Identify the range of the function shown in the graph.

Y-3=1/5(x+2) is the answer.

Answer:

(a) 30 feet

(b) 30 feet.

Step-by-step explanation:

Given that the opening of a tunnel that travels through a mountainside can be modeled by

[tex]y=\frac{-2}{15} (x-15)(x+15)[/tex], where x and y are measured in feet.

[tex]\Rightarrow y=\frac{-2}{15}(x^2-15^2}[/tex]

[tex]\Rightarrow y=\frac{-2}{15}{x^2-225}\cdots(i)[/tex]

(a) At the ground level, [tex]y=0[/tex]

So, the width of the tunnel at ground level is distance between the extreme point of the tunnel on the grount.

For, [tex]y=0[/tex], the extreme points of the tunnel.

[tex]0=\frac{-2}{15} (x-15)(x+15)[/tex]

[tex]\Rightarrow (x-15)(x+15) =0[/tex]

[tex]\Rightarrow x= 15, -15[/tex]

So, the extreme points of the tunnel are, [tex]x_1=15[/tex] and [tex]x_2=-15[/tex].

Hence, the width of the tunnel at the ground level

[tex]= | x_1 - x_2 |[/tex]

[tex]=|15-(-15)|[/tex]

[tex]=30[/tex] feet.

(b) The maximum height of the tunnel can be determiment by determining the maxima of the given function.

First determining the value of x for which the slope of the graph is zero.

[tex]\frac{dy}{dx}=0[/tex]

From equation (i),

-2x=0

[tex]\Rightarrow x=0[/tex]

And  [tex]\frac{d^2y}{dx^2}= -2[/tex]

which is always negative, so at x=0 the value of y is maximum.

Again, put x=0 in equation (i), we have

[tex]y=\frac{-2}{15}{0^2-225}[/tex]

[tex]\Rightarrow y=30[/tex] feet.

Hence, the tunnel is 30 feet tall.

Answer:

27

Step-by-step explanation:

Answer:

13/13.3 or 10

Step-by-step explanation:

You said she paid $10 to join, if she spent at least $40, then we subtract 10, then divide 30 by 3 then you would get 10.

If we don't have to subtract and she spent around $40 on only books, it would be 13/13.3

Answer:THE ANSWER IS BLOCKED AND DELETED FROM THE ACCOUNT OR THE INTERNET ACCESS IS LOW OR YOUR BATTERY IS NOT WORKING PROPERLY TRY AGAIN LATER

Answer:

1/36

Step-by-step explanation:

A dice have 6 faces, each face have 1/6 chance to land on, so the chance of landing on 3 two times in a row is 1/6 x 1/6 = 1/36

Answer:

(x+y+z)=79

5x+2y+z=859

2x+3y+9z=498

Step-by-step explanation:

Its writing 3 different equations that have the same value for the same variable.

Answer:

Correct Choice: Second Option

[tex]\displaystyle x=\frac{5\pm \sqrt{97}}{12}[/tex]

Step-by-step explanation:

Standard Form of Quadratic Function

The standard representation of a quadratic function is:

[tex]f(x)=ax^2+bx+c[/tex]

where a,b, and c are constants.

Solving with the quadratic formula:

[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

We have the following equation to solve:

[tex]5x = 6x^2 -3[/tex]

Rearranging all the terms to the left side:

[tex]6x^2 -5x- 3=0[/tex]

Comparing with the general form of the quadratic equation: a=6, b=-5, c=-3. Apply the formula:

[tex]\displaystyle x=\frac{-(-5)\pm \sqrt{(-5)^2-4(6)(-3)}}{2(6)}[/tex]

[tex]\displaystyle x=\frac{5\pm \sqrt{25+72}}{12}[/tex]

[tex]\boxed{\displaystyle x=\frac{5\pm \sqrt{97}}{12}}[/tex]

Correct Choice: Second Option

Answer:

5

Step-by-step explanation:

find the measure

Answer:

7425

Step-by-step explanation:

First let's make the last two fractions improper.

-4  1/2 = -9/2    -2  1/5 = -11/5

Now we have to find the least common denominator.

[tex]\frac{5}{6} *\frac{-9}{2}*\frac{-11}{5}[/tex]

The least common denominator is 30 because all the denominators can be multiplied by something to get 30.

