You live near a bridge that goes over a river. The underneath side of the bridge is an arch that can be modeled with the function y= -0.000475x^2 + 0.851x, where x and y in feet. How high above is the river bridge (the top of the arch)? How long is section of bridge above the arch?

A)The bridge is about 1,791.58 ft. above the river, and the length of the bridge above the arch is about 381.16 ft.

B)The bridge is about 1,791.58 ft. above the river, and the length of the bridge above the arch is about 895.79 ft.

C)The bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is about 895.79 ft.

D)The bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is about 1,791.58 ft

Answers

Answer 1

y= -0.000475x^2 + 0.851x

How high above is the river bridge (the top of the arch)?

You have to find the vertex of of the parabole: the y-coordinate is the highest point.

Remember that the x-coordinate of the vertex of a parabole is at - b / 2a.

That is x = - 0.851 / [ 2(-0.000475) = 895.79

The corresponden y is y = -0.000475(895.79)^2 + 0.851(895.79) = 381.16 feet above the river.

How long is section of bridge above the arch?

The section of the brige is equal to the difference of the two roots

Roots: y= -0.000475x^2 + 0.851x = 0

=> x( - 0.000475x + 0.851) = 0

=> x = 0 and x = 0.851 / 0.000475 = 1791.58

Then the section is 1791.58 feet long.

Therefore, the answer is the option D)The bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is about 1,791.58 ft

Related Questions

In 2010, the national debt of the United States was about 14 trillion dollars. In 2003 it was about 7 x 10 to the 12 dollars. About how many times larger was the national debt in 2010 than 2003? THIS IS SCIENTIFIC NOTATION

Answers

Okay. 10^12 is 1 trillion. 1 trillion * 7 is 7 trillion. 14 trillion / 7 trillion is 2. The national debt in 2010 is two times larger than in 2003. So that basically means that the national debt doubled from 2003 to 2010.

Answer: About 2 times.

Step-by-step explanation:

Given : In 2010, the national debt of the United States was about 14 trillion dollars.

We know that 1 trillion [tex]=1,000,000,000,000= 10^{12}[/tex]

then, In 2010, the national debt of the United States was about [tex]14\times10^{12}[/tex]

dollars.

In 2003 it was about [tex]7\times10^{12}[/tex] dollars.

Now, the number of times the national debt was larger in 2010 than 2003 :-

[tex]\dfrac{ 14\times10^{12}}{7\times10^{12}}\\\\=\dfrac{14}{7}\times10^{12-12}\\\\=2\times10^0=2[/tex]

Hence, national debt was about 2 times larger in 2010 than 2003 .

The probability of choosing either a girl or a boy is

Answers

It depends on the amount

No.of Girls / total no of boys and girls is boy's probabilty
And
No of boys / total no of boys and girls is girl's probabilty

two workers paint lines for angled parking spaces. One worker paints a line so that m<1= 65. The other worker paints a line so that m<2= 65. Are their lines parallel? Explain

Answers

Five questions in math for 25 points! 1. What is "a symbol for a number we don't know yet. It is often a letter like x or y." 2. What is a coefficient? 3. What is "a number on its own, it...Hans is planting a garden with snapdragons and daisies. The table shows some possible combinations of the two plants. If Hans plants 29 daisies, how many snapdragons will he plant? ANSWER If x-5 divided by x-1 and n(x) = x â€“ 3, what function has the same domainDoes the point (, square root of 7) lie on the circle shown? ExplainWhat are Opposite Operations (Inverse Operations)?Provide a counterexample to the statement below: "If two angles are a supplementary, then they are a linear pair" A. This statement is always true, no counterexample exists. B. Two non-adjacent...

