A train travels 480 miles at a constant speed (x), in miles per hour. Write an equation that can be used to find the speed of the train, if the time to travel 480 miles is 6 hours. you do not need to solve the equation

Answer:

100.8°

Step-by-step explanation:

∠POR = ∠POQ + ∠QOR

∠POQ is 20% of 360° ( measure of the angles in a circle )

= 0.2 × 360° = 72°

∠QOR is 8% of 360° = 0.08 × 360° = 28.8°

Hence

arc PR = ∠POR = 72° + 28.8° = 100.8°

Answer:

  B:  -34

Step-by-step explanation:

The given angles are supplementary, so you have ...

  (2x+146) + (4x+238) = 180

  6x +384 = 180 . . . . . simplify

  6x = -204 . . . . . . . . . subtract 384

  x = -34 . . . . . . . . . . . .divide by 6

_____

Check

angle F is (2·(-34)+146)° = 78°

angle C is (4·(-34)+238)° = 102°

These angles indeed are supplementary, so the answer checks OK.

X=-34; add both expressions together and solve for x

The work done by the force field  on the object moving on the parabola y=7x^2 from (0,0) to (4,112) is calculated by integrating the force along the path. The total work done is found to be 224 units of work.

To find the work done by a variable force on an object moving along a given curve, we utilize the concept of a line integral in vector calculus. Given the force field F =  and the parabolic path described by y = 7x2, from point (0,0) to (4,112), we want to integrate the force field along the curve. To calculate this line integral, we parameterize the curve using x as the parameter, since y is already expressed as a function of x. We then express the force field in terms of x, evaluate the dot product of the force field and the differential of the position vector, and integrate from the start to the end of the curve.

The work, W, is found by integrating the dot product of F and dx from the initial to the final position:
W = \\int (F . dx).

In our case, the force field becomes F(x, y(x)) = F<7x2, x> = <7x2, x>. The differential displacement along the parabola, expressed in vector form, is dx = <1, 14x>dx because dy/dx = d(7x2)/dx = 14x. Thus, the infinitesimal work is dW = F .dx = 7x2 * 1dx + x * 14xdx = 21x2dx. Finally, we integrate from x = 0 to x = 4 to find the total work:

W = \\int_{0}^{4} 21x2dx = 7x3\\right]_{0}^{4 = 7 * 43 = 224.

Therefore, the work done by the force field along the parabolic path from (0,0) to (4,112) is 224 units of work.

The work required to move an object along the parabola y = 7x^2 from (0,0) to (4,112) under the force field F = <y, x> is approximately 149.33 units.

To find the work required to move an object along a curve under the influence of a force field, we can use the line integral of the force field along the curve. The line integral is given by the formula:

∫ F · dr = ∫ (F1 dx + F2 dy)

Given the force field F = <y, x> and the parabola y = 7x^2, we need to parameterize the curve to express it in terms of a single variable.

Let's parameterize the curve using x as the parameter:

x(t) = t

y(t) = 7t^2

Now, we can calculate the differential elements dx and dy:

dx = x'(t) dt = dt

dy = y'(t) dt = 14t dt

Substitute the expressions for F, dx, and dy into the line integral formula:

∫ F · dr = ∫ (y dx + x dy)

            = ∫ (7t^2 dt + t * 14t dt)

            = ∫ (7t^2 + 14t^2) dt

            = ∫ 21t^2 dt

            = 7t^3 / 3 + C

Evaluate the integral from t = 0 to t = 4:

Work = [7(4)^3 / 3] - [7(0)^3 / 3]

    = (7 * 64 / 3) - 0

    = 448 / 3

    ≈ 149.33

Therefore, the work required to move an object along the parabola y = 7x^2 from (0,0) to (4,112) under the force field F = <y, x> is approximately 149.33 units.

he would hove to work 20 hours to meet the second job I think

To make the same total earnings at the first job as the second job (including benefits), Phillip would have to work an additional 4 hours (to account for the $100 benefits). If the workdays are 8 hours each, then for every two days (which is 16 hours) worked at job 2, Phillip would need to work an additional 4 hours at job 1, summing up to 20 hours.

This problem is about comparing the earnings from the two jobs. For the second job, Phillip earns $20 per hour and also gets benefits equivalent to $100 per pay period.

If Phillip wants to earn the same amount in the first job (which does not offer any benefits), we calculate how many hours he would need to work to earn an additional $100 (the value of the benefits).

