MATHEMATICS MIDDLE SCHOOL

Factor quadratic equation 6x.squared +41x + 63 = 0

Answers

Answer 1

Answer:

x1= -9/2 ; x2= -7/3

Step-by-step explanation:

Rewrite to 6x^2 + 27x +14x +63 = 0

Factor and get 3x(2x + 9) + 7(2x + 9) = 0

Factor again and get (2x + 9)(3x + 7) = 0

Separate into possible cases -> 2x + 9 = 0; 3x + 7 = 0

The equation has two solutions: x1 = -9/2 and x2 = -7/3

Hope this helped!!

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New Clarendon Park is undergoing renovations to its gardens. One garden that was originally a square is being adjusted so that one side is doubled in length, while the other side is decreased by three meters.The new rectangular garden will have an area that is 25% more that the original square garden. Write an equation that could be used to determine the length of a side of the original square garden.
Determine the area, in square meters, of the new rectangular garden.

Answers

The answer is 80 square meters.

The square area is expressed as:
A = a²,
where A is the area of the square, and a is the side of the square.

The rectangle area is expressed as:
A₁ = a₁ · b₁,
where A₁ is the area of the rectangle, and a₁ and b₁ are the sides of the rectangle.

After renovations, square garden becomes rectangular.

One side is doubled in length:
a₁ = 2a

The other side is decreased by three meters.
b₁ = a - 3

The new area is 25% than the original square garden:
A₁ = A + 25%A =
= A + 25/100·A
= A + 1/25·A
= a² + 1/25·a²
= a² + 0.25·a²
= 1.25·a²

If the starting equation is:
A₁ = a₁ · b₁

Thus, the equation is:
1.25a² = 2a·(a - 3)
1.25a² = 2a · a - 2a · 3
1.25a² = 2a² - 6a

Therefore, the equation that could be used to determine the length of a side of the original square garden is:
2a² - 6a = 1.25a²

Now, we will solve the equation:
2a² - 6a = 1.25a²
2a² - 1.25a² - 6a = 0
0.75a² - 6a = 0
⇒ a(0.75a - 6) = 0

From here, one of the multiplier must be zero - either a or (0.75a - 6). Since a could not be zero, (0.75a - 6) is:
0.75a - 6 = 0
0.75a = 6
a = 6 ÷ 0.75
a = 8

If the side of the square is 8, then the area of the rectangle is
A₁ = 1.25 · a²
A₁ = 1.25 ·8²
A₁ = 1.25 · 64
A₁ = 80

Therefore, the area of the new rectangle garden is 80 square meters.

Factor the gcf -6x ^ 4 y ^ 5 -15 x ^ 3 y ^ 2 + 9x ^ 2 y ^ 3

Answers

Answer:

-3x^2y^2(2x^2y^3 + 5x - 3y)

Adele started her homework at 9:10. she finished at 9:45. how long did she spend on her homework?

Answers

9:45-9:10=35
she spent 35 minutes

She spent 35 minutes because 9:45 - 9:10 is 35.

AssAssessment captures blank growth

Answers

What do you mean by this

David wants to build a pen for his goat. He wants the area of the pen be 48 square feet .if the length and width of the pen are whole numbers which of the following could be the perimeter of the pen.A. P= 26
B. P= 28
C. P= 30
D. P= 36
PLEASE HELP!

Answers

B.

The reason being said Area is l*w

or length*width

Try 8*6=48 sq ft.

But perimeter is the outer edge..

l+l+w+w=P

8+8+6+6=28

Simple.

Thus, B, is your answer.

Alrighty, pretty much, A=bh and P=(b=h)2
If you divide 28 by 6, you are left with 8, making h=6 and b=8
If you plug this in for perimeter, you have 28

The answer is B. P= 28 feet

I don't understand why I keep getting the answer 934.64 for 160.8 X 44.3

Answers

160.8*44.3=7123.44
Im assuming your multiplying wrong
You can compare your work to mine to see what you did wrong:)

You are so wrong try multipliying 3 times 8 without getting the result of 64 since 3 times 8 is 24 and 160 times 44 is 7,040 so the wright answer is 7,040.24

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