Which function is a quadratic function?

Which Function Is A Quadratic Function?

Answers

Answer 1
Answer:

The function which is quadratic is:

           [tex]y-3x^2=3(x^2+5)+1[/tex]

Step-by-step explanation:

We know that the general equation of a quadratic function is given by:

[tex]y=ax^2+bx+c[/tex]

where a , b and c are real numbers.

1)

[tex]y-3x^2=3(x^2+5)+1[/tex]

On solving we get:

[tex]y-3x^2=3x^2+15+1\\\\\\y=3x^2+3x^2+1+15\\\\\\y=6x^2+16[/tex]

Hence, the function is quadratic.

2)

[tex]y^2-7x=2(x^2+6)+7[/tex]

It is not a quadratic equation since we have a term as : [tex]y^2[/tex]

and hence the equation will not match the general equation of the quadratic function.

3)

[tex]y-2x^2=6(x^3+5)-4[/tex]

as it has a term of [tex]x^3[/tex]

Hence, it is a equation of a cubic function.

4)

[tex]y-5x=4(x+5)+9[/tex]

On solving we get:

[tex]y=9x+29[/tex]

It does not has any term of [tex]x^2[/tex]

Hence, the equation is not a quadratic function it represent a linear function.

Answer 2

The functions that are quadratic functions are [tex]y - 3x^2 = 3(x^2+5)+1\\[/tex] and [tex]y^2-7x= 2(x^2+6) +7[/tex].

The highest power of the polynomial is called the degree of the polynomial. The polynomial of degree two is called a quadratic polynomial.

According to the question,

1)

[tex]y - 3x^2 = 3(x^2+5)+1\\ y = 3x^2+ 15 + 3x^2 +1\\ y = 6x^2 +16[/tex]

Since the polynomial is of degree 1, It is a quadratic function.

2)

[tex]y^2-7x= 2(x^2+6) +7\\y^2= 2x^2 +7x+19[/tex]

The function is a quadratic function.

3)

[tex]y - 3x^2= 6(x^3+5)-4[/tex]

The degree of x is 3, so it is a cubic function.

4)

[tex]y - 5x = 4(x+5)+9 y \\= 4x + 5x+ 29y\\ = 9x+29[/tex]

The function is a linear function.

The functions which are quadratic equations are [tex]y - 3x^2 = 3(x^2+5)+1\\[/tex]and  [tex]y^2-7x= 2(x^2+6) +7[/tex] .

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Related Questions

What features do all right triangles have in common

Answers

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷The answer is that there is a right angle(90 degrees) and also there are three sides.

Explanation: Since all right triangles have a right angle, and also is a triangle, they have three sides and one is 90 degrees.

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

DOGE

The common features of all the right angled triangles are the highest angle is the right angle (90°), Pythagorean theorem is applicable.

What is a triangle?

Any figure bounded by 3 sides and the sum of all the internal angles is 180° is called a angled triangle.

What is a right angled triangle?

Any triangle whose one angle is 90° is called a right angled triangle.

How to find what features do all right triangles have in common?

The common features of all the right angled triangles are discussed below:

All the right angled triangles have one angle 90°.The side opposite to the right angle( 90° ) is the longest and is called the hypotenuse.Pythagorean Theorem is applicable which says that squares of the length of the hypotenuse is equal to the sum of the squares of the lengths of the base and perpendicular.

These are the common features.

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which of the following sets does the number 3.14 belong to ? -whole number , integers, rational numbers , irrational numbers, real numbers, non of the above . Select all that apply . ​

Answers

The number 3.14 is a rational number and since all rational numbers are real numbers, it is a real number too.

The set of numbers that 3.14 belongs to is a rational number and a real number.

A rational number simply means a number that has a whole number and a quotient. In this case, such a number has a whole number and decimal fractions.

Therefore, since the number given is 3.14, this implies that the number is a rational number. Also, it should be noted that a rational number is also a real number.

Therefore, 3.14 is a rational number and a real number

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Given: circle k(O), m AM=125°, m EF=31°, m∠MAF=75°. Find: m∠AME

Answers

Answer:

58°

Step-by-step explanation:

If m AM=125°, then m∠AOM=125°.

If m∠MAF=75°, then m∠MOF=150° (because central angle MOF subtends on the same arc as inscribed angle MAF).

