What is the range of the function?

The function f(x) = (x - 4)(x - 2) is shown.

10

O all real numbers less than or equal to 3

O all real numbers less than or equal to - 1

O all real numbers greater than or equal to 3

O all real numbers greater than or equal to - 1

Answers

Answer 1

Answer:

The range of the function is all real numbers greater than or equal to -1.

Step-by-step explanation:

Second order polynomials are continous and have an absolute maximum or minimum that restricts the set of the range associated with the function. A fair approach to estimate the range is rewritting the expression into parabola form, which is:

[tex]y - k = C \cdot (x-h)^{2}[/tex]

Where:

[tex]C[/tex] - Vertix parameter, dimensionless. If [tex]C > 0[/tex], then vertix is an absolute minimum, but if [tex]C < 0[/tex], vertix is an absolute maximum.

[tex]x[/tex] - Independent variable, dimensionless.

[tex]y[/tex] - Dependent variable, dimensionless.

[tex]h[/tex] - Location of the vertix with respect to the independent variable, dimensionless.

[tex]k[/tex] - Location of the vertix with respect to the dependent variable, dimensionless. This value restrics the set corresponding to the range of the polynomic function.

First, we have to expand polynomial into its standard form:

[tex]y = (x-4)\cdot (x-2)[/tex]

[tex]y = x^{2}-6\cdot x +8[/tex]

Now, we are going to complete the square and factorize the resultant expression until parabola form is obtained:

[tex]y = x^{2}-6\cdot x + 9 -9 + 8[/tex]

[tex]y = (x-3)^{2} -1[/tex]

[tex]y + 1 = 1 \cdot (x-3)^{2}[/tex]

Since the vertix parameter is positive, then vertix is an absolute minimum. The location of the vertix with respect ot the depedent variable is [tex]k = -1[/tex]. Therefore, the range of the function is all real numbers greater than or equal to -1.


Related Questions

Can somebody help me with this please ?? :)

Answers

yes they are congruent budy because they have given AC is equal to AD,, BC is equal to ED and angle BAC is equal to angle EAD.

For congruence of triangle ABC and triangle ADE we just need three parts that we got and therefore they are congruent..

don't forget to follow

Please help I don't understand

Answers

Answer:

C

Step-by-step explanation:

i just took the test

7. Express as a fraction in simplest form: 4 to 36

Answers

Answer:

4/36=2/18=1/9=1/9=1/9=1/9=1/9=1/9

Answer:

1/9

Step-by-step explanation:

4:36 as a ratio can be written in the form of a fraction.

4/36

Simplify the fraction using the highest common factor.

4÷4/36÷4

1(4)/9(4)

The 4's cancel.

1/9

Can someone make sure that I’m right I don’t know I think I’m wrong but I don’t know so can you help me

Answers

Answer:

2 sqrt(5)

Step-by-step explanation:

To find the geometric mean to two numbers

sqrt( x*y)

sqrt( 5*4)

sqrt(5) * sqrt(4)

2 sqrt(5)

suppose f(x)=x^2-4.Find the graph of f(3x)

Answers

Answer:

3(x²-4) or 3x²-12

Step-by-step explanation:

x²-4 times 3 is equal to 3x-12 which is also 3(x²-12)

Figure ABCD is a parallelogram.
What is the value of n?
3
5
17
25​

Answers

Answer:

n is equal to 17 if you want you can plug the number to both equation and try to see if both are equal if they are equal that means you did it right

Answer:

n = 17

Step-by-step explanation:

The opposite angles of a Parallelogram are equal.

So,

4n-2 = 2n+32

4n-2n = 32+2

2n = 34

Dividing both sides by 2

n = 17

solve 0.06*0.7+0.03=0.06*(-0.2)+0.03​

Answers

Answer 0.06*0.7+0.03=0.072 and 0.06*(-0.2)+0.03=0.018

(05.06) coordinate grid with plotted ordered pairs, point A at negative 5, 4 point B at 4, 7 point C at negative 2, 7 point D at negative 7, 1 point E at 4, negative 2 point F at 1, negative 6 point G at negative 3, negative 10 point H at negative 4, negative 4 point I at 9, 3 point J at 7, negative 4 and point K at 2, 3 The coordinate grid shows points A through K. Which points are solutions to the system of inequalities listed below? (2 points) 2x + y 8

Answers

Answer: I'm not sure if this is right but I believe its point E, F, G, J

Step-by-step explanation:

Don't use this without getting confirmation I don't want to trip anyone up!

