Suppose 3 is a root of the quadratic equation ax² – 2x – 21 = 0. Find the value of a and hence find the other
root of the equation.​

Answer:cost of each pound of apple= $3

And cost of each pound of orange =$2

Step-by-step explanation:

Step 1

Let cost of apples = x

And cost of Oranges =y

Let 6 pounds of apples and 3 pounds of oranges cost 24 dollars be represented as

6 x + 3y= 24----- equation 1

Also, Let 5 pounds of apples and 4 pounds of oranges cost 23 dollars be represented as

5x+ 4y= 23----- equation 2

Step 2

6 x + 3y= 24----- equation 1

5x+ 4y= 23----- equation 2

Using substitution method to solve the equation

6 x + 3y= 24

24-6x=3y

y= 24-6x/3 = 8-2x

Y= 8-2x

Substituting the value of y= 8-2x  into equation 2

5x+ 4( 8-2x)= 23

5x+ 32 -8x= 23

32-23= 8x-5x

9=3x

x=9/3

x=3

Putting the value of x= 3 in equation 1 and solving to find y

6 x + 3y= 24

6(3) +3y= 24

18+3y=24

3y= 24-18

3y=6

y=6/3= 2

Therefore the cost of each pound of apple= $3

And cost of each pound of orange =$2

56.1% is the average number of people at the games increase from 2005 to 2012

percentage, a relative value indicating hundredth parts of any quantity.

Given,

The average number of people who attended football games at a stadium in 2005 is 8000.

The average number of people who attended football games at a stadium in 2012 is 12500.

The difference from average number of people from 2005 to 2012

12500-8000

Twelve thousand five hundred minus eight thousand

4500

To find the percentage of increase we need to divide change in number by original number

4500/8000

0.561

Now multiply with 100 because it is a hundredth part.

0.561×100=56.1

Hence 56.1% is the average number of people at the games increase from 2005 to 2012

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Answer:

The Medinas left $9.78 for a tip

Step-by-step explanation:

Percentages

The Medinas went out to eat at Chilli's and the bill was $65.20. They tipped 15% to their server.

This percentage is calculated over the amount of the $65.20 bill, thus the tip was:

15% of 65.20 = 15/100 * $65.20 = $9.78.

The Medinas left $9.78 for a tip

Answer:

(1,5)  is your answer

Step-by-step explanation:

You would have to divide the

2 and 10 by 2 and you would get (1,5)

Hope that help!Have a GREAT day!!

And Brainiest is needed!

Answer: rectangular prism

Step-by-step explanation:

Answer:

2/12 is equivalent fraction for 2/3 divided by 4

Step-by-step explanation:

2

3

&

4

2

3

÷

4= ?

step 2 Multiply 2/3 with reciprocal of 4

=2

3

x1

4

=2

12

The Quotient is 1/3.

One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things.

Given:

2/3 divided by 4

As, division is not possible in fraction so we will perform the multiplication

= 2/3  ÷ 4

= 2/3 x 1/4

= 2/6

= 1/3

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Answer:

Thanks, check out my music please. Its Colter Wall on yt

Step-by-step explanation:

Answer:

thx for the 50 points

Answer:

25

Step-by-step explanation:

By prime factorisation, we get:

5 | 625

5 | 125

5 | 25

5 | 5

| 1

. So the prime factors are:

625 = 5 x 5 x 5 x 5

625 = 25 x 25

√625 = 25

Rectangle have four edges.

Answer:

D - 353.7

Step-by-step explanation:

Edge 2020

Answer:

option d

Step-by-step explanation:

edge 2023

Answer:

Step-by-step explanation:

hi

Answer: 22 person-hours

Step-by-step explanation:

It takes 14 hours to break up the driveway and then to clear away the rubble.

Then it takes 8 hours to pour the concrete and smooth it.

Total time it will take to break up a driveway, clear away the rubble, pour the concrete, and smooth the concrete will therefore be;

= 14 + 8

= 22 person-hours

Answer:

The two numbers are 6 and 15.

Step-by-step explanation:

[tex]x+y=21\\y=21-x\\x^{2} +y^{2} =261\\x^{2} +(21-x)^{2}=261\\x^{2} +441-42x+x^{2} =261\\2x^{2} -42x+180=0\\x^{2} -21x+90=0\\(x-6)(x-15)=0\\[/tex]

x=6 and x=15

Answer:

i think 6(k)^2 ?