[tex](\frac{5}{5})*\frac{5}{6}* (\frac{15}{15})*\frac{-9}{2}* (\frac{6}{6})*\frac{-11}{5}[/tex] Simplify

[tex]\frac{25}{30}*\frac{-135}{30}*\frac{-66}{30}[/tex] simply

[tex]\frac{-3375}{30}*\frac{-66}{30}[/tex]

[tex]\frac{222750}{30}[/tex] simply

7425

Answer: y= (4/5)x+6

Step-by-step explanation:

(0,6) is the y intercept/b . Use y2-y1 for the slope/m. Y= Mx+b now is y=(4/5)x+6.

Answer:8 over 4

Step-by-step explanation:

Rise over run

Answer:

x = 17, angle 1 and 2 = 45

Step-by-step explanation:

Answer:

8 teams is answer

Step-by-step explanation:

Answer: 1/2

Step-by-step explanation: got it right

The slope of the line that passes through the points (8,7) and (4, 5) is 1/2.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

The given coordinate points are (8, 7) and (4, 5).

Substitute (x₁, y₁)= (8, 7) and (x₂, y₂)= (4, 5) in slope formula, we get

Slope = (5-7)/(4-8

= -2/(-4)

= 1/2

Therefore, the slope of the line that passes through the points (8,7) and (4, 5) is 1/2.

To learn more about the slope of a line visit:

https://brainly.com/question/14511992.

#SPJ6

Answer:

Yes, but doing so will clear out his account.

Step-by-step explanation:

CHECK THE COMPLETE QUESTION BELOW

Aaron's bank account has a balance of $1213.69 before he starts spending money. He makes the following transactions:

Transaction

Cost ($)

Car payment

260.16

Groceries

97.98

Parking ticket

75.00

DVD box set

115.35

Antique lamp

68.53

Suit

331.84

Aaron is considering getting his car a new paint job. Doing so will have a total cost of $264.83. Can Aaron afford this? Explain a. Yes, he can make the purchase and still have money left over. b. Yes, but doing so will clear out his account. c. No, purchasing that would overdraw his account. d. No, he is overdrawn already

Aaron's bank account balance=$1213.69

He made all this transactions below;

Car payment

260.16

Groceries

97.98

Parking ticket

75.00

DVD box set

115.35

Antique lamp

68.53

Suit

331.84

The summation of all his transactions is;260.16+97.98+75.00+115.35+68.53+

331.84= $948.86

Which means after performing those transactions above, he was left with $948.86.

We were informed that Aaron is considering getting his car a new paint job. Doing so will have a total cost of $264.83.

For him to paint his car now he will spend $264.83, if we add with the previous transactions it sum up to $1213.69 which was actual amount he has at hand. I.e ($264.83+$948.86)=

$1213.69

Therefore, the answer is Yes, but doing so will clear out his account.

Answer:

y= -7x+22/-4

Step-by-step explanation:

Answer:

y=7/4x-11/2

Step-by-step explanation:

Move the Y and x values to separate sides

-4y=-7x+22

divide whatever it takes to make y alone (dived by -4)

y=7/4x-11/2

Answer:

Value over a defined period of time, and it represents the momentum of a variable. ✨

Step-by-step explanation:

Answer:

283.75

Step-by-step explanation:

  525/4=131.25

131.25+110=241.25

525-241.25=283.75

Answer:

O-O omg i feel u i have like the same question

Step-by-step explanation:

sorry couldn't help

Answer:

Hello! I'm pretty sure you aren't expecting an answer now. If no one else answers the points would be lost so I'm answering right now. If you were, I'm really sorry and you can report this answer so that it gets deleted and another person can answer! :)

Answer:

55 r5

Step-by-step explanation:

Answer:

390/7=55 with a remainder of 5.

Step-by-step explanation:

we can get this answer by subtracting fifty-five sevens from three-hundred ninty.

390-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7=5

Answer:

can you comment the real question because this is just gibrish

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

210 Pink cakes and 0 Yellow cakes

Step-by-step explanation:

Since the Yellow cake takes about %33.3 more time to prepare but only about %16.6 more revenue, it's always more profitable to make Pink cakes.

Answer:

2.26 hours

Step-by-step explanation:

Given that:

Stock 1:

Initial price = 13.17

Rate of increase = $0.11 per hour

13.17 + 0.11h - - - (1)

Stock 2 :

Initial price = 13.69

Rate of decrease = 0.12 per hour

13.69 - 0.12h - - (2)

13.17 + 0.11h = 13.69 - 0.12h

0.11h + 0.12h = 13.69 - 13.17

0.23h = 0.52

h = 0.52 / 0.13

h = 2.26 hours