Thus,

m∠FOA=360°-150°-125°=85°.

If mEF=31°, then m∠EOF=31° (as central angle subtended on the arc EF).

Hence,

m∠EOA=m∠EOF+m∠FOA=31°+85°=116°.

Angle EOA is central angle subtended on arc EA, angle AME is inscribed angle subtended on arc AE, thus

m∠AME=1/2m∠EOA=58°.

The elevations of three cities in the Netherlands are shown below. Which comparison is true?

Answers

Answer:

The answer is the first choice "A"

Step-by-step explanation:

I have done this test

The comparison which is true is Amsterdam is the same distance from sea level as Drachten.

How to find which comparison is true?Here negative sign indicates the direction.

So, we can see the Amsterdam is at same distance from sea level as Drachten. The negative sign indicates that Amsterdam is 2 m below the sea level.

So, option A is correct.

Drachten is 2 m higher then the sea level and is clearly higher than Rotterdam which is 4 m below the sea level.

So, option B is incorrect.

The distance of Rotterdam from sea level is 4 m whereas that of Drachten is 2 m. So the distance of Rotterdam from sea level is greater than that of Drachten.

So option C is incorrect.

Rotterdam which is 4 m below the sea level and is clearly lower than Amsterdam which is 2 m below the sea level.

So option D is incorrect.

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Last year Jo paid £245 for her car insurance. This year she has to pay £883 for her car insurance. Work out the percentage increase in the cost of her car insurance.

Answers

Answer:

260%

Step-by-step explanation:

To solve how much the percentage increase cost of Jo's car insurance is, we first need to list down our variables.

1st year = £245

2nd year = £883

First off, we need to find the difference of the two.

Increase = £883 - £245

Increase = £638

Now to find the percentage increase, we take our increase and divide it by our 1st year's payment and multiply it by 100.

Percentage increase = [tex]\dfrac{638}{245}*100[/tex]

Percentage increase = [tex]2.60*100[/tex]

Percentage increase = 260%

So the percentage increase of last years payment to this years payment is 260%.

Apply the definition of subtraction and properties of operations to find the result.



1/8-3/7-1/8

Answers

Final answer:

To find the result of 1/8 - 3/7 - 1/8, we need to find a common denominator for the fractions and then subtract them.

Explanation:

To find the result of 1/8 - 3/7 - 1/8, we need to apply the definition of subtraction and properties of operations. First, let's find a common denominator for the fractions. The common denominator for 8 and 7 is 56. Multiply the numerator and denominator of 1/8 by 7 to get 7/56. Multiply the numerator and denominator of 3/7 by 8 to get 24/56. Now subtract the fractions: (7/56) - (24/56) = -17/56. Finally, subtract 1/8 from -17/56. Multiply the numerator and denominator of 1/8 by 7 to get 7/56. Subtract the fractions: (-17/56) - (7/56) = -24/56.

1.) In a class of 45 students , 80% received A’s on a Math test . How many students received an A?


2.) Mary spent 15 dollars. If this was 20% of her earnings, how much money did she earn ?

Answers

Step-by-step explanation:

1) 45 times 0.8 (which is equivalent to 80 percent) is 36 students.

2) 15 divided by 0.2 is 75, so she earned 75 dollars

Smart growth is an urban planning theory that promotes the development of suburbs surrounding major city centers.



True or False

Answers

the answer is false, i hope this helps

Answer:

The given statement is false.

Step-by-step explanation:

Smart growth is an urban planning theory that promotes the development of suburbs surrounding major city centers.

Rather smart growth is defined as a well planned economic development and community development with an aim to curb urban fall out and reduce the worsening environmental conditions.

Plz help me!!!!!!!!!!!

Answers

imaginary, you cannot form the square root of a negative #

Answer:  c) imaginary

Step-by-step explanation:

(√5) is irrational but (√-1 )is not a valid number, therefore, (√-5) is imaginary.

How long does it take for a deposit of $1400 to double at 2% compounded continuously?

