Give an example of a quadratic function that has a maximum value. How do you know that it has a maximum value?

Answers

Answer 1

An example of a quadratic function that has a maximum value is the parabola defined by the equation y = -(x-3)^2 + 4.

What is quadratic function?

A quadratic function is a type of polynomial function that can be written in the form y = ax^2 + bx + c, where a, b, and c are constants and x is the variable. The graph of a quadratic function is a parabola, which can either open upward or downward depending on the value of the leading coefficient (a).

What is equation?

An equation is a mathematical statement that asserts the equality of two expressions. It is usually written with an "=" sign between the two expressions, such as y = 2x + 3 or x^2 + y^2 = 1. Equations can be used to model real-world situations, and solving an equation means finding the values of the variables that make the equation true.

We can determine that this function has a maximum value by looking at the leading coefficient of the quadratic term (x^2). In this case, the coefficient is -1, which means that the parabola opens downward. Therefore, since the parabola opens downward, the vertex of the parabola is the highest point of the parabola, which means that it is a maximum point.

Also we can find the vertex of the parabola by using the formula x = -b/2a, in this case x= -0 / 2*-1 = 3/2 =1.5, and using this value in the function, we get the y value which is 4, so the vertex is (1.5,4) which confirms that the function has a maximum value at (1.5,4)

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Related Questions

5 times a number,incrased by 8

Answers

45 is the answer hope this helps

Answer:

5 × x + 8

Would be the equation you are looking for.

What is the area in square feet for this shape?

Answers

Answer:

Area of figure = 68.13 feet² (Approx.)

Step-by-step explanation:

Given:

Length of rectangle = 9 ft

Width of rectangle = 6 ft

Diameter of semicircle = 6 ft

Find:

Area of figure

Computation:

Radius of semicircle = Diameter of semicircle / 2

Radius of semicircle = 6 / 2

Radius of semicircle = 3 ft

Area of figure = Area of rectangle + Area of semicircle

Area of figure = [Length x( Width] + [πr²]/2

Area of figure = [9 x 6] + [(3.14)(3)²]/2

Area of figure = [54] + [(3.14)(9)]/2

Area of figure = [54] + [28326]/2

Area of figure = [54] + [14.13]

Area of figure = 68.13

Area of figure = 68.13 feet² (Approx.)

Julie remembered that the 4 digits of her locker combination were 4, 9, 15, and 22, but not their order. What is the maximum
number of attempts Julie has to make to find the correct combination?

Answers

Answer:

256

Step-by-step explanation:

4^(4)=256, I'm pretty sure that's the answer. i looked up and after some research found that.

Answer: 256

Step-by-step explanation:

Easiest way is to do 4x4x4x4

Factorize 4x squared - 25y squared

Answers

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

here we go~

[tex]\qquad \sf  \dashrightarrow \: 4x {}^{2} - 25y {}^{2} [/tex]

[ identity : a² - b² = (a + b)(a - b) ]

[tex]\qquad \sf  \dashrightarrow \: (2x) {}^{2} - (5y) {}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (2x + 5y)(2x - 5y)[/tex]

The sum of two numbers is -6. Their difference is 36. What is the smallest number?

Answers

Let first number be x.

Let second number be y.

According to question,

x+y=36…….(equation 1)

and

x-y=6…..(equation 2)

equation 2 can be written as , x=6+y……(equation 3)

Put equation 3 in equation 1,

6+y+y=36

6+2y=36

2y=36–6

2y=30

y=30/2

y=15

now, put y=15 in equation 1,

x+15=36

x=36–15

x=21

So, numbers are 21 and 15.

What happens when you log an e?

Answers

When you log an e, you are essentially taking the natural logarithm of the number. This means that you are taking the logarithm of a number to the base e, which is about 2.718. The result of this calculation is the number of times the number must be multiplied by itself to get the original number.

For example, if you were to log an e, it would be equal to 1, since e x e = e. If you log a number bigger than e, such as 8, the result would be equal to 2.079, which means that 8 must be multiplied by itself twice (2.079 times) to get the original 8.

In general, when you log a number, you can think of it as a way of seeing how many times that number needs to be multiplied by itself to get the original number. This can be useful in many fields, from mathematics to engineering to physics, to find the mathematical relationship between two numbers.

