[10 points]
find the range of each of the following function. All the function are definied for all values of x.

f(x) = 3(x+5)² +2

Can you give the answer and explanation?
what does 'all the function are definied for all values of x'?

Heldpdlsoemss​

Answers

Answer 1

Answer:

y ≥ 2

Step-by-step explanation:

The range is all of the values that f(x) can have. In order to find the range, let's first find the vertex. That's pretty easy to do since f(x) is already written in vertex notation (vertex notation is f(x) = a(x - c)² + d where (c, d) is the vertex). Since c = -5 and d = 2, the vertex is (-5, 2). Because the value of a is positive (a = 3 in this case, which is positive) we know that the parabola opens upward, therefore the vertex is the minimum. This means that the y-coordinate of the vertex is the smallest possible y-value of the function, therefore, since the y-coordinate of the vertex is 2, the range is y ≥ 2. Note that we use ≥ and not >, this is because y can be 2, therefore, it is included in the solution set.

Answer 2

Answer:

Hey there!

First, we must understand what range is. Range is just another word for all the possible y values of the equation.

This equation, f(x) = 3(x+5)² +2 is in vertex form. We see that this creates a parabola with a vertex at (-5, 2) and opens up.

Thus, the range of this graph would be: [2,∞) in interval notation. Note, the [ is used for greater than or equal to, or less than or equal to, and the ")" is used for less than or greater than.

We use ) for ∞, because ∞ is just a concept, not a real number.

Finally, all functions are defined for all values of x means that this is an f(x) function, and the f(x) is equal to something that can be written in terms of x.

Let me know if this helps :)


Related Questions

5-2(2x - 3) = 12

Cual es el resultado de x?

Answers

Answer:

[tex]x = - \frac{1}{4} [/tex]

Step-by-step explanation:

5-2(2x - 3) = 12

Expanda los términos en el corchete

Eso es

5 - 4x + 6 = 12

Agrupar términos similares

Envíe las constantes al lado derecho de la ecuación y aquellas con variables al lado izquierdo

Tenemos

- 4x = 12 - 5 - 6

- 4x = 1

Divide ambos lados entre - 4

[tex] - \frac{4x}{ - 4} = - \frac{1 }{4} [/tex]

Tenemos la respuesta final como

[tex]x = - \frac{1}{4} [/tex]

Espero que esto te ayude

1
Which sentence contains a spelling error?
A. Kallie possesses a good sense of humor, but she can be very mischievous at times.
OB.
You don't need to keep your receipt because the computer will record the transaction.
C. Tina's mother is a promanent member of the Volunteers Association of America.
OD
The movie will portray the life and death of Lieutenant Colonel Rodriquez-Smith.
Reset
Submit

Answers

Answer:

D prominent is spelled wrong that's how you spell it

Step-by-step explanation:

A manufacturer drills a hole through the center of a metal sphere of radius R = 8. The hole has a radius r. What value of r will produce a ring whose volume is exactly half the volume of the sphere? (Round your answer to two decimal places.)

Answers

Answer:

New radius(r) = 3.65 (Approx)

Step-by-step explanation:

Given:

Radius of sphere(R) = 8

Find:

New radius(r)

Computation:

Volume of sphere = (4/3)πR³

Volume of sphere = (4/3)π(6)³

Volume of sphere = 288π

Volume of ring = (4/3)π(R²-r²)³/²

Half volume of sphere = Volume of ring

288π / 2 = (4/3)π(R²-r²)³/²

144 = (4/3)(6²-r²)³/²

108 = (6²-r²)³/²

New radius(r) = 3.65 (Approx)

How do I solve for y in this equation? 3xy-28=15x

Answers

Answer:

  x = 28/(3y -15)

Step-by-step explanation:

Put the x-terms on the same side of the equal sign and everything else on the other side. Divide by the coefficient of x.

  3xy -28 = 15x . . . . . . given

  -28 = 15x -3xy . . . . . subtract 3xy

  -28 = x(15 -3y) . . . . . factor out x

  -28/(15 -3y) = x . . . . . . divide by the coefficient of x

We prefer to have a positive sign where possible, so we can multiply this by -1/-1 to get ...

  x = 28/(3y -15)

URGENT!!! What is the real part of 4−5i?

