The front of a storage bunker can be modeled by y=-5/216(x-72)(x+72), where x and y are measured in inches. The x axis represents the ground. Find the width of the bunker at ground level.

Answers

Answer 1
as far as I can make out this one.

the bunker is a 3D object, it has a height, with and length, however we're only concerned with the 2D front face, which has a length and width only.

we know the x-axis is the ground level, so the y-axis must be the scale for the length.

if we can find, using the provided model, the x-intercepts, namely where the x-axis gets touched, we can just get the distance between them and that's the ground level width.

keeping in mind that when the graph touches the x-axis, an x-intercept, "y" is 0.

[tex]\bf y=-\cfrac{5}{216}(x-72)(x+72)\implies \stackrel{y}{0}=-\cfrac{5}{216}(x-72)(x+72) \\\\\\ 0=\stackrel{\textit{difference of squares}}{(x-72)(x+72)}\implies 0=x^2-72^2\implies 72^2=x^2 \\\\\\ \pm\sqrt{72^2}=x\implies \pm 72=x[/tex]

now, the distance from (-72, 0) and (72, 0) is just 72 +72, or 144.
Answer 2
Final answer:

The width of the bunker at ground level is 14.58 inches.

Explanation:

The x-axis is the ground level, so the y-axis must be the scale for the length. Using the provided model, the x-intercepts, namely where the x-axis gets touched, we can just get the distance between them and that's the ground-level width.

The width of the bunker at ground level can be found by substituting x = 0 into the equation y = -5/216(x-72)(x+72).

This equation represents a quadratic function, which means it is a parabola.

By substituting x = 0, we get y = -5/216(-72)(72)

= 14.58 inches.


Related Questions

What is the area of this triangle in the coordinate plane? 25.0 units²
27.5 units²
50.0 units²
55.0 units²

Answers

25.0 

using the formula 

The base is 10 and the height is 5
27.5 units²

the base is 11 (I think I make no mistake), and the height is 5.

Please help me with this one. WILL MARK BRAINLIEST

Answers

1. Yes.
cranberry juice : total cups = 1 : 5 in all cases

2. Yes.
cranberry juice : total cups = 2 : 5 in all cases

3. No.
1 : 5 is not the same as 2 : 5.

Explain which type of graph would best, display the data showing the temperature of a liquid being heated in a science experiment?

Answers

I would have to say a line graph due to the facts that you can see the rising and falling of temperature.
Most likely a line graph.  Line graphs are best used to track data containing modifications over long and short periods of time. 

Two step equation; 0.7t - 3.2 = 1.7

Answers

0.7t = 1.7+3.2

0.7t = 4.9

0.7t/0.7 = 4.9/0.7

t=7

hope it helps
t=7. needs to be atleast 20 characters long oops

Chord AC intersects chord BD at point P in circle Z.

AP=3.5 in.
DP=4 in.
PC=6 in.



What is BP?

Answers

1. To solve this problem and find the value of BP, you must apply the "Intersecting chords theorem".

 2. You have that:

 AP=3.5 in
 PC=6 in
 DP=4 in

 3. Then, by applying the "Intersecting chord theorem", you have:

 (AP)(PC)=(BP)(DP)

 4. When you substitute the values into (AP)(PC)=(BP)(DP), you obtain:

 (3.5 in)(6 in)/BP(4 in)

 5. Now, you must clear BP. Then:

 (3.5 in)(6 in)/4 in=BP
 21 in^2/4 in=BP

 6. Therefore, the value of BP is:

 BP=5.25 in

Answer:

5.25

Step-by-step explanation:

converse of the Pythagorean theorem

Answers

i only know how to do # 7.

7. 4.5^2 + 6^2 = 7.5^2
20.25 + 36 = 56.25
56.25 = 56.25

yes, the card is a right triangle because A and B added together equals the same as C

Answer:

I hope this helps u can use this u see this is how the Pythagorean theorem works a^2 + b^2 = c^ i hope this helps have a great day bye please mark as brainliest :D

Step-by-step explanation:

whats the equation for this problem?

