is it legal to drive at 80 mph if everyone is driving at that same speed, even though the posted speed limit is 65 mph?

The constant of proportionality is 12, and the  equation to represent the direct proportion is y = 12x

A proportion is a comparison of two numbers that each represent the parts of a whole.

Given that, Karl hikes 3 km in 36 minutes, his distance is directly proportional to the time he walks,

The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other.

Put y = 36 and x = 3, to find the constant of proportionality,

k = 36/3

y = 12

Therefore, the constant of proportionality is 12,

The equation to represent the direct proportion =

y = 12x

Hence, the constant of proportionality is 12, and the  equation to represent the direct proportion is y = 12x

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Answer:

a= 17* √2

Step-by-step explanation:

a=17*cosec45

Step-by-step explanation:

x=97+40 degree (being sum of two interior angle is equal to one exterior angle)

The inequality used to determine v, the minimum number of visits Taylor needs to earn her first free movie ticket is 75 + 6.5v ≥ 100.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Given,

Points for signing up = 75 points

Points for each visit to the movie theater = 6.5 points

Let v be the minimum number of visits Taylor needs to earn her first free movie ticket.

Points earned for v visits = 6.5v

She needs at least 100 points for a free movie ticket.

75 + 6.5v will be the points she earn for a free movie ticket.

This expression must be greater than 100, which is the required points for a free movie.

75 + 6.5v ≥ 100

Hence the inequality representing the situation is 75 + 6.5v ≥ 100.

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Answer: Let's call the measure of the angle x.

The complement of the angle is (90 - x) degrees, and the supplement is (180 - x) degrees.

So, using the information given in the problem, we can set up an equation:

5 * (90 - x) = 2 * (180 - x) - 24

Expanding both sides and simplifying, we get:

450 - 5x = 360 - 2x - 24

Solving for x, we get:

6x = 294

x = 49

Therefore, the measure of the angle is 49 degrees.

Step-by-step explanation:

The sketch of cylinder is shown in the figure.

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \pi r^2 h \: \rm unit^3[/tex]

Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.

Given;

Volume=36pi

Diameter=6cm

Now,

Radius=6/2=3cm

Volume= 36pi

pi*R^2*h=36pi

3^2*h=36

h=36/6

h=6cm

Therefore, by the given volume the radius and height will be 3cm and 6cm.

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Work Shown:

A = the 1st marble is blue

B = the 2nd marble is green

Replacement is applied. This makes A and B independent.

P(A) = (4 blue)/(10 total) = 4/10 = 2/5

P(B) = (2 green)/(10 total) = 2/10 = 1/5

P(A and B) = P(A)*P(B) ... see note below

P(A and B) = (2/5)*(1/5)

P(A and B) = 2/25

Note: The equation is valid because events A and B are independent.

Answer:

[tex]\frac{597}{283750}+3*10^8[/tex]

Step-by-step explanation:

[tex]((2848*838449)/(294949*3848483))+300,000,000\\or\\\frac{2848*838449}{294949*3848483}+300,000,000\\\\\frac{2.388*10^9}{1.135*10^{12} } +3x10^8\\\\\\\frac{597}{283750}+3*10^8[/tex]

Answer: 31457261583.3

Step-by-step explanation:

Step-by-step explanation:

Find 1/4 of 56

56 / 4 = 14

Now

56-14=42

Now

42/7=6

6x4=24

42-24=18

18 copies left

Answer:

850 miles on 25 gallons

Step-by-step explanation:

Answer: 850 miles on 25 gallons is more efficient, meaning it covers a greater distance per gallon of fuel.

