A diver dives from the board at a local swimming pool. Her height, y, in metres, above the water in terms of her horizontal distance, x, in metres, from the end of the board is given by y= -x^2 + 2x + 3. What is the diver's maximum height?

Answers

Answer 1

Answer:

4 meters

Step-by-step explanation:

Given a quadratic equation in which the coefficient of [tex]x^2[/tex] is negative, the parabola opens up and has a maximum point. This maximum point occurs at the line of symmetry.

Since the divers height, y is modeled by the equation

[tex]y= -x^2 + 2x + 3[/tex]

Step 1: Determine the equation of symmetry

In the equation above, a=-1, b=2, c=3

Equation of symmetry, [tex]x=-\dfrac{b}{2a}[/tex]

[tex]x=-\dfrac{2}{2*-1}\\x=1[/tex]

Step 2: Find the value of y at the point of symmetry

That is, we substitute x obtained above into the y and solve.

[tex]y(1)= -1^2 + 2(1) + 3=-1+2+3=4m[/tex]

The maximum height of the diver is therefore 4 meters.


Related Questions

What is the y-intercept of the line given by the equation below? y = 4/17x + 5​

Answers

Answer:

(0,5)

Step-by-step explanation:

100 points. WILL MARK BRAINLIEST. EASY QUESTION
Topic: Fractions.

ONLY COMPLETE QUESTION 2

Answers

Answer:

see below

Step-by-step explanation:

2 1/2+ 3 3/16 + 7/8

Get a common denominator of 16

2 8/16 + 3 3/16 + 14/16

5 25/16

5 + 16/16 + 9/16

6 9/16

Subtract this from 8 ft

8 - 6 9/16

Borrow 1 from 8 in the form of 16/16

7 16/16 - 6 9/16

1 7/16

b  1 7/16 - 1 1/3

The common denominator is 48

1 21/48    - 1 16/48

5/48

To the nearest tenth, which is the perimeter of △ABC

Answers

Answer:

My best guess is 24

Step-by-step explanation:

idk if this is right or not, but the triangle could be a 3 4 5 right triangle.

3 x 2 = 6

4 x 2 = 8

5 x 2 = 10.

6 + 8 + 10 = 24

this is the best answer i got. Don't know if it's going to help...

Express the required calculation in terms of it and then round to the nearest tenth.

How much fencing is required to enclose a circular garden whose radius is 20 meters?

There are of fencing required.

(Simplify your answer. Type an exact answer in terms of 7.)

There are approximately

of fencing required.

(Round to the nearest tenth as needed.)

Answers

Answer:

126m

Step-by-step explanation:

The circumference of the circle would be the amount of fencing required for the circular garden.

Circumference, C = 2πr

π = [tex]\frac{22}{7}[/tex]

C = 2*20*[tex]\frac{22}{7}[/tex]

C = 125.71 m

We need 125.71 meters to fence the garden.

There are y boats on a lake there are 6 people in each boat write an expression in term of y for the total number of people in the boats

Answers

Answer:

6y people are in the boats

Step-by-step explanation:

Here, we are interested in writing an expression for the total number of people in the boats.

We have 6 people in each of the boats and there are a total of y boats.

The total number of people in the boats is thus y * 6 = 6y people

-2 1/3-(-5) can someone help me

Answers

convert the mixed numbers to improper fractions then find the LCD and combine.
exact form: 8/3
decimal form: 2.6
mixed number form: 2 2/3

Emery bought three cans of beans I had a total weight of 2.4 pounds each can of beans with the same amount which model correctly illustrates the relationship check all that apply

Answers

Answer:

Figure 2 and 3 are correct

Step-by-step explanation:

This question is incomplete, the figures are attached.

