Find the value of d such that the system of equations

Is the equation 3+z= -9 true false or open

Harrizon [31]

Subtract 3 from both sides

(z = -9 - 3)

Simplify -9 - 3 to -12

z = -12

3 + -12 = -9 so this is true.

6 0

2 years ago

Which equation is y = –6x^2 + 3x + 2 rewritten in vertex form? y = negative 6 (x minus 1) squared + 8 y = negative 6 (x + one-fo

mart [117]

Answer:

$y = -6(x - \frac{1}{2})^2 -\frac{7}{2}$

Step-by-step explanation:

Given:

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

Required

Rewrite in vertex form

The vertex form of an equation is in form of: $y = a(x - h)^2+ k$

Solving: $y = -6x^2 + 3x + 2$

Subtract 2 from both sides

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

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

Factorize expression on the right hand side by dividing through by the coefficient of x²

$y - 2 = -6(x^2 + \frac{3x}{-6})$

$y - 2 = -6(x^2 - \frac{3x}{6})$

$y - 2 = -6(x^2 - \frac{x}{2})$

Get a perfect square of coefficient of x; then add to both sides

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<em>Rough work</em>

The coefficient of x is $\frac{-1}{2}$

It's square is $(\frac{-1}{2})^2 = \frac{1}{4}$

Adding inside the bracket of $-6(x^2 - \frac{x}{2})$ to give: $-6(x^2 - \frac{x}{2} + \frac{1}{4})$

To balance the equation, the same expression must be added to the other side of the equation;

Equivalent expression is: $-6(\frac{1}{4})$

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The expression becomes

$y - 2 -6(\frac{1}{4})= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

$y - 2 -\frac{6}{4}= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

$y - 2 -\frac{3}{2}= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

Factorize the expression on the right hand side

$y - 2 -\frac{3}{2}= -6(x - \frac{1}{2})^2$

$y - (2 +\frac{3}{2})= -6(x - \frac{1}{2})^2$

$y - (\frac{4+3}{2})= -6(x - \frac{1}{2})^2$

$y - (\frac{7}{2})= -6(x - \frac{1}{2})^2$

$y +\frac{7}{2} = -6(x - \frac{1}{2})^2$

Make y the subject of formula

$y = -6(x - \frac{1}{2})^2 -\frac{7}{2}$

<em>Solved</em>

7 0

3 years ago

Read 2 more answers

What is the definition of marginal utility? A. The average utility from consuming a good or service multiplied by the number of

Ilya [14]

Answer: Option 'E' is correct.

Step-by-step explanation:

Marginal utility is the addition utility derived from each successive unit of a particular good.

so, marginal utility is the change in utility from consuming an addition unit of a good or service.

Mathematically, it is expressed as

$MU=\dfrac{\Delta TU}{\Delta Q}$

Hence, Option 'E' is correct.

4 0

3 years ago

Meghan has her own business. When she makes money, it is called income. When she spends money, it is called expenses. Choose the

Dmitry_Shevchenko [17]

Answer:

Meghan should use positive integers to represent income. Income is money that flows into the business, and it is always positive. The higher the income, the more money a business will have.

On the other hand, expenses must be represented by negative integers. Expenses are money that flows out of a business, and is always negative. The higher the expenses, the less money the business will have. Expenses reduce a business's net income.

4 0

2 years ago

Pls please please answer !!!

KatRina [158]

Answer:

B) 120

Step-by-step explanation:

hope this helpssssss

5 0

2 years ago

Read 2 more answers