Answer: EFG is correct

Step-by-step explanation:

I did the quiz

The table represents an exponential function. What is the multiplicative rate of change of the function?
1/3
2/3
2
9

Answers

The answer would be 2/3 I took the test and passed it

The multiplicative rate of change of the function is 2.

What is the rate of change?

The pace at which one quantity changes in relation to another quantity is known as the rate of change function. The rate of change will be calculated by the ratio of the change of the dependent variable to the change of the independent variable.

Given that the values of the variables x and y are,

x    y

1     6

2    4

The rate of change will be calculated as,

Rate  of change  = ( y₂ - y₁ ) / ( x₂ - x₁ )

Rate  of change  = (4 - 6 ) / ( 2 - 1 )

Rate of change = -2

The multiplicative rate of change will be 2.

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What is the measure of a 137 degree angle

Answers

Answer: 137 degrees

Step-by-step explanation:

It's in the sentences, the angle is 137 degrees

Mark dropped an object from a bridge 400 feet above the ground level with an initial velocity of 0. He knows that the gravitational pull of the earth is about 16 feet per second squared. wants to find how many seconds,t, it will take the object to hit the ground. Match each expression with the correct equation that models this situation or solution.

Answers

Answer:

The first listed equation is the correct equation to solve

The correct answer is: t = 5 seconds

Step-by-step explanation:

Let me mention first that there is an error in the statement that the gravitational pull of the Earth is 16 ft/s^2. It is in fact 32 ft/s^2, and the actual equation uses half of the acceleration multiplied by the square of the variable time, so it gives as final expression :

[tex]y(t)=-16\,t^2+ 0 \,t +400[/tex]

and we want to find the value/s for "t" that make this equation equal zero (when it reaches the ground and the object just touches the ground. This makes the equation we want to solve:

[tex]0=-16\,t^2+ 0 \,t +400\\16\,t^2+0\,t -400=0[/tex]

which solving for "t" becomes:

[tex]16\,t^2-400 =0\\16\,t^2=400\\t^2=\frac{400}{16} \\t^2=25\\t= +/- 5\,\,sec[/tex]

So we adopt the positive answer (positive time) since the negative value has no physical meaning for this problem.

That is: t = 5 seconds

correct equation: -16t^2 + 0t + 400 = 0

solution: 5 seconds

i just did the workbook and got it correct!

i will mark brainliest!!!!!!!!!!!!!!!!!

Answers

Answer:

C

Step-by-step explanation:

Macy didnt correctly find the equivalent fraction with the denominator of 30

4/5 is 24/30 not 18/30.

this is because 4×6 is 24 which is the numerator and 5×6 is 30 which is the denominator

Answer:

Macy did not correctly find the equivalent fraction with the denominator of 30.

Step-by-step explanation:

What Macy should have written:

[tex]\frac{4}{5} ?\frac{18}{30} =\\\\\frac{24}{30} >\frac{18}{30}[/tex]

What Macy wrote:

[tex]\frac{4}{5} ?\frac{18}{30} =\\\\\frac{18}{30} <\frac{19}{30}[/tex]

[tex]\frac{4*6}{5*6}[/tex] does not equal [tex]\frac{18}{30}[/tex]

Which of the following decimals is equivalent to the common fraction four-fifth? a. 0.80 b. 0.75 c. 0.65 d. 0.45 Other:

Answers

Answer:

The answer is option a

0.8

4/5 = 0.8

Hope this helps.

In 2010, Rafik bought a house. In 2015, Rafik sold the house to Bianca. He made a 20% profit on the sale. In 2019, Bianca sold the house for £193800. She made a 5% loss. Work out how much Rafik paid for the house in 2010.