Number of cans of beans bought by Emery = 3

Total weight of cans = 2.4 pounds

Therefore the weight of each can = 2.4/4 = 0.8 pounds

The can be represented by the equation:

y = 0.8x,   where x is the number of cans and y represents the total weight

From the graph of figure 1, weight of each can =  20/16 = 1.25 pounds. This is not correct

From the graph of figure 2, weight of each can =  8/10 = 0.8 pounds. This is correct

From the table of figure 3, weight of each can =  4/5 = 0.8 pounds. This is  correct

From the table of figure 4, weight of each can =  5/4 = 1.25 pounds. This is not correct

Please help it’s worth 80 points

Answers

The answer should be (D)

Answer:

D

Step-by-step explanation:

There are 2 triangles on the sides. On the bottom we have one rectangle, than we have the tilted rectangle, and the straight rectangle.

Solve for j.

–9.3j + 12.34 = –14.64 − 5.2j − 6j

Answers

So the value of j is -14.2

look at the attached picture

Hope it will help you

Good luck on your assignment

-9.3j + 12.34 = -14.64 - 5.2j - 6j
-9.3j + 5.2j + 6j = -14.64 - 12.34
1.9j = -26.98
j= -26.98 /1.9
j= -14.2

If f(x) = 3/x+2 - √x-3, complete the following statement (round to the nearest hundredth) f(7)=

Answers

Answer:

f(7) = -5/2

Step-by-step explanation:

Substituting 7 for x in f(x) = 3/x+2 - √x-3, we get:

f(7) = 3/(7+2) - √(7-3)

Note:  the parentheses are required / mandatory

We get   f(7) = 3/9 - 2, or 1/3 - 2, or  f(7) = -5/2

write the rule for f(h(x))

Answers

F(x) = x-7
H(x)= 2x+3
F(H(x)) = (2x + 3) -7 = 2x - 4

Answer:

F(x) = x-7,H(x)= 2x+3,F(H(x)) = (2x + 3) -7 = 2x - 4

Step-by-step explanation:

f(x)is a function so is the others so pair all then solve :)

"What is the theoretical probability of rolling a prime number on a standard number cube?"

Answers

Answer:

There are three prime numbers and 3 even numbers on a number cube, so the probability of each is 3/6 = 1/2

Step-by-step explanation:

Probability of rolling a prime number on a standard number cube is  [tex]\frac{1}{2}[/tex] or 0.5.

What is theoretical probability?

The theoretical probability is defined as the ratio of the number of favorable outcomes to the number of possible outcomes.

Numbers on a cube are {1, 2, 3, 4, 5, 6}

Total number of favorable outcomes = 6

Number of prime numbers in {1, 2, 3, 4, 5, 6} are {2, 3, 5}.

Number of favorable outcomes = 3

Probability of rolling a prime number on a standard number cube

P = [tex]\frac{Number of favorable outcomes}{Total number of favorable outcomes }[/tex]

P = [tex]\frac{3}{6}[/tex]

P = [tex]\frac{1}{2}[/tex]

Hence, probability of rolling a prime number on a standard number cube is  [tex]\frac{1}{2}[/tex] or 0.5.

Learn more about theoretical probability here

https://brainly.com/question/12543071

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algebra 1 : ordered pairs kinda dont get it

Answers

Answer:

Option C; 3x - y = -27 and x + 2y = 16

Step-by-step explanation:

1. Let us consider the equation 21x - y = 9. In this case it would be best to keep the equation in this form, in order to find the x and y intercept. Let us first find to y - intercept, for the simplicity ⇒ 21 * ( 0 ) - y = 9 ⇒ y = - 9 when x = 0. Now if we take a look at the first plot of line q, we can see that the x value is -9 rather than the y value, so this equation doesn't match that of line q. This would eliminate the first two options being a possibility.

2. Now let us consider the equation 3x - y = -27. Let us consider the x-intercept in this case. That being said, ⇒ 3x - ( 0 ) = -27 ⇒ 3x = -27 ⇒ x = -9 when y = 0. As we can see, this coordinate matches with one of the coordinates of line q, which might mean that the second equation could match with the equation for line v.

