If the sum and product
of roots of a quadratic
equation are -7/2 and
5/2 respectively,then
the equation is :​

Answers

Answer 1

Answer:

The equation is y = 2x² + 7x + 5

Step-by-step explanation:

In the quadratic equation y = ax² + bx + c

The roots of it are the values of x at y = 0The sum of the two roots = [tex]\frac{-b}{a}[/tex]The product of the two roots = [tex]\frac{c}{a}[/tex]

∵ The sum of the roots is [tex]\frac{-7}{2}[/tex]

∵ The product of the roots is [tex]\frac{5}{2}[/tex]

→ By using the rules above

∴ [tex]\frac{-b}{a}[/tex] = [tex]\frac{-7}{2}[/tex]

∴ [tex]\frac{c}{a}[/tex] = [tex]\frac{5}{2}[/tex]

→ Compare between them

a = 2

∴ -b = -7 ⇒ divide both sides by -1

b = 7

c = 5

∵ The form of the quadratic function is y = ax² + bx + c

→ Substitute the values of a, b, and c in it

∴ y = 2x² + 7x + 5

The equation is y = 2x² + 7x + 5


Related Questions

The mean lifetime of a tire is 48 months with a standard deviation of 77 months. If 147 tires are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 0.83 months?

Answers

Answer:

0.55199

Step-by-step explanation:

When we have a random number of samples, We solve using z score formula

z = (x-μ)/σ/√n where

x is the raw score

μ is the population mean

σ is the population standard deviation

n is random number of samples

z = 0.83/77/√147

z = 0.13069

Probabilty value from Z-Table:

P(x<48.83) = 0.55199

The probability that the mean of the sample would differ from the population mean by less than 0.83 months is 0.55199

Refer to the accompanying data set and construct a ​% confidence interval estimate of the mean pulse rate of adult​ females; then do the same for adult males. Compare the results. Click the icon to view the pulse rates for adult females and adult males. Construct a ​% confidence interval of the mean pulse rate for adult females. nothing bpm nothing bpm ​(Round to one decimal place as​ needed.) Construct a ​% confidence interval of the mean pulse rate for adult males. nothing bpm nothing bpm ​(Round to one decimal place as​ needed.) Compare the results.
A. The confidence intervals​ overlap, so it appears that there is no significant difference in mean pulse rates between adult females and adult males.
B. The confidence intervals​ overlap, so it appears that adult males have a significantly higher mean pulse rate than adult females.
C. The confidence intervals do not​ overlap, so it appears that adult females have a significantly higher mean pulse rate than adult males.
D. The confidence intervals do not​ overlap, so it appears that there is no significant difference in mean pulse rates between adult females and adult males.

Answers

Complete Question

The complete question is shown on the first uploaded image

Answer:

The 95% confidence interval of mean pulse rate for adult female is [tex]71.98 <  \mu <  79.88 [/tex]

The 95% confidence interval of mean pulse rate for adult male is  [tex]62.89 <  \mu <  70.57 [/tex]

The correct option is  C

Step-by-step explanation:

  Generally the sample mean for Male pulse rate is mathematically represented as

       [tex]\= x_1 = \frac{\sum x_i }{n}[/tex]

= >    [tex]\= x_1 = \frac{81 + 74 + \cdots + 59 }{40 }[/tex]

= >    [tex]\= x_1 = 66.73[/tex]

Generally the standard deviation for male pulse rate is mathematically represented as

      [tex]\sigma_1 = \sqrt{\frac{\sum (x - \= x)^2 }{n-1 } }[/tex]

=>   [tex]\sigma_1 = \sqrt{\frac{\sum (81 - 66.73 )^2 + (74 - 66.73 )^2+ \cdot + (59 - 66.73 )^2 }{40-1 } }[/tex]

=>   [tex]\sigma_1 = 12.24[/tex]

From the question we are told the confidence level is  95% , hence the level of significance is    

      [tex]\alpha = (100 - 95 ) \%[/tex]