Answers

i know that x is equal to 11 and i hope it helps you 
if so please mark as Brainliest
i think they may be right

A junior baseball team plays 16 games each summer. Last summer the team scored an average of 3.25 runs per game during the first half of the season. The tteam scored a total of 29 runs during the second half of the season. How many runs were scored by the team last season?

Answers

Final answer:

To determine the total number of runs scored by the team last season, we calculate the runs from both halves of the season. The team scored 55 runs in total, with 26 runs in the first half and 29 runs in the second half.

Explanation:

To calculate the total number of runs scored by the junior baseball team last season, we need to add the runs from the first half of the season to the runs from the second half of the season. The team played a total of 16 games, so the first half constitutes 8 games. They scored an average of 3.25 runs per game during the first half. To find the total runs for the first half, we multiply the average runs per game by the number of games:

First-half runs = Average runs per game × Number of games in the first half

First -half runs = 3.25 runs/game × 8 games = 26 runs

For the second half of the season, the team scored a total of 29 runs. Therefore, the total runs scored last season is the sum of the first and second halves:

Total runs = First half runs + Second half runs

Total runs = 26 runs + 29 runs = 55 runs

So, the team scored 55 runs in total last season.

The total area of the state of tennessee is 69,919 square miles. The area of Nashville is 604 square miles. if a meteor were its land somewhere in the state, estimate the probability that it would land within the city limits of the capital.

Answers

22.8 square miles (59 km2) is land and 0.1 square miles (0.26 km2) (0.61%) is water. Portions of the Percy Priest Lake reservoir lies within the town limits. The two main waterways are Stones River and Stewarts ..

Answer:

44000

Step-by-step explanation:

e

i have done this before

Jerry will roll a number cube numbered 1-6 twice what is the probability of rolling an even number, then the number 3

Answers

6 possible outcomes on a dice, which means you roll it it could be any of them. Because 3 is one of the 6 the answer would be 1/6

Answer: ITS NOT 1/6, ITS 1/12

Step-by-step explanation:

I took the test :)

Would this be correct?

Answers

It would be D because store N sold me tires then store M all together and it would be B because the number are bigger in the store N collumn then the M collumn.

Your school gets a dunk tank for its spring fair. The tank is in the shape of a cylinder that is 5 feet high and has a radius of 3 feet. About how much water can the dunk tank hold? Use 3.14 for pi.

Answers

3*3*3.14*5= 141.3
3 squared times pi for the circle area times 5 for the cylinder volume


Answer:

140

Step-by-step explanation:

that's the answer on ttm

a female bunny gained one pound per week for six weeks. a male bunny gained two pounds per week for six weeks. how many more pounds did the male bunny gain than the female bunny. two pieces of information are missing

Answers

Answer:

6 lbs

Step-by-step explanation:

Female: 1 lb/week

Male: 2 lbs/week

How much did the Female gain in 6 weeks?

1 x 6= 6 lbs.

How much did the Male gain in 6 weeks?

2 x 6= 12 lbs.

How much more did the Male gain than the female?

12-6=6

The male gained 6 more lbs than the female

6 pounds more the male bunny gain than the female bunny.

What is Unitary Method?

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees

Given:

A female bunny gained one pound per week for six weeks.

So, Female Bunny Weigh in Six weeks= 6 Pounds.

Now, male bunny gained two pounds per week for six weeks.

So, Male Bunny Weigh in Six weeks= 12 Pounds.

Thus, Male Bunny weigh more by (12 - 6)= 6 pounds.

Hence, Male Bunny has 6 Pounds more than female Bunny.

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True or false? if the sample mean of a random sample from an x distribution is relatively small, then the confidence interval for μ will be relatively short. g

Answers

Answer: False.

The sample mean does not determine how wide the confidence interval would be. The sample mean determines the center of the confidence interval. The confidence level, standard deviation, and the sample size would determine the confidence interval width. 

Suppose u1, u2, ..., un are independent random variables and for every i = 1, ..., n, ui has a uniform distribution over [0, 1]. define z = min(u1, ..., un). find the
c.d.f. and the p.d.f of z.

