MATHEMATICS HIGH SCHOOL

What is the missing number that will complete the factorization? a2 + 8a + 12 = (a + 2)(a + )

Answers

Answer 1

Answer:

Answer:

The missing number that will complete the factorization is 6 .

Step-by-step explanation:

Given : Polynomial $a^2+8a+12$

We have to factorize the given Polynomial $a^2+8a+12$ and complete the given factorization.

Consider the given Polynomial $a^2+8a+12$

Simplifying using middle term splitting method,

Writing 8a as the sum of two terms such that the product of these term is the product of remaining two terms.

8a can be written as 2a + 6a

We get,

$a^2+8a+12$ as $a^2+2a+6a+12$

Taking a common from first two term and 6 common from last two terms, we have,

$a^2+2a+6a+12=a(a+2)+6(a+2)$

Simplifying, we get,

$a(a+2)+6(a+2)=(a+6)(a+2)$

Thus, the missing number that will complete the factorization is 6 .

Answer 2

Answer: It is 6. I found this by diving 12 by 2 because 2 and the missing number need to have a product of 12. Here's the proof if you want it!

(a+2)(a+6)

a^2 + 2a + 6a + 12

a^2 + 8a + 12

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Jake wants to enlarge his 12-foot by 14-foot garden. If he multiplies the dimensions by 2, how will the area of the garden be affected?

Answers

Area = L*W
Original Area = 12*14 = 168
Multiply the dimensions by 2 = 12*2 = 24 and 14*2 = 28
New Area = 24 *28 = 672

New Area divided by original area = 672/168 = 4

The garden will be 4 times bigger in area

Adam volunteers once a month to make meals for shut-ins. He has 14 pieces of chicken and 21 pieces of corn. He needs to put the same number of pieces of chicken and corn on each plate. what is the greatest number of plates he can make? How many pieces of corn and chicken will he put on each plate?

Answers

7 seems to be the common factor between these two numbers so we shall divide 14 and 21 to get 2&3. So He can make 7 plates with 2 pieces of chicken and 3 pieces of corn

Joe will go to the swimming pool on 20 different days this month. • a one-day pass to the pool is $2.25. • a monthly pass to the pool is $30.00. how much money will joe save by buying a monthly pass

Answers

Joe will save 20 dollars buying a monthly pass

An iron tank is constructed in the form of an isosceles trapezoid. Each base angle measures 105°, the length of the base is 10 feet, and each of the nonparallel sides is 12 feet long. Determine the length of a diagonal brace to the nearest whole number.10 ft
13 ft
18 ft
24 ft

Answers

The right answer for the question that is being asked and shown above is that: "13 ft."An iron tank is constructed in the form of an isosceles trapezoid. Each base angle measures 105°, the length of the base is 10 feet, and each of the nonparallel sides is 12 feet long. The length of a diagonal brace to the nearest whole number is 13 ft

Answer:

Its 18ft

Step-by-step explanation:

since the angle is so large it travels further out than you think

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!! I CANNOT RETAKE THIS!!What are the factors of the polynomial function?

Use the rational root theorem to determine the factors.

Answers

Answer: (x - 2)(x + 2)(2x + 1)

Step-by-step explanation:

q p

f(x) = 2x³ + x² - 8x - 4

rational root theorem: $(p)/(q) = +/- (1, 2, 4)/(1, 2)$ so the possible roots are: +/- 1, 2, 4, $(1)/(2)$

Let's try x = 2

2 | 2 1 -8 -4

| ↓ 4 10 4

2 5 2 0 remainder is 0 so (x - 2) is a factor

0 = (x - 2) (2x² + 5x + 2)

0 = (x - 2) (x + 2)(2x + 1)

Answer: X - 2 ( X + 2) (2 x + 1)

a local business was looking to hire a landscaper to work on their property. they narrowed their choices to two companies. flourish landscaping company charges a flat rate of $120 per hour. green thumb landscapers charge $70 per hour plus a $1600 equipment fee. write a system of equations representing how much each company chargers. determine and state the number of hours that must be worked for the cost of each company to be the same. if it is estimated to take at least 35 hours to complete the job, which company will be less expensive? justify your answer

Answers

Flourish- 120x
Green Thumb- (70x)=1600

Flourish- 120*35= $4200
Green Thumb- (70*35)+1600= $4050

It would be less expensive to hire Green Thumb Landscapers. There is a $150 difference between the two

It would take 32 hours of work for the cost to be the same for both companies

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