Mrs. Howard is hosting a catered dinner party to celebrate her daughter's graduation. The catering company she plans to use charges $13.50 per plate of food and an additional fee of $540 to cover linens and tableware. The total bill for the catering services is $1,512. Which equation can be used to determine the total number of guests, g, who attend the dinner party? 13.50g + 540 = 1,512 13.50g - 1,512 = 540 5400g + 13.50 = 1,512 540g - 1,512 = 13.50

Answers

13.50g+540=1512

hope this helps :)

Answer:

The equation can be used to determine the total number of guests is 13.50g + 540 = 1512 and the total number of guest are 72 .

Step-by-step explanation:

As given

Mrs. Howard is hosting a catered dinner party to celebrate her daughter's graduation.

The catering company she plans to use charges $13.50 per plate of food and an additional fee of $540 to cover linens and tableware.

The total bill for the catering services is $1,512.

Total number of guests, g .

Than the equation becomes

1512 = 540 + 13.50 g

1512 - 540 = 13.50 g

972 = 13.50 g

[tex]g = \frac{972}{13.50}[/tex]

g = 72

Therefore the equation can be used to determine the total number of guests is 13.50g + 540 = 1512 and the total number of guest are 72 .

Amy, who is 17 years old, is 5 years older than twice Moe's age.Write an equation that you could solve to find Moe's age. Solve the equation and describe your steps.

Answers

(17-5) divided by 2 = 6 years old

First, take Amy’s age (17) and subtract it by 5, to get 12 ( 12 is 2 Times moe’s age). Then, divide 12 by 2 to get 6 ( since moe’s age was multiplied, you have to change it back by dividing).

Twice a number, increased by one, is between negative three and seven. find all the numbers.

Answers

Final answer:

To solve the inequality -3 < 2x + 1 < 7 for the number x, subtract 1 from all parts and then divide by 2. The solution is the range of numbers greater than -2 and less than 3.

Explanation:

The problem statement here results in an inequality that can be expressed algebraically. If 'x' represents the unknown number, we can write the inequality as -3 < 2x + 1 < 7.

To solve for 'x', we will isolate the variable on one side by following the rules of inequalities similar to solving equations.

First, subtract 1 from all parts of the inequality to get the pure inequality without a constant.

-4 < 2x < 6

Now, divide all parts of the inequality by 2, which yields:

-2 < x < 3

All numbers greater than -2 and less than 3 satisfy the original problem statement. Therefore, the range of numbers that solve the inequality is from -2 to just below 3.

What is the sum of 4 times a number and 3 is bigger than 15, but also -21 at most?

Answers

4x + 3 + 15 - 21
4x + 18 - 21
4x - 3
Answer: 4x - 3

if TRAP is an isosceles trapezoid what is the value of x ?

Answers

The answer I got is E. 19

the answer to this question is 19!

what is the answer to y-3.5=-2.1

Answers

y - 3.5 = -2.1
y = -2.1 +3.5
y =1.4

The value of variable y in y - 3.5 = -2.1 is 1.4 .

Given , equation : y-3.5=-2.1

To get the value of y isolate the variable y.

y - 3.5 = -2.1

Combine like terms,

Take -3.5 from LHS to RHS . The sign will be changed from negative to positive.

y = 3.5 - 2.1

y = 1.4

Therefore the value of y that will satisfy the equation is 1.4 .

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There are 18 boys and 60 girls working on a community service project. they work in groups where each group has the same number of boys and the same number of girls. what is the first step to finding the greatest number of groups possible? what is the greatest number of groups possible? what is the first step in finding the solution?

Answers

First you need to list the factors of each number

18: 1,2,3,6,9,18
60:1,2,3,4,5,6,10,12,15,20,30,60
Look for the common, in this case is 6
Solution is 6 groups, 3 boys and 10 girls on each group

The law of detachment can be used to draw a conclusion from the following statements: "It will be sunny on Tuesday." "I will always go outside if the weather is nice."

Answers

Final answer:

Using the law of detachment, if it is sunny on Tuesday and there is a habit of going outside in nice weather, one can conclude that they will go outside on Tuesday.

Explanation:

The law of detachment is a concept in logic used to form conclusions given a conditional statement and its hypothesis being true. For instance, in the scenario provided:

If it is sunny on Tuesday (hypothesis).