Answers

Answer:

  4

Step-by-step explanation:

The real part of a complex number is the part that does not have "i" as a factor.

Here, the real part is 4.

What’s the measure of X in this short answers are fine

Answers

Answer:

28 = x

Step-by-step explanation:

62 =  angle BAC  since they are vertical angles

angle ABC is a right angle since KL is perpendicular to FG

Adding the angles in triangle ABC

BAC + ABC + BCA = 180

62 + 90 + BCA = 180

152 + BCA = 180

BCA = 180-152

BCA = 28

BCA = x since they are vertical angles

28 = x

Evaluate the expression when m = 4 and n = 7.
n+5m

Answers

Answer:

27

Step-by-step explanation:

If you substitute the two give numbers and follow BEDMAS, you can calculate the answer.

n+5m

n = 7 and m = 4

=(7)+(5(4))

=7+20

=27

1а - За =
o4a
O
-2а
О2а
О-4а

Answers

Answer:

-2a

Step-by-step explanation:

[tex]1a - 3a \\ = - 2a[/tex]

Use the number line below, where RS = 7y +5, ST = 2y + 7, and RT = 14y - 28.
a. What is the value of y?
b. Find RS, ST, and RT.

Answers

Answer:

a. 8

b. 61, 23, 84

Step-by-step explanation:

As we can see, point S is between points R and T, therefore:

RS + ST = RT7y + 5 + 2y + 7 = 14y - 289y + 12 = 14y - 2814y - 9y = 12 + 285y = 40y = 40/5y = 8

------------

RS = 7y+5 = 61ST = 2y + 7= 23RT = 14y - 28 = 84

A van can travel 18 miles on each gallon of gasoline. At that rate, how many miles can the van travel on 15 gallons of gasoline? -33 miles -83 miles -120 miles -270 miles

Answers

Answer:

Hey there!

1 gallon of gas is equal to 18 miles of road.

15 gallons of gas is equal to 18(15) miles, or 270 miles of road.

Let me know if this helps :)

Answer:

D) because if you take 18 times 15 you would get 270

Step-by-step explanation:

Stay safe, positive, and healthy C:

Have a wonderful morning c:

Identify the number that does not belong with the other three. Explain your reasoning (24 points)​

Answers

Answer:

See explanation

Step-by-step explanation:

The number that would not belong is [tex]\sqrt{48}[/tex] since it is irrational

Answer:

[tex]\sqrt{48}[/tex]

Step-by-step explanation:

Looking at the numbers, we can see that the first number, third, and fourth number are all rational numbers since they either repeat or terminate.

On the other hand, let's try and simplify the square root of 48:

[tex]\sqrt{48}=\sqrt{16\cdot3}=\sqrt{16}\cdot\sqrt3=4\sqrt3[/tex]

The square root of 3 is irrational. Therefore, 4 times the square root of 3 is also irrational. All of the given numbers are rational instead of the second one. So, the second number does not belong .

negative plus a positive equals

Answers

Answer:  multiplied together or divided, the answer is positive. If two negative numbers are multiplied together or divided, the answer is positive.

Step-by-step explanation:

The result of adding a negative number and a positive number will depend on the magnitude of the two numbers and which one is larger.

What is the Subtraction operation?

Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

In mathematics, adding a negative number and a positive number involves combining two quantities with opposite signs. When we add a negative number and a positive number, we can think of it as "subtracting the absolute value of the negative number from the positive number."

For example, if we have -3 + 5, we can rewrite it as 5 - 3, which equals 2. In this case, we are subtracting the absolute value of the negative number (3) from the positive number (5).

Similarly, if we have -7 + 2, we can rewrite it as 2 - 7, which equals -5. In this case, we are subtracting the absolute value of the negative number (7) from the positive number (2), but since the negative number has a larger absolute value, the result is negative.

So, the result of adding a negative number and a positive number will depend on the magnitude of the two numbers and which one is larger.

Learn more about subtraction here:

https://brainly.com/question/1927340

#SPJ2

The complete question is as follows:

What is a negative plus a positive?

don’t understand why I have to type a question each time when I have a picture but anyone know this?!