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Frank has constructed a tent in the shape of a square pyramid.



The peak of the tent is at 30 feet and is at a horizontal distance of 20 feet from the left edge. The height of the tent varies at a rate of 1. 5 feet with the horizontal distance from the left edge.

The equation that models the height of the tent, h, in feet, with respect to the horizontal distance in feet from the left edge, d, is h = |d − | +. The height of the tent is 22. 5 feet at a horizontal distance of feet

Answers

The equation that models the height of the tent, h, in feet, with respect to the horizontal distance in feet from the left edge, d, is h = 1.5 d + h0.

The height of the tent is 22. 5 feet at a horizontal distance of 15 feet.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The height of the tent varies at a rate of 1. 5 feet with the horizontal distance from the left edge.

This can be written as -

h = 1.5 d, where d is the distance.

So, the equations that models the situation is -

h = 1.5 d + h0

The peak of the tent is at 30 feet and is at a horizontal distance of 20 feet from the left edge.

So, when d =20, then h =30.

Plugging the values in the equation -

30 = 1.5 (20) + h0

30 = 30 + h0

h0 = 0

The height of the tent is 22. 5 feet.

So, now h = 1.5 d and h = 22.5.

Equating these two -

22.5 = 1.5 d

d = 22.5/1.5

d = 15

Therefore, the distance value is obtained as 15 feet.

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rotation definition math

Answers

Answer: a circular movement

Step-by-step explanation: rotation has a central point that stays fixed and everything else moves around that point in a circle.

EX) a full rotation is 360

PLA HELP WILL MARK BRAINLEST AND GIVE 100 points

Answers

Answer:

B) measures of variability

Hope this helped :)

select a graph that shows the relationship between the height form which the ball is dropped , x, and the height of the first bounce y

Answers

Answer:

a?

Step-by-step explanation:

How do i show my working when trying to work out 3 1/3 divided by 4?

Answers

Answer:

5/6

Step-by-step explanation:

When dividing fractions, we use a rule where we keep the first number, change the sign, and flip the second number.

3 1/3 must be converted to an improper fraction before we can do this, though.

3 1/3 is 10/3 because we multiply 3 by the denominator, also 3, and then add one, so 10/3.

Now we can divide. Remember 4 is the same thing as 4/1

10/3 ÷ 4/1

Keep the first fraction the same, change the division sign into a multiplication sign, and divide by flip the second fraction.

It ends up looking like 10/3 x 1/4

Multiply: 10 x 1 and 3 x 4

It's 10/12, but we can simplify that by dividing both the top and the bottom by 2.

The final answer is 5/6

The distance between two points A and B on latitude 60°S along their parallel of latitude is 2816km. Calculate the angular difference in their longitudes. If A is due west of B and on longitude 20°W, find the longitude of B

Answers

Answer:

Part A

The angular difference of their longitude is approximately 50.65°

Part B

The location of B is on the longitude of approximately 30.65°E

Step-by-step explanation:

Part A

The given parameters are;

The location of the points A and B = Along the parallel of latitude 60°

The radius of the Earth, R = 6,371 km

The radius at the 60° parallel of latitude, r = R × cos(θ)

∴ r = 6,371 × cos(60°) = 3,185.5

The circumference of the 60° parallel of latitude, C₆₀ = 2 × π × 3,185.5

The angle subtended by the arc formed by their distance apart, θ₁, is given as follows;

θ₁ = 2,816/(2 × π × 3,185.5) × 360 ≈ 50.65°

The angular difference of their longitude, θ₁ ≈ 50.65°

Part B

Given that the location of A is on the longitude 20°W and A is due west of B, we have the location of B is on the longitude (50.65° - 20°)E = 30.65°E

The location of B is on the longitude of approximately 30.65°E.

Can I please have help? No files please!

Answers

Answer:

[tex]J.(x,y)[/tex] → [tex](9x,9y)[/tex]

[tex]--------[/tex]

hope it helps..

have a great day!!

