Three tickets to attend an Off-Broadway show cost $81, 4 tickets cost $108, and 5 tickets cost $135. Show that the relationship between number and the cost is a proportional relationship by making a table of tickets for 1 to 5 tickets. Show your work. Number of Tickets 1 2 3 4 5 Total Cost ($) What is the constant of proportionality, k? Write and Equation for the relationship. (Remember to state what the variables represent)

Answer:

(a)19.6 meters

(b) 1 seconds

(c)30.625 meters

Step-by-step explanation:

The height of the balloon is modeled by the equation:

[tex]h = -4.9t^2- 14.7t + 19.6[/tex]

(a)Since the balloon is thrown from the top of the house,  the height of the house is at t=0

When t=0

[tex]h(0) = -4.9(0)^2- 14.7(0) + 19.6\\h=19.6$ meters[/tex]

The height of the house is 19.6 meters.

(b)When the balloon hits the ground

Its height, h(t)=0

Therefore, we solve h(t)=0 for values of t.

[tex]h = -4.9t^2- 14.7t + 19.6=0[/tex]

[tex]-49t^2-147t+196=0\\-49(t^2+3t-4)=0\\t^2+4t-t-4=0\\t(t+4)-1(t+4)=0\\(t+4)(t-1)=0\\t+4=0$ or $t-1=0\\t=-4$ or t=1[/tex]

Therefore, the ball hits the ground after 1 seconds.

(c)To determine the maximum height, we take the derivative of the function and solve it for its critical point.

[tex]If$ h = -4.9t^2- 14.7t + 19.6\\h'(t)=-9.8t-14.7\\$Setting the derivative equal to zero$\\-9.8t-14.7=0\\-9.8t=14.7\\t=-1.5\\$Therefore, the maximum height, h(t) is:\\h(1.5) = -4.9(-1.5)^2- 14.7(-1.5) + 19.6\\=30.625$ meters[/tex]

Answer:

∈

Step-by-step explanation:

∈ symbol indicates the data set on the left side is fully included in the data set on the right side

Answer:

Step-by-step explanation:

The question is not properly structured. Here is the complete question.

For cones with radius 6 units, the equation V=12\pi h relates the height h of the cone, in units, and the volume V of the cone, in cubic units. Sketch a graph of this equation on the axes.

The formula for calculating the volume of a cone is expressed as shown;

[tex]V = \frac{1}{3} \pi r^{2} h[/tex] where r is the radius and h is the height.

Given radius r = 6units, on substituting;

[tex]V = \frac{1}{3}*\pi *6^{2}*h\\ V = \frac{36\pi h}{3}\\V = 12\pi h... (1)[/tex]

It can be seen from the derived volume of the cone that it is linear in nature. The volume of the cone has a linear relationship with its height. As the volume increases, the height also increases and vice versa.

Generally for a direct variation

[tex]if\ y\ \alpha x \ \\y = kx[/tex]

where k is the constant of proportionality. comparing to equation 1, k = 12π.

Find the graph attached

All real numbers because any value of x works

It takes 48 hours if 12 people built the same wall.

Please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Answer:

3 x 12 x 129

Step-by-step explanation:

You can get your answer

Step-by-step explanation:

1 business = 736800 ÷ 9 = 81866.66

Each business associates 81866.66

Answer:

The answer to your question is C.

Step-by-step explanation:

Have a nice day :)

The values of c and d are c = 4.2, d=−12, c = −5, d=−8/4 and c = −1/5, d=11

The complete question is added as an attachment

From the question, we have the following parameters that can be used in our computation:

d = integers

c = rational numbers

Integers are numbers without decimal and rational numbers can be expressed as fractions

Using the above as a guide, we have the following possible values

c = 4.2, d=−12, c = −5, d=−8/4 and c = −1/5, d=11

Read more about numbers at

https://brainly.com/question/10853762

#SPJ1

Answer:

Step-by-step explanation:

Statement A is closest to being correct.  To get the graph of g(x), we compress the graph of f(x) vertically due to multiplying f(x) by (1/4).

Answer:

C. The graph of g(x) is the graph of f(x) horizontally stretched by a factor of 4.

Step-by-step explanation:

a p e x

Answer:

D Over the interval [4, 7], the local minimum is -7.

