What is the relation between 1 and 2?

f(x) = ax² + bx + c

f(1) = 6

f(2) = 11

f(3) = 18

value of a,b,c​

Substitute x = 1 , 2 , 3 in the given polynomial.

★ f(1) = a(1)² + b(1) + c

⟹ 6 = a + b + c -- equation (1)

Similarly,

★ f(2) = a(2)² + b(2) + c

⟹ 11 = 4a + 2b + c -- equation (2)

★ f(3) = a(3)² + b(3) + c

⟹ 18 = 9a + 3b + c -- equation (3)

Subtract equation (1) from (2).

⟹ 4a + 2b + c - (a + b + c) = 11 - 6

⟹ 4a + 2b + c - a - b - c = 5

⟹ 3a + b = 5 -- equation (4).

From equation (3) ,

⟹ 18 - c = 9a + 3b

⟹ 18 - c = 3(3a + b)

Substitute the value of 3a + b from equation (4).

⟹ 18 - c = 3 * 5

⟹ 18 - 15 = c

⟹ 3 = c

substitute the value of c in equation (1).

⟹  6 = a + b + 3

⟹ 6 - 3 = a + b

⟹ 3 = a + b -- equation (5)

Subtract equation (5) from equation (4).

⟹ 3a + b - (a + b) = 5 - 3

⟹ 3a + b - a - b = 2

⟹ 2a = 2

⟹ a = 1

Substitute a value in equation (5).

⟹ 1 + b = 3

⟹ b = 3 - 1

⟹ b = 2

Therefore,

a = 1

b = 2

c = 3.

I hope it will help you.

Regards.

Answer:

145.9°C

Step-by-step explanation:

Given that :

Lowest temperature recorded (Soviet Vostock station Antarctica) = - 89.2°C

Highest temperature recorded (Greenland Ranch California) = 56.7°C

Difference between the highest and lowest recorded temperature :

(Highest temperature - lowest temperature)

(56.7°C - (-89.2°C))

= 56.7°C + 89.2°C

= 145.9°C

Answer:

8 wristbands

Step-by-step explanation:

Let us assume that both of the company were ordered to deliver w wristbands.

The amount of money charged by company 1 who sells at $2 and offers free shipping is given as:

2w

The amount of money charged by company 2 who sells at $1.25 and $6 for shipping per order given as:

1.25w + 6

If both companies charge the same amount, hence:

2w = 1.25w + 6

2w - 1.25w = 6

0.75w = 6

w = 6/0.75

w = 8

The two companies charge the same amount for 8 wristbands

Answer:

Step-by-step explanation:

Any number or variable to the power of 0 is 1

(7^3 x^4)^0 = 1

Answer:

Measure all the sheets together and divide by 200

Step-by-step explanation:

An average mean is the sum of something divided by how many things there are.  In this case, it is the sum of the thickness of 200 pages, divided by the number of pages, 200.

Answer:

Step-by-step explanation:

5/6 - (2/5 + 1/3)

25/30 - (12/30 + 10/30)

25/30 - 22/30 = 3/30 = 1/10

answer is b

Answer:

Purchases= production + desired ending inventory - beginning inventory

Step-by-step explanation:

Giving the following information:

Two pounds of raw materials are needed to produce one product.

The desired ending balance of raw materials is 10% of the next month's production needs.

The beginning inventory of raw materials is 4,000 pounds.

The raw material cost per unit is $0.50 per pound.

To calculate the direct material purchase required for a given month, we need the production for each month. I will provide the formula and a small example to guide an answer.

To calculate the purchase required, we need to use the following formula:

Purchases= production + desired ending inventory - beginning inventory

For example:

Production:

January= 5,000 units

February= 4,500 units

Direct material purchases January:

Production= 5,000*2= 10,000

Desired ending inventory= (4,500*2)*0.1= 900

Beginning inventory= (4,000)

Total purchase in pounds= 6,900

Total direct material cost= 6,900*0.5= $3,450

Answer: 11 1/3 (eleven and one third)

Step-by-step explanation:

Answer:

Kindly check explanation

Step-by-step explanation:

3 boxes or less = Cost of tiles = $48

4 - 8 boxes ;  cost = $45

9 - 19 boxes ; cost = $42

> 19 boxes ; cost = $38

Cost of purchasing 5 boxes of tiles :

$45 * 5 = $225

Cost of purchasing 19 boxes :

$42 * 19 = $798

Answer:

F.

Step-by-step explanation:

Prime means that it is only divisible by 1 and itself, and we know that it is also divisible by 7, therefore it is a composite number because it has 1, 7, and 49 as factors.

Answer:

Simplify the expression.

Exact Form:

41 /12

Decimal Form:

3.41 6

Mixed Number Form:

3  5 /12

Answer:

0.24$

Step-by-step explanation:

Each egg costs 1/12 of 2.88.

So either you multiply 2.88 by 1/12

or you divde 2.88 by 12

Answer:

0.24

Step-by-step explanation:

you would divide 2.88 by 12 hope this helps.

The name of my shape is a parallelogram. The sides are:

The perimeter is 34 feet because:

Step 1: Add smaller groups.