3. To see whether Option 3 is applicable, we must take a look at the 2nd equation x + 2y = 16. Let us calculate the y - intercept here: ( 0 ) + 2y = 16 ⇒ 2y = 16 ⇒ y = 8 when x = 0. Here we can see that this coordinate matches with that of the second coordinate provided as one of the points in line v. That means that ~ Answer: Option C

A bag contains 16 lottery balls, numbered 1-16. A ball is drawn, not replaced, then another is drawn. The events are:
independent or dependent?

Answers

Answer:

independent

Step-by-step explanation:

QUICK HELP PLS

Evaluate the questions below and select the statistical ones.
A
What is the mass of earth?
B
What is the mass of Halley's Comet?
C
How massive are asteroids in the asteroid belt?

Answers

Answer:

C

Step-by-step explanation:

A only gives one answer.(5.972 × 10^24 kg to be precise)

B It is only one thing so it has one mass, not providing a range of answers

C= There are many asteroids so a range of answers are made

Which of the following represents 3π, rounded to the nearest tenths?

Answers

Answer:

9.4

Step-by-step explanation:

pi = 3.1415...

3.1415*3 = 9.4

What is the measure of JKL? A. 60° B. 80° C. 110°D. 120 from edge 2020

Answers

Answer:

If its from the Ed assignment, it would be D. 120. Though this is a late reply.

The value of the measure of JKL is,

⇒ ∠ JKL = 120°

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In the triangle JKH is,

∠ JHK = 24°

∠ HJK = 96°

Hence, We can formulate;

⇒ ∠ JKL = ∠ JHK + ∠ HJK

Substitute the given values we get;

⇒ ∠ JKL = 24° + 94°

⇒ ∠ JKL = 120°

Thus, The value of the measure of JKL is,

⇒ ∠ JKL = 120°

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ6

HELP PLEASE! Im struggling

Answers

Answer:

c. [tex] \dfrac{2}{3} [/tex]

Step-by-step explanation:

Let the common ratio be r.

[tex] a_2 = \dfrac{2}{5} [/tex]

[tex] a_3 = \dfrac{2}{5}r [/tex]

[tex] a_4 = \dfrac{2}{5}r^2 [/tex]

[tex] a_5 = \dfrac{2}{5}r^3 [/tex]

We are told that [tex] a_5 = \dfrac{16}{135} [/tex].

[tex] \dfrac{2}{5}r^3 = \dfrac{16}{135}[/tex]

[tex] \dfrac{5}{2} \times \dfrac{2}{5}r^3 = \dfrac{5}{2} \times \dfrac{16}{135}[/tex]

[tex] r^3 = \dfrac{8}{27} [/tex]

[tex] r = \sqrt[3]{\dfrac{8}{27}} [/tex]

[tex] r = \dfrac{2}{3} [/tex]

Answer: c. [tex] \dfrac{2}{3} [/tex]

El tema es de polinomios

Answers

Answer:

Tu imagen no es muy clara, así que no puedo entenderla.

Step-by-step explanation:

solve the inequality 1/2y>5​

Answers

Answer:

y > 10

Step-by-step explanation:

1/2y>5​

Multiply each side by 2

2* 1/2y>5​*2

y > 10

Answer:

y > 10

Step-by-step explanation:

Inequality:

1/2y>5​

We need to isolate the variable y.

Since it is being multiplied by 1/2, we need to multiply by the reciprocal, or opposite, on both sides. The reciprocal of 1/2 is 2. (Check by multiplying both numbers and making sure the product is 1.)

Multiply:

1/2y>5​

x2     x2

y > 10

Therefore, the simplified inequality is y > 10.

what is the surface area of a prism 8,6,10,12



Please give me proper and right answers


i am begging you

Answers

Answer:

618.4 unit^2.

Step-by-step explanation:

We have 6 surfaces  ( 3 pairs of equal area) so it is:

2 * 8.6*10 + 2 * 8.6*12 + 2 * 10*12

=  2 * 86 + 24*8.6 + 2 * 120

= 618.4.