=>   [tex]\alpha = 0.05[/tex]

Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is  

   [tex]Z_{\frac{\alpha }{2} } =  1.96[/tex]

Generally the margin of error is mathematically represented as  

      [tex]E = Z_{\frac{\alpha }{2} } *  \frac{\sigma_1 }{\sqrt{n} }[/tex]

=>    [tex]E = 1.96 *  \frac{12.4 }{\sqrt{40} }[/tex]

=>    [tex]E =3.84 [/tex]

Generally 95% confidence interval is mathematically represented as  

      [tex]\= x_1 -E <  \mu <  \=x_1  +E[/tex]

=>    [tex]66.73 -3.84 <  \mu < 66.73 +3.84 [/tex]

=>    [tex]62.89 <  \mu <  70.57 [/tex]

  Generally the sample mean for Female pulse rate is mathematically represented as

       [tex]\= x_2 = \frac{\sum x_i }{n}[/tex]

= >    [tex]\= x_2 = \frac{81 + 94 + \cdots + 73 }{40 }[/tex]

= >    [tex]\= x_2 = 75.93[/tex]

Generally the standard deviation for Female  pulse rate is mathematically represented as

      [tex]\sigma_2 = \sqrt{\frac{\sum (x - \= x)^2 }{n-1 } }[/tex]

=>   [tex]\sigma_2 = \sqrt{\frac{\sum (81 - 66.73 )^2 + (94 - 66.73 )^2+ \cdot + (73 - 66.73 )^2 }{40 } }[/tex]

=>   [tex]\sigma_2 = 12.73[/tex]

Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is  

   [tex]Z_{\frac{\alpha }{2} } =  1.96[/tex]

Generally the margin of error is mathematically represented as  

      [tex]E = Z_{\frac{\alpha }{2} } *  \frac{\sigma_2 }{\sqrt{n} }[/tex]

=>    [tex]E = 1.96 *  \frac{12.73 }{\sqrt{40} }[/tex]

=>    [tex]E =3.95 [/tex]

Generally 95% confidence interval is mathematically represented as  

      [tex]\= x_2 -E <  \mu <  \=x_2  +E[/tex]

=>    [tex]75.93 -3.95 <  \mu < 75.93 + 3.95 [/tex]

=>    [tex]71.98 <  \mu <  79.88 [/tex]


Please help me please

Answers

Answer:

Step-by-step explanation:

110_5

The length of a rectangle is 97 meters and the width is 14 meters. Find the area. Give your answer without units.
Provide your answer below:

Answers

Use the formula, l•w (length times width)
The length is 97 and the width is 14
97•14=1358

The area of a rectangle is the product of length and width thus the area will be 1358 square meters.

What is a rectangle?

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

The perimeter of the rectangle = 2( length + width).

It is known that,

Area of rectangle = length × width.

Area = 97 x 14 = 1358 sqare meters

Hence "The area of a rectangle is the product of length and width thus the area will be 1358 square meters".

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How many 1 6 cup servings are in 3 4 cups of popcorn? (in simplest fraction form)

Answers

Answer: 8/17

Step-by-step explanation: 16 ÷ 34 = 8/17

Hope this helps ^_^

The average monthly cost of basic cable TV was $9.73 in 1985 and has increased by about $1.35 each year since then. Let t be the number of years since 1985.
1. Use function notation to write an equation giving the monthly cost of basic cable TV as a function of t.
f(t)=____t+____
2. Using the function from above what is the average monthly cost of basic cable TV for this year?
3. Using the function from 1, what year was the average monthly cost of basic cable TV $23.23?​

Answers

Answer:

$50.23

Step-by-step explanation:

f(t)=1.35(t)+9.73

First I found out how many years are after 1985 so you would do 2020-1985 which equals 30.