Step-by-step explanation:

Answer: 180 houses

Step-by-step explanation:

From the question, we are informed that in a village the number of houses and the number of flats are in the ratio 9:5 while the number of flats and the number of bungalows are in the ratio 10:3 and that there are 30 bungalows in the village.

Since the ratio of the number of flats and the number of bungalows are in the ratio 10:3 and there are 30 bungalows in the village, the number of flats will be:

= 10/3 × 30

= 10 × 10

= 100 flats

Since we are told that the ratio of the number of houses to the number of flats are in the ratio 9:5 and we've gotten the number of flats as 100, then the number of houses will be:

= 9/5 × 100

= 9 × 20

= 180 houses

Answer:

Macy’s

Step-by-step explanation:

let’s find the cost of each shirt

JCPenny’s: 14.99 x 0.80 = $11.99

                   11.99 x 1.06 = $12.70

                   The final cost of the JCPenny shirt is $12.70

Macy’s: 17.99 x 0.65 = $11.69

             11.69 x 1.07 = $12.51

             The final cost of the Macy’s shirt is $12.51

$12.51 is less than $12.70

So, the Macy’s shirt is the better deal :)

Answer:

2

Step-by-step explanation:

the - means you have to subtract to add. so subtract 3 over 4 and you get 2

Answer:

simplified expression for √x^2+6x+9 if x≥3

is x+3

Step-by-step explanation:

[tex]\sqrt{x^2+6x+9} \\=>\sqrt{x^2+3x+3x+9} \\=>\sqrt{x(x+3)+3(x+3)} \\=>\sqrt{(x+3)(x+3)} \\=>\sqrt{(x+3)^2}\\=>(x+3) \ or -(x+3)[/tex]

but given that x≥3

then we have to negate solution -(x+3)\

Then simplified expression for √x^2+6x+9 if x≥3

is x+3

Answer:

see below

Step-by-step explanation:

4. If ∠AYX = 25.5° that means that ∠XYZ = 25.5 * 2 = 51° because YA is the angle bisector.

5. If ∠XYZ = 64°, ∠AYZ = 64 / 2 = 32°.

6. You can construct ∠P and PQ by using a protractor. I'm not sure how to attach an image so I'll just tell you the answer I got for c which is about 3 cm.

Answer:

1/2

Step-by-step explanation:

The constant of variation is the same as the slope. From the graph, the slope is 1/2.

Answer:

I believe the answer is 2

Answer:

10 units

Step-by-step explanation:

Let us find the volume of Haley's prism and compare it with the volume of Jeremiah's.

The volume of Haley's prism is:

V = 5 * 3 * 4 = 60 cubic units

Jeremiah's prism has twice the volume of Haley's:

V(J) = 2 * 60 = 120 cubic units

This implies that:

120 = 4 * 3 * h

where h = height of prism

=> 120 = 12h

=> h = 120 / 12 = 10 units

Jeremiah's prism is 10 units tall.

Answer:

(6, - 3 )

Step-by-step explanation:

Given f(x) then f( x + c) represents a horizontal translation of f(x)

• If c > 0 then a shift to the left of c units

• If c < 0 then a shift to the right of c units, thus

y = f(x - 4) represents a shift to the right of 4 units, so

(2, - 3 ) → (2 + 4, - 3 ) → (6, - 3 )

The maximum point on the graph after translation y = f( x -4) is (6 , -3)

Translation of a graph is the movement of the graph either in horizontal direction or vertical direction .

Horizontal translation to the left is given by f (x+ c) ,c >0

: (x, y) → (x- c , y)

Horizontal translation to the right is given by f (x- c) ,c >0

: (x, y) → (x+ c , y)

Given that the maximum point on the graph of the equation

y = f(x) is (2,-3)

To find the maximum point on the graph of the equation y = f(x-4)

f(x -4) is Horizontal Translation to the right with 4 units , c= 4

then  (x, y) → (x+ c , y)

Thus the maximum point (2,-3) is moved to ( 2 +c , -3)

⇒ (2+ c , -3) = (2+4 , -3) = ( 6 , -3)

Therefore, the maximum point of the graph of the equation  y = f(x-4) becomes (6,-3)

Also, Learn more abut translation of graphs from the link below:

https://brainly.com/question/11805053

#SPJ5

Answer:

5/3

Step-by-step explanation:

multiply the whole thing by y to get 3y/x=5 and then divide by 3 to get y/x=5/3

Answer:

y/x=5/3

Step-by-step explanation:

3/x=5/y ⇒ y/x=5/3  replacing y with 3

Answer:

Hope it helps!