Will mark as brainliest if correct

Answers

Answer:

X = 1.09

Step-by-step explanation:

6 to the 1.09th power is 7.04993094301076 so when it is rounded it is 7.

Answer:

the answer is 7

Step-by-step explanation:

log10(6x)=log10(7)

x•log10(6)=log10(7)

x = log10(7)/log10(6)

this works because of

logb(x y) = y ∙ logb(x)

I figured this out from the internet!!

source:TigerAlegbra

john charges a fee of $50 to figure out what is wrong with a customers car. then he charges $75 per hour to fix the car. if john charged a customer $237.50 how long did he work on the car?
please answer fast.

Answers

Answer:

2 hours and 30 minutes.

Step-by-step explanation:

First you must add $50 and $75. Then add two $75, to get $200. Then, Multiply $1.25 by 30.

Hope this helps :)

(If it did please make this brainliest.)

3х - 40 °
30°
х+ 20
whats x?

Answers

So the right answer is 42.5

look at the attached picture

Hope it will help you

Good luck on your assignment

Write an addition equation or a subtraction equation to describe the diagram

Answers

Answer:

add the diagram

Step-by-step explanation:

what perfect square goes into the square root of 108

Answers

We can rewrite 27 as 9 × 3, where 9 is a perfect square, then take it through our steps. Since 3 doesn't have any perfect square factors, √(3) is as simplified as possible, so we have that the square root of 108 in radical form is 6 × √(3), or 6√(3).

Answer:

[tex]6\sqrt{3}[/tex]

Step-by-step explanation:

so we are going to create a factor tree which is the .The factor tree is any two numbers that equal to 108.

next we are going to pull out our pairs.so there are one pair of two's and one pair of threes

[tex]\sqrt[2]{108} =2*3\sqrt{3} =6\sqrt{3}[/tex]

pls mark me brainliest

40 PTS!!How many possible outcomes exist when four fair coins are flipped? 2 4 8 16

Answers

Answer:

16

Step-by-step explanation:

4 coins 2 out comes each

2 X 2 X 2 X 2 = 16

2^4 = 16

Hope i helped you

Answer:

16

Step-by-step explanation:

What is the solution to this system of equations?

On a coordinate plane, 2 lines intersect at (negative 6, negative 2).

What is the solution to the system of equations?
(–6, –2)
(–2, 6)
(6, 2)
(–2, –6)
pls hurry up im being
timed

Answers

Answer:

(-6,-2)

Step-by-step explanation:

Since they intersect at (negative 6, negative 2) and the solution to the two equations is their point of intersection, then you just need to convert the words to numbers in the form (-6,-2). Hope this helps!

Answer:

It is A

Step-by-step explanation:

I just took the test and got 100 eny answer ask me :D

Correct answers only!

To the nearest cent, how much will she have in 3 years?

Use the formula B = p(1 + r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

Answers

Answer:

4444.63

Step-by-step explanation:

after 1st year money will be 3000 + 0.14 *3000 =3420

after 2nd year 3420 + 0.14*3420 =3898.80

after 3rd yeaar 3898.80 + 0.14*3898.80 = 4444.632

In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If 15 boys and 4 girls are competing, how many different ways could the six medals possibly be given out?

Answers

Answer:

There are a total of possible 1820 results.

Step-by-step explanation:

Since there are two competitions, one for boys and one for girls, and we want all the possible results we will calculate the possible combinations for the boys and multiply them by the possible combinations for the girls. This is shown below:

[tex]Boys = \frac{15!}{3!(15 - 3)!} = \frac{15!}{3!12!} = \frac{15*14*13*12!}{3!12!}\\Boys = \frac{15*14*13}{3*2*1}\\Boys = \frac{15*14*13}{3*2*1}\\Boys = 455[/tex]

[tex]Girls = \frac{4!}{3!*(4 - 3)!}\\Girls = \frac{4*3!}{3!}\\Girls = 4[/tex]

Total number of possible results:

[tex]results = 4*455\\results = 1820[/tex]

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