I plug it in for t.

f(t)=1.35(30)+9.73

Then you multiply 1.35 and 30 which would leave us with.

f(t)=40.5+9.73

Add them and you get $50.23

PLS HELP I WILL MARK BRAINLIEST SINCE YOIR WRITING FOR ME

Answers

The answer is -0.5
if you add 0.5 to -0.5 you will get 0
if you add 1.5 to -1.5 you will get 0
thus 0.5 is the answer due to it needing a lesser value to be added to obtain the value 0

Answer:

-0.5. -0.5 is to the right of -1.5

Complete the steps to solve 4.5 ÷ 0.5

Answers

Answer:

9

Step-by-step explanation:

4.5/0.5=9

9*0.5=4.5

hope this helps :3

if it did pls mark brainliest

Answer:

4.5 ÷ 0.5

45/10 ÷ 5/10

45/10 × 10/5

450/50

45/5

= 9

Step-by-step explanation:

Answer correctly and I will mark you brainless ❤️

Answers

The y intercept is b=7/1000

Lou deposited $3,500 into a savings account. The simple interest rate is 4%. How much interest will the account earn in 10 years?

Answers

Answer:

2 years : $280

10 years: $1400

Step-by-step explanation:

The amount of interest earned in 10 years will be $1,400.

What is simple interest?

Let P be the principal, R be the rate of interest, and T be the time. Then the interest rate is given as,

The formula for interest is written as,

I = (PRT)/100

$3,500 was put into a savings account Lou. 4% is the simple interest rate.

The amount of interest after 10 years is calculated as,

I = ($3,500 x 4 x 10) / 100

I = $1,400

The amount of interest earned in 10 years will be $1,400.

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Examine the equation. 4(x – 3) = 4x – 12 Which of the following is true? (Check all that apply.) It is a true statement. Any input will result in an equivalent equation. It is equivalent to an equation of the form a = a. It has no solution. Only one input will result in a true statement.

Answers

Answer:

A, B, and C.

Step-by-step explanation:

We have the equation:

[tex]4(x-3)=4x-12[/tex]

Let’s distribute the left. This yields:

[tex]4x-12=4x-12[/tex]

Let’s add 12 to both sides:

[tex]4x=4x[/tex]

And subtract 4x from both sides:

[tex]0=0[/tex]

We get the true statement 0=0.

Hence, A is correct.

Because it is a true statement, any input will yield an equivalent output.

Hence, B is also correct.

We also have the form a=a, where a is 0.

Hence, C is also correct.

Therefore, our correct answers are A, B, and C.

Answer:

It is a true statement.

Any input will result in an equivalent equation.

It is equivalent to an equation of the form a = a.

Maggie has a 2-gallon pitcher of lemonade. How many liters of lemonade did she make?

I'LL GIVE BRAINLIEST!

Answers

Answer:

2 gallons converted to liters is 7.57 or 8 liters rounded

Maggie made 2 more gallons

What is the constant of proportionality in the equation y = 5/9x

Answers

Answer:   5/9

This is assuming the equation is y = (5/9)x

Note it is in the form y = kx with k = 5/9 as the constant of proportionality.

A pool that is being drained contained 18,000 gallons of water. After 2 hours, 12, 500
Gallons of water remain. Write an equation in all 3 forms to model this situation,
HELLPPP PLLEASEEEE!!!!!

Answers

Answer:

y-18,000=2,750(x-0) --> point-slope

y=2,750x+18,000   --> slope-intercept

-2,750x + y = 18,000  --> standard

Step-by-step explanation:

Linear Modeling

Some situations can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.

The pool being drained contained initially 18,000 gallons of water. If we set the variable x as the time in hours and y as the remaining gallons of water in the pool, this first point is (0;18,000).

We are also aware that after 2 hours 12,500 gallons of water remain. This gives us the second point as (2;12,500).