Answers

[tex]Z=U_{(1)}=\min\{U_1,\ldots,U_n\}[/tex]

has CDF

[tex]F_Z(z)=1-(1-F_{U_i}(z))^n[/tex]

where [tex]F_{U_i}(u_i)[/tex] is the CDF of [tex]U_i[/tex]. Since [tex]U_i[/tex] are iid. with the standard uniform distribution, we have

[tex]F_{U_i}(u_i)=\begin{cases}0&\text{for }u_i<0\\u_i&\text{for }0\le u_i<1\\1&\text{for }u_1\ge1\end{cases}[/tex]

and so

[tex]F_Z(z)=1-(1-F_{U_i}(z))^n=\begin{cases}0&\text{for }z<0\\1-(1-z)^n&\text{for }0\le z<1\\1&\text{for }z\ge1\end{cases}[/tex]

Differentiate the CDF with respect to [tex]z[/tex] to obtain the PDF:

[tex]f_Z(z)=\dfrac{\mathrm dF_Z(z)}{\mathrm dz}=\begin{cases}n(1-z)^{n-1}&\text{for }0<z<1\\0&\text{otherwise}\end{cases}[/tex]

i.e. [tex]Z[/tex] has a Beta distribution [tex]\beta(1,n)[/tex].

Figure FGH has vertices located at F(1, 3), G(–1, 2), and H(2, 1). The figure is rotated using the origin as the center of rotation. The image has vertices located at F’(3, –1), G’(2, 1), and H’(1, –2). Which rotation could have taken place?
a 45° clockwise rotation
a 90° clockwise rotation
a 90° counterclockwise rotation
a 180° counterclockwise rotation

Answers

using a graph tool
see the attached figure

the answer is the option 
a 90° clockwise rotation

Answer:  The correct option is

(B) a 90° clockwise rotation.

Step-by-step explanation:  Given that the co-ordinates of the vertices of figure FGH are  F(1, 3), G(–1, 2) and H(2, 1).

The figure FGH is rotated using origin as the center of rotation and the the co-ordinates of the vertices of image figure F'G'H' are  F'(3, -1), G'(2, 1) and H'(1, -2).

We are to select the type of rotation that could have taken place.

The transformation from the vertices of FGH to the vertices of image F'G'H' is

F(1, 3)  ⇒   F'(3, -1),

G(-1, 2)  ⇒   G'(2, 1),

H(2, 1)  ⇒   H'(-1, 2).

Therefore, the transformation rule is  (x, y)  ⇒   (y, -x). This gives the rotation about origin through an angle of 90°.

Thus, the rotation of 90° clockwise taken place from figure FGH to image F'G'H'.

Option (B) is correct.

The graphic compares two basketball shoes.

After researching many different shoes, Chris narrows down his choice to these two. Which shoes are the best deal?

1 the Hyper-Dunks because they will last for two seasons
2 the Air Slammers because they are the best price
3 the Hyper-Dunks because his favorite pro player wears them
4 the Air Slammers because those are what his teammates chose

Answers

2 the Air Slammers because they are the best price.
According to the information given to receive the best deal, he would choose the Air Slammers because the price is the cheapest, and even if the hyper dunks would last 2 seasons if the air slammers lasted 1 season each the total would be less than the Hyper Dunks.

Answer:

the answer is B

Step-by-step explanation:

convert
11 m^2 to yd^2

Answers

1 yd = 3 m

11/3 = 3.667 (rounded

11m^2 = 3.667yd^2

hope this helps

A new washing machine used 3 2/4 gallons of water per full load to clean cloths. If John washed 2 2/3 loads of clothes, how many gallons of water would be used?

