A train travels at 80 miles per hour. An equation can be written that compared that the time(t) with the distance(d). What is the domaine and range?

If the Area= Length × Width

Then, The width of the rectangle is (x -1).

We know that area of rectangle is the number of unit square within the boundary of the rectangle.

The formula of area of rectangle is:

    Area = Length × width

⇒ Width = Length / Area

Given that,  

(x⁴ +4x³ + 3x² -4x -4) / (x³ + 5x² + 8x + 4 ) = Width   ----------------- (1)

Let's simply the expression :

Note that: x=1 is a zero of the numerator since the sum of the coefficient is zero.

So, (x-1) is a factor:

Putting the values in equation (1)

(x⁴ +4x³ + 3x² -4x -4) = (x-1)  (x³ + 5x² + 8x + 4 )

(x⁴ +4x³ + 3x² -4x -4) / (x³ + 5x² + 8x + 4 ) = (x-1)

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Answer:

D on Edge 23

Step-by-step explanation:

because i said so

The possible values of k that forms a triangle with an area of 1.5 square units are 1 and 2/3

A triangle is a three sided polygon.

The equation of the parabola is; y = 0.5•(x - 3)•(x + k)

The area of the triangle = 1.5 square units

A x-intercept of the equation, y = 0.5•(x - 3)•(x + k) is x = 3.

The area of a triangle, A, is found from the equation

A = 0.5 × Base length × Height

When x = 3, the height of the triangle is therefore;

A = 1.5 = 0.5 × 3 × Height

Height = 1.5 ÷ (0.5 × 3) = 1

Similarly, when the height is 3, the base length is 1

The y-intercept has a value of y = 0.5•(0 - 3)•(0 + k) = -1.5•k

Area of triangle = 0.5 × 1.5•k × k = 1.5

k = 1

When the x-intercept is 3, we have;

0.5 × 1.5•k × 3 = 1.5

k = 1/(1.5) = 2/3

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Explanation:

0.4 = 4/10 = 2/5

The original slope as a fraction is 2/5

Flip the fraction to get 5/2, then flip the sign to get -5/2 which is the perpendicular slope

The orginal slope 2/5 and perpendicular slope -5/2 multiply to -1. This is true of any pair of perpendicular lines where neither line is vertical nor horizontal.

Rephrased another way: -5/2 is the negative reciprocal of 2/5.

Answer:

See below

Step-by-step explanation:

I hope this is what you're looking for!

Some examples include:

Answer:

$6.30

Step-by-step explanation:

The state sales tax rate in North Carolina is 4.5% estimate the state sales tax on a model of the wright brothers’ airplane that costs $139.99.

You are asked to estimate meaning $139.99 should be rounded to $140. Because 4.5% = 0.045

sales tax (estimated):

0.045 * $140 = $6.30

CHECK:

Exact amount is:

0.045 * 139.99 = $6.29955

Answer: \frac{2x^3-3x^2+5}{x-4}

Step-by-step explanation:

Answer:

  600 ft by 1200 ft

Step-by-step explanation:

You want the dimensions of the largest rectangular area that can be enclosed on three sides with 2400 feet of fencing.

Let x represent the dimension of the field that is parallel to the river, and y the dimension out from the river. The sum of the three side lengths is ...

  x + 2y = 2400

Solving for y gives ...

  y = (2400 -x)/2

The area is the product of the two dimensions:

  A = xy = x(2400 -x)/2

We observe that this is the factored form of a quadratic with zeros at x=0 and x=2400. Its leading coefficient is negative, so the graph opens downward, and the vertex is the point where area is a maximum.

The vertex is located on the line of symmetry at the x-value that is halfway between the zeros:

  x = (0 +2400)/2 = 1200

  y = (2400 -x)/2 = (2400 -1200)/2 = 600

The dimensions of the field that has the largest area are 600 ft by 1200 ft.

__

Additional comment

As we observed here, the side parallel to the "river" will use 1/2 of the fencing, and the remaining two sides will each use 1/4 of the fencing. This is the general solution to such a fencing problem.