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

Let's find the equation of the line with the 2 points:

[tex]\displaystyle y-18,000=\frac{18,000-12,500}{2-0}(x-0)[/tex]

Calculating:

[tex]\displaystyle y-18,000=\frac{5,500}{2}(x-0)[/tex]

[tex]y-18,000=2,750(x-0)[/tex]

The equation above is the point-slope form of the line

Simplifying and adding 18,000:

[tex]y=2,750x+18,000[/tex]

The equation above is the slope-intercept form of the line

Moving all the variables to the left side:

[tex]-2,750x + y = 18,000[/tex]

The equation above is the standard form of the line

Answer:

y-18,000=2,750(x-0) --> point-slope

y=2,750x+18,000   --> slope-intercept

-2,750x + y = 18,000  --> standard

The value of 100 pennies is ___% of the value of a dollar

Answers

Answer:

The type of coins =pennies  has = 100 pennies.

servant has a total number of 100 coins

The sum of the percentage and pennies = $100

Let us represent the number of nickels as which is _% = 55.4

The number of pennies as y

Step-by-step explanation:

PLEASE HELP URGENT WILL GOVE BRAINLIEST

Answers

it is b and there is no explanation

What type of number is 739?.
A. Neither
B. Prime
C. Composite ​

Answers

ANSWER

For 739, the answer is: prime anslo written as B

Step-by-step explanation:

739 is a prime number because it has only two distinct divisors: 1 and itself (739).

HAVE A GOOD DAY!

Answer:

its neither

Step-by-step explanation:

a pump moves 42 gallons in 7 minutes

Answers

Answer:

The correct answer is 6

Step-by-step explanation:

Divide 42 divided by 7 to get 6.

Answer:

What is the question?

Step-by-step explanation:

The pump moves 6 gallons in 1 minute

Divide 42 by 7 = 6

But I don't know the question so I can't tell you the best correct answer.

I just took a guess at what you wanted

Solve the equations:

2^(3x−4) = −2

Answers

Answer:

x=NaN your welcome hehe

Please help I will mark the brainiest answer please

Answers

Answer:

Part A 40

Part B 90

part C show your work

please mark brainliest i need it

Hope helps

^ABC is similar to ^EDC shown below.
Which equation could be used to determine x, the
length of CD?

Answers

Answer:

last one 12/8 = 9/X

Step-by-step explanation:

according to the rule of similarity in triangles

The equation that can be used to find the length of CD is 9/x = 12/8.

Where x is CD.

Option D is the correct answer.

What is a triangle?

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

ΔABC ≅ ΔEDC

We can write:

BC/BA = CD/DE

9/12 = x/8

9/x = 12/8

Thus,

The equation 9/x = 12/8 can be used to find x.

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To demonstrate probabilities, a mathematics teacher had students draw cards from a bag which contained 26 red cards and
26 black cards. During class, the bag was dropped, and 5 red cards and 1 black card were lost.
Tell whether the loss of cards changes the probability of drawing a black card from the bag.
If so, was the probability increased or decreased? Support your answer by calculating the probability for each situation.

Answers

Answer:

decreased

Step-by-step explanation:

Keith wants to plot -8 and -9 and on a number line. Which statement is true? *

Answers

Where the statements at lol

A 2-column table with 6 rows. Column 1 is labeled Tables with entries 1, 2, 3, 4, 5, 6. Column 2 is labeled Chairs with entries 6, 12, 18, 24, 30, 36.
Rachel needs two tables for her birthday party. How many chairs will she need?

Answers

i think the answer is The 1st table represents a function

Lets explain how to solve the problem

- Function is a relation where each input has a single output

- The notation of the function is f(x) = y , where x is the input of the

function and y is the out put of the function

-  The domain of the function is x and the range of the function is y

* Lets find which table represent a function

# First table:

     x      y

    -3      -1

     0      0

    -2      -1

- In the first table

∵ -3 has only -1

∵ 0 has only 0

∵ -2 has only -1

∵ 8 has only 1

∵ Every x has a single y

∴ The table represents a function

∴ The 1st table represents a function

- In the second table

   x       y

   -5       -5

    0       0

   -5       5

    6       -6

∵ x = -5 has y = -5 and y = 5

∴ One x has two values of y

∴ The table doesn't represent a function

- In the third table

    x          y

   -4         8

   -2         2

   -2         4

    0         2

∵ x = -2 has y = 2 and y = 4

∴ One x has two values of y

∴ The table doesn't represent a function

- In the fourth table

    x          y

   -4         2

    3         5

   -4         0

∵ x = -4 has y = 2 and y = 0

∴ One x has two values of y

∴ The table doesn't represent a function

Answer:

