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3 years ago

11

Consider the equation below.

1 answer:

Lerok [7]3 years ago

8 0

Answer:

See explanation

Step-by-step explanation:

Given

$-2(5x+8)=14+6x$

Required

Complete the steps

$-2(5x+8)=14+6x$

Multiply 5x and 8 by -2

$-10x - 16 = 14 + 6x$

Subtract by 6x

$-10x - 6x- 16 = 14 + 6x - 6x$

$-16x- 16 = 14$

Add 16

$-16x- 16 + 16= 14 + 16$

$-16x= 30$

Divide by -16

$x= \frac{30}{-16}$

$x= -\frac{15}{8}$

<em>See attachment</em>

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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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<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: $-6(\frac{1}{4})$

------------------------------------------------------------------------------------

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

4 years ago

Read 2 more answers

Item 13<br> Graph.<br><br><br><br> y−5=4/3(x−5)<br><br> pls help

grin007 [14]

Answer:

I cant graph it for you but i can tell u the answer! i just saw that it has the full explanation better than mine!

Step-by-step explanation

3 0

3 years ago

Day X = 33; Day Y = 44. What is the percent change from day X to day Y?

Serhud [2]

Answer: 33.3% increase, pretty sure

Step-by-step explanation: Big number- Small number, and then divided by the first number: 44-33=11. 11 divided by 33 ( original) is 0.3333, and then change the decimal to a percent, which is 33.3%.

5 0

3 years ago

Factor this polynomial completely.<br> 6x2 + 7x - 20

Papessa [141]

It’s the third answer
(2x + 5) x ( 3x -4)

3 0

3 years ago

Help me if you can please

Luden [163]

Answer:

the question is not visible

8 0

3 years ago