1. If 5(x − 6) = − 8, then x = ?
a. -38/5
b. -8/5
c. -2/5
d. 2/5
e. 22/5

Answers

Answer:

the answer is e. i hope this helps :)))

The answer is e.22/5 hope this helps bud

According to the synthetic division below, which of the following statements are true? Check all that apply.
A. (x+2) is a factor of 5x2-16x + 12.
B. (x-2) is a factor of 5x2-16x + 12.
C. (5x2 - 16x+12) + (x - 2) = (5x-6)
D. (5x2-16x +12) + (x + 2) = (5x-6)
E. The number -2 is a root of F(x) = 5x2 - 16x + 12.
F. The number 2 is a root of F(X) = 5x2 - 16x+ 12.​

Answers

Answer:

Correct answer just took the quiz

Step-by-step explanation:

The correct option for the given statement is that (x-2) is a factor of [tex]5x^{2} -16x+12[/tex].

What is a factor?

It is a number by which the number whose it is a factor can be divided.

How to divide an equation?

To check factor of an equation we need to divide it with so to check (x-2) a factor of [tex]5x^{2} -16x+12[/tex] we need to divide the equation by x-2

=( [tex]5x^{2} -16x+12[/tex])/x-2

=5x-6

So it is a factor of the given equation.

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Is the triangle formed by points A, B, and C a right triangle?

Answers

Answer:Yes

Step-by-step explanation: It is a right triangle as if you imagine it, you can see that is half of a square, holding a right angle within it.

Fill in the blank question.
Miss Wade's science class of 20 students is going on a field trip to the zoo. Each student will also take a train ride around the zoo. Mr. Sexton's class of 25 students is going on a field trip to the state park and will take a canoe trip. Admission to the zoo is twice that of the state park's entry fee as shown in the table. Each group will spend the same total amount of money.

Answers

Answer:

The total cost of the science class trip to the zoo is $1200

Step-by-step explanation:

The cost of the science class trip to the zoo is $1200, and the cost of Mr. Sexton's class trip to the state park is $1000.

Given P(A and B)= 0.09, P(B)= 0.25. FIND P(A given B)
A:0.34
B:0.29
C:0.02
D:0.36

Answers

The answer to your question is A:0.34

HELP ME ASAP AND I MEAN ASAP

Answers

Answer:

9miles

Step-by-step explanation:

Answer:

Step-by-step explanation:

In a right triangle, if the length of the hypotenuse is 5 and the length of one of the other sides is 3, what is the length of the third side?​

Answers

Answer:

a^2+b^2=c^2

a^2+9=25(5*5)

therefore ,a^2=25-9=16

√16=4

   sides are 4 cm,3 cm,5 cm

Step-by-step explanation:

[tex]4.[/tex]

Step-by-step explanation:

Pythagoras theorem says that "In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides". As the Hypotenuse side is already yet given and one of the side of a triangle value is given. Now we should find the value for other side of a triangle. In order to find the value of other side, we should use the Pythagoras theorem formula.

AC² = AB² + BC²

Let AC be the Hypotenuse side, AB and BC be the other two sides of a triangle.

Given:-

AC = 5, AB = 3, BC = ?

Use Pythagoras theorem formula

AC² = AB² + BC²

5² = 3² + BC²

25 = 9 + BC²

25 - 9 = BC²

16 = BC²

16 = BC

BC = 4.

9/11 - 1/2 in it's simplest form​

Answers

Answer:

7/22 or 0.31818...

Step-by-step explanation:

have a good day!! :)

which country are you from?

Answers

Answer:

Whom are you asking????

<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3

Answer:

America

<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3

please help thxsssssssssssssssssssssssssssss

Answers

Answer:

x≤3.5

Step-by-step explanation:

=>7-2x≤0=>-2x+7≤0=>-2x≤-7 divide 2 by 2 and by 7=>x≤3.5

hello please help i’ll give brainliest

Answers

It’s the third one c

Answer:

C.

Step-by-step explanation:

PLEASE BRAINLIEST

PLEASE HELP AMD SHOW WORKING.
Find the y-intercept of the equation 5x-2y=28
a._14
b.-5/2
c.5/2
d.14​

Answers

Rewrite the equation in slope-intercept form

5x -2y = 28

Subtract 5x from both sides

-2y = -5x + 28

Divide both sides by -2

Y = 5/2x -14

The y intercept is -14

Answer:

Solution given:

5x-2y=28

5x-28=2y

y=5/2x-14

comparing above equation with y=MX+c

where

c=y intercept=-14

-14 is a required answer.