Step-by-step explanation:

The general form of a cubic function is y = ax3 + bx + cx + d where a , b, c and d are real numbers and a is not zero. We can graph cubic functions by plotting points.

A cubic function is any function of the form y = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants, and a is not equal to zero, or a polynomial functions with the highest exponent equal to 3. These types of functions are extremely prevalent in applications involving volume.

Credits;

Graphs of Cubic Functions (solutions, examples, videos)

Cubic Function: Definition, Formula & Examples - Video & Lesson

Answer:

C

Step-by-step explanation:

Option c gives the actual representation of the question

Answer:

(-3, 1.5)

Step-by-step explanation:

Take the averages of the x-coordinates and y-coordinates of the 2 points

-5.5 + -0.5 = -6. Divide by 2 to get the average: -6/2 = -3. So, -3 will be the x coordinate of the midpoint.

-6.1 + 9.1 = 3. Divide by 2 to get the average: 3/2 = 1.5. So, 1.5 will be the y coordinate of the midpoint.

The midpoint will be (-3, 1.5)

Answer:

The TV has a length of 61.01" and a height of 34.32"

Step-by-step explanation:

The size of a TV is given by the length of it's diagonal, in this case the diagonal of the TV is 70". The ratio of the screen is 16:9, which means that for every 16 units on the length of the tv there are 9 inches on its height. The diagonal of the screen forms a right angle with the length and the width, therefore we can apply Pythagora's theorem as shown below:

[tex]diagonal^2 = height^2 + length^2\\\\height^2 + length^2 = (70)^2\\\\height^2 + length^2 = 4900[/tex]

Since the ratio is 16:9, we have:

[tex]9*length = 16*height[/tex]

[tex]length = \frac{16}{9}*height[/tex]

Applying this on the first equation, we have:

[tex]height^2 + (\frac{16}{9}*height)^2 = 4900\\\\height^2 + \frac{256}{81}*height^2 = 4900\\\\\frac{337}{81}*height^2 = 4900\\\\height^2 = \frac{4900*81}{337}\\\\height^2 = \frac{396900}{337}\\\\height^2 = 1177.744\\\\height = \sqrt{1177.744}\\\\height = 34.32[/tex]

[tex]length = \frac{16}{9}*34.32\\\\length = 61.01[/tex]

The TV has a length of 61.01" and a height of 34.32"

Answer:

Your Answer is $43.7

Step-by-step explanation:

Take the initial $38 and Multiply it by the .15 (15%) tip

You get a $5.7 tip

Add that to the meal cost of $38 and you get $43.7

Answer:

Step-by-step explanation:

The only valid expression from the given list is the one that uses the arctangent ([tex]tan^{-1}(0.75)[/tex] ) function.

Recall that the tangent of an acute angle in a right angle triangle is defined as:

[tex]tan(B)=\frac{opposite}{adjacent}[/tex]

therefore in our case we have:

[tex]tan(B)=\frac{opposite}{adjacent} \\tan(B) = \frac{12}{16} \\tan(B)=0.75\\B=arctan(0.75)[/tex]

Answer:

the median increases by 0

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The matrices are conformable for multiplication.

Multiply and sum the product of corresponding elements in row 1 of matrix A with elements in column of matrix B.

AB = [tex]\left[\begin{array}{ccc}5(2)+2(3)\\3(2)-1(3)\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}10+6\\6-3\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}16\\3\\\end{array}\right][/tex] → C

Answer:

m = 3.86

Step-by-step explanation:

D = 6 / 7

D = m + 3

6 / 7 = m + 3

6 / 7 + 3 = m

m = 3.86