To do this, we divide $100 (benefits of the second job) by the first job's hourly pay rate ($25) which results in 4 hours.

So, Phillip must work an additional 4 hours to make up for the benefits. Meaning, for any given number of hours he would work at the second job, he would need to work an extra 4 hours at the first job to get the same total earnings.

Therefore, the right answer is not among the choices given because we have an extra step to add to each option. If we consider a standard 8-hour workday, working at the second job for two days gives 16 hours with an additional $100 for benefits. To make the same in the first job, Phillip would need to work, 16 hours (from the second job) + 4 hours (to compensate for the $100 benefits) = 20 hours.

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Answer:

[tex]0.4n+0.1n^2\ miles[/tex]

Step-by-step explanation:

The first time he trains, he runs 0.5 mile, then the first term of the arithmetic sequence is [tex]a_1=0.5.[/tex]

Each subsequent time he trains, he runs 0.2 mile farther than he did the previous time, then the difference of the arithmetic sequence is [tex]d=0.2.[/tex]

The nth term of the arithmetic sequence can be found using formula

[tex]a_n=a_1+(n-1)d,[/tex]

hence

[tex]a_n=0.5+0.2(n-1)\\ \\a_n=0.5+0.2n-0.2\\ \\a_n=0.3+0.2n.[/tex]

The total distance after Miguel has trained n times can be found using formula

[tex]S_n=\dfrac{a_1+a_n}{2}\cdot n,[/tex]

thus, the total distance is

[tex]S_n=\dfrac{0.5+0.3+0.2n}{2}\cdot n=\dfrac{0.8+0.2n}{2}\cdot n=(0.4+0.1n)n=0.4n+0.1n^2.[/tex]

Answer:

First answer is C. (0.3+0.2K)

Second one is 15 Times

Step-by-step explanation:

Answer on EDG hope it helps :)

Answer:

Step-by-step explanation:

(7y)² = 7²×y² = 49y²

In order to simplify the expression (7y)^2, we need to apply the exponent to both the numerical coefficient and the variable inside the parentheses. Here's how to do it step-by-step:
1. The expression (7y)^2 denotes that everything inside the parentheses is to be squared. That means we multiply 7y by itself.
2. When squaring a product, we square each factor separately. So we have to square both the 7 and the y.
3. Squaring 7 gives us 7^2, which equals 49.
4. Squaring the variable y gives us y^2.
5. Now, we multiply 49 by y^2 to combine our results.
Putting these steps together, we see that (7y)^2 simplifies to 49y^2.
The final simplified expression without parentheses is 49y^2.

The correct answer is A. 46%

answer for this question is (b)2X

The phrase "the product of 2 and a number" written as a mathematical expression is 2x

Given:

The product of 2 and a number

Let

The unknown number = x

So,

The product of 2 and a number

= 2 × x

= 2x

Therefore, the product of 2 and a number is written as 2x

Learn more about maths expression:

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Answer:

96in^2

Step-by-step explanation:

because first find the area of two sides (Length*Height)*2 sides.

Find the area of adjacent sides (Width*Height)*2 sides.

Find the area of ends (Length*Width)*2 ends.

Add the three areas together to find the surface area.

Example: The surface area of a rectangular prism 5 cm long, 3 cm.

Answer:

96

Step-by-step explanation:

Did quiz

ANSWER

y = 3x + 6.50

EXPLANATION

The $3 for each downloaded movie is the unit rate of change.

This is represent the slope of the linear function that models this situation.

The monthly fee of monthly fee of $6.50 the constant rate.

It represents the y-intercept of the function.

The linear function is given by

[tex]y = mx + b[/tex]

The correct choice is y = 3x + 6.50

the answer would be C. y = 3x + 6.50, for every movie you buy (which is x), they would be 3$. therefore it would be 3x, and the monthly fee would just be added with that. :P

Answer: [tex]x\geq0[/tex] or [tex][0,\infty)[/tex]

Step-by-step explanation:

You have the function:

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

The domain of the function is the set of all the possible input values that the function can has.

We know that the square root of a negative number is not defined in the Real numbers. Therefore, "x" cannot be a negative number.

Then the domain of f(x) will be:

[tex]x\geq0[/tex] or [tex][0,\infty)[/tex]

Answer:

Step-by-step explanation:

Can you write this as y = √x?