Step-by-step explanation:

Answer:

For exercise 11: x = 64

For exercise 12: x = 66

For exercise 13: x = 89

For exercise 14: x = 99

Step-by-step explanation:

The sum of interior angles of an n-sided polygon = [tex](n- 2 )[/tex] x [tex]180^{o}[/tex]

where n = number of sides

For all the four figures in this exercise, n = 4

Therefore, Sum of interior angles = [tex](4 - 2)[/tex] x [tex]180^{o}[/tex]

                                                          = 2 x [tex]180^{o}[/tex]

                                                          = [tex]360^{o}[/tex]

For Exercise 11:

[tex]x^{o} + 100^{o} + 130^{o} + 66^{o} = 360^{o}[/tex]

[tex]x^{o} + 296^{o} = 360^{o}[/tex]

[tex]x = 360 - 296[/tex]

x = [tex]64^{o}[/tex]

Apply the above stated concept in the other three exercises

Answer: Their car got an average of 23.6 miles per gallon.

BTW I just searched it up so I'm sorry if it is wrong.

The new co-ordinates of the point after transformation is (-3,9)

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates,

Given here: The point g'(4,6)

The point transforms to  (x-7,y+3)

Thus the new points are 4⇒4-7=-3

6⇒6+3=9

Thus, The new co-ordinates of the point after transformation is (-3,9)

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Answer:

In the case presented, the range is the difference between the maximum value and the minimum value of the data. The range describes the breadth of the data and how much they vary from the minimum value to the maximum value. Therefore, the range indicates the dispersion of the data.

The statement indicates that the range is 5, which means that the most flights made by students is 5. Since the data has a narrow dispersion, we can conclude that most students have taken a similar number of flights, implying that most students have flown an amount close to the maximum number observed.

Therefore, the option that best describes the dispersion of the data is: "The data has a range of 5, which is a narrow dispersion. This means that most students have taken a similar number of flights."

Step-by-step explanation:

The possible dimensions of rectangular room A are 9 and 3x - 2.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle.

Given:

A fitness center has several rectangular rooms where exercise classes are held.

The area of Room A is 27x − 18 square units.

The area of the rectangle = length x width

27x − 18 = length x width

9 (3x - 2) = length x width.

Therefore, 9 and 3x - 2 are the dimensions.

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The average rate of change of the temperature from 0 to 2 minutes is given as follows:

-6ºC per minute.

The average rate of change of a function is given by the change in the output divided by the change in the input.

The temperatures for this problem are given as follows:

Hence the change in the output is given as follows:

62 - 74 = -12ºC.

The change in the input is of:

2 - 0 = 2 minutes.

Hence the rate is given as follows:

-12/2 = -6ºC per minute.

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Answer: It is 34$ per one ticket

Step-by-step explanation:

$374 divided by 11 is 34

Answer:

$34 per ticket

Step-by-step explanation:

We were told $374/11tickets.

We are looking for how much per 1 ticket.

Divide to find the per-ticket cost.

Use either 374÷11

374/11 .

374÷11 = 34

This means $34 per ticket.

Using the Pythagorean theorem, if AL is perpendicular to BD and CM is perpendicular to BD, then quadrilateral ABCD is a parallelogram.

In a parallelogram, the opposite sides are equal in length, i.e. AL = CD and BM = AD.

By the Pythagorean theorem, we know that the length of the diagonal BD can be found as the square root of the sum of the squares of AL and CM:

BD = √(AL^2 + CM^2)

Since AL = CD, the area of quadrilateral ABCD can be found as:

ar (quad.ABCD) = AL × BD

Substituting BD = √(AL^2 + CM^2) and combining the two equal length sides, we get:

ar (quad.ABCD) = (AL + CM) × √(AL^2 + CM^2) / 2

Finally, dividing both sides by √(AL^2 + CM^2) and using the fact that BD = √(AL^2 + CM^2), we get:

ar (quad.ABCD) = 1/2 × BD × (AL + CM)

Thus, we have proved that the area of quadrilateral ABCD is equal to 1/2 × BD × (AL + CM).

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Answer:

  (x, y) = (4, 0)

Step-by-step explanation:

You want the solution to the system of equations ...

It often works well to start the solution process by putting both equations into standard form. We do that by removing any common factors from the coefficients. Here, we see that the second equation's coefficients each have a factor of 3, so we can remove that and rewrite the system as ...

Changing the coefficient of the y-term has no effect, telling us that y=0, and the equation reduces to ...

