A football is kicked at 40 yards away from a goal post that is 10 feet high. Its path is modeled by y = -0.03x 2 + 1.6x, where x is the horizontal distance in yards traveled by the football and y is the corresponding height above the ground in feet.

Does the football go over the goal post? How far above or below the goal post is the football? Use two or more complete sentences to explain your answers. (Hint: The unit conversion is built into the given function.)

Answers

Answer 1
[tex]y(40)=-0.03(40^{2})+1.6(40)=16feet[/tex]
16>10

Yes, the ball clears the goal by 6 feet.

Related Questions

NEED URGENT HELP!

Match the graph with the correct equation.

y – 5= –(x + 3)

y – 3 = –(x + 5)

y – 3 = (x + 5)

y + 3 = –(x + 5)

Answers

(0, -2) (-2, 0)

slope = 2/-2 = -1

if x = -5, y = 3

equation
y - 3 = -1(x +5)
y - 3 = - (x + 5)

answer

y – 3 = –(x + 5)

Answer:  The correct option is (B) [tex]y-3=-(x+5).[/tex]

Step-by-step explanation:  We are given to match the graph shown with the correct equation.

From the graph, we note that

(-5, 3) and (0, -2) are two points that lie on the line graph.

So, the slope of the given graph is

[tex]m=\dfrac{-2-3}{0-(-5)}\\\\\\\Rightarrow m=\dfrac{-5}{5}\\\\\Rightarrow m=-1.[/tex]

Since the point (-5, 3) lies on the line, so its equation in point-slope form will be

[tex]y-3=m(x-(-5))\\\\\Rightarrow y-3=-(x+5).[/tex]

Thus, option (B) is CORRECT.

A sailfish can swim up to 68 miles per hour. At this rate, how far can a sailfish swim in 1 fourth hour?

Answers

1/4 of an hour

68 miles per hour

 multiply 68 by 1/4 = 68/1 *1/4 = 68/4

divide 68 by 4

68/4 =17

 it can swim 17 miles

17 miles 
you just divide 1/4 by 68 and you get 17

Dominick is planning to take a vacation to either Orlando or Tampa Bay. He wants to go to the city that is warmer, on average. The box plot below shows the temperatures from the previous year during the time that Dominick will take his vacation: box plot labeled Orlando with min at 64.5, Q1 at 65.5, median at 67.5, Q3 at 71.5, max at 72.5. Box plot labeled Tampa Bay with min at 60, Q1 at 63.5, median at 66.25, Q3 at 72.5, max at 74 Which city should Dominick visit, and why?

Answers

Orlando

Median = 67.5 
Interquartile Range = Q₃ - Q₁ = 71.5 - 65.5 = 6
Range = Max Value - Min Value = 72.5 - 64.5 = 8

Tampa Bay

Median = 62.25
Interquartile Range = Q₃ - Q₁ = 72.5 - 63.5 = 9
Range = Max Value - Min Value = 74 - 60 = 14

From the three values that we can read from the box plots, Orlando has the higher median, lower interquartile range and lower range.

Lower interquartile range and range indicates a more consistent data, so we can say that Orlando has more consistent warmer temperature than Tampa Bay. 

Dominick should visit Orlando

Answer:

He should visit Orlando. The median is higher and the range is smaller, so the temperature is higher on average.

Step-by-step explanation:

one light flashes every 18 seconds and the other flashes every 12 seconds. If they flash together at 8:00pm, what is the next time that they will flash together?

Answers

ur basically looking for the lowest common multiple...and it is 36...so they will flash together again in 36 seconds....so its still gonna be 8:00 pm...just 36 seconds later
What these types of problems want you to find is the least common multiple.

The LCM will be the product of the highest occurring primes of the numbers prime factorization.

12=2*2*3, 18=2*3*3

So the LCM is 2*2*3*3=36

So the lights will flash again at the same time 36 seconds after 8 pm, or if you prefer:

8:00:36

The sum of two numbers is 72. The greater number is 8 more than the smaller number. Which equation can be used to solve for the smaller number? x − (x + 8) = 72 x + (x + 8) = 72 x(x + 8) = 72 x(x − 8) = 72

Answers

let x is the smaller number
bigger number is x + 8

The sum of two numbers is 72
so
 x + (x+8) = 72

answer
x + (x + 8) = 72
x + y = 72
y = x + 8......y is the greater number

x + (x + 8) = 72 <==

A bedroom is 5.2 meters wide. find it's width in feet (1 meter= 3.28 feet)

Answers

17.056 because if you multiply the amount of feet in a meter by how many meters there are then you get your answer.