The domain of the function y = √x is [0, ∞ ).  In elementary algebra, before you encounter imaginary numbers, y = √x is not defined for negative x.

Answer:

  $2169.49

Step-by-step explanation:

The mortgage payment is ...

  A = (210,000·0.95)(0.045/12)/(1 -(1 +0.045/12)^(-12·15)) ≈ 1526.16

The monthly set-aside for taxes is ...

  3.5%·200,000/12 = 583.33

The monthly set-aside for insurance is ...

  720/12 = 60

So the total of P&I + taxes + insurance will be ...

  $1526.16 +583.33 +60.00 = $2169.49

Answer:

2202.72

Step-by-step explanation:

just got the answer right on the quiz

Answer:

Option a

[tex]f(x) = e^{x-1} -2[/tex]

Step-by-step explanation:

If the graph of the function [tex]y=f(x+h) +b[/tex]  represents the transformations made to the graph of [tex]y= f(x)[/tex]  then, by definition:

If [tex]b> 0[/tex] the graph moves vertically upwards b units.

If [tex]b <0[/tex] the graph moves vertically down  b units

If [tex]h<0[/tex] The graph moves horizontally h units to the right

If [tex]h>0[/tex] The graph moves horizontally h units to the left

In this problem we have the parent  function [tex]y=e^x[/tex]

We know that the parent function is translated 1 unit rigth and 2 units down.

This is:

[tex]h<0 = -1\\\\b < 0 = -2[/tex]

Finally the transformation is:

[tex]y=f(x-1) -2[/tex]

[tex]f(x) = e^{x-1} -2[/tex]

Answer:

z = [tex]\frac{5}{3}[/tex]

Step-by-step explanation:

Given z is directly proportional to x and inversely proportional to y then the equation relating them is

z = [tex]\frac{kx}{y}[/tex] ← k is the constant of proportionality

To find k use the condition x = 7, y = 7 and z = 2

k = [tex]\frac{zy}{x}[/tex] = [tex]\frac{2(7)}{7}[/tex] = 2

z = [tex]\frac{2x}{y}[/tex] ← equation of proportionality

When x = 10 and y = 12, then

z = [tex]\frac{2(10)}{12}[/tex] = [tex]\frac{20}{12}[/tex] = [tex]\frac{5}{3}[/tex]

Answer:

There similar

Answer: Similar and Same shape

Step-by-step explanation:

I got it wrong and these were the correct answers ON G

Answer:

16

Step-by-step explanation:

1 gallon is equal to 8 pints.

2 gallons is equal to 16 pints.

Answer:

y = 51.3°

Step-by-step explanation:

tan(y) = Opp./Adj

tan(y) = 10/8

tan(y) = 1.25

y = 51.3°

ANSWER

The next two terms are

338, 434

EXPLANATION

The given sequence is 14,38,74,122,182,254

Let us observe some pattern and use it to find the next two terms.

14+24=38

38+36=74

74+48=122

122+60=182

182+72=254

To get the next term we add 84 to 254

254+84=338

To get the next term,we add 96 to 338

338+96=434

Answer:

Question 1 -  f(x) = | x | - 2

First, let's find the 5 values requested:

x = -2 ==> | x | - 2 = | - 2 |  - 2 = 2 - 2 = 0

x = -1 ==> | x | - 2 = | - 1 |  - 2 = 1 - 2 = -1

x = -0 ==> | x | - 2 = | 0 |  - 2 = 0 - 2 = -2

x = 1 ==> | x | - 2 = | 1 |  - 2 = 1 - 2 = -1

x = 2 ==> | x | - 2 = | 2 |  - 2 = 0 - 2 = -2

You can see the plotted graph attached.

Question 1 -  f(x) = | x  - 1 | - 1

First, let's find the 5 values requested:

x = -2 ==> | x  -  1 | - 1 = | - 2 - 1 |  - 1 = | - 3 | - 1 = 3 - 1 = 2

x = -1 ==> | x  -  1 | - 1 = | - 1 - 1 |  - 1 = | - 2 | - 1 = 2 - 1 = 1

x = 0 ==> | x  -  1 | - 1 = | 0 - 1 |  - 1 = | - 1 | - 1 = 1 - 1 = 0

x = 1 ==> | x  -  1 | - 1 = | 1 - 1 |  - 1 = | 0 | - 1 = 0 - 1 = -1

x = 2 ==> | x  -  1 | - 1 = | 2 - 1 |  - 1 = | 1 | - 1 = 1 - 1 = 0

You can see the plotted graph attached.

