The Johnstown Inclined Plane in Pennsylvania is one of the longest and steepest hoists in the world. The railway cars travel a distance of 896.5 feet at an angle of approximately 35.4 degrees, rising to a height of 1693.5 feet above sea level. (Round your answers to two decimal places.)

(a) Find the vertical rise of the inclined plane: 519.33 ft

(b) Find the elevation of the lower end of the inclines plane: _____ ft

(c) The cars move up the mountain at a rate of 300 feet per minute. Find the rate at which they rise vertically: 173.78 ft/min

Answer:

Step-by-step explanation:

Assume the cost for a cup of coffee is x and the cost for a cup of tea is y.

For Alex: 4x+3y=6.95

For Ben 5x+2y=7.20

Then multiply Alex's cost by 2 and Ben's by 3 to cancel y.

8x+6y=13.90

15x+6y=21.60

Equation 2 minus equation 1 would be

15x+6y-(8x+6y)=15x+6y-8x-6y=7x

21.60-13.90=7.70

7x=7.70

Then x=1.10 and plugging it one of the equations,

y= 0.85

A cup of coffee costs 1.10 pounds and A cup of tea is 0.85 pounds

:)

Coordinate rule for the composition is w(-1,-2) → s(-1-1,-2-4) → s(-2,-4) , x(-2,0) → t(-2+0,0+2) → t(-2,2), y(1,2) → u(1+1,2+2) → u(2,4) , z(1,-1) → v(1+3,-1+1) → v(4,0).

Given:

w x y x has vertices w(-1,-2) , x(-2,0), y(1,2) and z(1,-1).

s t u v has vertices s(-2,-4) , t(-2,2) , u(2,4) and v(4,0).

The coordinate rule for transformation is:

w(-1,-2) → s(-1-1,-2-4) → s(-2,-4)

x(-2,0) → t(-2+0,0+2) → t(-2,2)

y(1,2) → u(1+1,2+2) → u(2,4)

z(1,-1) → v(1+3,-1+1) → v(4,0)

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The equation of line will be given as y = 3x + 24

Given,

The graph of a linear function passes through the points (4, 24) and (6, 30).

The equation of the line will be given as:-

y  -  y₁ = m ( x  -  x₁)

Slope m will be calculated as:-

m = (y₂ - y₁) / (x₂ - x₁) = (30 - 24) / (6 - 4) = 6/2 = 3

The equation will be:-

y  -  24  =  3 ( x - 4 )

y  = 3x - 12 + 24

y = 3x + 24

Therefore the equation of the line will be given as y = 3x + 24.

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Answer: 7.6

Step-by-step explanation:

19÷100×40 which will give you 7.6

The time taken by the object to hit the ground is 10 seconds , the correct option is (a) .

In the question ,

it is given that ,

the object is dropped from the height of 1600 feet ,

So , the height h(t) = 1600

the equation representing the height of the object at time t is ,

h(t) = 16t² + 155

Substituting the height h(t) = 1600

16t² + 155 = 1600

16t² = 1600 - 155

16t² = 1445

t² = 1445/16

t² = 90.31

t = √90.31

t = 9.503

t ≈ 10 seconds

Therefore , The time taken by the object to hit the ground is 10 seconds .

The given question is incomplete , the compete question is

An object is dropped from a height of 1,600 feet. The amount of time, in seconds, the object takes to hit the ground can be found by solving the equation 16t² + 155 = h(t) . How many seconds will it take to hit the ground ?

(a) 10

(b) 50

(c) 100

(d) 500

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The value of x for the given triangle is 4.5

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of all three angles of a triangle is always 180°

In the given triangle ABC,

∠A=(9x+16)°, ∠B=(6x+15)°

And the extrior angle ∠C=(19x+3)°

Use the external angle property,

The sum of two interior angles is equal to an exterior angle.

Therefor,

∠C=∠A+∠B

(19x+3)°=(9x+16)°+(6x+5)°

19x+3=15x+21

4x=18

x=4.5

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The area of the regular pentagon with sides of 7 cm is 84.30 cm²

The area of a regular pentagon can be determined if the side length (s) is given. The formula used for calculating the area of a regular pentagon is:

[tex]A = \frac{1}{4}\sqrt{5(5+2\sqrt{5})}s^{2}[/tex]

Given: side length (s) = 7 cm

Area (A) = 1/4×√( 5(5+2√5) ×7²  = 84.30 cm²

Therefore, the area of the pentagon is 84.30 cm²

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The quadrilateral with vertices (0,0), (5,0), (8,4), and (3,4) is a rhombus.

What is a rhombus?

A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal.

What is a distance formula?