I will always go outside if the weather is nice (conditional statement).

By applying the law of detachment, we can conclude that:

I will go outside on Tuesday (conclusion).

This logical reasoning assumes that a 'nice' weather includes a sunny day. Hence, if it is indeed sunny on Tuesday, the condition for going outside is met.

Luigi is an urban planner. as an independent contractor, he charges $140 fee plus $ 25 per hour for each contract with the city.

Write a function to represent this scenario where Y represents the total amount her changes for a project and x represents the number of hours worked on a project

Answers

x = hours 25 per hour = 25x

y = total

so y = 25x +140

Answer: y = 140+25x

Step-by-step explanation:

Since According to the question, Luigi initally charged $140.

And, per hour he charged an additional amount $25 for each contract with the city.

Here, x represents the number of hours worked on a project.

Thus the additional amount after x hours = 25x

So, the total amount he charged in x hours= 140+ 25x

And, according to the question y represents the above change.

Thus, we get a function for the given situtaion

which is , y= 140+ 25x , where x is number of hours and y is total amount charged.

Heather's fish tank has 18 liters of water in it. she plans to add 4 liters per minute until the tank has more than 58 liters. what are the possible numbers of minutes heather could add water?

Answers

It tank will be filled up in 40 mins cause every min you fill in 4 liters. Don’t take my word for this make sure you check my work.

parallelogram ESTA has vertices E (10,0), S(14,3),T(6,9) and A (2,6). to calculate its area, Jamal will first determine the equation of the line through point E and perpendicular to ST. What is the equation of this line?

Answers

closed line for the same equation. thanks for using brainly.

If CDEF ≅ MNPQ, then EF≅ _____

.

PQ.

QM.

MN.

NQ

Answers

Your answer would be PQ

Final answer:

In the context of congruent polygons, side EF of polygon CDEF is congruent to side PQ of polygon MNPQ due to the corresponding order of sides in congruent figures.

Explanation:

The question refers to congruent figures in geometry, specifically congruent polygons. If polygons are congruent, all corresponding sides and angles are congruent as well. Therefore, if CDEF ≅ MNPQ, then side EF must be congruent to the side of polygon MNPQ that corresponds to EF in the order of letters given. Following the order, side EF corresponds to side PQ.

which conjunction or disjunction is equivalent to the given absolute value inequality?
|x + 2| > 16

a. x + 2 > 16 and x + 2 < - 16
b. x + 2 < 16 and x + 2 > - 16

Answers

The correct answer is A. When dealing with an absolute value inequality, you want to flip the positive to a negative sign, as well as flip the inequality sign.

Answer:

Step-by-step explanation:

|x+2|>16

x+2>16 or x+2<-16

So, tecnically a and b are incorrect, but if you change the "and" to "or" the correct would be a.

anonymous 4 years ago A technical writer makes $45,000 per year and has just begun contributing 8% of her salary to her 401(k) plan. If her employer matches 6% of her contributions, how much will have been contributed to the 401(k) plan after 2 years?

Answers

add everything up except the 45,000 and 402(K). then subtract 45,000$ from 401. Then subtract your answers to both equations.

Answer:

$7,632 would have been contributed to the 401(k) plan after 2 years.

Step-by-step explanation:

A technical writer makes salary per year = $45,000

She contributing 8% of her salary to her 401(k) plan = 8% of 45,000

0.08 × 45,000 = $3,600

Her employer matches 6% of her contributions = 6% of 3,600

= 0.06 × 3,600 = $216.00

Total contribution for one year = 3,600 + 216.00 = $3,816

After 2 years = 3,816 × 2 = $7,632.00

$7,632 would have been contributed to the 401(k) plan after 2 years.

In a school election, 3/4 of the students vote. There are 1464 ballots. Write and solve and equation to find the number of students.

