Simplify .
7g - 12 = 3 + 7/3g

Answers

Answer 1

Answer: Hey there, first we simplify, 7g-12=7/3G+3, second, we subtract 7/3G from both sides, 7g-12-7/3g=7/3G+3-7/3g=14/3g-12=3, third, we add 12 to both sides, 14/3g-12+12=3+12=14/3g=15, now, we multiply both sides by 3/14, 3/14*14/3g=3/14*15=g=45/14. Therefore, the answer is g=45/14

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I know its a lot but i dont understand it i have tried to understand it

Answers

The method for this kind of thing is PEMDAS
1. Parentheses
2. Exponents
3. Multiply
4. Add
5. Subtract
Do it in this order.
Tell me if you need more help.

Two integers, a and b have product of -48 what is the greatest possible sum of a and b.

Answers

The factors of 48 are:
1 x 48
2 x 24
3 x 16
4 x 12
6 x 8
and visa versa: 48 x 1 etc.

To make the product negative, one of the factors has to be positive and one has to be negative. To find the greatest sum, make the bigger number the positive factor and the smaller number the negative factor. So, -1 x 48 = -48 and the sum of -1 + 48 = 47 which would be the greatest possible sum.

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.

The remainder obtained when x^4 + 3x^2 - 2x + 2 is divided by (x + b) is the square of the
remainder obtained when x^2 – 3 is divided by (x + b). Find the values of b.

Answers

Use the polynomial remainder theorem: the remainder upon dividing a polynomial $p(x)$ by $x-c$ is $p(c)$ .

$(-b)^4+3(-b)^2-2(-b)+2=b^4+3b^2+2b+2$

$((-b)^2-3)^2=b^4-6b^2+9$

Now

$b^4+3b^2+2b+2=b^4-6b^2+9\implies9b^2+2b-7=0$

$\implies(9b-7)(b+1)=0$

$\implies b=\frac79\text{ or }b=-1$

The output of a function table is 4 less than the input Angela says the function rule is x-4=y. Kara says the rule is 4-x=y who is correct?

Answers

Output = y
4 less = - 4 or y<
than the input = y < x by 4 or y + 4 = x
Happy to Help!

Given f (x) and g(x)+k look at the graph below and determine the value of K

Answers

Answer:

k=5

Step-by-step explanation:

Let's find the equation for both lines. For the line in blue we know that passes through points (0,-2) and (3,-1) with this information we can use the formula of the line:

$y-y_1=(y_2-y_1)/(x_2-x_1) (x-x_1)$