D = √(x₂ - x₁)² + (y₂ - y₁)²

Here, we have

Given vertices A(0,0), B(5,0), C(8,4), and D(3,4)

By applying the distance formula, we get

AB = √(5 - 0)² + (0 - 0)²  = 5

BC = √(8 - 5)² + (4 - 0)²  = 5

CD = √(3 - 8)² + (4 - 4)²  = 5

Hence, it's all sides are equal so it is a rhombus.

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The rewritten form of the given expression such that it is without absolute value notation is; 2b.

It follows from the task content that the rewritten form of the given expression; | 2b | is to be determined.

On this note, since it is given that the variable b is less than zero; i.e b < 0.

It follows that the expression evaluation of 2b yields a negative number.

However, the rewritten form of the expression without the absolute value notation since the value of b is unknown still remains; 2b.

Therefore, the required rewritten form is; 2b.

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a) An equation that models the amount of storage as a function of the number of songs is y = -0.005x + 16

b)  Slope of the equation is -0.005 and the intercept of the equation is 16

Slope intercept form

Slope intercept form presents the graph of a straight line and is represented in the form of

y = mx + c.

where

y = y coordinate

m = slope

x = x coordinate

b = y intercept

Given,

Here we have the  table shows the amount of storage y (in gigabytes) on a music-playing device when there are x songs on the device

Now, we have to find the following:

a) Equation of the table

b) Slope and intercept.

In order to find the equation, we have to identify the slope an intercept of the table.

So, to find that we have to take two points from the table.

Then the selected points are

(0, 16), (242, 14.8)

By using these point we have to calculate the slope as,

m = (14.8 - 16) / (242 - 0)

m = -1.2/242

m = -0.005

Now, the intercept is calculated by using the point (0, 16) and the slope -0.005, then we get,

16 = -0.005(0) + c

c = 16

Therefore, the equation is y = -0.005x + 16.

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Answer:

Step-by-step explanation:

For the first one, find the value of x:

[tex]3x-8=-2\\3x=8-2=6\\x=2[/tex]

Then, use the value of x to find the answer:

For the second one, find the value of y:

[tex]-2(3y+5)=-4\\-6y-10=-4\\-6y=10-4=6\\y=-1[/tex]

Then, use the value of y to find the answer:

[tex]5y=5(-1)=-5[/tex]

The amount that the salesman pay the manufacturer for the computer is $20800.

From the information, the salesman sold the computer for $15600 making a loss of 25%.

The amount that the salesman pay the manufacturer for the computer will be illustrated thus:

Since a 25% loss was made, the cost price will be: = 100% + 25% = 75%

Therefore, the cost price will be:

= Sales price / 125%

= $15600 / 0.75

= $20800

The amount is $20800.

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Answer:

38 songs in each group.

Step-by-step explanation:

Alexander has 418 songs on his MP3 player. he divides the songs into 11 equal groups. About how many songs are in each group. (round the numbers)

418/11 = 38 songs in each group.

Answer: Both p and q are 8cm long.

Step-by-step explanation:

BE created a similar triangle that is exactly half of the larger triangle.

So if BE is 4 and AE is 8 then we know that CD is 8 and AD is 16.

However we only need segment q which is half of AD so the answer is:

p=8 and q=8

;)

The account balance after 10 years is $7200.

It should be noted that simple interest is calculated as:

= (Principal × Rate × Time) / 100

= ($3000 × 1.4 × 10) / 100

= $4200

The total amount that will be in the account will be:

= Principal + Interest

= $3000 + $4200

= $7200

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Hi again! The equation to the function would be..

y = 1/2x + 1 (assuming that the initial value is one)

Answer: you did not put in the full equation but i got this right out of the box.

ˉx 28

r 0.82

Answer: (3x-2)(3x+2)

I knew the answer it was just hard to explain all of it. Sorry if this doesn't help

The given linear function is [tex]f (h) = - \frac{1}{5} x + 3[/tex]. The graph is attached at the end.

Let the independent variable be x.

It is given in the question:

Value of the function, h at 0 = 3

Thus, h(0) =3

Also, when the independent variable decreases by 5, the dependent variable increases by 1.

So, slope = -[tex]\frac{1}{5}[/tex]

y-intercept = 3

We know the linear equation is-

y = mx + b ... (i)

where y ⇒ linear function

m ⇒ slope of the line

x ⇒ independent variable

b ⇒ y-intercept

Putting the values of each term in equation (i), we get:

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

We can plot this equation in a graph, as attached below.

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The complete question is:
Graph the function with the given description. A linear function h models a relationship in which the dependent variable increases 1 unit for every 5 units the independent variable decreases. The value of the function at 0 is 3.