Answers

x = total number of students

equation is:

(3/4)x = 1464

to solve for x divide both sides by 3/4

x = 1464 / 3/4 = 1952

x = 1952

there are 1952 total students

Evan earns $12 an hour plus $15 an hour for every hour of overtime. Overtime hours are any hours more than 30 hours for the week. Part A: Create an equation that shows the amount of money earned, M, for working x hours in a week when there is no overtime. (3 points) Part B: Create an equation that shows the amount of wages earned, T, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 30 hours. (3 points) Part C: Evan earned $510 in 1 week. How many hours (regular plus overtime) did he work? Show your work. (4 points)

Answers

Part A: M = 12x. (x hours at the rate of $12/per hour) Part B: T = 12 * 30 + 15y. ( 30 hours per week at the rate of $12 per hour plus y hours at the rate of $15 per hour) Part C: Let us first find out the amount earned through regular working hours and overtime hours. Regular hours in a week is 30 at the rate of $12 per hour. It comes to 12*30 = $360 The remaining amount, 510-360 = 150, is earned through overtime. Overtime rate is $15 per hour. So the number of hours worked overtime = 150/15 = 10 Total hours worked during the week = 30 + 10 = 40.

You and your family attend your brother’s championship baseball game. Between innings you decide to go to the snack stand. You go to the snack stand with $15 and find that sodas are $2.50 and that popcorn is $3.75. Write an inequality that models the number of sodas you can buy if you get a bag of popcorn too. What is the maximum number of sodas you can buy in this situation?

Answers

4 sodas if you buy a bag of popcorn, if you dont buy popcorn you can buy 6 sodas

the expression 12x+15x-11x can be combined because of which property
A. commutative property of addition
B. distributive property
C. additive inverse property
D. multiplicative property

Answers

Final answer:

The expression 12x+15x-11x can be combined using the associative property of addition.

Explanation:

The expression 12x+15x-11x can be combined by using the associative property of addition.

First, combine the like terms which have the same variable, in this case 'x'. Add the coefficients of the like terms, which are 12, 15, and -11. 12x + 15x - 11x = (12 + 15 - 11)x = 16x.

Therefore, the simplified expression is 16x. The associative property of addition allows us to group the terms in any order and still get the same result.

Final answer:

The expression 12x + 15x - 11x can be simplified due to the associative property of addition, enabling terms to be grouped and combined to yield a simplified form of 16x. The correct option is not provided in the choices, but would be the associative property, not listed in the student's options.

Explanation:

The expression 12x + 15x - 11x can be simplified by combining like terms, which is possible because of the associative property of addition. This property allows us to group numbers in an addition expression in any way we choose without changing the result.

Therefore, using the associative property, we can group and combine the terms with 'x' to get (12x + 15x) - 11x, which simplifies to 27x - 11x, and then further to 16x.

The correct answer to the question is Option A: associative property of addition, though it is important to note that this option was not listed in the initial question provided. The commutative property allows us to change the order of the terms without changing the result, but does not directly apply to the combination of like terms.

Nevertheless, both the associative and commutative properties are used when combining like terms in algebra.

There are 300 coins of the same type in two stacks. One stack is 380 millimeters tall. The other is 220 millimeters tall. Find the thickness of one coin

Answers

Total coins = 300

Total thickness of the two stacks is
380 + 220 = 600mm

The thickness of a coin is
(600 mm)/(300 coins) = 2 mm per coin.

Answer: 2 millimeters

Hidemi is a waiter. He waits on a table of 4 whose bill comes to $69.98. If Hidemi receives a 20% tip, approximately how much will he receive?
$3.50
$14.00
$84.00
$7.00

Answers

$14.00 is the answer because you have to multiply $69.98 by 20% and that will give you 13.99 but you round it off and you will get $14.00

The answer is C! Have a great day!!!

Rose leaves her apartment to take her dog for a walk. She goes 3 blocks due south, 8 blocks due east, 5 blocks due north, and 8 blocks due west. At this point, where is Rose in relation to her apartment?

