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3 years ago

5x - 5 = 50 just to clarify is it 11

Mathematics

1 answer:

Alenkasestr [34]3 years ago

4 0

Add 5 to both sides

5x = 50 + 5

Simplify 50 + 5 to 55

5x = 55

Divide both sides by 5

x = 55/5

Simplify 55/5 to 11

x = 11

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20 points pls help quick

masha68 [24]

Answer:

$\displaystyle f(x) = 3x^2 + 2x + 5\text{ and } g(x) =2x^2 - 4x -2\text{ or } \\ \\ f(x) = 3x^2 + 5 \text{ and } g(x) = x^2 - 4x -2$

Step-by-step explanation:

We are given the two functions:

$\displaystyle f(x) = 3x^2 + mx +5 \text{ and } g(x) = nx^2 - 4x -2$

And that:

$\displaystyle h(x) = f(x)\cdot g(x)$

With the given conditions that (1, -40) and (-1, 24) satisfy the new function, we want to determine functions f and g.

First, find h:

$\displaystyle \begin{aligned} h(x) & = f(x)\cdot g(x) \\ \\ & = (3x^2 + mx +5)(nx^2 - 4x -2) \end{aligned}$

Because (1, -40) and (-1, 24) are points on the graph of h, we have that h(-1) = 40 and h(-1) = 24. In other words:

$\displaystyle \begin{aligned} h(1) = -40 & = (3(1)^2 + m(1) +5)(n(1)^2 - 4(1) -2) \\ \\ & = (3 + m +5)(n-4 -2) \\ \\ & = (m+8)(n-6) \\ \\ -40 &= mn-6m+8n-48 \end{aligned}$

And:

$\displaystyle \begin{aligned} h(-1) = 24 & = (3(-1)^2 + m(-1) +5)(n(-1)^2 -4(-1) -2) \\ \\ & = (3 - m +5)(n + 4 -2) \\ \\ & = (-m+8)(n+2) \\ \\ 24 & = -mn -2m + 8n +16 \end{aligned}$

Solve the system of equations. Adding the two equations together yield:

$\displaystyle -16 = -8m+16n - 32$

Solve for either m or n:

$\displaystyle \begin{aligned} -16 & = -8m + 16n - 32 \\ \\ 16 & = -8m + 16n \\ \\ 8m & = 16n - 16 \\ \\ m & = 2n -2\end{aligned}$

Substitute this into one of the two equations above and solve:

$\displaystyle \begin{aligned} -40 & = mn - 6m + 8n - 48 \\ \\ 0 & = (2n-2)n -6 (2n-2) + 8n -8 \\ \\ &= (2n^2 - 2n) + (-12n + 12) +8 n - 8 \\ \\ & = 2n^2 -6n + 4 \\ \\ & = n^2 - 3n + 2 \\ \\ &= (n-2)(n-1) \\ \\ & \end{aligned}$

Therefore:

$\displaystyle n = 2 \text{ or } n = 1$

Solve for m:

$\displaystyle \begin{aligned}m &= 2n-2 & \text{ or } m & = 2n-2 \\ \\ & = 2(2) - 1 &\text{ or } & =2(1) -2 \\ \\ &= 2 &\text{ or } & = 0 \end{aligned}$

Hence, the values of n and m are either: 2 and 2, respectively; or 1 and 0, respectively.

In conclusion, functions f and g are:

$\displaystyle f(x) = 3x^2 + 2x + 5\text{ and } g(x) =2x^2 - 4x -2\text{ or } \\ \\ f(x) = 3x^2 + 5 \text{ and } g(x) = x^2 - 4x -2$

7 0

2 years ago

7 x 5/6 simplified!!

mihalych1998 [28]

Answer:

5 5/6

Step-by-step explanation:

7 x 5 = 35

35/6 = 5 5/6

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3 years ago

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lawyer [7]

Answer:

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Step-by-step explanation:

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3 years ago

If $500 was earned on $10,000 total worth of sales, then the commission rate is:

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3 years ago

Please help me this is a test that is important

Margaret [11]

Answer:

implifying

2x + 2y = 4xy

Solving

2x + 2y = 4xy

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4xy' to each side of the equation.

2x + -4xy + 2y = 4xy + -4xy

Combine like terms: 4xy + -4xy = 0

2x + -4xy + 2y = 0

Add '-2y' to each side of the equation.

2x + -4xy + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0

2x + -4xy + 0 = 0 + -2y

2x + -4xy = 0 + -2y

Remove the zero:

2x + -4xy = -2y

Combine like terms: -2y + 2y = 0

2x + -4xy + 2y = 0

Factor out the Greatest Common Factor (GCF), '2'.

2(x + -2xy + y) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(x + -2xy + y)' equal to zero and attempt to solve:

Simplifying

x + -2xy + y = 0

Solving

x + -2xy + y = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1y' to each side of the equation.

x + -2xy + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0

x + -2xy + 0 = 0 + -1y

x + -2xy = 0 + -1y

Remove the zero:

x + -2xy = -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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3 years ago

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