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3 years ago

Determine the next step for solving the quadratic equation by completing the square.

Mathematics

1 answer:

Studentka2010 [4]3 years ago

4 0

Answer:

The solutions are $x=\frac{1+\sqrt{7}}{2}$ and $x=\frac{1-\sqrt{7}}{2}$

Step-by-step explanation:

we have

$0=-2x^{2}+2x+3$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$-3=-2x^{2}+2x$

Factor the leading coefficient

$-3=-2(x^{2}-x)$

Complete the square. Remember to balance the equation by adding the same constants to each side.

$-3-0.5=-2(x^{2}-x+0.5^{2})$

$-3.5=-2(x^{2}-x+0.5^{2})$

Rewrite as perfect squares

$-3.5=-2(x-0.5)^{2}$

$7/4=(x-0.5)^{2}$

square root both sides

$x-0.5=(+/-)\sqrt{\frac{7}{4}}$

$x-\frac{1}{2}=(+/-)\frac{\sqrt{7}}{2}$

$x=\frac{1}{2}(+/-)\frac{\sqrt{7}}{2}$

$x=\frac{1+\sqrt{7}}{2}$

$x=\frac{1-\sqrt{7}}{2}$

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Please i need help asap

Mademuasel [1]

You would have to divide the categories over the budget. after you divide, you would end up with a decimal, so you to convert it into a percentage, you would simply multiply it by 100.

clothing: 6%
housing: 22%
insurance: 8%

8 0

2 years ago

Read 2 more answers

Please help me with 2 and 3 and use the elimination process!

grandymaker [24]

Answer:

2. Judy =$5

Ben= $4

Step-by-step explanation:

2. Let Judy = x and Ben = y

8x + 10y = 80

9x + 5y = 65

Solve these simultaneous equations.

8 x + 10 y = 80

18 x + 10 y = 130

Take the second equation away from the first equation

− 10 x = − 50

x = 5

This means that Judy gets paid $5 an hour.

Therefore, Ben gets paid $4 an hour.

Answer:

3. 24 quarters and 16 dimes

Step-by-step explanation:

3. Let the number of dimes = x and the number of quarters = y

Value Value

Type Number of of

of of EACH ALL

coin coins coin coins

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

dimes x $0.10 $0.10x

quarters y $0.25 $0.25y

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

TOTALS 40 $7.60

x + y = 40

0.10x + 0.25y = 7.60

Get rid of decimals by multiplying every term by 100:

10x + 25y = 760

So we have the system of equations:

x + y = 40

10x + 25y = 760

We solve by substitution. Solve the first equation for y:

x + y = 40

y = 40 - x

Substitute (40 - x) for y in 10x + 25y = 760

10x + 25(40 - x) = 760

10x + 1000 - 25x = 760

-15x + 1000 = 760

-15x = -240

x = 16 = the number of dimes.

Substitute in y = 40 - x

y = 40 - (16)

y = 24 quarters.

$1.60 + $6.00 = $7.60

I hope that helped, sorry for taking so long :-)

8 0

3 years ago

If ∠1 = 3x, ∠2 = 5x + 18, and s ⊥ r, find m∠1.

Bingel [31]

I hope it will help you.

7 0

2 years ago

Read 2 more answers

Explain how to multiply the following whole numbers 21 x 14

Lesechka [4]

Answer:

$\begin{matrix}\space\space&\textbf{2}&\textbf{1}\\ \times \:&1&\textbf{4}\end{matrix}$

________

$\frac{\begin{matrix}\space\space&\textbf{0}&8&4\\ +&\textbf{2}&1&0\end{matrix}}{\begin{matrix}\space\space&\textbf{2}&9&4\end{matrix}}$

Step-by-step explanation:

Given

$21\:\times \:14$

Line up the numbers

$\begin{matrix}\space\space&2&1\\ \times \:&1&4\end{matrix}$

Multiply the top number by the bottom number one digit at a time starting with the ones digit left(from right to left right)

Multiply the top number by the bolded digit of the bottom number

$\begin{matrix}\space\space&\textbf{2}&\textbf{1}\\ \times \:&1&\textbf{4}\end{matrix}$

Multiply the bold numbers: 1×4=4

$\frac{\begin{matrix}\space\space&2&\textbf{1}\\ \times \:&1&\textbf{4}\end{matrix}}{\begin{matrix}\space\space&\space\space&4\end{matrix}}$

Multiply the bold numbers: 2×4=8

$\frac{\begin{matrix}\space\space&\textbf{2}&1\\ \times \:&1&\textbf{4}\end{matrix}}{\begin{matrix}\space\space&8&4\end{matrix}}$

Multiply the top number by the bolded digit of the bottom number

$\frac{\begin{matrix}\space\space&\textbf{2}&\textbf{1}\\ \times \:&\textbf{1}&4\end{matrix}}{\begin{matrix}\space\space&8&4\end{matrix}}$

Multiply the bold numbers: 1×1=1

$\frac{\begin{matrix}\space\space&\space\space&2&\textbf{1}\\ \space\space&\times \:&\textbf{1}&4\end{matrix}}{\begin{matrix}\space\space&\space\space&8&4\\ \space\space&\space\space&1&\space\space\end{matrix}}$

Multiply the bold numbers: 2×1=2

$\frac{\begin{matrix}\space\space&\space\space&\textbf{2}&1\\ \space\space&\times \:&\textbf{1}&4\end{matrix}}{\begin{matrix}\space\space&\space\space&8&4\\ \space\space&2&1&\space\space\end{matrix}}$

Add the rows to get the answer. For simplicity, fill in trailing zeros.

$\frac{\begin{matrix}\space\space&\space\space&2&1\\ \space\space&\times \:&1&4\end{matrix}}{\begin{matrix}\space\space&0&8&4\\ \space\space&2&1&0\end{matrix}}$

adding portion

$\begin{matrix}\space\space&0&8&4\\ +&2&1&0\end{matrix}$

Add the digits of the right-most column: 4+0=4

$\frac{\begin{matrix}\space\space&0&8&\textbf{4}\\ +&2&1&\textbf{0}\end{matrix}}{\begin{matrix}\space\space&\space\space&\space\space&\textbf{4}\end{matrix}}$

Add the digits of the right-most column: 8+1=9

$\frac{\begin{matrix}\space\space&0&\textbf{8}&4\\ +&2&\textbf{1}&0\end{matrix}}{\begin{matrix}\space\space&\space\space&\textbf{9}&4\end{matrix}}$

Add the digits of the right-most column: 0+2=2

$\frac{\begin{matrix}\space\space&\textbf{0}&8&4\\ +&\textbf{2}&1&0\end{matrix}}{\begin{matrix}\space\space&\textbf{2}&9&4\end{matrix}}$

Therefore,

$\begin{matrix}\space\space&\textbf{2}&\textbf{1}\\ \times \:&1&\textbf{4}\end{matrix}$

________

$\frac{\begin{matrix}\space\space&\textbf{0}&8&4\\ +&\textbf{2}&1&0\end{matrix}}{\begin{matrix}\space\space&\textbf{2}&9&4\end{matrix}}$

6 0

3 years ago

1.325 to the nearest hundreths

12345 [234]

Its 1.33 because you round up if its 5 or greater

4 0

3 years ago

Read 2 more answers