Answers

work shown above! in the end she is 2 blocks north of her apartment. hope this helps c:

Answer:

3 blocks due west

Step-by-step explanation:

Planes X and Y and points J, K, L, M, and N are shown.
Exactly how many planes contain points J, K, and N?

0
1
2
3

Answers

No plane contains these points, as we can see on the image, point J does not belong to any of the shown planes.

How many planes contain points J, K, and N?

A plane contains a point if the point lies on the plane. For example, here you can see that plane X contains the points K and N.

But, if you look at the image, no plane contains the point J, then there is no plane that contains the 3 points J, K, and N, so the correct option is 0.

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Complete the expression so it forms a perfect-square trinomial. x² +___ x + 49 A. 14 B. 7 C. 7/2

Answers

(x + 7)(x + 7)

x^2 + 14x + 49

14x is your answer

hope this helps

The expression so it forms a perfect square trinomial is 14x.

We have given that,

The expression so it forms a perfect-square trinomial.

We have to determine the x² +___ x + 49.

What is the factor?

A divisor of an integer n also called a factor of n, is an integer m that may be multiplied by some integer to produce n.

In this case, one also says that n is a multiple of m.

(x + 7)(x + 7)

x^2 + 14x + 49

The expression so it forms a perfect square trinomial is 14x.

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What is the greatest common factor of 60x4y7, 45x5y5, and 75x3y? 5xy 15x3y 45x3y5 75x5y7

Answers

Answer: 15x3y

Step-by-step explanation:

We rewrite the expressions by using factorisation method of their primes. This will give:

60x4y7= 2×2×3×5×x×x3×y×y6

45x5y5= 3×3×5×x×x4×y×y4

75x3y= 3×5×5×x×x2×y

Common factors= 3 × 5 × x3 × y

= 15x3y

Answer:

its B

Step-by-step explanation:

Amelia knits 1/10 of a scarf in 48 minutes. What fraction of a scarf can she knit in an hour? A. 5/24 B. 1/480 C. 1/8 D. 2/25

Answers

Aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

What is the solution of the linear quadratic system or equations?
Y=x^2+5x-3
Y-x=2

Answers

The solution to the system of equations are (1, 3) and (-5, -3)

Given the following functions

Y=x^2+5x-3

Y-x=2; y = x + 2

Equating both outputs will give

x^2+5x-3 = x + 2

x^2+5x-3 - x - 2 = 0

x^2 + 4x - 5 = 0

Factorize the equation

x^2 + 5x - x - 5=0

x(x+5) - 1(x+5) = 0

(x-1)(x+5) = 0

x = 1 and -5

Recall that y = x + 2

y = 3 and -3

Hence the solution to the system of equations are (1, 3) and (-5, -3)

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Final answer:

The solution to a linear quadratic system of equations can be found by substitifying one equation into the other and solving. In this case, the solutions are (1,3) and (-5,-3).

Explanation:

To find the solution of a linear quadratic system of equations, you need to substitute one equation into the other. In this case, for the equations [tex]Y = x^2 + 5x - 3[/tex] and [tex]Y - x = 2[/tex], you would first isolate Y in the linear equation, resulting in [tex]Y = x+2.[/tex]

Then, you substitute (x + 2) for Y in the quadratic equation, leading to [tex]x + 2 = x^2 + 5x - 3.[/tex]

Next, rearrange the equation to get it in the standard quadratic form: 0 = [tex]x^2 + 5x - x - 3 - 2.[/tex] Simplifying this results in the equation [tex]0 = x^2 + 4x - 5.[/tex]

Finally, solve this equation by factoring or using quadratic formula, which gives the solutions as x = 1, -5. Substituting both 1 and -5 into the equation Y = x + 2 gives the corresponding y-values, Y = 3 and -3. Therefore, the solutions to the system of equations are (1,3) and (-5,-3).

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A mathematical scale in which the concentration of hydrogen ions in a solution is expressed as a number from 0 to 14

Answers

That is the pH scale
pH = - log of the concentration of hydrogen ions in a solution.

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