Answers

Answer:

34.66 yr

Step-by-step explanation:

The formula for interest compounded continuously is

[tex]A = Pe^{rt}[/tex]

Data:

P = $1400

r = 2 % = 0.02

Calculations:

(a) Calculate A

A = 2 × 1400 = $2800

(b) Calculate t

 [tex]2800 = 1400e^{0.02t}[/tex]

        [tex]2 = e^{0.02t}[/tex]     Divided each side by 1400

 ln2 =  0.02t               Took the ln of each side

     t = ln2/0.02          Divided each side by 0.02

     t = 34.66 yr

It will take 34.66 yr for the investment to double at 2 % interest compounded continuously.

Check:

2800 = 1400e^{0.02×34.66}

2800 = 1400e^{0.6931}

2800 = 1400 × 2

2800 = 2800

WHich choice is equivalent to the expression below? √-125

Answers

Answer:

Final simplified form is [tex]5\sqrt{5}i[/tex]

Step-by-step explanation:

We have been given an expression [tex]\sqrt{-125}[/tex]

Now we need to simplify [tex]\sqrt{-125}[/tex] and check which choice matches with simplified form of [tex]\sqrt{-125}[/tex].

You missed to provide the choices but still we simplify that.

[tex]\sqrt{-125}[/tex]

[tex]=\sqrt{-5*5*5}[/tex]

[tex]=5\sqrt{-5}[/tex]

When there is negative sign inside square root then we replace that by "i" iota.

[tex]=5\sqrt{5}i[/tex]

Hence final simplified form is [tex]5\sqrt{5}i[/tex]

Lisa has 2 red dresses, 3 green dresses and x blue dresses hanging in her closet. If lisa chooses one dress at random, the probability that lisa will choose a red dress is 25%. How many blue dresses does lisa have?

Answers

Final answer:

Lisa has a total of 8 dresses in her closet. There are 2 red dresses, 3 green dresses, and the remaining 3 are blue dresses.

Explanation:

The subject of the question is probability in Mathematics. In the problem, Lisa has a total of 2 red dresses and 3 green dresses. The quantity of blue dresses is represented by 'x'. It is stated that the probability of choosing a red dress is 25%. Each dress in her closet is an outcome for this probability calculation.

So, in total, she has 2(red dresses) + 3(green dresses) + x(blue dresses) = 100% of the dresses or total outcomes. Since the probability of picking a red dress is 25%, then 2 (red dresses) are 25% of the total outcomes.

To work out the total number of outcomes (total dresses), we calculate 100% ÷ 25% = 4, and then multiply this by the number of red dresses (which is 2), giving us 4*2 = 8 dresses in total.

As we know there are 2 red dresses and 3 green dresses, that leaves 8 (total dresses) - 2 (red) -3 (green) = 3 blue dresses. Thus, Lisa has three blue dresses in her closet.

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Final answer:

Lisa has 6 blue dresses.

Explanation:

To find the number of blue dresses Lisa has, we need to set up an equation using the given information.

Lisa has 2 red dresses, 3 green dresses, and x blue dresses. The total number of dresses is 2 + 3 + x = 5 + x.

The probability of choosing a red dress is 25%, which can be written as 0.25.

This means that the number of red dresses divided by the total number of dresses equals 0.25. So, we have 2 / (5 + x) = 0.25.

Solving this equation for x, we find that Lisa has 6 blue dresses.

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i dont understand the question for D can someone please explain it ​

Answers

Answer:

71°

Step-by-step explanation:

The average temperature is calculated as

Average = [tex]\frac{sum}{count}[/tex]

let x be the temperature in October, then

[tex]\frac{25+70+65+85+92+82+x}{7}[/tex] = 70, that is

[tex]\frac{419+x}{7}[/tex] = 70 ( cross- multiply )

419 + x = 490 ( subtract 419 from both sides )

x = 71

Average temperature in October was 71°

What is the wavelength of a sound wave that has a speed of 250 m/s and a frequency of 400 Hz?

I will give brainest if you help me asap! 15 POINTS!!

Answers

0.50 m *100 Hz

= 50m/s I really hope this helps!

The density of a fish tank is 0.5 fish per feet3. There are 30 fish in the tank. What is the volume of the tank

Answers

Answer:

60 cubic feet.

Step-by-step explanation:

The fish are 0.5 per cubic foot. This means 1 fish occupies 2 cubic feet. So if there are 30 fishes then there must be 60 cubic feet.

