What is f(4) for the function f(x)= 6x+7?

The Fall Festival charges $0.75 per ticket for the rides. Kendall bought 18 tickets for rides and spent a total of $33.50 at the

PIT_PIT [208]

Part (a)

The variable y is the dependent variable and the variable x is the independent variable.

Part (b)

The cost of one ticket is $0.75. Therefore, the cost of 18 tickets will be:

$0.75\times 18=13.5$ dollars

Now, we know that Kendall spent her money only on ride tickets and fair admission and that she spent a total of $33.50.

Therefore, the price of the fair admission is: $33.50-$13.50=$20

If we use y to represent the total cost and x to represent the number of ride tickets, the linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission can be written as:

$y=0.75x+20$ ......Equation 1

Part (c)

The above equation is logical because, in general, the total cost of the rides will depend upon the number of ride tickets bought and that will be 0.75x. Now, even if one does not take any rides, that is when x=0, they still will have to pay for the fair admission, and thus their total cost, y=$20.

Likewise, any "additional" cost will depend upon the number of ride tickets bought as already suggested. Thus, the total cost will be the sum of the total ride ticket cost and the fixed fair admission cost. Thus, the above Equation 1 is the correct representative linear equation of the question given.

4 0

3 years ago

Ashleigh rode her bicycle 26.5 miles in 4 hours.which gives best estimate of how far Ashleigh rode in 1 hour

Firdavs [7]

Ashleigh rode her bicycle about 6 miles in 1 hour

4 0

3 years ago

Find the missing length.

Mandarinka [93]

The answer is 6 because 14+6=20

Hope this helps

4 0

3 years ago

How many dimensions are in a point? A. 0 B. 1 C. 2 D. 3

Juliette [100K]

Answer:

0 dimensions are in a point

6 0

3 years ago

Read 2 more answers

On a single set of axes, sketch a picture of the graphs of the following four equations: y = −x+ √ 2, y = −x− √ 2, y = x+ √ 2, a

Artist 52 [7]

Answer:

( 1/√ 2 , 1/√ 2 ) , ( 1/√ 2 , - 1/√ 2 ), ( -1/√ 2 , 1/√ 2 ) , ( -1/√ 2 , - 1/√ 2 )

y + 1 = - ( x + 2 ) + √ 2 , y + 1 = - ( x + 2 ) - √ 2 , y + 1 = ( x + 2 ) - √ 2

y + 1 = ( x + 2 ) + √ 2 , ( x + 2 )^2 + ( y + 1)^2 = 1

Step-by-step explanation:

Given:

- Four functions to construct a diamond:

y = −x+ √ 2, y = −x− √ 2, y = x+ √ 2, and y = x − √ 2.

Find:

a)Show that the unit circle sits inside this diamond tangentially; i.e. show that the unit circle intersects each of the four lines exactly once.

b)Find the intersection points between the unit circle and each of the four lines.

(c) Construct a diamond shaped region in which the circle of radius 1 centered at (−2, − 1) sits tangentially. Use the techniques of this section to help.

Solution:

- For first part see the attachment.

- The equation of the unit circle is given as follows:

x^2 + y^2 = 1

- To determine points of intersection we have to solve each given function of y with unit circle equation for set of points of intersection:

For: y = −x+ √ 2 , x - √ 2

And: x^2 + y^2 = 1

x^2 + (+/- * (x - √ 2))^2 = 1

x^2 + (x - √ 2)^2 = 1

2x^2 -2√ 2*x + 2 = 1

2x^2 -2√ 2*x + 1 = 0

2[ x^2 - √ 2] + 1 = 0

Complete sqr: (1 - 1/√ 2)^2 = 0

x = 1/√ 2 , x = 1/√ 2

y = -1/√ 2 + √ 2 = 1/√ 2

y = 1/√ 2 - √ 2 = - 1/√ 2

Points are: ( 1/√ 2 , 1/√ 2 ) , ( 1/√ 2 , - 1/√ 2 )

- Using vertical symmetry of unit circle we can also evaluate other intersection points by intuition:

x = - 1/√ 2

y = 1/√ 2 , -1/√ 2

Points are: ( -1/√ 2 , 1/√ 2 ) , ( -1/√ 2 , - 1/√ 2 )

- To determine the function for the rhombus region that would be tangential to unit circle with center at ( - 2 , - 1 ):

- To shift our unit circle from origin to ( - 2 , - 1 ) i.e two units left and 1 unit down.

- For shifts we use the following substitutions:

x = x + 2 ....... 2 units of left shift

y = y + 1 .......... 1 unit of down shift

- Now substitute the above shifting expression in all for functions we have:

y = −x+ √ 2 -----> y + 1 = - ( x + 2 ) + √ 2

y = −x− √ 2 -----> y + 1 = - ( x + 2 ) - √ 2

y = x- √ 2 -------> y + 1 = ( x + 2 ) - √ 2

y = x+ √ 2 ------> y + 1 = ( x + 2 ) + √ 2

x^2 + y^2 = 1 -----> ( x + 2 )^2 + ( y + 1)^2 = 1

- The following diamond shape graph would have the 4 functions as:

y + 1 = - ( x + 2 ) + √ 2 , y + 1 = - ( x + 2 ) - √ 2 , y + 1 = ( x + 2 ) - √ 2

y + 1 = ( x + 2 ) + √ 2 , ( x + 2 )^2 + ( y + 1)^2 = 1

- See attachment for the new sketch.

7 0

3 years ago