Convert these unlike fractions to equivalent like fractions and add them. You must use the LCD to get the answer correct. If possible, reduce the final sum.

Answers

Your final answer would be 2/3.

The LCD would be 12.

You would have to multiply both the top and bottom of 1/4 to get the denominator to 12.

To do this, you multiply it both the numerator and denominator by 3.

This would leave you with 3/12.

The second fraction already has a denominator of 12 so we will just leave it as is.

Then you add.

3/12 + 5/12

This would give you

8/12

Then you simplify it or "reduce it" by dividing both the top and bottom by 4 to get your final answer.

2/3

The simplest form expression for the addition of the fractions given using the lowest common multiple of of the denominator is 2/3.

Given the fractions :

1/4 + 5/12

The lowest common multiple of the denominator ;

Lowest common multiple of 4 and 12 = 12

1/4 + 5/12 = (3 + 5) / 12

1/4 + 5/12 = 8/12

Expressing in simplest form :

8/12 = 2/3

Therefore, the simplest form expression of the addition is 2/3

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Jackie's total number of coins is 204.. She has twice as many quarters as nickels and three times as many dimes as nickels.. How many of each coin does she have ??

Thank you so much :)

Answers

Call x the number of nickles that she has.

Then the number of quarters is twice x = 2x

And the number of dimes is three times x = 3x.

So, the total number of coins is x + 2x + 3x = 240

=> 6x = 240

=> x = 240 / 6

=> x = 40

=> Number of nickels = x = 40

Number of quarters = 2x = 80

Number of dimes = 3x = 120

Verification: 40 + 80 + 120 = 240

Answer: nickles 40, quarters 80, and dimes 120.

Triangle ABC is similar to triangle DEF. what is the value of x ? Pic attached :) thank you.

Answers

x=6 and 2/3 
the proportion is also 3:5

Given that triangles ABC and DEF are similar, the value of x is: D. 6⅔.

What are Similar Triangles?

If two triangles are similar, it means they have the same shape but different sides, and therefore, the ratio of their corresponding sides are equal.

Thus:

BC/EF = AC/DF

Substitute

8/2x = 3/5

Cross multiply

40 = 6x

Divide both sides by 6

x = 6⅔.

In summary, given that triangles ABC and DEF are similar, the value of x is: D. 6⅔.

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68.32 divided by 2.8

Answers

Answer:

24.4

Step-by-step explanation:

We are asked to divide 68.32 by 2.8.

First of all, we will write our given problem as a division problem.

[tex]\frac{68.32}{2.8}[/tex]

We can see that our numerator has two digits after decimal and denominator has one digit after decimal, so we will multiply numerator and denominator by 100 as:

[tex]\frac{68.32\times 100}{2.8\times 100}[/tex]

[tex]\frac{6832}{280}=24.4[/tex]

Therefore, the quotient of our given problem is 24.4.

24.4  

Further explanation  

We will determine the quotient of 68.32 against 2.8.  

Notes:

The division process is the arithmetic operation of the distribution of equal parts of a number.  The division is the opposite of the multiplication process.  

         24.4  __

2.8 )  6 8 . 3 2  

       - 6 7 . 2 [tex]\downarrow[/tex]  

             1 . 1 2  

          - 1 . 1 2  

                   0  

Please see the attached picture.

The terminology of the division operation associated with the above scheme is as follows:  

[tex]\boxed{ \ 68.32 \rightarrow the \ dividend \ }[/tex][tex]\boxed{ \ 2.8 \rightarrow the \ divisor \ }[/tex][tex]\boxed{ \ 24.4 \rightarrow the \ quotient \ }[/tex]  [tex]\boxed{ \ 0 \rightarrow the \ remainder \ }[/tex]

Therefore, 68.32 divided by 2.8 is divisible because the remainder is zero.

Thus, the quotient of 68.32 divided by 2.8 is 24.4.  

- - - - - - - - - -

Alternative Strategy

[tex]\boxed{ \ 68.32 = 56 + 12.32 \ }[/tex]

[tex]\boxed{ \ 68.32 \div 2.8 = (56 \div 2.8) + (12.32 \div 2.8) \ }[/tex]

[tex]\boxed{ \ 68.32 \div 2.8 = 20 + 4.4 \ }[/tex]

[tex]\boxed{\boxed{ \ 68.32 : 2.8 = 24.4 \ }}[/tex]

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Keywords: 68.32 divided by 2.8, find the quotient, 24.4, the division operation, dividend, divisor, the remainder, division scheme

Bryan is observing the velocity of a cyclist at different times. After four hours, the velocity of the cyclist is 15 km/h. After seven hours, the velocity of the cyclist is 12 km/h.

Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points)

Part B: How can you graph the equations obtained in Part A for the first 12 hours? (5 points)

Answers

Part A.

What we can do to solve this problem is to assume that the acceleration of Bryan is constant so that the velocity function is linear. The standard form of a linear function is in the form:

y = m x + b

or in this case:

v = m t + b

where v is velocity and t is time, b is the y –intercept of the equation

The slope m can be calculated by:

m = (v2 – v1) / (t2 – t1)

m = (12 – 15) / (7 – 4)

m = -1

Since slope is negative therefore this means the cyclist are constantly decelerating. The equation then becomes:

v = - t + b

Now finding for b by plugging in any data pair:

15 = - (4) + b

b = 19

So the complete equation is:

v = - t + 19

This means that the initial velocity of the cyclists at t = 0 is 19 km / h.

 

Part B. What we can do to graph the equation is to calculate for the values of v from t = 0 to 12, then plot all these values in the Cartesian plane then connect the dots.

Find the circumference of the following circle. (Use 3.14 for π.)



15.7 in.
78.5 in.
19.63 in.
31.4 in.

Answers

The formula for circumference is 2pi*r.
The given diameter is 5 and radius is half of diameter, so the radius is 2.5.
Plus that into the formula.
2*pi*2.5 equals approx. 15.7

The circumference of the circle is 15.7 inches.

What is circumference?

Circumference can be defined as the total distance around a circle.

To calculate the circumference of the circle, we use the formula below.

Formula:

P = πd............... Equation 1

Where:

P = Circumference of the circled = Diameter of the circleπ = pie.

From the question,

Given:

d = 5 inchesπ = 3.14

Substitute these values into equation 1

P = 3.14×5P = 15.7 inches.

Hence, The circumference of the circle is 15.7 inches.

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gross income £12000 tax free allowance £6475 what is taxable amount @20%, tax payable,net income and weekly net amount how to work out?

Answers

We calculate for the taxable income by subtracting the tax free allowance from the gross income.

          Taxable income = Gross income - tax free allowanc
           Taxable income = (£12,000 - £6,475)
                                    = £5,525

Hence, the taxable income is equal to £5,525.

Net income: 
This would be equal to the gross income minus the amount of taxes to be paid.
 
                 Net income = Gross income - amount of tax to be paid
                 Net income = (£12,000) - (0.20)($5,525)
                 Net income = $10,895

Therefore,
         ANSWER: $10,895

32.1in.×28.2in.×1ft.=

Answers

since 2 of the 3 are in inches convert the 3rd one to inches

1 foot = 12 inches

now multiply 32.1 x 28.2 x 12 = 10,862.64 cubic inches

-1 = n+5 what does n equal to

Answers

n equals -6.
-6 + 5 = -1.

Two equations are shown: Equation A y = 4 over x + 3 Equation B y = −2x − 4 Which statement best compares the graphs of the two equations? Both are nonlinear. Both are linear. Equation A is nonlinear and Equation B is linear. Equation A is linear and Equation B is nonlinear.

SHOW WORK!!

Answers

The given equations are
A. [tex]y= \frac{4}{x}+3 [/tex]
B. y = -2x - 4

Equation A is nonlinear.
Equation B is linear.
The graphs are shown below.

Answer:
Equation A is nonlinear and equation B is linear.

Answer:

The answer is C.  Equation A is nonlinear and Equation B is linear.

Hope This Helps!

X to the power of three equals 343

Answers

x^3= 343

Find the cube root of both sides
∛x^3 = ∛343

x= 7

Final answer: x=7

What is the value of x in the equation −x = 6 − 4x + 18?
24
8
−8
−24

Answers

−x = 6 − 4x + 18
3x = 24
x = 8

answer
8  (second choice)
-x=6-4x+18
4x-x=24
3x=24
x=24/3
x=8
:)

two consecutive even integers have a sum of 346. Find the smailler of these two numbers

Answers

Assume two numbers are n and n+2

Then n+ n+2 = 346 -> 2n = 344 -> n= 172

So the smaller one is 172, another one is 174

Answer:

Smallest number = 172

Step-by-step explanation:

Two consecutive even integers have a sum of 346.