Answers

we know that
3 2/4  -------------> is (3*4+2)/4--------> 14/4-------> 7/2
2 2/3 --------------> is (2*3+2)/3--------> 8/3

if a new washing machine used 7/2 gallons of water ------------> one full load cloths
 X gallons of water------------------------------------------------------> 8/3 of load cloths
X=(8/3)*(7/2)---------> X=56/6------->28/3 gallons of water
28/3--------> 9 1/3 gallons of water

the answer is
 9 1/3 gallons of water

Trapezoid JKLM is shown on the coordinate plane below:
If trapezoid JKLM is translated according to the rule ( x, y)—>(x + 5, y-4), What are the coordinates of point L’ ?
A. (3,-3)
B. (1, -6)
C. (8,-6)
D. (-1, 3)

Answers

the answer looks like it could be (3,-2)

Answer: (8,-6)


Step-by-step explanation:

the coordinates are  (3,-2)

(x+5, y-4)

(3+5,-2-4)

(8,-6)


Which expression is equivalent to 8x - 2y + x + x

Answers

10x - 2y .   Combine like terms (8x +1x + 1x) + 2y.                             

John drives 257 miles and uses 9 gallons of gas. How many miles per gallon did he get? Without calculating the answer, from the choices given, which is most reasonable? A. 100 miles per gallon B. –6 miles per gallon C. 30 kilometers per liter D. 25 miles per gallon

Answers

D) 25 miles per gallon. you have to divide 257 by 9
Hope i helped!!

Answer:

Option D

Step-by-step explanation:

Given that John drives 257 miles and uses 9 gallons of gas.

we can find unit rate as

Per galon mileage given = 257/9 = 28

ANd units are miles/gallon

100 miles per gallon is very far from 28 hence incorrect

6 miles per gallon is very low

30 is right but unit is wrong

Hence option D is the right answer.

2. Draw a line with 3 distinct points on it. Label each with a different letter. How many different rays can you name using only the three given points? (1 point) 8 6 4 2

Answers

I think it is 4 

Hope it is right
To my understanding the answer is indeed 4 

    -Kaylah

what's the lateral area of the square pyramid 8m 8m 22 m

Answers

i think the anwsers 1408

The formula for finding the lateral area of any square base pyramid is:

[tex] A=a\sqrt{a^2+4h^2} [/tex]

Where "a" is the base edge or the edge of the square and "h" is the height of the pyramid.

In our case, "a"=8 meters and "h"=22 meters

[tex] \therefore A=8\sqrt{8^2+4(22)^2} \approx357.77 [/tex] squared meters

Thus, the lateral area of the given square pyramid is 357.77 squared meters.

How many different outcomes are possible if you can choose between a bus or a train, full fare or concession and you can travel in the morning or the afternoon?

Answers

3 pairs of choices give rise to 2^3 = 8 possibilities:
.. bus, full, morning
.. bus, full, afternoon
.. bus, concession, morning
.. bus, concession, afternoon
.. train, full, morning
.. train, full, afternoon
.. train, concession, morning
.. train, concession, afternoon
Final answer:

Applying the multiplication principle in probability, there are eight different combinations possible when choosing between bus or train, full fare or concession, morning or afternoon for your travel.

Explanation:

Your question is asking how many different combinations of travel mode, fare type, and time of day are possible under given conditions. For this situation, we can apply simple probability rules with concept of multiplication principle, which states that if there are n ways to do something, and m ways to do another, then there are n * m ways to do both.

In this case, you have two choices for each category: mode of transportation (bus or train), fare type (full fare or concession), and time of day (morning or afternoon). The combination is simply 2 (mode of transport) * 2 (fare type) * 2 (time of day) = 8. So, there are eight possible outcomes.

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What is the measure of the angle formed by the minute hand and the hour hand of a clock when the clock shows 4:00?

Answers

The answer to this is 120. 

Answer:

[tex]120^o[/tex]

Step-by-step explanation:

We are asked to find the measure of the angle formed by the minute hand and the hour hand of a clock when the clock shows 4:00.

Since we know that clock is a circle made of 360 degrees.

Angle described by minute hand in one minute equals to 6 degrees (360/60). Angle described by hour hand in 1 hour equals 30 degrees (360/12).

At 4:00 minute hand will be at 12 and hour hand will be at 4. So we will multiply 4 by 30 to find the measure of angle formed when the clock shows 4:00.