Answer: x≤12

Step-by-step explanation: the room holds a max of 12 people, so the number of people will be less than or equal to 12

Answer:

6.68

Step-by-step explanation:

[tex]20.16+20.78+12.53 = 53.47[/tex]

[tex]53.47 \div 8 = 6.68375[/tex]

Answer:

No

Step-by-step explanation:

listen to guy above he opened my eyes

Answer:

the C(X) pattern is +4? i need more context but i can give u that much

Step-by-step explanation:

a. False, the slope of f(x) will be steeper than m(x).

b. False, the y-intercept of m(x) will be equal to f(x).

What is a slope?

Slope and slant both refer to an incline away from a reference surface or line that is generally straight. The definition of slope is "a vertical inclination in an oblique direction" Here, the land abruptly slopes either upward or downhill.

Here, we have

f(x) = x and m(x) = 3/5f(x)

a.  m₁ = slope of f(x) = x is 1

     m₂ = slope of m(x) = 3/5f(x) is 3/5

    m₁ >  m₂

f(x) = x is more steeper than m(x) = 3/5f(x).

b.  a₁ = intercept of f(x) = x is 0.

    b₁ = intercept of m(x) = 3/5f(x) is 0.

The y-intercept of m(x) will be equal to f(x).

Hence, a. False, the slope of f(x) will be steeper than m(x).

b. False, the y-intercept of m(x) will be equal to f(x).

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The probability that the number generated contains the digit 3 at least once is 0.7458.

Probability that there is digit 3 at least once =  1- P(no 3s in the number)

Total probability is, 10^13.

Here the digits are 0 to 9. we have 10 choices and the digits can be repeated hence the total probability is 10^13.

Now, if there is no 3, the choices will 9, hence the probability is 9^13.

Further, the probability of an event happening, is equal to the

favourable outcomes/total outcomes.

Hence, we get the probability of no 3's is 9^13/10^13

=0.2542

Probability that there is digit 3 at least once =  1- 0.2542

=0.7458

Therefore, the probability of at least one 3 is 0.7458.

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Answer:

Step-by-step explanation:

As we see the two expressions are equal in value

Answer:

log3 1/3 = logb 1/b

(Both expressions are equal)

Step-by-step explanation:

Now we have to,

→ find the expression with greater value.

Then the greatest value is,

→ log3 1/3 = logb 1/b

→ log3 3^(-1) = logb b^(-1)

→ -1 = -1

→ [ LHS = RHS ]

Hence, both have same value.

Answer:

24√2

Step-by-step explanation:

[tex]2 \sqrt{50} + 3 \sqrt{72} - \sqrt{32} [/tex]

[tex]2 \sqrt{25 \times 2} + 3 \sqrt{36 \times 2} - \sqrt{16 \times 2} [/tex]

[tex]2 \sqrt{25} \sqrt{2} + 3 \sqrt{36} \sqrt{2} - \sqrt{16} \sqrt{2} [/tex]

[tex]2(5 \sqrt{2} ) + 3(6 \sqrt{2} ) - 4 \sqrt{2} [/tex]

[tex]10 \sqrt{2} + 1 8\sqrt{2} - 4 \sqrt{2} [/tex]

[tex]24 \sqrt{2} [/tex]

The inequality can be simplified to:

-7 < x < 3

And the graph can be seen in the image at the end.

Here we have the inequality:

|x + 2| + 1 > 6

To solve this, we need to isolate the variable x, so if we first subtract 1 we get:

|x + 2| +1 - 1 > 6 - 1

|x + 2| > 5

The absolute value part can be decomposed into two.

-5 < x + 2 < 5

Now we can subtract 2 in all the inequality, so we get:

-5 - 2 < x + 2 - 2 < 5 - 2

-7 < x < 3

The graph of this can be seen below

Answer:12 1/2

Step-by-step explanation:

5725 is the height of the mountain prior to construction, represented by the variable h.

Two or more expressions with an Equal sign is called as Equation.

Given,

The mountain that contains Mount Rushmore is approximately 5,675 feet high.

The height of the mountain is 622.5 feet less than 1.1 times its height before construction began.

1.1h – 622.5 = 5,675 is the equation to find the height of the mountain prior to construction, represented by the variable h

1.1h – 622.5 = 5,675

We need to find the value of h

Add 622.5 on both the sides

1.1h=5675+622.5

1.1h=6297.5

Divide both sides by 1.1

h=6297.5/1.1

h=5725

Hence 5725 is the height of the mountain prior to construction, represented by the variable h.

