MATHEMATICS HIGH SCHOOL

1. Solve the following equation using the quadratic formula: 3x2 + 6x + 8 = 6.2. Is the quadratic formula the most efficient way to solve this equation? Why or why not?

Answers

Answer 1

Answer:

Answer:

1. $x=-(3+√(3))/(3)\text{ (or) }x=(-3+√(3))/(3)$

2. Quadratic formula is the most efficient way to solve this equation.

Step-by-step explanation:

We have been given an equation $3x^2+6x+8 = 6$ . We are asked to solve our given equation using quadratic formula.

$x=(-b\pm√(b^2-4ac))/(2a)$ , where,

b = Coefficient of x term,

c = Constant,

a = Coefficient of $x^2$ term.

$3x^2+6x+8-6=6-6$

$3x^2+6x+2=0$

Upon substituting our given values, we will get:

$x=(-6\pm√(6^2-4(3)(2)))/(2(3))$

$x=(-6\pm√(36-24))/(6)$

$x=(-6\pm√(12))/(6)$

$x=(-6\pm √(4\cdot 3))/(6)$

$x=(-6\pm 2√(3))/(6)$

$x=(-6-2√(3))/(6)\text{ (or) }x=(-6+2√(3))/(6)$

$x=(-2(3+√(3)))/(2*3)\text{ (or) }x=(2(-3+√(3)))/(2*3)$

$x=-(3+√(3))/(3)\text{ (or) }x=(-3+√(3))/(3)$

Therefore, the solutions for our given equation are $x=-(3+√(3))/(3)\text{ (or) }x=(-3+√(3))/(3)$ .

2. We cannot factor our given equation by splitting the middle term because there are no such numbers which add up-to 6 and whose product is 6.

Therefore, the quadratic formula is the most efficient way to solve this equation.

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In a family with 2 children, excluding multiple births, what is the probability of having a boy and a girl in any order?75%
25%
50%
60%

Answers

50% because it can either girl or boy first. I hope i helped

50% because 100% divided by 2 children would be 50% per child.

3x−8y+44=0 7x=12y−56

Answers

Answer:

(4, 7 )

Step-by-step explanation:

given the 2 equations

3x - 8y + 44 = 0 → (1)

7x = 12y - 56 ( subtract 12y - 56 from bpth sides )

7x - 12y + 56 = 0 → (2)

multiplying (1) by 7 and (2) by - 3 and adding the result will eliminate x

21x - 56y + 308 = 0 → (3)

-21x + 36y - 168 = 0 → (4)

add (3) and (4) term by term to eliminate x

(21x - 21x) + (- 56y + 36y) + (308 - 168) = 0

0 - 20y + 140 = 0 ( subtract 140 from both sides )

- 20y = - 140 ( divide both sides by - 20 )

y = 7

substitute y = 7 into either of the 2 orinal equations and solve for x

substituting into (1)

3x - 8(7) + 44 = 0

3x - 56 + 44 = 0

3x - 12 = 0 ( add 12 to both sides )

3x = 12 ( divide both sides by 3 )

x = 4

solution is (4, 7 )

The lines 3y-x=3 and y+3=3(x-1) are

Answers

lets change the form of the equations to the canonical line equation form:
y = mx + b

3y - x = 3
y = (1/3)x + 1

y + 3 = 3(x - 1)
y = 3x - 6

Solve for n round to the tenths place 14/21.2= n\15

Answers

Well.... first lets break this problem up. and work on the left side first
soo we solve this ↓
14/21.2 = 0.66
now lets plug in our values. The left side will just be replaced by 0.66
Soooo
0.66 = n/15
so this means we do the opposite on both sides of what n and 15 are doing
In this case they are dividing so yes we are doing the opposite by multiply.
sooooo
0.66 = n/15
×15 = x 15 they cancel out on the right hand side and lets solver for the left side.
0.66 x 15 = 9.9
so that means
n = 9.9
or we could round it and just say 10
n = 10
hope this helps:P

Whats the difference of 10 and u ?

Answers

The difference of 10 and u

Answer: 10 - u.

Goran made 6 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all 6 necklaces was $33.60 . If the beads cost $2.90 for each necklace, how much did each pendant cost?

Answers

2.90*6=17.40
33.60-17.40=$16.20
16.20/6=$4.05

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