Translate the triangle.
The enter the new coordinates.
A (-2,4)
C
(-3,2)
B
(1,1)
<-4, -1 >
A'(-6, [?])
B'([ ], [ ])
C'([], [])

Answers

Therefore , the solution of the given problem of triangle comes out to be  A'(1, 0) (1, 0) , B'(1, 2) (1, 2) and C'(3,-2) (3,-2).

Explain the triangle.

The fact that a triangle has four segments or vertices qualifies it as a polygon. It is an elementary geometric form. The name given to a triangle with endpoints A, B, then C is Triangle ABC. A singular plane and square are obtained in Euclidean geometry when the edges are not collinear. Any triangle that has three sides and three corners is a polygon. The triangle's corners are the spots at which its three sides intersect. 180 degrees is the result of three triangle angles.

Here,

The image A'B'C' is formed by our transformation rule, (+3,y-2)

So:

1. Describe the updated coordinates for points A', B', and C'?

In order to locate these new positions, we have:

A' (-23, 2-2)  =>    A'(1, 0) (1, 0)

B' => (-23, 4-2)    =>   B'(1, 2) (1, 2)

C'=> (0+3,0-2) => C'(3,-2) (3,-2)

2. Explain the qualities that would emerge if the respective vertices were linked together by lines.

We can notice the two triangles on the First Figure if we look closely. The green one is A'B'C, while the red one would be the triangle ABC.

The equivalent vertices with in second figure have been joined together by line segments, as shown by the green lines.

Two things can be said about those three lines: first, they are parallel, and second, they are all the same length.

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EASY BRAINLIEST PLEASE HELP!!
-if you answer correctly ill give you brainliest which will give you 100pts-

(if you put links or don't answer accordingly im reporting your account)

Answers

Parallelogram? I’m not sure
It could resemble a parallelogram at first sight but parallelograms have the opposite sides equal and parallel. In this case they are parallel but the sides on the left and on the right are neither.

ILL BRAINLIEST YOU PLEASE HELP ME

Answers

Answer

Option A

61 in, 60 in, 11 in. represents three sides of a right triangle

Step-by-step explanation:

By Using Pythagorean Triplet we can say that

61 in, 60 in, 11 in. represents three sides of a right triangle

FOR VERIFICATION ONLY:

(11)² + (60)² = (61)²

121 + 3600 = 3721

3721 = 3721

Thus, 3721 = 3721 represents three sides of a right triangle

-TheUnknownScientist

factor the polynomial completely and SHOW WORK i’ve been on it for the past 30 minutes and I want to cry 24x^3-78x^2+45x NO LINKS pls :))

Answers

9514 1404 393

Answer:

  3(x)(4x -3)(2x -5)

Step-by-step explanation:

First of all, recognize that all coefficients are multiples of 3, and all terms have x as a common factor. This means your first factorization is ...

  (3x)(8x^2 -26x +15)

Now, you can use the "X-method" or similar to factor the quadratic. Start by looking for factors of (8)(15) = 120 that have a total of -26. Both will be negative. Here is a list of the positive factor pairs.

  120 = 1·120 = 2·60 = 3·40 = 4·30 = 5·24 = 6·20 = 8·15 = 10·12

The sums of these factor pairs are ...

  121, 62, 43, 34, 29, 26, 23, 22

The pair with a sum of 26 is highlighted.

Using this information, you can complete the X-method diagram, or you can use these numbers to rewrite the quadratic x-term to have 2 parts:

  8x^2 -20x -6x +15

Now, the quadratic can be factored by grouping:

  =  (8x^2 -20x) +(-6x +15)

  = 4x(2x -5) +3(-2x +5)

Recognizing the sign difference between the parentheses contents, we can factor the quadratic to be ...

  = (4x -3)(2x -5) . . . . . note the sign gets attached to the 3

So, the complete factorization of the original expression is ...

  24x^3-78x^2+45x = 3(x)(4x -3)(2x -5)

Help I’m stuck on a question

Answers

Answer:

3rd one

Step-by-step explanation:

Third answer

0. 1200
<———————•
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