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The equation of the parallel line is y = -x

The equation is given as

y = -x - 2

The point is also given as

point = (2, -2)

The equation of a line can be represented as

y = mx + c

Where

slope = m

By comparing the equations, we have:

m = -1

This means that the slope of  y = -x - 2 is -1

The slopes of parallel lines are equal

This means that the slope of the other line is -1

The equation of the parallel line is then calculated as

y = m(x - x₁) +y₁

Where

m = -1

(x₁, y₁) = (2, -2)

So, we have

y = -1(x - 2) - 2

Open the brackets and evaluate

y = -x

Hence, the parallel line has an equation of y = -x

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Answer:

Step-by-step explanation:

Hi,  you are studying trigonometry :P  nice  

conterminal means stopping at the same place, right?  sooo what is the same place for 659°  compared to our only once around the circle of 360°   since 720° is twice around a circle our 659° is less than that so just subtract 360° from 659° to get the co-terminal angle.

659-360=299°

299° is the co-terminal angle

270 is the line between the 3rd and 4th quadrant,  so this is definitely in the 4th quadrant.

let's just count backwards (CW) from zero degrees till we get to our 299° angle going in the forward (CCW) direction.    so 299-360= -61°

the reference angle is 61°

Does all of this make sense?  :/  

Answer:

[tex]4 \alpha ngles[/tex]

4 angles

hope it help!

have a nice night

The following are the answers:

a) 7 / (2a)³

b) 1/(4m)³ + 10³

c) (5a)³ - (4b)³

d) 1/(3x)³ + 1/(5y)³

e) (0.5x - 0.6y)²

f) (-a - 0.3)²

g) ((3/4)²a² + (2/3)²a)²

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

a)

(8 - 1) / 8a^3

= 7 / (2a)³

b)

1/64m^3 + 1000

= 1/(4m)³ + 10³

c)

125a^3 - 64b^3

= (5a)³ - (4b)³

d)

1/27x^3 + 1/125y^3

= 1/(3x)³ + 1/(5y)³

Now,

Polynomial is an expression of writing with more than one term.

We will write it in the form of:

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

e)

0.25x^2 - 0.6xy + 0.36y^2

= (0.5x)² - 2 x 0.5 x 0.6 + (0.6y)²

= (0.5x - 0.6y)²

f)

-a^2 + 0.6a - 0.09

-a² - 2 x (-a) x 0.3 - (0.3)²

= (-a - 0.3)²

g)

9/16a^4 + a^3 + 4/9a^2

((3/4)²a²)² + 2 x (3/4)²a² x (2/3)²a + ((2/3)²a)²

= ((3/4)²a² + (2/3)²a)²

Thus,

The following are the answers:

a) 7 / (2a)³

b) 1/(4m)³ + 10³

c) (5a)³ - (4b)³

d) 1/(3x)³ + 1/(5y)³

e) (0.5x - 0.6y)²

f) (-a - 0.3)²

g) ((3/4)²a² + (2/3)²a)²

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The length of the ramp is [tex]\sqrt{410}[/tex] inches.

According to the question,

We have the following information:

A ramp is elevated to a height of 7 inches from the base. The horizontal distance between the lower end of the ramp and the base is 19 inches.

So, it will be a right-angled triangle.

Now, we can use Pythagoras theorem to find the length of the ramp which is the hypotenuse of the triangle.

Let's denote the length of the ramp to be l, elevated height to be p and horizontal distance to be b.

[tex]l^{2} =p^{2} +b^{2}[/tex]

[tex]l^{2} =7^{2} +19^{2}[/tex]

[tex]l^{2}[/tex] = 49+361

[tex]l^{2}[/tex] = 410

l = [tex]\sqrt{410}[/tex] inches

Hence, the length of the ramp is [tex]\sqrt{410}[/tex] inches.

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Answer:
x = 48/3

when Jack got 50 chocolates and has left 2, then Jack gave away 50-2=48 chocolates. When each friend got 3 chocolates, the number of friends x is equal to 48 divided by 3.

The total admission fee of the group is 22.5m + 51n + 48.

Given that the admission fee to a museum is $12.50 per nonsenior adult, $8 per child, and $6.50 per senior citizen.

Also, it was further stated that the tour group consists of m nonsenior adults, (5/4m +6) children, and 8n senior citizens.

The total amount for the fees will be:

= Non senior adults + Children + Senior citizen

= 12.5(m) + 8(1.25m + 6) + 6.50(8n)

= 12.5m + 10m + 48 + 51n

= 22.5m + 48 + 51n

= 22.5m + 51n + 48

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