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3 years ago

Write an equivalent expression by applying the distributive property (x-5)^2

Mathematics

1 answer:

tamaranim1 [39]3 years ago

4 0

Answer:

x^2 - 10x + 25

Step-by-step explanation:

Hope it helps.

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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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Rough work

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

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

Solved

7 0

4 years ago

Read 2 more answers

What is 10% of 50? A. 6.75 B. 7.5 C. 10.5 D. 5.25

nirvana33 [79]

Its 5. Its none of those.

10% of 50.00 = 5.0000

5 0

4 years ago

16.872 divided by 0.24 HELP I NEED HELP QUICJ

goldenfox [79]

Answer:

70.3

Step-by-step explanation:

16.872/.24= 70.3

6 0

3 years ago

Read 2 more answers

In an arithmetic sequence, the seventh term is −9 and the nineteenth term is 39.

Stella [2.4K]

Answer:

37.5% that is the answer

Step-by-step explanation:

3 0

3 years ago

How do you evaluate 3ab

dimaraw [331]

Lets say a=2 and b=5 you now plug in you numbers to get 3x2x5 we know 3x2=6 so now take 6 and multiply it by 5 so 6x5=30 you can also set this equal to 0 3ab=0 then divide by either a or b ill show you both if you divide by a you are left with 3b=a if you divide by b than you get 3a=b

5 0

3 years ago