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2w + 10 = 26 can you use to find w, the number of weeks the driving classes last the driving test will last for 8 weeks.

A linear equation is an algebraic equation of the form y = mx + b. involving only a constant and a first-order ( linear ) term, where m is the slope and b is the y - intercept.

If w is the number of weeks,

The equation to represent this equation is to be 2w + 10 = 26

2w = 26 - 10

2w = 16

w =  [tex]\frac{16}{2}[/tex]

w = 8

Hence the driving test will last for 8 weeks.

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The The temperature at midnight is -5.6°C.

What is the short definition of temperature?

It should be noted that there are 8 hours between midnight and 6 am.

Therefore, the equation will be:

x + (0.65 × 8) = -0.1

x + 5.5 = - 0.1

x = -0.1 - 5.5

x = - 5.6

The temperature at midnight is -5.6°C.

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Answer: 20

Step-by-step explanation:

5 boxes with 10, 10, 10, 10, and 10 donuts in each box.

She gives one box away, so that is 50-10=40

Then she gives 2 boxes away, which is 40-20=20, so she has 20 donuts left to share with her classmates.

Answer: 20

Step-by-step explanation:

5 x 10 = 50 Donuts

50 Donuts - 10       for the Bus driver

40 Donuts - 20      for the school principal

=20

She can share 20 Donuts with her classmates.

If the system of equations, A·x + B·y = C and P·x + Q·y = R has infinitely many solutions, then the relationship between the values, A, B, C, P, Q, and R is; A/P = B/Q = C/R

A system of linear equations can have no solutions, only one solution or infinitely many solutions.

Part of the question that appear missing is presented as follows;

The system of equations in the question is;

If the system has infinitely many solutions, then the equations (1) and (2) represent the same equation, such that equation (1) can be obtained directly from equation (2) and vice versa

This indicates that equation (1) is a multiple of equation (2)

Let the common factor be c, we have;

A = c·P

B = c·Q

C = c·R

Which gives;

A/P = B/Q = C/R = c

The relationship between the coefficient is that; A/P = B/Q = C/R

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The value of the expression -15x+14y as calculated from the given equations is 12.

The pair of simultaneous equations are given as

-9x+8y=3............................1

6x-6y=-3

Now we will solve these equation by elimination method.

6x-6y=-3

or, 2x-2y=-3.......................2

Now multiplying equation 2 by 4 and adding to equation 1 we get:

-9x+8y=3

8x - 8y = -12

or, -x = -9

or, x = 9

Now we use this value of x to find the value of y

-9x + 8y = 3

or , -81 -3 = -8y

or, y = 10.5  

Hence the value of the expression -15x+14y is

=-15(9) + (14)(10.5)

=12

The theory of linear systems serves as the foundation for the field of linear algebra, which is used in most branches of modern mathematics. Computing techniques for obtaining the solutions, which are essential to the disciplines of engineering, physics, chemistry, computer science, and economics are included in numerical linear algebra.

It is useful to approximate a system of nonlinear equations by a linear system when developing a mathematical model or computer simulation of a relatively complex system.

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Answer:

d) {(-2,0), (-1,0), (1,0), (2,0)}

Step-by-step explanation:

We know that,

→ A set function has different x values.

Then the set function will be,

a) {(1,0), (1,1), (2,2), (2,2)}

→ The x values underlined are repeated.

Hence, it is not a set function.

b) {(0,0), (1,1), (1,1), (3,3)}

→ The x values underlined are repeated.

Hence, it is not a set function.

c) {(0,-2), (0,-1), (0,1), (0,2)}

→ The x values underlined are repeated.

Hence, it is not a set function.

d) {(-2,0), (-1,0), (1,0), (2,0)}

→ There are no repeated values for x.

Hence, it is a set function.

Answer:

240?

Step-by-step explanation:

Answer:

That is a line. Here's two points that pass through the line:

Literally just graph a line that passes through those two points.

Answer:

Rs. 4000

Step-by-step explanation:

Profit = 80% = 180% of original price

Therefore, [tex]\frac{180}{100}x=7200\\ 180x=720000\\x=4000[/tex]

Answer:

9000

Step-by-step explanation:

80 percent *9000 =

(80:100)*9000 =

(80*9000):100 =

720000:100 = 7200