Step-by-step explanation:

Answer: pm • pn = p(m • n)

Step-by-step explanation:

Answer:

v = -4

Step-by-step explanation:

2(3v - 5) = 2(v - 11) - 4

6v - 10 = 2v - 22 - 4

     +10          +10

6v = 2v -12 - 4

-2v   -2v

4v = -16

divide both sides by 4

v = -4

Hope this helps!!

The value of v = - 4.

We have the following equation -

2(3v - 5) = 2(v - 11) - 4

We have to find out the value of the variable v.

The solution of an equation is the value of variable for which the left hand side is equal to right hand side.

We have the following equation -

2(3v - 5) = 2(v - 11) - 4

2 x 3v - 2 x 5 = 2v - 2 x 11 - 4

6v - 10 = 2v - 22 - 4

6v - 10 = 2v - 26

6v - 2v = - 26 + 10

4v = -16

v = - 4

Hence, the value of v = - 4.

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Answer:

14.3

Step-by-step explanation:

Remark

Make a rough sketch of the triangle.

Make F the right angle

Make <D = 66

E is the other angle.

Givens

EF = 32

<F = 90

<D = 66

Equation

Tan(D) = EF/FD

Solution

Tan(66) = 32/FD                  Multiply both sides by FD

FD*Tan(66) = 32            

Tan(66) = 2.246

2.246 * FD = 32                  Divide by 2.2246

FD = 32/2.246

FD = 14.25

FD = 14.3

Answer:

yes, phone companies, are only allowed to charge for the amount of data you use

Step-by-step explanation:

Answer:

I believe it's D. 17x-2

Answer:

D

Step-by-step explanation:

3(5x-6)+2(x+8)

=15x-18+2x+16

=15x+2x-18+16

=17x-2

Answer:

a

Step-by-step explanation:

1.cross multiplication

MARK ME BRAINELIST

Answer:

A. 29.93 grams

B. 29.925 grams

C. 0.005 grams

D. 5.985 grams per dose

Step-by-step explanation:

Chemical A = 10.357 grams

Chemical B = 12.062 grams

Chemical C = 7.506 grams

Number of doses of drugs = 5

A. About how much medicine in grams

Round each chemical to the nearest tenth

Chemical A = 10.36 grams

Chemical B = 12.06 grams

Chemical C = 7.51 grams

Total medicine in grams = chemical A + chemical B + chemical C

= 10.36 + 12.06 + 7.51

= 29.93 grams

B. Find the exact amount of medicine mixed by Dr. Stevens.

Total medicine in grams = chemical A + chemical B + chemical C

= 10.357 + 12.062 + 7.506

= 29.925 grams

C. What is the difference between the exact amount and the estimated amount of medicine

Difference = Estimated amount - Exact amount

= 29.93 grams - 29.925 grams

= 0.005 grams

D. How many grams are in one dose of medicine?

Grams in a dose = exact amount of chemicals / 5 doses

= 29.925 grams / 5

= 5.985 grams per dose

Approximately 5.99 grams per dose

Step-by-step explanation:

The given equation is :

[tex]\dfrac{14+10x}{12}=-3[/tex]

Cross multiply,

[tex]14+10x=-3\times 12\\\\14+10x=-36\\\\10x=-36-14\\\\10x=-50\\\\x=-5[/tex]

This equation will have only one solution.

We can check the solution as follows :

Put x = -5 in LHS of the the given equation.

[tex]\text{LHS}=\dfrac{14+10x}{12}\\\\=\dfrac{14+10(-5)}{12}\\\\=\dfrac{14-50}{12}\\\\=\dfrac{-36}{12}\\\\=-3[/tex]

= RHS

Hence, this is the required solution.

Answer: 1,120 frogs

Step-by-step explanation:

If 12 out of every 180 frogs in the population have spots on their backs, the number that do not are;

= 180 - 12

= 168 frogs

168 frogs out of every 180 do not have spots. Out of 1,200 that would be;

= 168/180 * 1,200

= 1,120 frogs

Answer: It should have been correct.

Step-by-step explanation:

Answer:

the simplest form of 15/20 is 3/4

Answer:

3 different ways

Step-by-step explanation:

Answer:

3 different ways

Step-by-step explanation:

hope this helps

example of the diffrent way to write a ratio :

5 to 10

5 : 10

[tex]\frac{5}{10}[/tex]