Answers

Answer:

3/8

Step-by-step explanation:

There are 8 boxes and 3 shaded columns

[tex]\frac{3}{4}\times \frac{1}{2} \\\\=\frac{3\times \:1}{4\times \:2}\\\\=\frac{3}{4\times \:2}\\\\=\frac{3}{8}[/tex]

Answer:

Hey there!

The correct answer is 1/2(3/4)=3/8

Hope this helps :)

x to the second power plus 4equals 40 solve for x

Answers

x^2 + 4 = 40

x^2 = 36

6^2 = 36

x = 6

Peter withdrew 1000 dollars from his bank account today. He uses 500 to fix his car. Then, he divided the money into 5 equal parts and gave away 4 parts and kept 1 part for himself. Finally, he took his wife to the restaurant and spent 60 dollars on meals. Write a numerical expression to represent this situation and then find how much money Peter has now?

Answers

Answer:

ok he has $40 left

Step-by-step explanation:

1000-500 = 500

500 - 400 = 100

100-60 = 40

Answer:

Money with Peter = $ 40

Step-by-step explanation:

Let 'x' be the money left with Peter

Money left with Peter after fixing his car = 1000 - 500 = 500

500 is divided into 5 equal parts and 4 parts he gave away. 500 - 400 = 100

x = (1000 - 500) - 400 - 60

= 500 - 400 - 60

= 100 - 60

x =$  40

25b +15b combine like terms

Answers

Answer:

40b

Step-by-step explanation:

25 + 15 = 40

Answer:

40b

Step-by-step explanation:

We are given the expression:

25b+15b

and asked to simplify.

To simplify, we must combine like terms. Let's analyze the terms.

25b ⇒ has a variable "b"

15b ⇒ also has a variable "b"

The like terms in this expression are the terms with a variable, b.

To combine like terms, add the coefficients and leave a b on the end.

(25+15)*b

(40)*b

40b

The expression 25b+15b simplified is 40b.

Simplify. (3i + 2) + (4 i+ 3) =

Answers

Answer:

5+7i

Step-by-step explanation:

associative prop of addition

then simply add

You are told a professional cyclist eats around 5120 calories everyday for the Tour de Abroad. Estimate how many calories a cyclist would eat during a 21 day race

Answers

Answer:

Total calories eat = 107,520 calories

Step-by-step explanation:

Given:

Number of calories everyday = 5120 calories

Number of days = 21

Find:

Total calories eat

Computation:

Total calories eat = Number of calories everyday × Number of days

Total calories eat = 5120 × 21

Total calories eat = 107,520 calories

What is the term, coefficient, constant, and factor of 1/2(base1 + base2)h? (Formula used to find area of trapezoid)

Answers

Answer:

i. Term = [tex]\frac{b_{1}h }{2}[/tex] + [tex]\frac{b_{2}h }{2}[/tex]

ii. Coefficient = [tex]\frac{1}{2}[/tex]

iii. Constant = [tex]\frac{1}{2}[/tex]

iv. Factor = [tex]\frac{h}{2}[/tex]

Step-by-step explanation:

A trapezoid is a quadrilateral which has its base parallel to the opposite side. It's area can be determined by;

Area of trapezium = [tex]\frac{1}{2}[/tex] ([tex]b_{1}[/tex] + [tex]b_{2}[/tex])h

Where [tex]b_{1}[/tex] is the measure of length of its fist base,  [tex]b_{2}[/tex] is the measure of its second base and h is its height.

Considering the given question,

Term = [tex]\frac{b_{1}h }{2}[/tex] + [tex]\frac{b_{2}h }{2}[/tex]

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

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

Factor = [tex]\frac{h}{2}[/tex]

describe a situation with an output of area in square feet that can be modeled using the function f(x) = (x)(2x + 5)

Answers

Answer: The  length of a rectangle is 5 more than two times the width. If the width of the rectangle  is represent by x  then what is the area of the rectangle?  

Step-by-step explanation:

Answer: 3 feet

Step-by-step explanation: The area of a rectangular garden can be represented by the function

f(x) = x(2x + 5)

Find the area if the length, x, is 3 feet.

What property allows us to multiply or
divide by one whole to make an equivalent
fraction?