Answer:Instead of dividing the diameter by two to get the radius, the coworker multiplied the diameter by two, getting a value of 340 feet for the radius. Here’s the incorrect calculation:

volume of a cylinder ≈ 3.14 × (radius)2 × height

= 3.14 × (340 ft)2 × (60 ft)

= 3.14 × (115,600 ft2) × (60 ft)

= 21,779,040 ft3

Step-by-step explanation:

Miss Penny inherits £390. She decides to save some of the money and spend the rest.
The ratio of savings to spending money is 5 : 8
How much does she save and how much does she spend?

Answers

Answer:

saving=150

spending=240

Step-by-step explanation:

390/13=30

savings=30*5

spending=30*8

Answer:

£150 saved; £240 spent.

Step-by-step explanation:

If the ratio of savings to spending is 5:8, we find the fractions representing the amount saved and the amount spent by adding up 5 and 8 and then forming fractions:

savings:  5/13

spending:  8/13

(5/13) of £390 is £150; this is the amount saved.

(8/13) of £390 is £240; this is the amount spent.

Find the area of the circle? Use 3.14 for pi.

Answers

Answer:

A = 50.24 mm

Step-by-step explanation:

A = Pi*r^2

A = Pi*(4)^2

A = 16*Pi

A = 50.24 mm

Best regards

Answer:

50.24

Step-by-step explanation:

area of circle: (pi)r^2

r is the radius

given: r = 4

pi = 3.14

3.14(4)^2

3.14*16

50.24

the value of y varies directly with x, and when x = 1/4 , y = 25. What is the value of y when x is 2 1/3 need help ASAP

Answers

Answer:

[tex]y=233\frac{1}{3}[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In this problem we have

For [tex]x=1/4, y=25[/tex]

Find the value of k (constant of proportionality)

[tex]y/x=k[/tex] -----> [tex]k=25/(1/4)=100[/tex]

The linear equation is

[tex]y=100x[/tex]

Find the value of y when the value of [tex]x=2\frac{1}{3}[/tex]

substitute the value of x in the equation but first convert to an improper fraction

[tex]x=2\frac{1}{3}=\frac{2*3+1}{3}=\frac{7}{3}[/tex]

[tex]y=100(\frac{7}{3})=\frac{700}{3}[/tex]

convert the result in mixed number

[tex]\frac{700}{3}=\frac{699}{3}+\frac{1}{3}=233\frac{1}{3}[/tex]

area of 2 triangles area of 3 rectangles surface area= total area of triangles and rectangles. the surface area

Answers

What do you mean? I dont understand.

Answer:

52.8cm

Step-by-step explanation:

Add the area of all the faces together and you get 52.8

The red line below is perpendicular to which of the following

Answers

Answer:

The y axis

Step-by-step explanation:

Perpendicular means for a line to create a 90 degree angle, like it does on the y axis.

Hope this helps!

Rugs sell for $8 per square foot Beth bought a 9-foot-long rectangular rug for $432 how wide was the rug

Answers

6 feet.



First, divide $432 by $8 to find the number of square feet.

You get 54 square feet.

Now, just divide by 9 feet to find the width.

54 / 9 = 6

The rug was 9 ft by 6 ft.

HELP URGENT! WILL GIVE BRAINLIEST!!

1) What is the value of 8!?

A) 8
B) 64
C) 512
D) 40,320

2) What is the value of 5P5?

A) 5
B) 25
C) 120
D) 125

3) What is the value of 8P4?

A) 40,320
B) 1,680
C) 32
D) 24

4) What is the value of 7P7?

A) 1
B) 14
C) 49
D) 5,040

5) Four out of nine performers will be chosen to in a row on stage. How many ways can the 4 performers stand in a row?

A) 362,880
B) 347,760
C) 15,120
D) 3,024

Answers

Answer:

1) 8    2) 125   3) 1,680   4) 5,040   5) 3,024

Step-by-step explanation:

Answer:

FRee points man idc about the question

Austin reads 8 books. He reads 4 more books than Emily. How many books does Emily read?

Answers

Answer: 4

Step-by-step explanation: Austin reads 8 he reads 4 more. 4+4=8

What is the distance ?