It is 12

Step-by-step explanation:

Sarah is training for a bike race. She rides her bike 5 3/4 miles in 1/3 hour. What is Sarah’s rate in miles per hour. Express your answer as a mixed number

Answers

Answer:no

Step-by-step explanation:

Answer:

17 [tex]\frac{1}{4}[/tex]

The cost of medical care abroad is often significantly less than in the United States. In 2014, the cost of knee replacement surgery in the United states was $34,000. This cost was $4000 more than four times the cost of knee replacement surgery in India. Find the cost of Knee replacement surgery in India.

Answers

Answer:

Cost in India: $7500

Step-by-step explanation:

Represent cost in India with I and cost in United States as U.

Given

[tex]U = 3400[/tex]

[tex]U = 4000 + 4 * I[/tex]

Required

Find I

Simply substitute 34000 for U in the second equation

[tex]34000 = 4000 + 4 * I[/tex]

[tex]34000 = 4000 + 4I[/tex]

Solve for 4I

[tex]4I = 34000 - 4000[/tex]

[tex]4I = 30000[/tex]

Solve for I

[tex]I = 30000/4[/tex]

[tex]I = 7500[/tex]

Hence, the cost in India is $7500

A football Waze proximately 0.42 kg. The physical education teacher needs to purchase a dozen footballs. What will be the total weight, in kilograms, of the footballs to calculate shipping and handling?

Answers

5.04kg
0.42(12)= 5.04 kg

If h(x) = g[f(x)], use the table of values for f, g, f'and g' to find the value of h'(1).
x f(x) g(x) f'(x) g'(x)
1 3
2
2
6
2 1
00
5
7
3
7
2
7
9
your answer goes here

Answers

Answer:

Hey there :)

h ( x ) = f [ g ( x ) ]

To find h ' ( x )  

We do → f ' [ g ( x ) ] × g ' ( x )  

This is called the chain rule

Given;

g ( 1 ) = 2  →  f ' ( 2 ) = 5

g ' ( 1 ) = 6

Apply the formula

h ' ( 1 ) = f ' [ g ( 1 ) ] × g ' ( 1 )

          = f ' ( 2 ) × 6

          = 5 × 6

h ' ( 1 ) = 30

If h(x) = g[f(x)], the value of h'(1) from the given table is calculated as 18.

To find the value of h'(1), we need to apply the chain rule. The chain rule states that if we have a composite function h(x) = g[f(x)], then its derivative h'(x) is given by [tex]\(h'(x) = g'(f(x)) \cdot f'(x)\)[/tex].

Let's use the table of values to find h'(1):

1. f(1) = 3

2. g(f(1)) = g(3) = 2

3. f'(1) = 2

4. g'(f(1)) = g'(3) = 9

Now, we can find h'(1) using the chain rule:

[tex]\[h'(1) = g'(f(1)) \cdot f'(1) = 9 \cdot 2 = 18.\][/tex]

Therefore, the value of h'(1) is 18.

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All of the following ordered pairs satisfy the function rule y = -2 x - 1 except _____.

(2, -5)
(-1, -3)
(-2, 3)
(0, -1)

Answers

Answer:

(-1, -3)

Step-by-step explanation:

A newborn giraffe weighs about 65 kilograms. How much does it weigh in grams?

Answers

Answer:

65,000 grams

Step-by-step explanation:

1 kilogram = 1,000 grams

The giraffe weighs 65,000 grams.

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