Answers

Answer:

Identity Property of Multiplication

Step-by-step explanation:

Required

State with property that describes the question

I'll answer this question using the following instances;

[tex]1.\ \frac{x}{3} = 1[/tex]

[tex]2.\ 3x = 1[/tex]

For the first expression, we multiply both sides by 3

[tex]3 * \frac{x}{3} = 1 * 3[/tex]

[tex]x = 1 * 3[/tex]

[tex]x = 3[/tex]

For the second; divide both sides by 2

[tex]\frac{3x}{3} = \frac{1}{3}[/tex]

[tex]x = \frac{1}{3}[/tex]

The property applied in both expressions is the identity property of multiplication

what is the length of a rectangle with width 16 in. and area 120 in^2

Answers

Answer:

It will have to be 7.5 inches.

Step-by-step explanation:

120 divided by 16 is 7.5 inches.

Answer:

Hey there!

A=LW

120=L16

L=7.5 in

Let me know if this helps :)

A 50 ft pole has a support wire that runs from its top to the ground with an angle of depression of 75°. To the nearest tenth of a foot, how much wire is used? Enter a number answer only.

Answers

Answer:

Step-by-step explanation:

Given:

height of pole = 50 ft

angle of depression = 75°

to find:

how much wire is used

Solution:

Let x be the wire used

sin 75° = 50/x

x = 50/sin 75°

  = 50 / 0.9659

  = 51.765

x = 51.8 ft

Hari borrowed Rs. 126000 from a money-lender at 15% per annum simple interest,
After 3 years, he paid Rs. 70700 and gave a buffalo to clear off the debt. What is the
cost of the buffalo?​

Answers

Answer:

Rs. 112000

Step-by-step explanation:

Borrowed money = Rs. 126000Interest rate = 15% PA simpleTime = 3 years

Hari is due to pay after 3 years:

126000* (1+ 3*15/100) = 182700

He pays Rs. 70700, remaining money is cleared by giving buffalo.

Cost of buffalo:

182700 - 70700= Rs. 112000

Answer is: Rs. 112000

Answer:

Solution,

principal(P)= Rs. 126000

Rate(R)=15%

Time(T)=3 years

Money paid=Rs.70700

Cost of buffalo=?

We know that,

                          Interest=P*T*R

                                           100

                                       = Rs. 126000*3*15

                                                         100

                                       = Rs. 56700

Now,

         Amount(A)=P+I

                           =Rs. ( 56700+126000)

                           = Rs.182700

Again,

          by the question,

                                    Cost of buffalo= Amount- Money paid

                                                             = Rs.(182700- 70700)

                                                              = Rs. 112000

Therefore, the cost of buffalo is Rs. 112000.

PLEASE HELP What is 16,448 written in scientific notation? A. 1.6448 x 10 B. 16.448 x 10 C. 1.6448 x 10 D. 1.6448 x 10

Answers

Answer:

1.6448 * 10^4.

Step-by-step explanation:

16448

There are 4 digits after the first so the exponent is 4.

1.6448 * 10^4.

an eraser company needs to ship erasers in bags of 780 plus or minus 9 erasers. what is the minimum and maximum erasers that could be in a bag?

Answers

Answer:

the minimum is 771 erasers while the maximum is 789 erasers

Step-by-step explanation:

you move 2 units and down 9 units. you end at (5, -5). where did you start​

Answers

3,10 is the answer in pretty sure
(3, 4) is where you started.

John and 4 friends are going out for pizza. They split one pizza and
5 drinks. The pizza cost $12.50 and they spent a total of $19.25.

Answers

Answer:

Step-by-step explanation:

If you are asking how much money were the drinks?

Then, the answer is $6.75. This is because 19.25 - 12.50 = 6.75

If you are asking how much money per drink, then the answer is $1.35

What is the question? If they’re asking how much each drink cost then the answer would be: $1.35 because you have to subtract $19.25-12.50=6.75 and then you divide that by the number of drinks which would be 6.75/5=$1.35

the area of a triangle is 54 cm. if the height is 3 cm more than the base, find the length of base​

Answers

it's 9 because 54/3 is 18 and that divided by 2 is the answer

A particular beach is eroding at a rate of 4 centimeters per year. A realtor converts this rate to millimeters per day. Which expression, when evaluated, results in the correct units and numerical value? algebra

Answers

Answer:

4cm        10mm         1year

         x               x                             its fractions

1 year       1cm        365days

Step-by-step explanation:

its all fractions

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