Answer:

∠H= 109º

∠F = 71º

∠G = 109º

Step-by-step explanation:

∠I = 71º

Interior opposite angles of parallel lines sums up to 180º.

∠H = 180 - 71 = 109º

Line IH is equal to Line FG.

∠F = ∠I

∠F = 71º

∠G = ∠H

∠G = 109º

ANSWER

Quadrant I

EXPLANATION

In the first quadrant all the trigonometric ratios are positive.

This implies that,both tanθ and secθ are positive in the first quadrant.

No two trigonometric ratios are positive in any other quadrant apart from the first quadrant.

Answer:

qaud I

Step-by-step explanation:

option B is right answer

Solving Trigonometric Equations Using Inverses Quiz part 1

1. -2

2. -0.36

3. C

4. tan^2theta = sin^2theta × sec^2theta (This Question)

5. 60 degrees

6. 0.71

7. 0.09

8. 2pi/3 , 4pi/3

9. pi/4 , 5pi/4

Step-by-step explanation: I just took it...

These are the correct answers you're welcome

this question isn't fully complete. comment a full question below and I'll try for ya ;) - Josie Annette

Final answer:

To calculate the commission, multiply the sale price of $8,800 by the commission rate of 5% to get a commission of $440.

Explanation:

The question is asking to calculate the commission a salesperson earns from selling a used car. The salesperson earns a 5% commission on the sale price of the car, which is $8,800. To find the commission, we multiply the sale price by the commission rate:

Sale Price = $8,800
Commission Rate = 5% (or 0.05 in decimal form)

Commission = Sale Price × Commission Rate
Commission = $8,800 × 0.05
Commission = $440

Therefore, the salesperson earns a commission of $440.

A flat circular plate has the shape of the region x 2 + y 2 ≤ 1. points on the plate have temperature t(x, y) = x 2 + 2y 2 − x. find the temperatures of the hottest and coldest points of the plate

Answer:5√2(cos(−π/4)+ isin(−π/4)) is in trig form

Step-by-step explanation:

Answer:

  see below

Step-by-step explanation:

The images are mirrored right/left, so the reflection must be across the y-axis. That only leaves two answer choices.

If you translate ABC to the left, you will put it entirely in quadrant II, so reflection across the y-axis will put it in quadrant I. Obviously, that is not the correct sequence of transformations.

If you translate ABC 3 units to the right, it will put line AB on x=2. Then reflection across the y-axis will put that vertical segment on x = -2, exactly where corresponding segment DE is located.

The appropriate choice is the one shown below:

Answer:

Step-by-step explanation:

Area of a circle is A = πr², and diameter of a circle is d = 2r.

d = 2r

72 = 2r

r = 36

A = πr²

A = π(36)²

A = 1296π

A ≈ 4069

Math is right about the answer

ANSWER

B.

[tex]112\pi \: {units}^{3} [/tex]

EXPLANATION

The volume of a cone is calculated using the formula:

[tex]Volume = \frac{1}{3} \pi {r}^{2}h[/tex]

where r=4 units is the base radius of the cone.

and h=21 units is the vertical height of the cone.

We plug in the values to get;

[tex]Volume = \frac{1}{3} \times \pi \times {4}^{2} \times 21[/tex]

[tex]Volume = 112\pi \: {units}^{3} [/tex]

Answer:

The correct answer is option B.  112π units ³

Step-by-step explanation:

Formula

Volume of cone = (πr²h)/3

Where r - Radius of cone and

h - Height of cone

To find the volume of cone

Here radius r = 4 units

Height h = 21 units

Volume = (πr²h)/3

= (π * 4² * 21)/3

= 112π units ²

Therefore the correct answer is option B.  112π units ³

Answer:

The diameter of the circle is [tex]D=36\ in[/tex] and the radius is [tex]r=18\ in[/tex]

Step-by-step explanation:

we know that

The circumference of a circle is equal to

[tex]C=\pi D[/tex]

where

D is the diameter of the circle

we have

[tex]C=113.04\ in[/tex]

substitute and solve for D

[tex]113.04=(3.14)D[/tex]

[tex]D=113.04/(3.14)[/tex]

[tex]D=36\ in[/tex]

Find the radius r

[tex]r=36/2=18\ in[/tex] -----> the radius is half the diameter