Answers

The solution is you need to subtract the y axis and x axis

A photograph measures 10 in. wide by 18 in. long. The picture is reduced so that the length is 6 in.
What is the new width?
a: 13 in
b: 313 in
c: 1045 in
d: 30 in
explain your answer please

Answers

Answer:

Step-by-step explanation:

The length has been reduced to 6 inches from 18 inches.

That means the length has been reduced to 6/18 = 1/3 of its original size.

So the width must be reduced to 1/3 * 10 which is roughly 3.333 inches.

It doesn't look like any of them are right. i don't know how to make it right from the answers given.

Jonas has two jobs last year and he received two W-2 forms on the first W-2 form the figure in box 1 was $19,328.98 while on second W-2 form the figure in box 1 was $7174.86 what was Jonas gross income from the two jobs last year?

Answers

Answer:

Gross income of Jonas from the two jobs is $ 26,503.84

Step-by-step explanation:

W-2 form is used in USA by to employees to show the money earned by them.

The gross income of Jonas will be the sum of two values.

Gross income= $19,328.98  + $7174.86

                      = $ 26,503.84

Answer:

$26,503.84

Step-by-step explanation:

What is the y intercept of the function f(x) = -2/3x + 1/3

Answers

Answer:

(0, 1/3)

Step-by-step explanation:

You find the y-intercept when the x value is 0, so plug in 0 for x and simplify

f(x) = -(2/9)(0) + 1/3

f(x) = 1/3

The y-intercept is at the point (0, 1/3)

huong and kathyrn each day impeoved their yards by planting rose bushes and ornamental grass. they bought their supplies from the same store. huong spent $70on 14 rose bushes and 7 bunches of ornamental grass. kathyrn spent $71 on 5 rose bushes and 14 bunches of ornamebtal grasa. what is the cost of one rose bush and the cost od ine bunch of ornamental geass?​

Answers

Answer:

One rose bush = $3

One bunch of ornamental grass = $4

Step-by-step explanation:

We can set up a system of equations to solve for this. Let cost of 1 rose bush be r and cost of 1 ornamental grass be g. Thus we can form 2 equations:

[tex]14r+7g=70\\5r+14g=71[/tex]

We can multiply the first equation by -2 so that we can eliminate g. Thus, we have:

[tex](*-2)14r+7g=70\\5r+14g=71\\-------\\-28r-14g=-140\\5r+14g=71\\--------\\-23r=-69\\r=\frac{-69}{-23}=3[/tex]

Thus, 1 rose bush is $3. Now plugging in r = 3 into the first original equation, we can solve for g:

[tex]14r+7g=70\\14(3)+7g=70\\42+7g=70\\7g=70-42\\7g=28\\g=\frac{28}{7}=4[/tex]

Thus, 1 bunch of ornamental grass is $4.

What is the factorization or the trinomial below? -2x^3+2x^2+12x

Answers

The answer is C because the 2x outside of the brackers must be negative to produce the beginning term. The next terms are positive and two negatives make a positive, therefore we can conclude that there must be a negative inside the brackets too.

Answer: C. −2x(x−3)(x+2)

Step-by-step explanation:

1. Find the Greatest Common Factor (GCF).

GCF=2x

2. Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

2x(2x^3/2x+−2x^2/2x+−12x/2x)

3. Simplify each term in parentheses.

−2x(x^2−x−6)

4. Factor x^2−x−6

−2x(x−3)(x+2)

Jimmy pays $2.52 for each gallon of gas. Which table best represents the relationship between g, the number of gallons purchased, and m, the amount he pays for gas?

Answers

The table that best represents the relationship between the number of gallons purchased, g, and the amount paid for gas, m, will list m as multiples of $2.52 as per the linear relationship g: $2.52 * g.

Jimmy pays $2.52 for each gallon of gas. To find the best table representing the relationship between g, the number of gallons purchased, and m, the amount he pays for gas, we need to create a table where each entry form is the product of g and the price per gallon, which is $2.52.

For each gallon g, the total cost m would be:

For 1 gallon: m = 1 * $2.52 = $2.52

For 2 gallons: m = 2 * $2.52 = $5.04

For 3 gallons: m = 3 * $2.52 = $7.56

...and so on.

This pattern will continue since the relationship is linear, and the table representing it will list the total cost m corresponding to the number of gallons g based on this constant rate of $2.52 per gallon.

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