[tex]\text{Measure of angle}=4\times 30^o[/tex]

[tex]\text{Measure of angle}=120^o[/tex]

Therefore, the measure of the angle formed by the minute hand and the hour hand of a clock, when the clock shows 4:00 is 120 degrees.

Which verbal expression best describes the algebraic expression 4x ÷ 6? (4 points)


The sum of four and some number divided by six

The quotient of four times some number and six

The product of some number and six divided by four

The quotient of four and some number times six

Answers

Answer:

its right i took test

Step-by-step explanation:

A baker needs 4 3⁄4 cups of flour. If she uses a 1 1⁄2 cup measuring scoop, how many scoops of flour must the baker use to have at least 4 3⁄4 cups?

Answers

Four. 1 1/2 + 1 1/2 = 3, + 1/12 = 4 1/2. But she still needs a fourth, so she'll need to use another scoop, so four.

Answer:

[tex]3\frac{1}{6}[/tex]

Step-by-step explanation:

Given : A baker needs  cups of flour =  [tex]4\frac{3}{4} =\frac{19}{4}[/tex]

Solution :

Since we are given that she uses  1 measuring scoop for cup of flour = [tex]1\frac{1}{2} =\frac{3}{2}[/tex]

She uses uses scoop for 1 cup of flour = [tex]\frac{1}{\frac{3}{2}}=\frac{2}{3}[/tex]

She uses scoops for [tex]\frac{19}{4}[/tex] cups of flour =  [tex]\frac{2}{3}*\frac{19}{4}[/tex]

=   [tex]\frac{19}{6}[/tex]

=   [tex]3\frac{1}{6}[/tex]

Thus   [tex]3\frac{1}{6}[/tex]   scoops of flour must the baker use to have at least 4 3⁄4 cups.

the sum of two numbers is 40. the sum of the smaller and 5 times the larger is 144. find the numbers.

Answers

x= smaller number
y= larger number

EQUATION 1:
the sum of two numbers is 40

x + y= 40

EQUATION 2:
the sum of the first number and 5 times the second is 144

x + 5y= 144

STEP 1:
Solve for one variable in equation 1.
x + y= 40
subtract y from both sides
x= 40-y

STEP 2:
Substitute x=40-y in equation 2.
x + 5y= 144
(40-y) + 5y= 144
combine like terms
40 + 4y = 144
subtract 40 from both sides
4y= 104
divide both sides by 4
y= 26 larger number

STEP 3:
Substitute y=26 in either equation to solve for x (smaller number).
x + 5y= 144
x + 5(26)= 144
x + 130= 144
x= 14 smaller number

CHECK:
14 + 26= 40
40= 40

ANSWER: The smaller number is 14 and the larger number is 26.

Hope this helps! :)
Final answer:

To find the two numbers, we can solve a system of equations. The smaller number is 14 and the larger number is 26.

Explanation:

To find the two numbers, we can solve a system of equations based on the given information. Let's represent the smaller number as x and the larger number as y.

From the first equation, we have x + y = 40.From the second equation, we have x + 5y = 144.

We can solve this system using substitution or elimination. Let's use substitution:

From the first equation, solve for x: x = 40 - y.Substitute this value of x into the second equation: (40 - y) + 5y = 144.Simplify the equation: 40 + 4y = 144.Subtract 40 from both sides: 4y = 104.Divide both sides by 4: y = 26.Substitute this value of y back into the first equation to find x: x + 26 = 40. Subtract 26 from both sides: x = 14.

Therefore, the smaller number is 14 and the larger number is 26.

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75 percent of 88 is the same as 60 percent of what number?

Answers

First we need to know 75% of 88.
To find this number we multiply 88 by 0.75. 
Hence, 0.75 * 88 = 66

Therefore, 60% of a certain number equals 66.
Then 1% of that certain number equals 66 / 60
Finally, to find our number (which equals 100%) we multiply by 100.
So 66 / 60 * 100 = 110.

Hence, 75 percent of 88 is the same as 60 percent of 110.
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