10 + 10 = 20

7 + 7 = 14.

Step 2: Add the two numbers.

14 + 20 = 34.

Hope this answer helps you!

I got 2 : 3. You didn’t give answer choices but after you commented the answer choices I was able to determine that 2:3 is the answer.

Answer:

Step-by-step explanation:

If Frederick can swim 25 yards in 23 seconds, then:

25 yards = 23 seconds

To determine how long it will take him to swim 175yards, we will say:

175 yards = x

Equating both expression:

25 yards = 23 seconds

175 yards = x

Cross multiply

25x = 23*175

25x = 4025

Divide both sides by 25

25x/25 = 4025/25

x = 161 secs

This means that it will take Frederick 161 secs to swim 175 yards

Answer:

x = 10

Step-by-step explanation:

8x + 14 = 6x + 34  (vertically opposite angles are equal)

Rearrange

2x = 20

x = 10

Answer:

x=10

Step-by-step explanation:

So we know that they are equal to each other.

so 6x+34=8x+14

-6x

34=2x+14

-14

20=2x

/2

x=10

Answer:

Orange with pink, Yellow with red, Purple with blue. Yellow should be 1x instead of 3x. Swotch the table under red with green aswell.

Answer:

3x+1

Step-by-step explanation:

(2x+x+3+6x)/3

9x+3/3

3x+1

The final result is a simplified algebraic expression 3x + 1 that represents the average of 2x, x + 3, and 6x.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The average of 2x, x + 3, and 6x can be represented by the algebraic expression (2x + (x + 3) + 6x)/3.

This expression takes the sum of 2x, x + 3, and 6x, and then divides that sum by 3, which is the number of terms being averaged.

Alternatively, the average can be represented by (2x + x + 6x + 3) / 3 = (9x + 3) / 3 = 3x + 1.

In either case, the final result is a simplified algebraic expression that represents the average of 2x, x + 3, and 6x.

Learn more about Expressions here :

brainly.com/question/21751419

#SPJ2

Answer:

10. Supplementary

11. Congruent

12. Congruent.

13 . congruent

14 supplement

15 supplementary

Answer:

its simple 5.90

Step-by-step explanation:

The statement that defines what a line segment is would be: B. All points between two given endpoints including the endpoints.

A line segment, in geometry, is defined as a line or part of a line having two endpoints.

A diagram showing a line segment with two distinct endpoints have been shown in the attachment below.

A line segment can also contain points between the two endpoints on the line.

Therefore, the statement that defines what a line segment is would be: B. All points between two given endpoints including the endpoints.

Learn more here:

https://brainly.com/question/24270297

Answer:

Maximum number of chairs is 7.

Step-by-step explanation:

We are told he has less than 120 minutes to spend painting furniture each day.

Now he has spent 30.5 minutes painting a desk.

Also, he wants to paint "x" number of chairs with each chair taking 12.5 minutes.

Thus, we have;

30.5 + 12.5x < 120

Subtract 30.5 from both sides to get;

12.5x < 120 - 30.5

12.5x < 89.5

x < 89.5/12.5

x < 7.16

Thus, maximum number of chairs he can paint is 7

Answer:

$64.20

Step-by-step explanation:

%7 of a dollar is .07

.07 × 60 = 4.20

4.20 + 60 = 64.20

Answer:

[tex](-∞,1) , (0,\frac{7}{4})[/tex]

Step-by-step explanation:

Factor:

x(4x³-3x-7)<0

This question is Incomplete

Complete Question

The bakery bought 4 bags of flour containing 3.5 kg each. 0.475 kg of flour is needed to make a batch of muffins, and 0.65 kg is needed to make a loaf of bread.

a. If 4 batches of muffins and 5 loaves of bread are baked, how much flour will be left? Give your answer in kilograms.

b. The remaining flour is stored in bins that hold 3 kg each. How many bins will be needed to store the flour? Explain your answer.

Answer:

a. 8.85kg of flour is left.

b. 2.95 bins

Step-by-step explanation:

The bakery bought 4 bags of flour containing 3.5 kg each.

Total kg of flour the Bakery bought : 4 × 3.5kg

= 14 kg of flour

0.475 kg of flour is needed to make a batch of muffins

1 batch of muffin = 0.475kg of flour

4 batches of muffins = ???

Cross Multiply

4 batches × 0.475kg/ 1 batch

= 1.9kg of flour was used.

0.65 kg is needed to make a loaf of bread.

1 loaf of bread = 0.65kg of flour

5 loaves of bread = ???

Cross Multiply

5 loaves × 0.65/1 loaf

= 3.25 kg of flour.

Total kg of flour used = 1.9kg + 3.25kg

= 5.15kg of flour.

The amount of flour left = 14kg - 5.15kg

= 8.85kg of flour is left.

b. The remaining flour is stored in bins that hold 3 kg each. How many bins will be needed to store the flour?

3 kg of flour is stored = 1 bin

8.85 kg of flour is stored = x

Cross Multiply

3kg × x = 8.85kg × 1 bin

x = 8.85 kg × 1 bin/3kg

x = 2.95 bins