Answers

9514 1404 393

Answer:

  £170,000

Step-by-step explanation:

Bianca bought the house for 1 +20% = 1.2 times Rafik's purchase price. She sold it for 1 -5% = 0.95 times what she bought it for. So, we have ...

  (Rafik's purchase price)×1.2×0.95 = £193800

  Rafik's purchase price = £193,800/(1.2×0.95) = £170,000

Rafik bought the house for £170,000.

Which expression is equivalent to the expression 4(6+y)+7?
0 24+ 4y
O 31+ 4y
o 31+By
O 24+ 7y

Answers

Answer:

31 + 4y

Step-by-step explanation:

4(6+y)+7

Expand the brackets.

24+4y+7

Rearrange.

4y + 24 + 7

Add the like terms.

4y + 31

Answer:

its B

Step-by-step explanation:

Clara is building a triangular garden. She wants the length of the longest side to be three more than twice as long as the length of the shortest side, and the third side will be twelve feet long.

Answers

Answer:

3s+15

Step-by-step explanation:

let 's' be the length of the shortest side

-> twice as long as the length of the shortest side =2s

->length of the longest side to be three more than twice as long as the length of the shortest side = 2s + 3

-> the third side= 12 feet

p = s + 12 + 2s+3

p= 3s+15

Find the solution set for this equation.
-m2 - 5m=0
Separate the two values with a comma.
Enter the correct answer.

Answers

Answer:

m = -5, 0

Step-by-step explanation:

Easiest and quickest way to do this is to graph the equation and find where it intersects the x-axis. If not, then use completing the square or quadratic formula to find your roots.

binomial numbers, Stifel

Answers

Answer:

binomiales, números combinatorios o combinaciones son números estudiados en combinatoria que corresponden al número

Step-by-step explanation:

Use a= √a b= √5 c= √10
to work out the value of ac/b
Give your answer in its simplest form.

Answers

Answer:

a = √a b = √5 c = √10

ac/b = (√a)(√10)/√5

= √ 10 × a /√5

= √10a / √5

Rationalize the surd

√10a ×√5/(√5)²

= √50a /5

= 5√2a/ 5

= √2a

The final answer is √2a

Hope this helps

In circle P, diameter QS measures 20 centimeters. Circle P is shown. Line segment Q S is a diameter. Line segment R P is a radius. Angle R P S is 123 degrees. What is the approximate length of arc QR? Round to the nearest tenth of a centimeter. 9.9 centimeters 19.9 centimeters 21.5 centimeters 43.0 centimeters

Answers

Answer:

Length of arc QR is [tex]\approx[/tex] 9.9 cm

Step-by-step explanation:

Given that circle P, i.e. center is point P.

QS is diameter with length 20 cm.

Given that RP is the radius with

[tex]\angle RPS = 123^\circ[/tex]

To find length of arc QR = ?

Solution:

Arc QR subtends the [tex]\angle QPR[/tex] on center P.

So, we need to find the angle [tex]\angle QPR[/tex] to find the length of arc QR.

QS is the diameter so [tex]\angle QPS = 180^\circ[/tex]

[tex]\angle QPS = 180^\circ = \angle QPR +\angle RPS\\\Rightarrow 180^\circ = \angle QPR +123^\circ\\\Rightarrow \angle QPR = 57^\circ[/tex]

Converting in radians,

[tex]\angle QPR = 57^\circ \times \dfrac{\pi}{180} = 0.99\ radians[/tex]

Using the formula for length of arc:

[tex]l = \theta \times R[/tex]

Where [tex]\theta[/tex] is the angle subtended by the arc on center.

R is the radius of circle.

Here,

[tex]\theta = 0.99\ radians\\R = 10\ cm[/tex]

[tex]l = 0.99 \times 10\\l = 9.9\ cm[/tex]

Length of arc QR is [tex]\approx[/tex] 9.9 cm

Answer:

9.9 cm

Step-by-step explanation:

How many cubes are needed to build this figure?