Let x be the smallest number.

We have other number = x + 2

We also have

           x + x + 2 = 346

           2x + 2 = 346

           2 x = 344

            x = 172

Smallest number = 172, Other number = 172 + 2 = 174

Smallest number = 172

if structural steel installed in 2.75 floors of a building 2 3/8 day , how long will it take to install steel in 11 floors

Answers

I will take 9.5 days, to install steel in 11 floors.

f (x) = x3 + 2, g(x) = x2 – 1, h(x) = 3x Evaluate. g(h( f ((–1))) = ?

Answers

h(f(x))=3(x^2+2)

h(f(x))=3x^2+6

g(h(f(x)))=(3x^2+6)^3+2

g(h(f(-1)))=(3(-1)^2+6)^2+2

g(h(f(-1)))=(3+6)^2+2

g(h(f(-1)))=81+2

g(h(f(-1)))=83

Answer:

It's 8

Step-by-step explanation:

Took one for the team and got it wrong to get the right answer which is 8. Just took it. Edg 2020. Hope this helps :)

Btw be confident today cause honey you are beautiful! Just see what a little confidence in yourself can do <3

17.16 is 62.4%of what

Answers

divide

17.16/0.624 = 27.5

You begin solving the equation 3+4x=51 by subtracting 3 from both sides. Which is the best choice for Step 2? Subtract 48 from both sides. Multiply both sides by 4. Divide both sides by 4. Divide both sides by 48.

Answers

You will divide both sides by 4.

The solution of the given equation is x=12. Therefore, option C is the correct answer.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 3+4x=51.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Subtract 3 from both sides, we get

4x=48

Divide both sides by 4, we get

x=12

Therefore, option C is the correct answer.

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A telephone pole casts a shadow that is 37 m long. Find the height of the telephone pole if a statue that is 33 cm tall casts a shadow 83 cm long.

Answers

By similar triangles...

p/37=33/83

p=37(33)/83

p=1221/83 m

p≈14.711 m  (to nearest thousandth of a meter, or nearest millimeter)

Can a triangle be drawn with the following angle measures? Why or why not?
50°, 70°, 70°

Answers

no, the 3 angles of a triangle need to equal 180 degrees

70 +70 +50 = 190 degrees so it cant be a triangle.

Yes. It could, but if the angle measures more than 180, it would be an obtuse triangle. 

Two spheres of the same density have a ratio of 9 to 16 in surface area. If the small sphere weighs 15 kg, what does the large sphere weigh?

Answers

surface area of a sphere = 4 pi r^2

radius of small sphere =  sqrt (9/4pi) =   0.8463

radius  of larger one  = sqrt (16/4pi)  =  1.1284

ratio of the weights is 1.1284^3 : 0.8463^3  =   2.37

large sphere weighs  15 * 2.37 =  35.55 kg

How does a digit in the ten thousands place compare to a digit in the thousands place

Answers

Well technically they mean nothing to each other in a sense. But for a purpose the digit in the Ten Thousands place holds a stronger/higher value. Meaning that the number in the Ten Thousands place is worth more than a number in the Thousands place.

graph the opposite of the number shown on each number line

Answers

Okay so for number 3 the answer would be 8. For the number 4 the answer would be -4. For number 7 the answer would be -3 and number 9 would be just 0.

4.35 / 5 show the work

Answers

You can use long division. There are 0 5's in 4, so put a 0. Then put the demical point next. Bring the 3 down. How many 5's are in 43? 8. Put 8 next to the right of the decimal point. 3 is a remainder. Bring down the 5. That makes 35. There are 7 5's in 35, so you put 7 next to the 8. 0.87 is the answer. There is no remainder, so you do not have to worry about anything like that.
     _0.86_______
5  I 4.30
     -0.0
   = 4 3 0  
   -  4 3 0
    =   0

So, your answer is 0.86

1.If 70% is £14, what is the full cost
2.4 bags of cement do 18msquared, how many msquared can be done with 7 bags
3.5x+1=3
4.find the nthe term of this sequence 7,12,17,22,27
4.if t(n)=6n+2 what is the 3rd term

Answers

1) £20
2) 18/4 * 7 = 31,5msquared
3) X= (3-1)/5 = 2/5 = 0.4
4) A(n) = 2 + 5n
5) t(3) = 6*3 + 2 = 20
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