The simplified expression 2-6/-2-4-12/6x-3 is given as follows:

-2 - 2x.

The expression for this problem is defined as follows:

[tex]2 - \frac{6}{-2} - 4 - \frac{12x}{6} - 3[/tex]

The division operation has a higher precedence over the subtraction operations, hence:

Hence the expression can be written as follows:

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

Then combining the like terms, which are the constant, the simplified expression is given as follows:

-2 - 2x.

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By applying rate of change concept it can be concluded that the area will change at a rate of 176 cm² / minute.

Rate of change is the change in values of a dependent variable concerning the independent variables.

The rate of change of a function shows how the function is changing from one x value to another. Whilst, differentiation is when you have an instantaneous rate of change at a single point.

We have the following information:

The rate of change of a circle = 7 cm/minute = dr/dt

We have to find the rate of change of the circle when r = 4 cm

To do so, we will use the derivative of the circle area:

A = πr²

dA/dr = 2πr

dA/dt = dA/dr × dr/dt

         = 2πr × 7  

         = 14πr

Now we input r = 4 cm into this equation:

rate of change of the area =  14*22/7*4

                                            =  176 cm² / minute

Thus, when r = 4 cm, the area will change at a rate of 176 cm² / minute.

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Answer:

Step-by-step explanation:

[tex]x_{1}[/tex] = - 5 , f( [tex]x_{1}[/tex] ) = 0 ;

[tex]x_{2}[/tex] = - 2 , f( [tex]x_{2}[/tex] ) = 0 ;

[tex]x_{3}[/tex] = 4 , f( [tex]x_{3}[/tex] ) = 0 ;

The slope-intercept form of the linear equation is:

y = 7 + (7/3)*x

A linear equation in the slope-intercept form is:

y = a*x + b

So, to write the given line in that form, we just need to isolate the variable x.

We have the equation:

-7x + 3y = 21

3y = 21 + 7x

y = (21 + 7x)/3

y = 7 + (7/3)*x

That is the equation in the slope-intercept form.

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Answer:

Geometry in Mathematics is the study of shape and figures.

Answer:

Geometry refers to a branch of mathematics which is focused on the measurement and relationship of lines, angles, surfaces, solids and points. For instance, the calculation of a triangle's angles is an example of geometry.

The zeroes of the quadratic function 2x² - 7x - 4 is 1 and 4,

known as roots.

A quadratic equation is an algebraic expression in the form of variables and constants.

itsA quadratic equation has two roots as it's degree is two.

We know, The general form of a quadratic equation is x² + bx + c.

Let, y = x² + bx + c.

At, (0, - 2).

- 2 = 0 + 0 + c.

c = - 2.

At, (4, 0).

0 = 4² + 4b - 2.

0 = 14 + 4b.

b = - 7/2.

So, It is x² - (7/2)x - 2 = 0.

2x² - 7x - 4 = 0.

2x² - 8x + x - 4 = 0.

2x(x - 4) - 1(x - 4) = 0.

(x - 4)(x - 1) = 0.

So, the zeroes of the function are 4 and 1.

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Answer:

Step-by-step explanation:

To find the value of "a" in the equation y = a(x + 3)(x - 5), we can use the fact that the function passes through the point (6, 45).

Step 1: Substitute the x and y values of the point into the equation:

45 = a(6 + 3)(6 - 5)

45 = a(9)(1)

Step 2: Solve for "a":

45 = 9a

a = 45/9

a = 5

The value of "a" in the equation y = a(x + 3)(x - 5) is 5.

The distributive property is often used to simplify algebraic expressions.

Algebra refers to the involving of unknown quantities into the block relationship between variables.

In this example, the expression 2(-3x + 5) can be simplified using the distributive property. The distributive property states that for any two numbers a and b, and a third number c, a(b + c) = ab + ac. Applying this property to our expression, 2(-3x + 5) = 2(-3x) + 2(5).

By expanding the expression, we see that 2(-3x + 5) = -6x + 10. This simplified expression is much easier to work with than the original expression. The distributive property can be applied to any expression in order to simplify it, making it easier to solve.

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Step-by-step explanation:

in geometry it is a plane figure with at least three straight sides and angles, and typically five or more.

Answer:

x = 0.4

Step-by-step explanation:

1.5 * x = 0.6

x = 0.6 / 1.5

x = 0.4

Answer:

0.4

Step-by-step explanation:

To solve the equation 1.5 * ? = 0.6 for the value of ?, we need to isolate the variable ? on one side of the equation.

First, we can divide both sides of the equation by 1.5 to isolate the variable:

1.5 * ? / 1.5 = 0.6 / 1.5

Simplifying, we get:

? = 0.4

Therefore, the value of ? that makes the equation 1.5 * ? = 0.6 true is 0.4.

5.8 + (-8.45)

Remove the plus sign and parentheses:

5.8 - 8.45

-2.65

That's your answer. Hope this helped!

Answer:

-2.65

Step-by-step explanation:

Hope this will help