Answers

Answer:

3 cubes are needed are needed to build the figure

6 cubes are used in this diagram

Which of the following values are in the domain of the function graphed below?check all that apply

Answers

Answer:

a,c, from l to be a great idea to be at the house by the way the time to do it on a hard time that I can help with the rest of the cause you found it on my phone and it do not have a circunr on my computer and

Step-by-step explanation:

yourwelcome

Answer: 7,0,2,3

Step-by-step explanation: nodadnotoday on Spotify

Which of these sequences is a geometric sequence?

Answers

Answer:

The answer is option d.

Hope this helps you.

Answer:

D

3,9,27,81,243,729

Step-by-step explanation:

You have a 90% as your grade and on your final you get 80%. Your current grade is 20%of your grade and your final is 80% of your grade. What percent for your grade would you get in the end?

Answers

Answer:

82%

Step-by-step explanation:

(20×90+80×80) / (20+80) = 8200 / 100 = 82.00

the grade would be 83%,

Make L the subject of the formula T=2π√L\G​ ​

Answers

Answer:

[tex]L=(\frac{TG}{2\pi })^2[/tex]

Step-by-step explanation:

[tex]T=2\pi \sqrt{L}/G[/tex]

[tex]TG=2\pi \sqrt{L}[/tex]

[tex]\frac{TG}{2\pi } =\sqrt{L}[/tex]

[tex](\frac{TG}{2\pi })^2 =L[/tex]

Answer:

[tex]l = {( \frac{tg}{2\pi}) }^{2} [/tex]

hope this helps you.

brainliest appreciated

good luck! have a nice day!

Pls answer i will mark as branliest

Answers

Answer:

A) Corresponding Angles Theorem (They correspond to each other)

B) If <XBC = 55 Then <XCB = 55

(Because they both are opposite to equal sides)

Now, Finding <BXC:

=> <BXC = 180-55-55 (Angles of a triangle add up to 180 degrees)

=> <BXC = 70 degrees

What is the standard form for the quadratic function? f(x)=(x−3)2+5 f(x)=x2−4
f(x)=x2+14
f(x)=x2−6x+14
f(x)=x2+6x−4

Answers

Answer:

x^2-6x + 14

Step-by-step explanation:

Here, we want to

write the standard form of the quadratic equation in the question.

This can be written by expanding the bracket.

F(x) = (x-3)^2 +5

F(x) = (x-3)(x-3) + 5

F(x) = x(x-3)-3(x-3) +5

F(x) = x^2 -3x-3x + 9 + 5 = x^2-6x + 14

Find the area of a circle with diameter 10cm use the value 3.14

Answers

Answer:

78.5 cm

Step-by-step explanation:

The area of a circle is represented by A = πr². Since we are replacing the value of pi(π) with 3.14, and the diameter is 10, meaning the radius(r) is 5, we can plug both values into the equation, to get A = 3.14(5^2). This simplifies to 78.5.

Answer:

78.5 cm^2

[tex]solution \\ diameter = 10 \: cm \\ radius = \frac{10}{2} = 5 \: cm \\ area \: of \: circle = \pi \: {r}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3.14 \times {5}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3.14 \times 5 \times 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3.14 \times 25 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 78.5 {cm}^{2} [/tex]

hope this helps...

Good luck on your assignment...

If triangle DEF has a 90° angle at vertex E, which statements are true? Select two options.
Triangle DEF is an obtuse triangle.
The angle at vertex D is acute.
The angle at vertex F is obtuse.
Triangle DEF is a right triangle,
The angle at vertex D is obtuse.

Answers

Answer:

The angle at vertex D is acute

Triangle DEF is a right triangle

Step-by-step explanation:

Acute means that the angle is smaller that 90degrees

Correct statement are,

The angle at vertex D is acute.

And, Triangle DEF is a right triangle,

What is mean by Angle?

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

We have to given that;

Triangle DEF has a 90° angle at vertex E.

Since, In triangle DEF,

vertex E has 90 degree.

So, Possible value of angle E and F are less than 90 degree

Hence, The angle at vertex D is acute.

And, Triangle DEF is a right triangle,

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I NEED HELP ASAP Which equation is equivalent to: −10r−6=115
A. 10r=−115+6
B. −10r=115+6
C. −10r=115−6
D. 10r=115−6

Answers

You answer is B

-10r=-115+6
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