  5x = 20

  x = 4

More formally, if we subtract the first equation from the second, we get ...

  (5x +2y) -(5x -3y) = (20) -(20)

  5y = 0 . . . . . . simplify

  y = 0 . . . . . . . divide by 5

The solution is (x, y) = (4, 0).

Answer:

x = -16 and x = 1

Step-by-step explanation:

"Finding the roots" means solving the equation. We'll set the equation equal to 0 (replace f(x) with zero) and factor.

0 = x^2 + 15x - 16

0 = (x + 16)(x - 1)

This is factored.

Using the Zero Product Property, we separate this into two small equations.

x+16 = 0 and x-1 = 0

Solve these one-step equations.

x = -16 and x = 1

These are the roots (and roots are solutions, are zeros, are x-intercepts) If the question ask for zeros, roots, solutions or x-intercepts, set it equal to 0, factor and solve.

Answer:

4.5 inches

Step-by-step explanation:

Answer:

0 < a < 6

or

(0, 6) in interval notation

Step-by-step explanation:

The area of the triangle is
[tex]Area \;A = \dfrac{1}{2}(base \cdot height)\\[/tex]

We are given base = 6 in, height = a and area A < 18 in²

Using the formula for area we get

[tex]A = (1/2)(6 \cdot a) = 3a[/tex]

We know this area is < 18

So 3a < 18

Dividing both sides by 3 gives us
3a/3 < 18/3

a < 6

So height a must be less than 6 inches.
Height cannot be 0 so the lower bound on height is

a > 0

Putting these together we get the rang of a as
0 < a < 6

In Interval notation this is written as (0, 6)

Hope that helps you. Have confidence in yourself and seek help for your doubts here or elsewhere on the net. You will succeed

Using equations, we know that the age of Geraldine and Steven is t - 4 and 2t - 8 respectively.

It basically consists of a variable, perhaps with an additional numerical constant.

To easily understand this concept, consider the example below. 3x – 4 = 5. It is a straightforward class 7 equation.

The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.

So, we have the following algebraic expression after converting the word problem:

To Geraldine:

g = t - 4

To Steven:
s = 2g

Inputting Tom's age into equation 1 results in:

g = t - 4

To determine Steven's age:

s = 2(t-4)

s = 2t - 8

Therefore, using equations, we know that the age of Geraldine and Steven is t - 4 and 2t - 8 respectively.

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Answer:

y = - [tex]\frac{5}{2}[/tex] x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, - 2) ← 2 points on the line

m = [tex]\frac{-2-3}{0-(-2)}[/tex] = [tex]\frac{-5}{0+2}[/tex] = - [tex]\frac{5}{2}[/tex]

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = - [tex]\frac{5}{2}[/tex] x - 2 ← equation of line

Answer:

(7^2)^2

Step-by-step explanation:

(7^-2)*(7^6)=7^-2+6

......since the base 7 is the same, when u multiply them, you should add the exponents and keep 7 as it is. That will be 7^4, which in equivalent to ans D(7^2)^2

Answer: -3/16

Step-by-step explanation:

When there is a negative exponent like x^-2 it equals 1/(x^2) the negative puts the number as a fraction so continuing...

-12(x^-2) (y^-2) can be rewritten as

-12 (1/x^2) (1/y^2) now we plug in x = -2 and y = 4

-12 (1/(-2^2) (1/(4^2)); -2^2 = 4 , 4^2 = 16

-12 (1/4) (1/16)

-3 (1/16)

= -3/16

Answer: $3,000

(There are 7 days in a week) I don't know if i'm correct or not but it should be the answer.

Answer:

y = -x +8

Step-by-step explanation:

The line crosses the x axis at 8. So we know when y = 0 then x = 8

The line cross the y axis at 8. so we know when x = 0 then y = 8

the equation of a line we know to take the form y = mx + c

When x = 0 and y = 8, and y = mx+ c then then c =8

when y = 0 x = 8. y = mx + c, 0 = m(8) +8. for this to be true m must be equal to -1

so the equation of the line, the inequality is y = -x +8